Cancel revision 64607. There had been a problem with the branch.
| ------------------------------------------------------------------------ | r64607 | efif | 2011-07-05 17:27:04 +0200 (Tue, 05 Jul 2011) | 1 line | | Merged feature-branch Aos_2-new_functors-tau into next | ------------------------------------------------------------------------
This commit is contained in:
Laurent Rineau
+23
-17
@@ -452,7 +452,6 @@ Arrangement_on_surface_2/doc_tex/Arrangement_on_surface_2/fig/unb_dcel.gif -text
|
||||
Arrangement_on_surface_2/doc_tex/Arrangement_on_surface_2/fig/unb_dcel.pdf -text svneol=unset#application/pdf
|
||||
Arrangement_on_surface_2/doc_tex/Arrangement_on_surface_2_ref/Arr_algebraic_segment_traits.tex -text
|
||||
Arrangement_on_surface_2/doc_tex/Arrangement_on_surface_2_ref/Arr_halfedge_direction.tex -text
|
||||
Arrangement_on_surface_2/doc_tex/Arrangement_on_surface_2_ref/Arr_rational_function_traits.tex -text
|
||||
Arrangement_on_surface_2/doc_tex/Arrangement_on_surface_2_ref/arr_do_intersect.tex -text
|
||||
Arrangement_on_surface_2/doc_tex/Arrangement_on_surface_2_ref/arr_zone.tex -text
|
||||
Arrangement_on_surface_2/doc_tex/Sweep_line_2/fig/Curve_intersections_2.png -text
|
||||
@@ -653,11 +652,10 @@ Arrangement_on_surface_2/test/Arrangement_on_surface_2/data/conics/vertex.pt -te
|
||||
Arrangement_on_surface_2/test/Arrangement_on_surface_2/data/conics/vertex.xcv -text
|
||||
Arrangement_on_surface_2/test/Arrangement_on_surface_2/data/conics/xcurves -text
|
||||
Arrangement_on_surface_2/test/Arrangement_on_surface_2/data/empty.zero -text
|
||||
Arrangement_on_surface_2/test/Arrangement_on_surface_2/data/linear/lines/compare_x_at_limit -text
|
||||
Arrangement_on_surface_2/test/Arrangement_on_surface_2/data/linear/lines/compare_x_near_limit -text
|
||||
Arrangement_on_surface_2/test/Arrangement_on_surface_2/data/linear/lines/boundary_near_x -text
|
||||
Arrangement_on_surface_2/test/Arrangement_on_surface_2/data/linear/lines/boundary_near_y -text
|
||||
Arrangement_on_surface_2/test/Arrangement_on_surface_2/data/linear/lines/compare_y_at_x -text
|
||||
Arrangement_on_surface_2/test/Arrangement_on_surface_2/data/linear/lines/compare_y_at_x_left -text
|
||||
Arrangement_on_surface_2/test/Arrangement_on_surface_2/data/linear/lines/compare_y_near_boundary -text
|
||||
Arrangement_on_surface_2/test/Arrangement_on_surface_2/data/linear/lines/curves -text
|
||||
Arrangement_on_surface_2/test/Arrangement_on_surface_2/data/linear/lines/intersect -text
|
||||
Arrangement_on_surface_2/test/Arrangement_on_surface_2/data/linear/lines/is_vertical -text
|
||||
@@ -735,11 +733,8 @@ Arrangement_on_surface_2/test/Arrangement_on_surface_2/data/polylines/split.xcv
|
||||
Arrangement_on_surface_2/test/Arrangement_on_surface_2/data/polylines/vertex -text
|
||||
Arrangement_on_surface_2/test/Arrangement_on_surface_2/data/polylines/vertex.pt -text
|
||||
Arrangement_on_surface_2/test/Arrangement_on_surface_2/data/polylines/vertex.xcv -text
|
||||
Arrangement_on_surface_2/test/Arrangement_on_surface_2/data/rational_arcs/compare_x_at_limit -text
|
||||
Arrangement_on_surface_2/test/Arrangement_on_surface_2/data/rational_arcs/compare_x_near_limit -text
|
||||
Arrangement_on_surface_2/test/Arrangement_on_surface_2/data/rational_arcs/compare_y_at_x -text
|
||||
Arrangement_on_surface_2/test/Arrangement_on_surface_2/data/rational_arcs/compare_y_at_x_left -text
|
||||
Arrangement_on_surface_2/test/Arrangement_on_surface_2/data/rational_arcs/compare_y_near_boundary -text
|
||||
Arrangement_on_surface_2/test/Arrangement_on_surface_2/data/rational_arcs/curves -text
|
||||
Arrangement_on_surface_2/test/Arrangement_on_surface_2/data/rational_arcs/intersect -text
|
||||
Arrangement_on_surface_2/test/Arrangement_on_surface_2/data/rational_arcs/is_vertical -text
|
||||
@@ -771,15 +766,14 @@ Arrangement_on_surface_2/test/Arrangement_on_surface_2/data/segments/split.xcv -
|
||||
Arrangement_on_surface_2/test/Arrangement_on_surface_2/data/segments/vertex -text
|
||||
Arrangement_on_surface_2/test/Arrangement_on_surface_2/data/segments/vertex.pt -text
|
||||
Arrangement_on_surface_2/test/Arrangement_on_surface_2/data/segments/xcurves -text
|
||||
Arrangement_on_surface_2/test/Arrangement_on_surface_2/data/spherical_arcs/boundary_near_x -text
|
||||
Arrangement_on_surface_2/test/Arrangement_on_surface_2/data/spherical_arcs/boundary_near_y -text
|
||||
Arrangement_on_surface_2/test/Arrangement_on_surface_2/data/spherical_arcs/compare -text
|
||||
Arrangement_on_surface_2/test/Arrangement_on_surface_2/data/spherical_arcs/compare.pt -text
|
||||
Arrangement_on_surface_2/test/Arrangement_on_surface_2/data/spherical_arcs/compare.xcv -text
|
||||
Arrangement_on_surface_2/test/Arrangement_on_surface_2/data/spherical_arcs/compare_x_near_boundary -text
|
||||
Arrangement_on_surface_2/test/Arrangement_on_surface_2/data/spherical_arcs/compare_x_on_boundary -text
|
||||
Arrangement_on_surface_2/test/Arrangement_on_surface_2/data/spherical_arcs/compare_y_at_x -text
|
||||
Arrangement_on_surface_2/test/Arrangement_on_surface_2/data/spherical_arcs/compare_y_at_x.pt -text
|
||||
Arrangement_on_surface_2/test/Arrangement_on_surface_2/data/spherical_arcs/compare_y_at_x.xcv -text
|
||||
Arrangement_on_surface_2/test/Arrangement_on_surface_2/data/spherical_arcs/compare_y_near_boundary -text
|
||||
Arrangement_on_surface_2/test/Arrangement_on_surface_2/data/spherical_arcs/curves -text
|
||||
Arrangement_on_surface_2/test/Arrangement_on_surface_2/data/spherical_arcs/intersect -text
|
||||
Arrangement_on_surface_2/test/Arrangement_on_surface_2/data/spherical_arcs/is_vertical -text
|
||||
@@ -824,7 +818,6 @@ Arrangement_on_surface_2/test/Arrangement_on_surface_2/test_do_equal.cpp -text
|
||||
Arrangement_on_surface_2/test/Arrangement_on_surface_2/test_do_intersect.cpp -text
|
||||
Arrangement_on_surface_2/test/Arrangement_on_surface_2/test_observer.cmd -text
|
||||
Arrangement_on_surface_2/test/Arrangement_on_surface_2/test_observer.cpp -text
|
||||
Arrangement_on_surface_2/test/Arrangement_on_surface_2/test_rational_function_traits_2.cpp -text
|
||||
Arrangement_on_surface_2/test/Arrangement_on_surface_2/test_traits_adaptor.cpp -text
|
||||
Arrangement_on_surface_2/test/Arrangement_on_surface_2/test_traits_adaptor.h -text
|
||||
Arrangement_on_surface_2/test/Arrangement_on_surface_2/test_zone.cpp -text
|
||||
@@ -1241,12 +1234,6 @@ Circular_kernel_2/benchmark/readme.doc -text svneol=unset#application/msword
|
||||
Circular_kernel_2/benchmark/readme.pdf -text svneol=unset#application/pdf
|
||||
Circular_kernel_2/benchmark/readme.sxw -text
|
||||
Circular_kernel_2/changes -text
|
||||
Circular_kernel_2/demo/Circular_kernel_2/Qt3/README -text
|
||||
Circular_kernel_2/demo/Circular_kernel_2/Qt3/help/get_arc.jpeg -text svneol=unset#image/jpeg
|
||||
Circular_kernel_2/demo/Circular_kernel_2/Qt3/help/index.html svneol=native#text/html
|
||||
Circular_kernel_2/demo/Circular_kernel_2/Qt3/help/planar_map_icon.jpeg -text svneol=unset#image/jpeg
|
||||
Circular_kernel_2/demo/Circular_kernel_2/Qt3/help/sweeper.jpeg -text svneol=unset#image/jpeg
|
||||
Circular_kernel_2/demo/Circular_kernel_2/Qt3/help/trash.jpeg -text svneol=unset#image/jpeg
|
||||
Circular_kernel_2/doc_tex/Circular_kernel_2/fig/Boolean_operation.png -text
|
||||
Circular_kernel_2/doc_tex/Circular_kernel_2/fig/Boolean_operation_detail.png -text
|
||||
Circular_kernel_2/doc_tex/Circular_kernel_2_ref/GeomFunctorsCompute.tex -text
|
||||
@@ -1425,9 +1412,16 @@ Convex_decomposition_3/test/Convex_decomposition_3/star.nef3 -text
|
||||
Convex_hull_2/demo/Convex_hull_2/help/index.html svneol=native#text/html
|
||||
Convex_hull_2/doc_tex/Convex_hull_2/convex_hull.png -text
|
||||
Convex_hull_2/doc_tex/Convex_hull_2/saarhull.png -text svneol=unset#image/png
|
||||
Convex_hull_3/benchmark/Convex_hull_3/compare_different_approach.cpp -text
|
||||
Convex_hull_3/benchmark/Convex_hull_3/is_on_positive_side.cpp -text
|
||||
Convex_hull_3/demo/Convex_hull_3/CMakeLists.txt -text
|
||||
Convex_hull_3/doc_tex/Convex_hull_3/bunny.png -text
|
||||
Convex_hull_3/doc_tex/Convex_hull_3/bunny.wrl.gz -text
|
||||
Convex_hull_3/doc_tex/Convex_hull_3/chull_bimba.png -text
|
||||
Convex_hull_3/doc_tex/Convex_hull_3_ref/convex_hull_3_to_polyhedron_3.tex -text
|
||||
Convex_hull_3/examples/Convex_hull_3/incremental_hull_class_3.cpp -text
|
||||
Convex_hull_3/include/CGAL/convex_hull_3_to_polyhedron_3.h -text
|
||||
Convex_hull_3/test/Convex_hull_3/quick_hull_default_traits.cpp -text
|
||||
Developers_manual/doc_tex/Developers_manual/fig/Cartesian_ipoint.gif -text svneol=unset#image/gif
|
||||
Developers_manual/doc_tex/Developers_manual/fig/Cartesian_orientation.png -text svneol=unset#image/png
|
||||
Developers_manual/doc_tex/Developers_manual/fig/Object.gif -text svneol=unset#image/gif
|
||||
@@ -2016,6 +2010,7 @@ Maintenance/infrastructure/matisse.geometryfactory.com/reference-platforms/setup
|
||||
Maintenance/infrastructure/matisse.geometryfactory.com/reference-platforms/x86-64_Linux-2.6_IntelCompiler-11.0-with-g++-4.5.1_F14/setup -text
|
||||
Maintenance/infrastructure/matisse.geometryfactory.com/reference-platforms/x86-64_Linux-2.6_IntelCompiler-11.1-with-g++-4.5.1_F14-strict-ansi/setup -text
|
||||
Maintenance/infrastructure/matisse.geometryfactory.com/reference-platforms/x86-64_Linux-2.6_IntelCompiler-11.1-with-g++-4.5.1_F14/setup -text
|
||||
Maintenance/infrastructure/matisse.geometryfactory.com/reference-platforms/x86-64_Linux-2.6_IntelCompiler-12.0-with-g++-4.5.1_F14/setup -text
|
||||
Maintenance/infrastructure/matisse.geometryfactory.com/reference-platforms/x86-64_Linux-2.6_g++-4.5-branch_CXX0X-F14/setup -text
|
||||
Maintenance/infrastructure/matisse.geometryfactory.com/reference-platforms/x86-64_Linux-2.6_g++-4.5-branch_Release-F14/setup -text
|
||||
Maintenance/infrastructure/matisse.geometryfactory.com/reference-platforms/x86-64_Linux-2.6_g++-4.5.1_F14-MATCHING-BUG-6/setup -text
|
||||
@@ -2042,6 +2037,8 @@ Maintenance/public_release/announcement/CGAL-3.7 -text
|
||||
Maintenance/public_release/announcement/CGAL-3.7-beta1 -text
|
||||
Maintenance/public_release/announcement/CGAL-3.8 -text
|
||||
Maintenance/public_release/announcement/CGAL-3.8-beta -text
|
||||
Maintenance/public_release/announcement/CGAL-3.8.1 -text
|
||||
Maintenance/public_release/announcement/CGAL-3.9 -text
|
||||
Maintenance/public_release/scripts/precompiled_demos_zips -text
|
||||
Maintenance/public_release/scripts/prepare_release -text
|
||||
Maintenance/release_building/BUGFIX_NUMBER -text
|
||||
@@ -3443,13 +3440,22 @@ Snap_rounding_2/doc_tex/Snap_rounding_2/sr1.pdf -text svneol=unset#application/p
|
||||
Snap_rounding_2/test/Snap_rounding_2/cgal_test eol=lf
|
||||
Snap_rounding_2/test/Snap_rounding_2/cgal_test_base -text
|
||||
Snap_rounding_2/test/Snap_rounding_2/cgal_test_with_cmake eol=lf
|
||||
Spatial_searching/TODO.txt -text
|
||||
Spatial_searching/benchmark/Spatial_searching/Compare_ANN_STANN_CGAL.cpp -text
|
||||
Spatial_searching/demo/Spatial_searching/Qt3/help/index.html svneol=native#text/html
|
||||
Spatial_searching/doc_tex/Spatial_searching/Fig1.gif -text svneol=unset#image/gif
|
||||
Spatial_searching/doc_tex/Spatial_searching/windowQuery.png -text
|
||||
Spatial_searching/doc_tex/Spatial_searching_ref/Distance_adapter.tex -text
|
||||
Spatial_searching/doc_tex/Spatial_searching_ref/RangeSearchTraits.tex -text
|
||||
Spatial_searching/doc_tex/Spatial_searching_ref/Search_traits_adapter.tex -text
|
||||
Spatial_searching/examples/Spatial_searching/searching_with_point_with_info.cpp -text
|
||||
Spatial_searching/examples/Spatial_searching/searching_with_point_with_info_inplace.cpp -text
|
||||
Spatial_searching/examples/Spatial_searching/searching_with_point_with_info_pmap.cpp -text
|
||||
Spatial_searching/include/CGAL/Search_traits_adapter.h -text
|
||||
Spatial_searching/include/CGAL/internal/K_neighbor_search.h -text
|
||||
Spatial_searching/include/CGAL/internal/bounded_priority_queue.h -text
|
||||
Spatial_searching/test/Spatial_searching/Compare_methods.cpp -text
|
||||
Spatial_searching/test/Spatial_searching/Point_with_info.h -text
|
||||
Spatial_sorting/doc_tex/Spatial_sorting/fig/Hilbert-median.gif -text
|
||||
Spatial_sorting/doc_tex/Spatial_sorting/fig/Hilbert-median.pdf -text
|
||||
Spatial_sorting/doc_tex/Spatial_sorting/fig/Hilbert-middle.gif -text
|
||||
|
||||
+15
@@ -309,6 +309,16 @@ Maintenance/infrastructure/matisse.geometryfactory.com/reference-platforms/x86-6
|
||||
Maintenance/infrastructure/matisse.geometryfactory.com/reference-platforms/x86-64_Linux-2.6_IntelCompiler-11.1-with-g++-4.5.1_F14/localtestscript
|
||||
Maintenance/infrastructure/matisse.geometryfactory.com/reference-platforms/x86-64_Linux-2.6_IntelCompiler-11.1-with-g++-4.5.1_F14/localtestscript-redo-results-collection
|
||||
Maintenance/infrastructure/matisse.geometryfactory.com/reference-platforms/x86-64_Linux-2.6_IntelCompiler-11.1-with-g++-4.5.1_F14/src
|
||||
Maintenance/infrastructure/matisse.geometryfactory.com/reference-platforms/x86-64_Linux-2.6_IntelCompiler-12.0-with-g++-4.5.1_F14/CGALConfig.cmake
|
||||
Maintenance/infrastructure/matisse.geometryfactory.com/reference-platforms/x86-64_Linux-2.6_IntelCompiler-12.0-with-g++-4.5.1_F14/CMakeCache.txt.backup
|
||||
Maintenance/infrastructure/matisse.geometryfactory.com/reference-platforms/x86-64_Linux-2.6_IntelCompiler-12.0-with-g++-4.5.1_F14/Makefile
|
||||
Maintenance/infrastructure/matisse.geometryfactory.com/reference-platforms/x86-64_Linux-2.6_IntelCompiler-12.0-with-g++-4.5.1_F14/config
|
||||
Maintenance/infrastructure/matisse.geometryfactory.com/reference-platforms/x86-64_Linux-2.6_IntelCompiler-12.0-with-g++-4.5.1_F14/include
|
||||
Maintenance/infrastructure/matisse.geometryfactory.com/reference-platforms/x86-64_Linux-2.6_IntelCompiler-12.0-with-g++-4.5.1_F14/lib
|
||||
Maintenance/infrastructure/matisse.geometryfactory.com/reference-platforms/x86-64_Linux-2.6_IntelCompiler-12.0-with-g++-4.5.1_F14/localbuildscript
|
||||
Maintenance/infrastructure/matisse.geometryfactory.com/reference-platforms/x86-64_Linux-2.6_IntelCompiler-12.0-with-g++-4.5.1_F14/localtestscript
|
||||
Maintenance/infrastructure/matisse.geometryfactory.com/reference-platforms/x86-64_Linux-2.6_IntelCompiler-12.0-with-g++-4.5.1_F14/localtestscript-redo-results-collection
|
||||
Maintenance/infrastructure/matisse.geometryfactory.com/reference-platforms/x86-64_Linux-2.6_IntelCompiler-12.0-with-g++-4.5.1_F14/src
|
||||
Maintenance/infrastructure/matisse.geometryfactory.com/reference-platforms/x86-64_Linux-2.6_g++-4.5-branch_CXX0X-F14/CGALConfig.cmake
|
||||
Maintenance/infrastructure/matisse.geometryfactory.com/reference-platforms/x86-64_Linux-2.6_g++-4.5-branch_CXX0X-F14/CMakeCache.txt.backup
|
||||
Maintenance/infrastructure/matisse.geometryfactory.com/reference-platforms/x86-64_Linux-2.6_g++-4.5-branch_CXX0X-F14/Makefile
|
||||
@@ -349,6 +359,11 @@ Maintenance/infrastructure/matisse.geometryfactory.com/reference-platforms/x86-6
|
||||
Maintenance/infrastructure/matisse.geometryfactory.com/reference-platforms/x86-64_Linux-2.6_g++-4.5.1_F14-ansi/localtestscript
|
||||
Maintenance/infrastructure/matisse.geometryfactory.com/reference-platforms/x86-64_Linux-2.6_g++-4.5.1_F14-ansi/localtestscript-redo-results-collection
|
||||
Maintenance/infrastructure/matisse.geometryfactory.com/reference-platforms/x86-64_Linux-2.6_g++-4.5.1_F14-ansi/src
|
||||
Maintenance/infrastructure/matisse.geometryfactory.com/reference-platforms/x86-64_Linux-2.6_g++-4.5.1_F14-m32/CGALConfig.cmake
|
||||
Maintenance/infrastructure/matisse.geometryfactory.com/reference-platforms/x86-64_Linux-2.6_g++-4.5.1_F14-m32/config
|
||||
Maintenance/infrastructure/matisse.geometryfactory.com/reference-platforms/x86-64_Linux-2.6_g++-4.5.1_F14-m32/include
|
||||
Maintenance/infrastructure/matisse.geometryfactory.com/reference-platforms/x86-64_Linux-2.6_g++-4.5.1_F14-m32/lib
|
||||
Maintenance/infrastructure/matisse.geometryfactory.com/reference-platforms/x86-64_Linux-2.6_g++-4.5.1_F14-m32/src
|
||||
Maintenance/infrastructure/matisse.geometryfactory.com/reference-platforms/x86-64_Linux-2.6_g++-4.5.1_F14/CGALConfig.cmake
|
||||
Maintenance/infrastructure/matisse.geometryfactory.com/reference-platforms/x86-64_Linux-2.6_g++-4.5.1_F14/CMakeCache.txt.backup
|
||||
Maintenance/infrastructure/matisse.geometryfactory.com/reference-platforms/x86-64_Linux-2.6_g++-4.5.1_F14/Makefile
|
||||
|
||||
@@ -1,5 +1,5 @@
|
||||
\begin{ccPkgDescription}{Algebraic Kernel \label{Pkg:AlgebraicKerneld}}
|
||||
\ccPkgHowToCiteCgal{cgal:bht-ak-11}
|
||||
\ccPkgHowToCiteCgal{cgal:bht-ak-11b}
|
||||
\ccPkgSummary{
|
||||
Real solving of polynomials is a fundamental problem with a wide application range.
|
||||
This package is targeted to provide black-box implementations of state-of-the-art
|
||||
|
||||
@@ -11,6 +11,7 @@
|
||||
//
|
||||
// ============================================================================
|
||||
|
||||
#include <CGAL/config.h>
|
||||
#include <CGAL/Algebraic_kernel_d/flags.h>
|
||||
|
||||
// Switches on/off tests for Sqrt-extension types
|
||||
|
||||
@@ -11,6 +11,7 @@
|
||||
//
|
||||
// ============================================================================
|
||||
|
||||
#include <CGAL/config.h>
|
||||
#include <CGAL/Algebraic_kernel_d/flags.h>
|
||||
|
||||
// Switches on/off tests for Sqrt-extension types
|
||||
|
||||
@@ -1,6 +1,6 @@
|
||||
|
||||
\begin{ccPkgDescription}{2D Apollonius Graphs (Delaunay Graphs of Disks)\label{Pkg:ApolloniusGraph2}}
|
||||
\ccPkgHowToCiteCgal{cgal:ky-ag2-11}
|
||||
\ccPkgHowToCiteCgal{cgal:ky-ag2-11b}
|
||||
\ccPkgSummary{
|
||||
Algorithms for computing the Apollonius
|
||||
graph in two dimensions. The Apollonius graph is the dual of the
|
||||
|
||||
@@ -1335,13 +1335,13 @@ public:
|
||||
x_real(first_x, xfirst2);
|
||||
y_real(first_y, yfirst2);
|
||||
|
||||
// double xmin, xmax, ymin, ymax;
|
||||
// if (x < xfirst2) { xmin = x; xmax = xfirst2; }
|
||||
// else { xmin = xfirst2; xmax = x; }
|
||||
// if (y < yfirst2) { ymin = y; ymax = yfirst2; }
|
||||
// else { ymin = yfirst2; ymax = y; }
|
||||
double distx = xfirst2 - x;
|
||||
double disty = yfirst2 - y;
|
||||
double xmin, xmax, ymin, ymax, distx, disty;
|
||||
if (x < xfirst2) { xmin = x; xmax = xfirst2; }
|
||||
else { xmin = xfirst2; xmax = x; }
|
||||
if (y < yfirst2) { ymin = y; ymax = yfirst2; }
|
||||
else { ymin = yfirst2; ymax = y; }
|
||||
distx = xfirst2 - x;
|
||||
disty = yfirst2 - y;
|
||||
move_center(distx, disty);
|
||||
on_first = FALSE;
|
||||
}
|
||||
|
||||
@@ -29,8 +29,3 @@ concept related to unbounded curves.
|
||||
Version~3.7 introduced a geometry-traits class
|
||||
that handles planar algebraic curves of arbitrary degree.
|
||||
It was developed by Eric Berberich and Michael Kerber.
|
||||
|
||||
Version~3.9 introduced a new geometry-traits class that handles
|
||||
rational arcs. It was developed by Oren Salzman and Michael Hemmer.
|
||||
It replaced an old traits, which handled the same family of
|
||||
curves, developed by Ron Wein.
|
||||
|
||||
@@ -87,7 +87,7 @@ on the \dcel\ data structure see~\cite[Chapter~2]{bkos-cgaa-00}.
|
||||
\end{ccTexOnly}
|
||||
\begin{ccHtmlOnly}
|
||||
<p><center>
|
||||
<img src="./fig/arr_segs.gif" border=0 alt="Arrangement of segments">
|
||||
<img src="./fig/arr_segs.gif" border=0 alt="Arrangement of sgements">
|
||||
</center>
|
||||
\end{ccHtmlOnly}
|
||||
\caption{An arrangement of interior-disjoint line segments with some
|
||||
@@ -106,22 +106,6 @@ hole is comprised of two edges. $f_1$ also contains two isolated
|
||||
vertices $u_1$ and $u_2$ in its interior.\label{arr_fig:seg_dcel}}
|
||||
\end{figure}
|
||||
|
||||
The $x$-monotone curves of an arrangement are embedded in an
|
||||
rectangular two-dimensional area called the parameter
|
||||
space.\footnote{The term parameter space stems from a major
|
||||
extension the arrangement package is going through to support
|
||||
arrangements embedded on certain two-dimensional parametric
|
||||
surfaces in three-dimensions (or higher).} The parameter space is
|
||||
defined as $X \times Y$, where $X$ and $Y$ are open, half-open, or
|
||||
closed intervals with endpoints in the compactified real line
|
||||
$\mathbb{R} \cup \{-\infty,+\infty\}$. Let $b_l$, $b_r$, $b_b$, and
|
||||
$b_t$ denote the endpoints of $X$ and $Y$, respectively. We
|
||||
typically refer to these values as the left, right, bottom, and top
|
||||
sides of the boundary of the parameter space. If the parameter space
|
||||
is, for example, the entire compactified plane, which is currently
|
||||
the only option supported by the package, $b_l = b_b = -\infty$ and
|
||||
$b_r = b_t = +\infty$.
|
||||
|
||||
The rest of this chapter is organized as follows: In
|
||||
Section~\ref{arr_sec:arr_class} we review in detail the interface
|
||||
of the \ccc{Arrangement_2} class-template, which is the central
|
||||
|
||||
@@ -9,7 +9,6 @@ mention throughout the chapter that there are different levels of
|
||||
requirements from the traits class, namely the traits class can model
|
||||
different concept refinement-levels.
|
||||
|
||||
%--------------------------------------------------
|
||||
\subsection{The Hierarchy of Traits-Class Concepts
|
||||
\label{arr_sssec:tr_concepts}}
|
||||
%--------------------------------------------------
|
||||
@@ -22,65 +21,93 @@ A model of the basic concept, \ccc{ArrangementBasicTraits_2},
|
||||
needs to define the types \ccc{Point_2} and
|
||||
\ccc{X_monotone_curve_2}, where objects of the first type are
|
||||
the geometric mapping of arrangement vertices, and objects of the
|
||||
latter type are the geometric mapping of edges. Such a model has to
|
||||
support in addition the following set of operations:
|
||||
\begin{description}
|
||||
\item[\ccc{Compare_x_2}:] Compares the $x$-coordinates of two points.
|
||||
%
|
||||
\item[\ccc{Compare_xy_2}:] Compares two points lexicographically, by
|
||||
their $x$-coordinates and then (in case of equality) by their
|
||||
$y$-coordinates.
|
||||
%
|
||||
\item[\ccc{Construct_min_vertex_2},\ccc{Construct_max_vertex_2}:]
|
||||
Returns the left endpoint (similarly, the right endpoint) of
|
||||
an $x$-monotone curve.
|
||||
%
|
||||
\item[\ccc{Compare_y_at_x_2}:] Given an $x$-monotone curve $c$ and a
|
||||
point $p$ that lies in its $x$-range, this predicate determines
|
||||
whether $p$ lies below, above or on $c$.
|
||||
%
|
||||
\item[\ccc{Compare_y_at_x_right_2}:]
|
||||
Given two $x$-monotone curves $c_1$ and $c_2$ that share a common
|
||||
left endpoint $p$, this predicate determines whether $c_1$ lies
|
||||
above or under $c_2$ immediately to the right of $p$, or whether the
|
||||
two curves coincide there.
|
||||
\item[\ccc{Equal_2}:] Checks two points and two curves for equality
|
||||
(two curves are equal if their graph is the same).
|
||||
%
|
||||
\item[\ccc{Is_vertical_2}:]
|
||||
Determines whether an $x$-monotone curve is vertical.
|
||||
\end{description}
|
||||
latter type are the geometric mapping of edges. In addition, it has to
|
||||
support the following set of predicates:
|
||||
\begin{itemize}
|
||||
\item Compare the $x$-coordinates of two points $p$ and $q$.
|
||||
%
|
||||
\item Compare two points $p$ and $q$ lexicographically, by their
|
||||
$x$-coordinates and then (in case of equality) by their
|
||||
$y$-coordinates.
|
||||
%
|
||||
\item Return the left endpoint (similarly, the right endpoint) of
|
||||
an $x$-monotone curve $c$.
|
||||
%
|
||||
\item Given an $x$-monotone curve $c$ and a point $p$ that lies in its
|
||||
$x$-range, determine whether $p$ lies below, above or on $c$.
|
||||
%
|
||||
\item Given two $x$-monotone curves $c_1$ and $c_2$ that share a
|
||||
common left endpoint $p$, determine whether $c_1$ lies above or under
|
||||
$c_2$ immediately to the right of $p$, or whether the two curves coincide
|
||||
there.
|
||||
\item Check two curves for equality (two curves are equal if their
|
||||
graph is the same).
|
||||
\end{itemize}
|
||||
|
||||
This basic set of predicates is sufficient for constructing
|
||||
arrangements of bounded $x$-monotone curves and points that
|
||||
are pairwise disjoint in their interiors and for answering
|
||||
point-location queries and vertical ray-shooting queries.
|
||||
In order to support unbounded curves we add the following
|
||||
predicates, involving curve-ends that coincide with the imaginary
|
||||
boundaries of the arrangement. We say that such curves have
|
||||
{\em boundary conditions} in $x$ or in $y$:
|
||||
\begin{itemize}
|
||||
\item
|
||||
Determine if the left end (similarly, the right end) of an
|
||||
$x$-monotone curve $c$ has a boundary condition in $x$. Namely,
|
||||
we say that its boundary condition is \ccc{MINUS_INFINITY} if
|
||||
it lies at $x = -\infty$, \ccc{PLUS_INFINITY} if it lies at
|
||||
$x = +\infty$, and \ccc{NO_BOUNDARY} otherwise.
|
||||
|
||||
Similarly, we need a predicate for determining whether a given
|
||||
curve-end (the left end or the right end of a given $x$-monotone
|
||||
curve) has a boundary condition in $y$, namely whether it lies
|
||||
at $y = \pm\infty$. Note that we can construct the left endpoint
|
||||
(or the right endpoint) of $c$ only if the corresponding curve-end
|
||||
is bounded (i.e., has no boundary conditions in $x$ or in $y$).
|
||||
%
|
||||
\item
|
||||
Given two $x$-monotone curve $c_1$ and $c_2$, both defined at $x =
|
||||
-\infty$, determine whether $c_1$ lies above or under $c_2$ at $x =
|
||||
-\infty$ (similarly, at $x = \infty$).
|
||||
%
|
||||
\item
|
||||
Compare the $x$-position of an unbounded curve-end with a
|
||||
finite $x$-coordinate and an infinite $y$-coordinate with a
|
||||
vertical line that passes through a given query point.
|
||||
%
|
||||
\item
|
||||
Compare the $x$-position of two unbounded curve-ends with finite
|
||||
$x$-coordinates and infinite $y$-coordinates.
|
||||
\end{itemize}
|
||||
Each model of the concept \ccc{ArrangementBasicTraits_2}
|
||||
needs to define a tag named \ccc{Has_left_category}. It determines
|
||||
needs to define a tag named \ccc{Has_boundary_category},
|
||||
which should be either \ccc{Tag_true} or \ccc{Tag_false}.
|
||||
In the latter case, the tag marks the fact that the traits
|
||||
class does not support unbounded curves (for example, the
|
||||
\ccc{Arr_segment_traits_2} class we have encountered in the
|
||||
previous sections), and it does not have to provide the
|
||||
predicates listed above.
|
||||
|
||||
An additional tag, named \ccc{Has_left_category}, determines
|
||||
whether the traits class supports the following predicate:
|
||||
\begin{description}
|
||||
\item[\ccc{Compare_y_at_x_left_2}:]
|
||||
Given two $x$-monotone curves $c_1$ and $c_2$ that share a common
|
||||
right endpoint $p$, this predicate determines whether $c_1$ lies
|
||||
above or under $c_2$ immediately to the left of $p$, or whether the
|
||||
two curves coincide there.
|
||||
\end{description}
|
||||
\begin{itemize}
|
||||
\item
|
||||
Given two $x$-monotone curves $c_1$ and $c_2$ that share a common
|
||||
right endpoint $p$, determine whether $c_1$ lies above or under
|
||||
$c_2$ immediately to the left of $p$, or whether the two curves
|
||||
coincide there.
|
||||
\end{itemize}
|
||||
This predicate is optional, as it can be answered using the
|
||||
other traits-class primitives, and we wish to alleviate the
|
||||
need to implement an extra method that is not absolutely
|
||||
necessary. However, as implementing the predicate directly
|
||||
may prove to be more efficient, the traits-class
|
||||
implementer may choose to provide it.
|
||||
implementer may choose to provide it. As we will see, the
|
||||
usage of tags makes it easier to implement new traits
|
||||
classes and allows for more flexibility in their design.
|
||||
|
||||
The basic set of predicates is sufficient for constructing
|
||||
arrangements of $x$-monotone curves that do not reach or approach the
|
||||
boundary of the parameter space. The nature of the input curves, i.e.,
|
||||
whether some of them are expected to reach or approach the left, right,
|
||||
bottom, or top side of the boundary of the parameter space, must be
|
||||
conveyed by the traits class. This is done through the definition of
|
||||
four additional nested types, namely \ccc{Left_side_category},
|
||||
\ccc{Right_side_category}, \ccc{Bottom_side_category}, and
|
||||
\ccc{Top_side_category}. Each of those types must be convertible to
|
||||
the type \ccc{Arr_oblivious_side_tag} for the class to be a model of
|
||||
the concept \ccc{ArrangementBasicTraits_2}.
|
||||
|
||||
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
\subsubsection{The Landmarks Concept
|
||||
\label{arr_sssec:tr_lanmarks_concept}}
|
||||
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
@@ -91,54 +118,49 @@ instantiated with a model of the refined
|
||||
\ccc{ArrangementLandmarkTraits_2} traits concept. A model of this
|
||||
concept must define a fixed precision number type (typically
|
||||
\ccc{double}) and support the additional operations:
|
||||
\begin{description}
|
||||
\item[\ccc{Approximate_2}:]
|
||||
Given a point \ccc{p}, approximate the $x$ and $y$-coordinates
|
||||
of \ccc{p} using the fixed precision number type. We use this
|
||||
operation for approximate computations---there are certain
|
||||
operations in the search for the location of the point that need not
|
||||
be exact and we can perform them faster than other operations.
|
||||
\begin{itemize}
|
||||
\item Given a point \ccc{p}, approximate the $x$ and $y$-coordinates
|
||||
of \ccc{p} using the fixed precision number type. We use this operation
|
||||
for approximate computations --- there are certain operations in the
|
||||
search for the location of the point that need not be exact and we can
|
||||
perform them faster than other operations.
|
||||
%
|
||||
\item[\ccc{Construct_x_monotone_curve_2}:] Given two points $p_1$ and
|
||||
$p_2$, this predicate constructs an $x$-monotone curve connecting
|
||||
$p_1$ and $p_2$.
|
||||
\end{description}
|
||||
\item Given two points $p_1$ and $p_2$, construct an $x$-monotone
|
||||
curve connecting $p_1$ and $p_2$.
|
||||
\end{itemize}
|
||||
|
||||
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
\subsubsection{Supporting Intersecting $x$-Monotone Curves
|
||||
\subsubsection{Supporting Interesecting $x$-Monotone Curves
|
||||
\label{arr_sssec:tr_xmon_concept}}
|
||||
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
|
||||
A traits class that models the \ccc{ArrangementXMonotoneTraits_2}
|
||||
concept, which refines the \ccc{ArrangementBasicTraits_2}
|
||||
concept, has to support the following functions:
|
||||
\begin{description}
|
||||
\item[\ccc{Intersection_2}:]
|
||||
Computes all intersection points and overlapping sections of
|
||||
two given $x$-monotone curves. If possible, computes also the
|
||||
multiplicity of each intersection point.\footnote{If the two
|
||||
curves intersect at a point $p$ but have different tangents, $p$
|
||||
is of multiplicity 1. If the tangents are also equal but the their
|
||||
curvatures are not the same, $p$ is of multiplicity 2, etc.}
|
||||
Knowing the multiplicity of an intersection point is not required,
|
||||
but it can speed up the arrangement construction.
|
||||
\begin{itemize}
|
||||
\item Compute all intersection points and overlapping sections of
|
||||
two given $x$-monotone curves. If possible, compute also the
|
||||
multiplicity of each intersection point.\footnote{If the two
|
||||
curves intersect at a point $p$ but have different tangents, $p$
|
||||
is of multiplicity 1. If the tangents are also equal but the their
|
||||
curvatures are not the same, $p$ is of multiplicity 2, etc.}
|
||||
Knowing the multiplicity of an intersection point is not required,
|
||||
but it can speed up the arrangement construction.
|
||||
%
|
||||
\item[\ccc{Split_2}:] Splits an $x$-monotone curve $c$ into two subcurves
|
||||
at a point $p$ lying in the interior of $c$.
|
||||
\item Split an $x$-monotone curve $c$ into two subcurves at a point
|
||||
$p$ lying in the interior of $c$.
|
||||
%
|
||||
\item[\ccc{Are_mergeable_2}:] Given two $x$-monotone curve $c_1$ and
|
||||
$c_2$ that share a common endpoint, this predicate determines
|
||||
whether $c_1$ and $c_2$ are \emph{mergeable}, that is, whether they
|
||||
can be merged to form a single continuous $x$-monotone curve of the
|
||||
type supported by the traits class.
|
||||
\item Given two $x$-monotone curve $c_1$ and $c_2$ that share a
|
||||
common endpoint, determine whether $c_1$ and $c_2$ are {\em
|
||||
mergeable}, that is, whether they can be merged to form a
|
||||
single continuous $x$-monotone curve of the type supported by the
|
||||
traits class.
|
||||
%
|
||||
\item[\ccc{Merge_2}:] Merges two mergeable $x$-monotone curves.
|
||||
\end{description}
|
||||
\item Merge two mergeable $x$-monotone curve $c_1$ and $c_2$.
|
||||
\end{itemize}
|
||||
Using a model of the \ccc{ArrangementXMonotoneTraits_2}, it is
|
||||
possible to construct arrangements of sets of $x$-monotone curves
|
||||
(and points) that may intersect one another.
|
||||
|
||||
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
\subsubsection{Supporting Arbitrary Curves
|
||||
\label{arr_sssec:tr_full_concept}}
|
||||
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
@@ -146,215 +168,37 @@ possible to construct arrangements of sets of $x$-monotone curves
|
||||
The concept \ccc{ArrangementTraits_2} refines the
|
||||
\ccc{ArrangementXMonotoneTraits_2} concept by adding the notion
|
||||
of a general, not necessarily $x$-monotone (and not necessarily
|
||||
continuous) curve. A model of this concept must define the
|
||||
\ccc{Curve_2} type and support the subdivision of a curve into a
|
||||
set of continuous $x$-monotone curves and isolated points using
|
||||
the predicate \ccc{Make_x_monotone_2}. For example, the curve
|
||||
$C:\ (x^2 + y^2)(x^2 + y^2 - 1) = 0$ is the unit circle (the loci
|
||||
of all points for which $x^2 + y^2 = 1$) with the origin $(0,0)$
|
||||
as a singular point in its interior. $C$ should therefore be
|
||||
divided into two circular arcs (the upper part and the lower part
|
||||
of the unit circle) and a single isolated point.
|
||||
connected) curve. A model of this concept must define the
|
||||
\ccc{Curve_2} type and support the division of a curve into a
|
||||
set of continuous $x$-monotone curves and isolated points. For
|
||||
example, the curve $C:\ (x^2 + y^2)(x^2 + y^2 - 1) = 0$ is the
|
||||
unit circle (the loci of all points for which $x^2 + y^2 = 1$)
|
||||
with the origin $(0,0)$ as a singular point in its interior. $C$
|
||||
should therefore be divided into two circular arcs (the upper
|
||||
part and the lower part of the unit circle) and a single isolated
|
||||
point.
|
||||
|
||||
Note that the refined model \ccc{ArrangementTraits_2} is required
|
||||
only when using the free \ccc{insert()} functions (see
|
||||
Section~\ref{arr_sec:gl_funcs}), which accept a \ccc{Curve_2} object
|
||||
in the incremental version, or a range of \ccc{Curve_2} objects in the
|
||||
aggregated version. In all other cases it is sufficient to use a model
|
||||
of the \ccc{ArrangementXMonotoneTraits_2} concept.
|
||||
|
||||
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
\subsubsection{Supporting Unbounded Curves}
|
||||
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
%
|
||||
An arrangement that supports unbounded $x$-monotone curves maintains
|
||||
an implicit bounding rectangle in the \dcel{} structure; see
|
||||
Section~\ref{arr_ssec:unb_rep}. The unbounded ends of vertical rays,
|
||||
vertical lines, and curves with vertical asymptotes are represented
|
||||
by vertices that lie on the bottom or top sides of this bounding
|
||||
rectangle. These vertices are not associated with points, but are
|
||||
associated with (finite) $x$-coordinates. The unbounded ends of all
|
||||
other curves are represented by vertices that lie on the left or
|
||||
right sides of this bounding rectangle. These vertices are not
|
||||
associated with points either. Edges connect these vertices and the
|
||||
four vertices that represents the corners of this bounding rectangle
|
||||
to form the rectangle.
|
||||
|
||||
Several predicates are required to handle $x$-monotone curves that
|
||||
approach infinity and thus approach the boundary of the parameter
|
||||
space. These predicates are sufficient to handle not only curves
|
||||
embedded in an unbounded parameter space, but also curves embedded
|
||||
in a bounded parameter space with open boundaries. Let $b_l$ and
|
||||
$b_r$ denote the $x$-coordinates of the left and right boundaries of
|
||||
the parameter space, respectively. Let $b_b$ and $b_t$ denote the
|
||||
$y$-coordinates of the bottom and top boundaries of the parameter
|
||||
space, respectively. Recall that currently the general code of the
|
||||
arrangement only supports the case where the parameter space is the
|
||||
entire compactified plane, thus $b_l = b_b = -\infty$ and
|
||||
$b_r = b_t = +\infty$. Nonetheless, when the parameter space is
|
||||
bounded, it is the exact geometric embedding of the implicit bounding
|
||||
rectangle. In the following we assume that an $x$ monotone
|
||||
curve $C$ can be considered as a parametric curve $C(t) = (X(t),Y(t))$
|
||||
defined over a closed, open, or half open interval with endpoints~$0$
|
||||
and~$1$.
|
||||
|
||||
%% The additional requirements are organized in four different concepts,
|
||||
%% one for each side. Models of the concept associated with the bottom
|
||||
%% and top sides can only handle curves with finite $x$-coordinates.
|
||||
%% Curves with negative infinite and positive infinite $x$-coordinates
|
||||
%% are handled by models of concepts associated with the left and right
|
||||
%% sides, respectively. We defer the introducing of the four individual
|
||||
%% concepts to a later release to avoid clutter. Instead, we introduce
|
||||
%% the single concept \ccc{ArrangementOpenBoundaryTraits_2}, which
|
||||
%% combines all the four concepts. The combined concept refines the
|
||||
%% concept \ccc{ArrangementBasicTraits_2}. The arrangement template
|
||||
%% instantiated with a traits class that models this combined concept
|
||||
%% can handle curves that are unbounded in any direction.
|
||||
Models of the concept \ccc{ArrangementOpenBoundaryTraits_2} handle
|
||||
curves that approach the boundary of the parameter space. This concept
|
||||
refines the concept \ccc{ArrangementBasicTraits_2}. The arrangement
|
||||
template instantiated with a traits class that models this concept
|
||||
can handle curves that are unbounded in any direction. If some curves
|
||||
inserted into an arrangement object are expected to be unbounded, namely,
|
||||
there exists $d \in \{0,1\}$ such that
|
||||
$\lim_{t \rightarrow d}X(t) = \pm\infty$ or
|
||||
$\lim_{t \rightarrow d}y(t) = \pm\infty$
|
||||
holds for at least one input curve $C(t) = (X(t),Y(t))$, the arrangement
|
||||
template must be instantiated with a model of the
|
||||
\ccc{ArrangementOpenBoundaryTraits} concept.\footnote{We
|
||||
intend to enhance the arrangement template to handle curves confined
|
||||
to a bounded yet open parameter space. A curve that reaches the
|
||||
boundary of the parameter space in this case is bounded and open.}
|
||||
|
||||
All the four types \ccc{Left_side_category},
|
||||
\ccc{Right_side_category}, \ccc{Bottom_side_category}, and
|
||||
\ccc{Top_side_category} nested in a model of the concept
|
||||
\ccc{ArrangementOpenBoundaryTraits} must be convertible to
|
||||
\ccc{Arr_open_side_tag}.\footnote{The tags
|
||||
\ccc{Arr_oblivious_side_tag} and \ccc{Arr_open_side_tag} are only
|
||||
two out of a larger number of options for the side categories
|
||||
included in major extension the code is going through.}
|
||||
For example, the \ccc{Arr_rational_arc_traits_2} traits-model supports
|
||||
unbounded curves; see Section~\ref{arr_ssec:tr_ratfunc}. Thus, all
|
||||
four nested types are defined as \ccc{Arr_open_side_tag}.
|
||||
Adversely, all four types nested in the \ccc{Arr_segment_traits_2}
|
||||
traits-model (see Section~\ref{arr_ssec:tr_segs}) are defined as
|
||||
\ccc{Arr_oblivious_side_tag}, as segments are always
|
||||
bounded.\footnote{We intend to introduce more concepts that require
|
||||
only a subset of the categories to be convertible to
|
||||
\ccc{Arr_open_side_tag}.}
|
||||
|
||||
A model of the concept \ccc{ArrangementOpenBoundaryTraits_2} must provide
|
||||
the additional predicates listed below.
|
||||
$x$-coordinates and $y$-coordinates are differently handled. This
|
||||
asymmetry is brought on by the various algorithms applied to
|
||||
arrangements, the input and output arguments of which are $x$-monotone
|
||||
curves. Indeed, all curves maintained by any arrangement are
|
||||
continuous weakly $x$-monotone curves. A non $x$-monotone curve is
|
||||
divided into $x$-monotone sub curves (and perhaps points) before it
|
||||
is inserted into an arrangement. This asymmetry is also reflected in
|
||||
the additional predicates listed below.
|
||||
%% Notice that curves that reach
|
||||
%% the left or right boundary sides are handled by the two predicates
|
||||
%% \ccc{Parameter_space_in_x_2} and \ccc{Compare_y_near_boundary_2},
|
||||
%% while the handling of curves that reach the bottom or top boundary
|
||||
%% sides is performed by the three predicates
|
||||
%% \ccc{Parameter_space_in_y_2}, \ccc{Compare_x_at_limit_2}, and
|
||||
%% \ccc{Compare_x_near_limit_2}.
|
||||
|
||||
\begin{description}
|
||||
\item[\ccc{Parameter_space_in_x_2}:]
|
||||
Given a parametric $x$-monotone curve $C(t) = (X(t),Y(t))$ and an
|
||||
enumerator that specifies either the minimum end or the maximum end
|
||||
of the curve, and thus maps to a parameter value $d \in \{0,1\}$,
|
||||
this predicate determines the location of the curve end along the
|
||||
$x$-dimension. Formally, the predicate determines whether
|
||||
$\lim_{t \rightarrow d} X(t)$ evaluates to $b_l$, $b_r$, or a value
|
||||
in between.
|
||||
%
|
||||
\item[\ccc{Compare_y_near_boundary_2}:]
|
||||
Given two $x$-monotone curves $C_1$ and $C_2$ and an enumerator $i$
|
||||
that specifies either the minimum ends or the maximum ends of the
|
||||
two curves, this predicate compares the $y$-coordinates of the
|
||||
curves near their respective ends. That is, the predicate compares
|
||||
the $y$-coordinates of the vertical projection of a point $p$ onto
|
||||
$C_1$ and onto $C_2$. If the enumerator $i$ specifies the minimum
|
||||
ends, the curves must approach the left boundary-side. In this case
|
||||
$p$ is located far to the left, such that the result is invariant
|
||||
under a translation of $p$ farther to the left. If $i$ specifies the
|
||||
maximum ends, the curves must approach the right boundary-side. In
|
||||
that case $p$ is located far to the right in a similar manner.
|
||||
%
|
||||
\item[\ccc{Parameter_space_in_y_2}:]
|
||||
Given a parametric $x$-monotone curve $C(t) = (X(t),Y(t))$ and an
|
||||
enumerator that specifies either the minimum end or the maximum end
|
||||
of the curve, and thus maps to a parameter value $d \in \{0,1\}$,
|
||||
this predicate determines the location of the curve end along the
|
||||
$y$-dimension. Formally, the predicate determines whether
|
||||
$\lim_{t \rightarrow d} Y(t)$ evaluates to $b_b$, $b_t$, or a value
|
||||
in between.
|
||||
%
|
||||
\item[\ccc{Compare_x_at_limit_2}:]
|
||||
Two versions of this predicate are provided:
|
||||
(i) Given a point $p$, a parametric $x$-monotone curve
|
||||
$C(t) = (X(t),Y(t))$, and an enumerator that specifies either the
|
||||
minimum end or the maximum end of the curve, and thus maps to a
|
||||
parameter value $d \in \{0,1\}$, this predicate compares the
|
||||
$x$-coordinate of $p$ and $\lim_{t \rightarrow d} X(t)$. If the
|
||||
parameter space is unbounded, a precondition assures that $C$
|
||||
has a vertical asymptote at its $d$-end; that is
|
||||
$\lim_{t \rightarrow d} X(t)$ is finite.
|
||||
(ii) Given two parametric $x$-monotone curves
|
||||
$C_1(t) = (X_1(t),Y_1(t))$ and $C_2(t) = (X_2(t),Y_2(t))$ and two
|
||||
enumerators that specify either the minimum end or the maximum
|
||||
end of each curve, and thus map to parameter values
|
||||
$d_1\in \{0,1\}$ and $d_2 \in \{0,1\}$ for $C_1$ and for $C_2$,
|
||||
respectively, this predicate compares
|
||||
$\lim_{t \rightarrow d_1} X_1(t)$ and $\lim_{t \rightarrow d_2} X_2(t)$.
|
||||
If the parameter space is unbounded, a precondition assures that
|
||||
$C_1$ and $C_2$ have vertical asymptote at their respective ends;
|
||||
that is $\lim_{t \rightarrow d_1} X_1(t)$ and
|
||||
$\lim_{t \rightarrow d_2} X_2(t)$ are finite.
|
||||
%
|
||||
\item[\ccc{Compare_x_near_limit_2}:]
|
||||
Given two $x$-monotone curves $C_1$ and $C_2$ and an enumerator $i$
|
||||
that specifies either the minimum ends or the maximum ends of the
|
||||
two curves, this predicate compares the $x$-coordinates of the
|
||||
curves near their respective ends. That is, the predicate compares
|
||||
the $x$-coordinates of the horizontal projection of a point $p$
|
||||
onto $C_1$ and onto $C_2$. If the parameter space is unbounded, a
|
||||
precondition assures that $C_1$ and $C_2$ have vertical asymptote
|
||||
at their respective ends. Furthermore, both curves approach the
|
||||
same boundary-side, either the bottom or the top, at their
|
||||
respective ends. If both curves approach the bottom boundary-side,
|
||||
$p$ is located far to the bottom, such that the result is invariant
|
||||
under a translation of $p$ farther to the bottom. If both curves
|
||||
approach the top boundary-side, $p$ is located far to the top in a
|
||||
similar manner. Another precondition assures that the
|
||||
$x$-coordinates of the limits of the curves at their respective
|
||||
ends are equal. That is, the predicate \ccc{Compare_x_at_limit_2}
|
||||
applied to $C_1$, $C_2$, and $i$ evaluates to \ccc{EQUAL}.
|
||||
\end{description}
|
||||
only when using the free \ccc{insert()} and
|
||||
\ccc{insert()} functions (see Section~\ref{arr_sec:gl_funcs}),
|
||||
which accept a \ccc{Curve_2} object in the incremental version,
|
||||
or a range of \ccc{Curve_2} objects in the aggregated version.
|
||||
In all other cases it is sufficient to use a model of the
|
||||
\ccc{ArrangementXMonotoneTraits_2} concept.
|
||||
|
||||
In the rest of this section we review the traits classes
|
||||
included in the public distribution of \cgal, that handle line
|
||||
segments, polylines, conic arcs, rational functions, and arcs of
|
||||
B\'{e}zier and algebraic curves.
|
||||
The last subsection overviews
|
||||
segments, polylines and conic arcs. The last subsection overviews
|
||||
decorators for geometric traits classes distributed with \cgal,
|
||||
which extend other geometric traits-class by attaching auxiliary
|
||||
data with the geometric objects.
|
||||
|
||||
%--------------------------------------------------------------
|
||||
\subsection{Traits Classes for Line Segments and Linear Objects
|
||||
\label{arr_ssec:tr_segs}}
|
||||
%--------------------------------------------------------------
|
||||
|
||||
The \ccc{Arr_segment_traits_2<Kernel>} class used so far in most
|
||||
example programs in this chapter is a model of the concepts
|
||||
\ccc{ArrangementTraits_2}, \ccc{ArrangementLandmarkTraits_2},
|
||||
and \ccc{ArrangementDirectionalXMonotoneTraits_2}; the later
|
||||
enables Boolean set operations. It is parameterized by a
|
||||
The \ccc{Arr_segment_traits_2<Kernel>} class used so far
|
||||
in most example programs in this chapter is parameterized by a
|
||||
geometric kernel and uses the \ccc{Kernel::Point_2} type as it
|
||||
point type. However, neither the \ccc{Curve_2} nor the
|
||||
\ccc{X_monotone_curve_2} types are identical to the
|
||||
@@ -460,13 +304,11 @@ data is stored with the line segments.
|
||||
|
||||
The class \ccc{Arr_non_caching_segment_traits_2<Kernel>} inherits
|
||||
from \ccc{Arr_non_caching_segment_basic_traits_2<Kernel>} and
|
||||
extends it to be a model of the concepts \ccc{ArrangementTraits_2},
|
||||
\ccc{ArrangementLandmarkTraits_2},and
|
||||
\ccc{ArrangementDirectionalXMonotoneTraits_2}. It may thus be used to
|
||||
construct arrangement of intersecting line segments, but as explained
|
||||
above, for efficiency reasons it is recommended to use it only when
|
||||
the arrangement is very sparse and contains hardly any intersection
|
||||
points.
|
||||
extends it to be a model of the \ccc{ArrangementTraits_2} concept.
|
||||
It may thus be used to construct arrangement of intersecting line
|
||||
segments, but as explained above, for efficiency reasons it is
|
||||
recommended to use it only when the arrangement is very sparse and
|
||||
contains hardly any intersection points.
|
||||
|
||||
In the following example we read an input file containing a set of
|
||||
line segments that are pairwise disjoint in their interior. As the
|
||||
@@ -494,9 +336,8 @@ from a \ccc{Kernel::Segment_2} object. Just like the default
|
||||
segment-traits class, the linear-traits class also use caching
|
||||
techniques to speed up its predicates and constructions.
|
||||
|
||||
%------------------------------------------------------------------
|
||||
\subsection{The Polyline-Traits Class\label{arr_ssec:tr_polylines}}
|
||||
%------------------------------------------------------------------
|
||||
%-------------------------------------
|
||||
|
||||
The \ccc{Arr_polyline_traits_2<SegmentTraits>} class can be used
|
||||
to maintain arrangements of polylines (a.k.a. poly-segments),
|
||||
@@ -557,9 +398,7 @@ polylines:
|
||||
|
||||
\ccIncludeExampleCode{Arrangement_on_surface_2/polylines.cpp}
|
||||
|
||||
%--------------------------------------------------------------
|
||||
\subsection{A Traits Class for Circular Arcs and Line Segments
|
||||
\label{arr_ssec:tr_circ_seg}}
|
||||
\subsection{A Traits Class for Circular Arcs and Line Segments\label{arr_ssec:tr_circ_seg}}
|
||||
%--------------------------------------------------------------
|
||||
|
||||
Circles and circular arcs are the simplest form of non-linear curves.
|
||||
@@ -585,14 +424,9 @@ of dilated polygons.
|
||||
|
||||
The \ccc{Arr_circle_segment_traits_2<Kernel>} class-template is designed
|
||||
for efficient handling of arrangements of circular arcs and line segments.
|
||||
It is a model of the concepts \ccc{ArrangementTraits_2} and
|
||||
\ccc{ArrangementDirectionalXMonotoneTraits_2}; the later enables
|
||||
Boolean set operations. Note that it is not a model of
|
||||
\ccc{ArrangementLandmarkTraits_2} concept, so it is impossible to
|
||||
use the landmark point-location strategy. The traits class template
|
||||
is parameterized by a geometric kernel, and can handle arrangements of
|
||||
It is parameterized by a geometric kernel, and can handle arrangements of
|
||||
segments of \ccc{Kernel::Circle_2} objects (full circles are also supported)
|
||||
or of \ccc{Kernel::Line_2} objects---namely circular arcs and line segments.
|
||||
or of \ccc{Kernel::Line_2} objects --- namely circular arcs and line segments.
|
||||
It is important to observe that the nested \ccc{Point_2} type defined by the
|
||||
traits class, whose coordinates are typically algebraic numbers of degree 2,
|
||||
is {\em not} the same as the \ccc{Kernel::Point_2} type, which is capable of
|
||||
@@ -668,9 +502,8 @@ purposes, are based on different concepts, and posses different
|
||||
characteristics. You are encouraged to experiment with both, compare
|
||||
their performance, and use the most suitable for your case.
|
||||
|
||||
%------------------------------------------------------------------
|
||||
\subsection{A Traits Class for Conic Arcs\label{arr_ssec:tr_conic}}
|
||||
%------------------------------------------------------------------
|
||||
%-----------------------------------------
|
||||
|
||||
A {\em conic curve} is an algebraic curve of degree 2. Namely, it
|
||||
is the locus of all points $(x,y)$ satisfying the equation $C:\ r
|
||||
@@ -759,7 +592,7 @@ computations on the number types it defines.
|
||||
\end{itemize}
|
||||
|
||||
The \ccc{Arr_conic_traits_2} models the \ccc{ArrangementTraits_2} and
|
||||
\ccc{ArrangementLandmarkTraits_2} concepts. (It supports
|
||||
the \ccc{ArrangementLandmarkTraits_2} concepts. (It supports
|
||||
the landmark point-location strategy). Its \ccc{Point_2} type is
|
||||
derived from \ccc{AlgKernel::Point_2}, while the \ccc{Curve_2}
|
||||
type represents a bounded, not necessarily $x$-monotone, conic arc.
|
||||
@@ -777,7 +610,6 @@ special cases, such as circular arcs or line segments. The
|
||||
also support basic access functions such as \ccc{source()},
|
||||
\ccc{target()} and \ccc{orientation()}.
|
||||
|
||||
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
\subsubsection{Examples for Arrangements of Conics}
|
||||
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
|
||||
@@ -826,91 +658,53 @@ multiplicity $1$:
|
||||
|
||||
\ccIncludeExampleCode{Arrangement_on_surface_2/conic_multiplicities.cpp}
|
||||
|
||||
%---------------------------------------------------------
|
||||
\subsection{A Traits Class for Arcs of Rational Functions\label{arr_ssec:tr_ratfunc}}
|
||||
%---------------------------------------------------------
|
||||
|
||||
The traits class
|
||||
\ccc{Arr_rational_function_traits_2<AlgebraicKernel_d_1>} handles
|
||||
bounded and unbounded arcs of rational functions, referred to as
|
||||
\emph{rational arcs} (in particular, such an arc may correspond to the
|
||||
entire graph of a rational function), and enables the construction and
|
||||
maintenance of arrangements of such arcs. Rational functions, and
|
||||
polynomial functions in particular, are not only interesting in their
|
||||
own right, they are also very useful for approximating or
|
||||
interpolating more complicated curves; see,
|
||||
A {\em rational function} is given by the equation $y =
|
||||
\frac{P(x)}{Q(x)}$, where $P$ and $Q$ are polynomials of arbitrary
|
||||
degrees. In particular, if $Q(x) = 1$, then the function is a
|
||||
simple polynomial function. A bounded {\em rational arc} is
|
||||
defined by the graph of a rational function over some interval
|
||||
$[x_{\rm min}, x_{\rm max}]$, where $Q$ does not have any real
|
||||
roots in this interval (Thus, the arc does not contain any poles).
|
||||
Rational functions, and polynomial functions in particular, are
|
||||
not only interesting in their own right, they are also very useful
|
||||
for approximating or interpolating more complicated curves; see,
|
||||
e.g.,~\cite[Chapter~3]{cgal:ptvf-nrcpp-02}.
|
||||
|
||||
\ccc{Arr_rational_function_traits_2<AlgebraicKernel_d_1>} is a model
|
||||
of the concepts \ccc{ArrangementTraits_2},
|
||||
\ccc{ArrangementOpenBoundaryTraits_2}, and
|
||||
\ccc{ArrangementDirectionalXMonotoneTraits_2}; the later enables
|
||||
Boolean set operations. Note that it is not a model of
|
||||
\ccc{ArrangementLandmarkTraits_2} concept, so it is impossible to use
|
||||
the landmark point-location strategy with this traits class.
|
||||
%\footnote{This requires a relaxation of \ccc{ArrangementLandmarkTraits_2},
|
||||
%which will be submitted separately.}
|
||||
The computations with rational arcs are guaranteed to be robust and
|
||||
exact, assuming that the coefficient of the polynomials $P$ and $Q$
|
||||
are rational numbers. The $x$-values that determine the interval
|
||||
over which the arc is defined can however be arbitrary algebraic
|
||||
numbers.
|
||||
|
||||
A rational function $y = \frac{P(x)}{Q(x)}$ is defined by two
|
||||
polynomials $P$ and $Q$ of arbitrary degrees. If $Q(x) = 1$ then
|
||||
the function is a simple polynomial function. Usually the domain is
|
||||
$\R$ but the function may also be restricted to a bounded interval
|
||||
$[x_{\rm min}, x_{\rm max}]$ or defined over a ray
|
||||
$(-\infty, x_{\rm max}]$ or $[x_{\rm min}, \infty)$. Rational
|
||||
functions are represented by the nested type \ccc{Curve_2}.
|
||||
A rational arc is always $x$-monotone in the mathematical
|
||||
sense. However, it is not necessarily continuous, as it may have
|
||||
singularities. An arc that has singularities must
|
||||
be split into continuous portions before being inserted into the
|
||||
arrangement. Arbitrary rational functions are represented by the
|
||||
nested type \ccc{Curve_2} and continuous portions of rational
|
||||
functions are represented by the nested type
|
||||
\ccc{X_monotone_curve_2}. Constructors for both types are provided by
|
||||
the traits. A \ccc{Curve_2} may be split up into several
|
||||
\ccc{X_monotone_curve_2} using \ccc{Make_x_monotone_2}.
|
||||
Using the \ccc{Arr_rational_arc_traits_2<AlgKernel, NtTraits>} class
|
||||
template it is possible to construct and maintain arrangement of
|
||||
rational arcs. The template parameters are very similar to the
|
||||
ones used by the \ccc{Arr_conic_traits_2} class template; see
|
||||
the previous section. However, no rational kernel is needed. Also
|
||||
in this case it is recommended to use the
|
||||
\ccc{CORE_algebraic_number_traits} class, with a kernel instantiated
|
||||
with the \ccc{Algebraic} type defined by this class.
|
||||
|
||||
Using the \ccc{Arr_rational_function_traits_2<AlgebraicKernel_d_1>}
|
||||
class template it is possible to construct and maintain arrangement
|
||||
of rational arcs. The template parameter of the traits must be a model
|
||||
of the concept \ccc{AlgebraicKernel_d_1}. A rational function is
|
||||
represented as the quotient of two polynomials $P$ and $Q$ of type
|
||||
\ccc{AlgebraicKernel_d_1::Polynomial_1} and an $x$-interval over which
|
||||
the polynomials are defined. The type of the polynomial coefficients,
|
||||
namely \ccc{AlgebraicKernel_d_1::Coefficient}, cannot be algebraic.
|
||||
Moreover, it is recommended that this type is not made rational either,
|
||||
since using rational, as opposed to integral, coefficients does not
|
||||
extend the range of the rational arcs and is typically less efficient.
|
||||
The type of the interval bounds, namely
|
||||
\ccc{AlgebraicKernel_d_1::Bound}, however, can be algebraic. A point is
|
||||
represented by a rational function and its $x$-coordinate, which is of
|
||||
type \ccc{AlgebraicKernel_d_1::Algebraic_real_1}. Note that an explicit
|
||||
representation of the $y$-coordinate is only computed upon request, as
|
||||
it can be a rather costly operation.
|
||||
The \ccc{Arr_rational_arc_traits_2} is a model of the
|
||||
\ccc{ArrangementTraits_2} concept (but not of the
|
||||
\ccc{ArrangementLandmarkTraits_2} concept, so it is not possible
|
||||
to use the landmark point-location strategy for arrangements of
|
||||
rational arcs). Its \ccc{Point_2} type is derived from
|
||||
\ccc{AlgKernel::Point_2}, while the \ccc{Curve_2} and
|
||||
\ccc{X_monotone_curve_2} types refer to the same class (note that
|
||||
a rational arc is always $x$-monotone). The traits class also
|
||||
defines the \ccc{Rat_vector} type, representing a vector of
|
||||
rational coefficients, (whose type is \ccc{NtTraits::Rational}). A
|
||||
rational arc can be constructed from a single vector of
|
||||
coefficients, specifying the polynomial $P$ alone (and $Q(x) =
|
||||
1$), or from two vectors of coefficients, specifying both $P$ and
|
||||
$Q$.
|
||||
|
||||
The constructed rational functions are cached by the traits class. The
|
||||
cache is local to each traits class object. It is therefore necessary
|
||||
to construct curves using only the constructor objects provided by
|
||||
member functions of the traits class.
|
||||
%This is also the reason why IO is not handled via the usual stream operators.
|
||||
Moreover, a curve must only be used by the traits class object that
|
||||
was used to construct it. The cache is automatically cleaned up from
|
||||
time to time. The amortized clean up costs are constant. In addition,
|
||||
there is also a separate member function that cleans up the cache on
|
||||
demand.
|
||||
|
||||
The curve constructors have an additional advantage. They conveniently
|
||||
enable the provision of two polynomials that define a rational arc
|
||||
using rational coefficients. For example, let $P$ and $Q$ denote two
|
||||
polynomials with integral coefficients that define a rational arc at
|
||||
interest, and let $P'$ and $Q'$ denote two polynomials with rational
|
||||
coefficients that define the same rational arc; that is, the quotients
|
||||
$P/Q$ and $P'/Q'$ are identical. You can construct the rational arc
|
||||
providing the coefficients of $P'$ and $Q'$ to the constructor. In this
|
||||
case the constructor normalizes the coefficients and stores the desired
|
||||
polynomials $P$ and $Q$.
|
||||
|
||||
\begin{figure}[h]
|
||||
\begin{ccTexOnly}
|
||||
\begin{figure}[t]
|
||||
\begin{ccTexOnly}
|
||||
\begin{center}
|
||||
\includegraphics{Arrangement_on_surface_2/fig/ex_16}
|
||||
\end{center}
|
||||
@@ -929,11 +723,9 @@ arrangement of rational arcs depicted in
|
||||
Figure~\ref{arr_fig:ex_16}. Note the usage of the two
|
||||
constructors, for polynomial arcs and for rational arcs:
|
||||
|
||||
\pagebreak[3]
|
||||
|
||||
\ccIncludeExampleCode{Arrangement_on_surface_2/rational_functions.cpp}
|
||||
|
||||
\begin{figure}[h]
|
||||
\begin{figure}[t]
|
||||
\begin{ccTexOnly}
|
||||
\begin{center}
|
||||
\includegraphics{Arrangement_on_surface_2/fig/ex_unb_rat}
|
||||
@@ -950,8 +742,8 @@ constructed in
|
||||
\end{figure}
|
||||
|
||||
The following example demonstrates the construction of an
|
||||
arrangement of six rational arcs---four unbounded arcs and two
|
||||
bounded ones---as depicted in Figure~\ref{arr_fig:ex_unb_rat}. Note
|
||||
arrangement of six rational arcs --- four unbounded arcs and two
|
||||
bounded ones --- as depicted in Figure~\ref{arr_fig:ex_unb1}. Note
|
||||
the usage of the constructors of an entire rational function and of
|
||||
an infinite ``ray'' of such a function. Also observe that the hyperbolas
|
||||
$y = \pm\frac{1}{x}$ and $y = \pm\frac{1}{2x}$ never intersect, although
|
||||
@@ -960,9 +752,8 @@ unbounded faces are created between them:
|
||||
|
||||
\ccIncludeExampleCode{Arrangement_on_surface_2/unbounded_rational_functions.cpp}
|
||||
|
||||
%----------------------------------------------------------------------------
|
||||
\subsection{A Traits Class for Planar B\'ezier Curves\label{arr_ssec:tr_bez}}
|
||||
%----------------------------------------------------------------------------
|
||||
%---------------------------------------------------------
|
||||
|
||||
A planar {\em B\'ezier curve} $B$ is a parametric curve defined by a sequence
|
||||
of {\em control points} $p_0, \ldots, p_n$ as follows:
|
||||
@@ -1004,7 +795,7 @@ See the Reference Manual for the exact interface of the \ccc{Point_2},
|
||||
|
||||
The \ccc{Arr_Bezier_curve_traits_2} is a model of the
|
||||
\ccc{ArrangementTraits_2} concept (but not of the
|
||||
\ccc{ArrangementLandmarkTraits_2} concept, so it is impossible
|
||||
\ccc{ArrangementLandmarkTraits_2} concept, so it is not possible
|
||||
to use the landmark point-location strategy for arrangements of
|
||||
rational arcs).
|
||||
|
||||
@@ -1033,10 +824,9 @@ Figure~\ref{arr_fig:ex_bez}.
|
||||
|
||||
\ccIncludeExampleCode{Arrangement_on_surface_2/Bezier_curves.cpp}
|
||||
|
||||
%-------------------------------------------------------------------------
|
||||
\subsection{A Traits Class for Planar Algebraic Curves of Arbitrary Degree
|
||||
\label{arr_ssec:tr_alg}}
|
||||
%-------------------------------------------------------------------------
|
||||
\subsection{A Traits Class for Planar Algebraic Curves
|
||||
of Arbitrary Degree\label{arr_ssec:tr_alg}}
|
||||
%---------------------------------------------------------
|
||||
|
||||
An algebraic curve $C$ in the plane is defined as the (real) zero locus
|
||||
of a polynomial $f(x,y)$ in two variables. The curve is uniquely defined
|
||||
@@ -1061,7 +851,7 @@ we support unbounded curves, vertical curves or segments, and isolated points.
|
||||
|
||||
The \ccc{Arr_algebraic_segment_traits_2<Coefficient>} class template
|
||||
is a model of the \ccc{ArrangementTraits_2} concept (but not of the
|
||||
\ccc{ArrangementLandmarkTraits_2} concept, so it is impossible
|
||||
\ccc{ArrangementLandmarkTraits_2} concept, so it is not possible
|
||||
to use the landmark point-location strategy for arrangements of
|
||||
algebraic curves).
|
||||
The template argument \ccc{Coefficient} determines
|
||||
@@ -1157,7 +947,7 @@ its $x$-range contains no critical point in its interior.
|
||||
\end{ccTexOnly}
|
||||
\begin{ccHtmlOnly}
|
||||
<p><center>
|
||||
<img src="./fig/cylindrical_decomposition.gif" border=0 alt="The algebraic curves">
|
||||
<img src="./fig/cylindrical_decomposition.gif" border=0 alt="The braic curves">
|
||||
</center>
|
||||
\end{ccHtmlOnly}
|
||||
\caption{The critical $x$-coordinates of an algebraic curve (dashed lines),
|
||||
@@ -1212,9 +1002,8 @@ Figure~\ref{arr_fig:ex_alg_segments}.
|
||||
|
||||
\ccIncludeExampleCode{Arrangement_on_surface_2/algebraic_segments.cpp}
|
||||
|
||||
%-----------------------------------------------------------
|
||||
\subsection{Traits-Class Decorators\label{arr_ssec:meta_tr}}
|
||||
%-----------------------------------------------------------
|
||||
%-----------------------------------
|
||||
|
||||
Geometric traits-class decorators allow you to attach auxiliary
|
||||
data to curves and to points. The data is automatically manipulated
|
||||
@@ -1291,7 +1080,6 @@ between two $x$-monotone curves $c_1$ and $c_2$ with associated data sets
|
||||
$S_1$ and $S_2$, respectively, the overlapping subcurve is associated with
|
||||
the consolidated set $S_1 \cup S_2$.
|
||||
|
||||
%~~~~~~~~~~~~~~~~~~~~~~~
|
||||
\subsubsection{Examples}
|
||||
%~~~~~~~~~~~~~~~~~~~~~~~
|
||||
|
||||
|
||||
@@ -11,7 +11,7 @@ lines and rays.
|
||||
%--------------------------------------------
|
||||
|
||||
Consider the arrangement induced by the two lines $y = x$ and
|
||||
$y = -x$. These two lines intersect at the origin, such that the
|
||||
$y = -x$. These two line intersect at the origin, such that the
|
||||
arrangement contains a single vertex $v = (0,0)$, with four infinite
|
||||
rays emanating from it. Each ray corresponds to an arrangement edge,
|
||||
and these edges subdivide the plane into four unbounded faces.
|
||||
@@ -151,11 +151,11 @@ Halfedges are drawn as thin arrows. The vertices $v_1, \ldots, v_8$
|
||||
lie at infinity, and are not associated with valid points. The
|
||||
halfedges that connect them are fictitious, and are not associated
|
||||
with concrete curves. The face denoted $f_0$ (lightly shaded)
|
||||
is the fictitious ``unbounded face'' which lies outside the bounding
|
||||
is the fictitious ``unbounded face'' which lies outside the imaginary
|
||||
rectangle (dashed) that bounds the actual arrangement. The four
|
||||
fictitious vertices $v_{\rm bl}, v_{\rm tl}, v_{\rm br}$ and
|
||||
$v_{\rm tr}$ represent the four corners of the bounding
|
||||
rectangle.\label{arr_fig:unb_dcel}}
|
||||
$v_{\rm tr}$ represent the four corners of the imaginary bounding
|
||||
rectangle..\label{arr_fig:unb_dcel}}
|
||||
\end{figure}
|
||||
|
||||
Given a set $\calC$ of unbounded curves, a simple approach for
|
||||
@@ -167,7 +167,7 @@ $\calC$. This process would result in a set $\calC$ of bounded curves
|
||||
straightforward to compute the arrangement induced by this set.
|
||||
However, we would like to operate directly on the unbounded curves
|
||||
without having to preprocess them. Therefore, we use an implicit
|
||||
bounding rectangle embedded in the \dcel{} structure.
|
||||
bounding rectangle embedded in the \dcel\ structure.
|
||||
Figure~\ref{arr_fig:unb_dcel} shows the arrangement of four lines
|
||||
that subdivide the plane into eight unbounded faces and two bounded
|
||||
ones. Notice that in this case the unbounded faces have outer
|
||||
@@ -179,57 +179,57 @@ infinity, and the halfedges connecting them are \emph{fictitious}, and
|
||||
represent portions of the bounding rectangle. Note that the outer CCBs
|
||||
of the unbounded faces contain fictitious halfedges. The twins of these
|
||||
halfedges form together one connected component that corresponds to
|
||||
the entire bounding rectangle, which forms a single hole in a face
|
||||
$f_0$. We say that $f_0$ is \emph{fictitious}, as it does
|
||||
not correspond to a real two-dimensional cell of the arrangement.
|
||||
the entire imaginary rectangle, which forms a single hole in a face
|
||||
$\tilde{f}$. We say that $\tilde{f}$ is \emph{fictitious}, as it does
|
||||
not corresponds to a real two-dimensional cell of the arrangement.
|
||||
|
||||
Observe that there are four extra vertices at infinity that do not lie
|
||||
on any curve; they are denoted as $v_{\rm bl}, v_{\rm tl},
|
||||
v_{\rm br}$, and $v_{\rm tr}$, and represent the bottom-left, top-left,
|
||||
bottom-right, and top-right corners of the bounding rectangle,
|
||||
respectively. Similarly, there are fictitious halfedges that lie on
|
||||
the top, the bottom, the left, or the right edge of the bounding
|
||||
rectangle. When the arrangement is empty, there are exactly
|
||||
the top, the bottom, the left, or the right edge of the imaginary
|
||||
bounding rectangle. When the arrangement is empty, there are exactly
|
||||
four pairs of fictitious halfedges, that divide the plane into two
|
||||
faces, namely a fictitious face lying outside of the bounding
|
||||
rectangle and a single unbounded face bounded by the bounding rectangle.
|
||||
faces, namely a fictitious face lying outside of the imaginary bounding
|
||||
rectangle and a single unbounded face bounded by the imaginary
|
||||
bounding rectangle.
|
||||
|
||||
Summarizing the above, there are four types of arrangement vertices,
|
||||
which differ from one another by their location with respect to the
|
||||
bounding bounding rectangle:
|
||||
which differ from one another by their location on the imaginary
|
||||
bounding rectangle:
|
||||
\begin{enumerate}
|
||||
\item\label{type-normal}
|
||||
A vertex, associated with a point in $\real^2$ whose
|
||||
coordinates are bounded. Such a vertex always lies inside the
|
||||
bounding rectangle.
|
||||
\item\label{type-unbounded}
|
||||
A vertex that represents an unbounded end of an $x$-monotone curve
|
||||
that is defined at $x = -\infty$ or at $x = \infty$. In case of
|
||||
a horizontal line or a curve with a horizontal asymptote, the
|
||||
$y$-coordinate of the curve end may be finite (see for example the
|
||||
vertices $v_2$ and $v_7$ in Figure~\ref{arr_fig:unb_dcel}), but in
|
||||
general the curve end also goes to $y = \pm\infty$ (see for instance
|
||||
the vertices $v_1$, $v_3$, $v_6$ and $v_8$ in
|
||||
Figure~\ref{arr_fig:unb_dcel}). For our convenience, we will always
|
||||
take a ``tall'' enough bounding rectangle and treat such vertices as
|
||||
lying on either the left or right rectangle edges (that is, if a curve
|
||||
is defined at $x = -\infty$, its left end will be represented by
|
||||
a vertex on the left edge of the bounding rectangle, and if it is
|
||||
defined at $x = \infty$, its right end will be represented by a
|
||||
vertex of the right edge).
|
||||
\item\label{type-unbounded-vertical}
|
||||
A vertex that represent the unbounded end of a vertical line or of a
|
||||
curve with a vertical asymptote (finite $x$-coordinate and an
|
||||
unbounded $y$-coordinate). Such a vertex always lies on one of the
|
||||
horizontal edges of the bounding rectangle (either the bottom one if
|
||||
$y = -\infty$, or the top one if $y = \infty$). The vertices $v_4$
|
||||
and $v_5$ in Figure~\ref{arr_fig:unb_dcel} are of this type.
|
||||
\item\label{type-fictitious}
|
||||
The fictitious vertices that represent the four corners of the
|
||||
bounding bounding rectangle.
|
||||
\item
|
||||
A ``normal'' vertex, associated with a point in $\real^2$ whose
|
||||
coordinates are bounded. Such a vertex always lies inside the
|
||||
bounding rectangle.
|
||||
\item
|
||||
A vertex that represent an unbounded end of an $x$-monotone curve
|
||||
that is defined at $x = -\infty$ or at $x = \infty$. In case of
|
||||
a horizontal line or a curve with a horizontal asymptote, the
|
||||
$y$-coordinate of the curve end may be finite (see for example the
|
||||
vertices $v_2$ and $v_7$ in Figure~\ref{arr_fig:unb_dcel}), but in
|
||||
general the curve end also goes to $y = \pm\infty$ (see for instance
|
||||
the vertices $v_1$, $v_3$, $v_6$ and $v_8$ in
|
||||
Figure~\ref{arr_fig:unb_dcel}). For our convenience, we will always
|
||||
take a ``tall'' enough bounding rectangle and treat such vertices as
|
||||
lying on either the left or right rectangle edges (that is, if a curve
|
||||
is defined at $x = -\infty$, its left end will be represented by
|
||||
a vertex on the left edge of the bounding rectangle, and if it is
|
||||
defined at $x = \infty$, its right end will be represented by a
|
||||
vertex of the right edge).
|
||||
\item
|
||||
A vertex that represent the unbounded end of a vertical line or of a
|
||||
curve with a vertical asymptote (finite $x$-coordinate and an
|
||||
unbounded $y$-coordinate). Such a vertex always lies on one of the
|
||||
horizontal edges of the bounding rectangle (either the bottom one if
|
||||
$y = -\infty$, or the top one if $y = \infty$). The vertices $v_4$
|
||||
and $v_5$ in Figure~\ref{arr_fig:unb_dcel} are of this type.
|
||||
\item
|
||||
The fictitious vertices that represent the four corners of the
|
||||
imaginary bounding rectangle.
|
||||
\end{enumerate}
|
||||
A vertex (at infinity) of Type~\ref{type-unbounded} or
|
||||
Type~\ref{type-unbounded-vertical} above always has
|
||||
A vertex at infinity of types 1--3 above always has
|
||||
three incident edges: one concrete edge that is associated with an
|
||||
unbounded portion of an $x$-monotone curve, and two fictitious edges
|
||||
connecting the vertex to its neighboring vertices at infinity.
|
||||
@@ -243,48 +243,44 @@ following methods, in addition to the ones listed in
|
||||
Section~\ref{arr_ssec:traverse}:
|
||||
\begin{itemize}
|
||||
\item
|
||||
The \ccc{Vertex} class provides three-valued predicates
|
||||
\ccc{parameter_space_in_x()} and \ccc{parameter_space_in_y()}, which
|
||||
return the location of the geometric embedding of the vertex in the
|
||||
parameter space. In particular, the former returns
|
||||
\ccc{ARR_LEFT_BOUNDARY}, \ccc{ARR_INTERIOR}, or
|
||||
\ccc{ARR_RIGHT_BOUNDARY}, and the latter returns
|
||||
\ccc{ARR_BOTTOM_BOUNDARY}, \ccc{ARR_INTERIOR}, or
|
||||
\ccc{ARR_TOP_BOUNDARY}. As the package currently supports only the
|
||||
case where the parameter space is the compactified plane, the former
|
||||
returns \ccc{ARR_INTERIOR} if the $x$-coordinate associated with the
|
||||
vertex is finite, \ccc{ARR_LEFT_BOUNDARY} if it is $-\infty$, and
|
||||
\ccc{ARR_RIGHT_BOUNDARY} if it is $\infty$. The latter returns
|
||||
\ccc{ARR_INTERIOR} if the $y$-coordinate associated with the vertex
|
||||
is finite, \ccc{ARR_BOTTOM_BOUNDARY} if it is $-\infty$, and
|
||||
\ccc{ARR_TOP_BOUNDARY} if it is $\infty$. The Boolean predicate
|
||||
\ccc{is_at_open_boundary()} is also provided. You can access the
|
||||
point associated with a vertex only if it is not a vertex at an open
|
||||
boundary (recall that a vertex at an open boundary is not associated
|
||||
with a \ccc{Point_2} object).
|
||||
The \ccc{Vertex} type provides the three-valued predicates
|
||||
\ccc{parameter_space_in_x()} and \ccc{parameter_space_in_y()}.
|
||||
The former returns \ccc{ARR_INTERIOR} if the point associated with the
|
||||
vertex has a finite $x$-coordinate, \ccc{ARR_LEFT_BOUNDARY}
|
||||
if the vertex lies on the left boundary of the parameter space, and
|
||||
\ccc{ARR_RIGHT_BOUNDARY} if the vertex lies on the right boundary of
|
||||
the parameter space. Similarly, \ccc{parameter_space_in_y()} returns
|
||||
\ccc{ARR_INTERIOR}, \ccc{ARR_BOTTOM_BOUNDARY}, or
|
||||
\ccc{ARR_TOP_BOUNDARY} depending on whether the point associated with
|
||||
the vertex has a finite $y$-coordinate, lies on the bottom boundary of
|
||||
the parameter space, or lies on the top boundary. The Boolean predicate
|
||||
\ccc{is_at_open_boundary()} is also supported. It checks whether the
|
||||
vertex lies at infinity. You can access the point associated with a
|
||||
vertex only if it does not lie at infinity (recall that a vertex at
|
||||
infinity is not associated with a \ccc{Point_2} object).
|
||||
%
|
||||
\item
|
||||
The nested \ccc{Halfedge} class provides the Boolean predicate
|
||||
\ccc{is_fictitious()}. The $x$-monotone curve associated with
|
||||
a halfedge can be accessed by the \ccc{curve()} method only if the
|
||||
halfedge is not fictitious.
|
||||
The nested \ccc{Halfedge} class provides the Boolean predicate
|
||||
\ccc{is_fictitious()}. The $x$-monotone curve associated with
|
||||
a halfedge can be accessed by the \ccc{curve()} method only if the
|
||||
halfedge is not fictitious.
|
||||
%
|
||||
\item
|
||||
The nested \ccc{Face} class provides the Boolean predicate
|
||||
\ccc{f.is_fictitious()}. The method \ccc{outer_ccb()} has the
|
||||
precondition that the face is not fictitious. Note that non-fictitious
|
||||
unbounded faces always have valid CCBs (although this CCB may
|
||||
comprise only fictitious halfedge in case the arrangement contains
|
||||
only bounded curves).
|
||||
The nested \ccc{Face} class provides the Boolean predicate
|
||||
\ccc{f.is_fictitious()}. The method \ccc{outer_ccb()} has the
|
||||
precondition that the face is not fictitious. Note that valid
|
||||
unbounded faces always have valid CCBs (although this CCB may
|
||||
comprise only fictitious halfedge in case the arrangement contains
|
||||
only bounded curves).
|
||||
\end{itemize}
|
||||
|
||||
The method \ccc{arr.number_of_edges()} does not count the number of
|
||||
fictitious edges, (which is always
|
||||
\ccc{arr.number_of_vertices_at_infinity() + 4}), and the iterators
|
||||
returned by \ccc{arr.edges_begin()} and \ccc{arr.edges_end()} specify
|
||||
a range of non-fictitious edges. Similarly, \ccc{arr.number_of_faces()}
|
||||
does not count the fictitious face. However, the
|
||||
\ccc{Ccb_halfedge_circulator} of the outer boundary of an
|
||||
a range of valid edges. Similarly, \ccc{arr.number_of_faces()} does not
|
||||
count the fictitious face.
|
||||
However, the \ccc{Ccb_halfedge_circulator} of the outer boundary of an
|
||||
unbounded face or the \ccc{Halfegde_around_vertex_circulator} of a vertex
|
||||
at infinity do traverse fictitious halfedges. For example, it is possible
|
||||
to traverse the outer boundaries of the unbounded arrangement edges
|
||||
|
||||
@@ -9,7 +9,7 @@
|
||||
|
||||
\label{chapterArrangement_on_surface_2}
|
||||
\ccChapterRelease{\ArrangementOnSurfaceRev. \ \ArrangementOnSurfaceDate}
|
||||
\ccChapterAuthor{Ron Wein, Efi Fogel, Baruch Zukerman, Dan Halperin, Eric Berberich, and Oren Zalzman}
|
||||
\ccChapterAuthor{Ron Wein, Efi Fogel, Baruch Zukerman, Dan Halperin, and Eric Berberich}
|
||||
|
||||
\input{Arrangement_on_surface_2/PkgDescription.tex}
|
||||
|
||||
|
||||
+159
-31
@@ -18,18 +18,23 @@ continuous $x$-monotone curves (a vertical segment is also considered to be
|
||||
to be pairwise disjoint in their interiors, so they do not intersect
|
||||
except at their endpoints.
|
||||
|
||||
The \ccc{X_monotone_curve_2} curves of an arrangement are confined to an
|
||||
iso-rectangular area called the parameter space. The iso-rectangule can
|
||||
be unbounded, open, or closed. The set of predicates provided by a model
|
||||
the concept \ccRefName{} is sufficient for constructing arrangements of
|
||||
$x$-monotone curves that do not reach or approach the boundary of the
|
||||
parameter space. The nature of the input curves, whether they are
|
||||
expected to reach or approach the left, right, bottom, or top side of the
|
||||
boundary of the parameter space, are conveyed through the definition of
|
||||
four additional nested types, namely \ccc{Left_side_category},
|
||||
\ccc{Right_side_category}, \ccc{Bottom_side_category}, and
|
||||
\ccc{Top_side_category}. Each such type must be convertible to the type
|
||||
\ccc{Arr_oblivious_side_tag}.
|
||||
The $x$-monotone curves may be {\em unbounded}, namely they may have unbounded
|
||||
ends that lie at infinity, or {\em bounded}, in which case their have finite
|
||||
endpoints are representable as \ccc{Point_2} objects. An $x$-monotone curve
|
||||
may also have one unbounded end and one finite endpoint (e.g. a ray).
|
||||
If unbounded curves are supported, the requirements from the traits class
|
||||
are extended a bit, as described below. In particular, the traits class needs
|
||||
to support comparisons at infinity, where we interpret comparisons at infinity
|
||||
as follows: Suppose we wish to compare the $y$-position of the hyperbolas
|
||||
$y_1 = \frac{1}{x}$ and $y_2 = \frac{2}{x}$ at $x = \infty$; than since there
|
||||
exists $x_0$ such that for each finite $x > x_0$ we have $y_2(x) > y_1(x)$
|
||||
(in our case we can take $x_0 = 0$), we say that $y_2$ is {\em above} $y_1$ at
|
||||
infinity. Similarly, when comparing the $x$-positions of the vertical line
|
||||
$x = 0$ and the $xy$-minimal end of parabola $y = \frac{1}{x}$ for $x > 0$
|
||||
(which has a vertical asymptote at $x = 0$), we define that the line lies to
|
||||
the {\em left} of the hyperbola. Namely, comparing curves at their unbounded
|
||||
ends should return the comparison result \ccc{EQUAL} only if the curves
|
||||
overlap.
|
||||
|
||||
\ccRefines{DefaultConstructible, CopyConstructible, Assignable}
|
||||
|
||||
@@ -46,14 +51,18 @@ four additional nested types, namely \ccc{Left_side_category},
|
||||
{indicates whether the nested functor \ccc{Compare_at_x_left_2} is
|
||||
provided.}
|
||||
|
||||
\ccNestedType{Left_side_category}
|
||||
{Must be convertible to \ccc{Arr_oblivious_side_tag}.}
|
||||
\ccNestedType{Bottom_side_category}
|
||||
{Must be convertible to \ccc{Arr_oblivious_side_tag}.}
|
||||
\ccNestedType{Top_side_category}
|
||||
{Must be convertible to \ccc{Arr_oblivious_side_tag}.}
|
||||
\ccNestedType{Right_side_category}
|
||||
{Must be convertible to \ccc{Arr_oblivious_side_tag}.}
|
||||
\ccNestedType{Arr_left_side_category}
|
||||
{indicates the type of the left boundary-side. Must be either
|
||||
\ccc{Arr_oblivious_side_tag} or \ccc{Arr_open_side_tag}.}
|
||||
\ccNestedType{Arr_bottom_side_category}
|
||||
{indicates the type of the bottom boundary-side. Must be either
|
||||
\ccc{Arr_oblivious_side_tag} or \ccc{Arr_open_side_tag}.}
|
||||
\ccNestedType{Arr_top_side_category}
|
||||
{indicates the type of the top boundary-side. Must be either
|
||||
\ccc{Arr_oblivious_side_tag} or \ccc{Arr_open_side_tag}.}
|
||||
\ccNestedType{Arr_right_side_category}
|
||||
{indicates the type of the right boundary-side. Must be either
|
||||
\ccc{Arr_oblivious_side_tag} or \ccc{Arr_open_side_tag}.}
|
||||
|
||||
\ccHeading{Functor Types}
|
||||
% =======================
|
||||
@@ -63,6 +72,16 @@ four additional nested types, namely \ccc{Left_side_category},
|
||||
\ccGlue
|
||||
\ccNestedType{Compare_xy_2}{models the concept \ccc{ArrTraits::CompareXy_2}.}
|
||||
\ccGlue
|
||||
\ccNestedType{Parameter_space_in_x_2}
|
||||
{models the concept \ccc{ArrTraits::ParameterSpaceInX_2}.
|
||||
Required only if the traits class supports unbounded curves
|
||||
(the \ccc{Has_boundary_category} category is defined as \ccc{Tag_true}).}
|
||||
\ccGlue
|
||||
\ccNestedType{Parameter_space_in_y_2}
|
||||
{models the concept \ccc{ArrTraits::ParameterSpaceInY_2}.
|
||||
Required only if the traits class supports unbounded curves
|
||||
(the \ccc{Has_boundary_category} category is defined as \ccc{Tag_true}).}
|
||||
\ccGlue
|
||||
\ccNestedType{Construct_min_vertex_2}
|
||||
{models the concept \ccc{ArrTraits::ConstructMinVertex_2}.}
|
||||
\ccGlue
|
||||
@@ -72,17 +91,30 @@ four additional nested types, namely \ccc{Left_side_category},
|
||||
\ccNestedType{Is_vertical_2}{models the concept \ccc{ArrTraits::IsVertical_2}.}
|
||||
\ccGlue
|
||||
\ccNestedType{Compare_y_at_x_2}
|
||||
{models the concept \ccc{ArrTraits::CompareYAtX_2}.}
|
||||
{models the concept \ccc{ArrTraits::CompareYAtX_2}.
|
||||
If the traits class supports unbounded curves (i.e., the
|
||||
\ccc{Has_boundary_category} category is defined as \ccc{Tag_true}), then
|
||||
the type models the concept \ccc{ArrTraits::CompareYNearBoundary_2}.}
|
||||
\ccGlue
|
||||
\ccNestedType{Compare_y_at_x_left_2}
|
||||
{models the concept \ccc{ArrTraits::CompareYAtXLeft_2}.
|
||||
Required only if the \ccc{Has_left_category} category is convertible to
|
||||
Required only if the \ccc{Has_left_category} category is defined as
|
||||
\ccc{Tag_true}.}
|
||||
\ccGlue
|
||||
\ccNestedType{Compare_y_at_x_right_2}
|
||||
{models the concept \ccc{ArrTraits::CompareYAtXRight_2}.}
|
||||
\ccGlue
|
||||
\ccNestedType{Equal_2}{models the concept \ccc{ArrTraits::Equal_2}.}
|
||||
\ccGlue
|
||||
\ccNestedType{compare_x_near_boundary_2}
|
||||
{models the concept \ccc{ArrTraits::CompareXNearBoundary_2}.
|
||||
Required only if the traits class supports unbounded curves
|
||||
(the \ccc{Has_boundary_category} category is defined as \ccc{Tag_true}).}
|
||||
\ccGlue
|
||||
\ccNestedType{compare_y_near_boundary_2}
|
||||
{models the concept \ccc{ArrTraits::CompareYNearBoundary_2}.
|
||||
Required only if the traits class supports unbounded curves
|
||||
(the \ccc{Has_boundary_category} category is defined as \ccc{Tag_true}).}
|
||||
|
||||
% \ccCreation
|
||||
\ccCreationVariable{traits}
|
||||
@@ -109,6 +141,14 @@ four additional nested types, namely \ccc{Left_side_category},
|
||||
\ccMethod{Compare_y_at_x_right_2 compare_y_at_x_right_2_object() const;} {}
|
||||
\ccGlue
|
||||
\ccMethod{Equal_2 equal_2_object() const;} {}
|
||||
\ccGlue
|
||||
\ccMethod{Parameter_space_in_x_2 parameter_space_in_x_2_object() const;} {}
|
||||
\ccGlue
|
||||
\ccMethod{Parameter_space_in_y_2 parameter_space_in_y_2_object() const;} {}
|
||||
\ccGlue
|
||||
\ccMethod{Compare_x_near_boundary_2 compare_x_near_boundary_2_object() const;} {}
|
||||
\ccGlue
|
||||
\ccMethod{Compare_y_near_boundary_2 compare_y_near_boundary_2_object() const;} {}
|
||||
|
||||
\ccHasModels
|
||||
% ==========
|
||||
@@ -167,7 +207,7 @@ Represents a planar (weakly) $x$-monotone curve.
|
||||
% =================
|
||||
\ccRefPageBegin
|
||||
\begin{ccRefConcept}{ArrTraits::CompareX_2}
|
||||
\ccRefines{AdaptableBinaryFunction}
|
||||
\ccRefines{Functor}
|
||||
|
||||
\ccHasModels\ccc{ArrangementBasicTraits_2::Compare_x_2}
|
||||
|
||||
@@ -183,7 +223,7 @@ Represents a planar (weakly) $x$-monotone curve.
|
||||
% ==================
|
||||
\ccRefPageBegin
|
||||
\begin{ccRefConcept}{ArrTraits::CompareXy_2}
|
||||
\ccRefines{AdaptableBinaryFunction}
|
||||
\ccRefines{Functor}
|
||||
|
||||
\ccHasModels\ccc{ArrangementBasicTraits_2::Compare_xy_2}
|
||||
|
||||
@@ -199,7 +239,7 @@ Represents a planar (weakly) $x$-monotone curve.
|
||||
% ===========================
|
||||
\ccRefPageBegin
|
||||
\begin{ccRefConcept}{ArrTraits::ConstructMinVertex_2}
|
||||
\ccRefines{AdaptableUnaryFunction}
|
||||
\ccRefines{Functor}
|
||||
|
||||
\ccHasModels\ccc{ArrangementBasicTraits_2::Construct_min_vertex_2}
|
||||
|
||||
@@ -213,7 +253,7 @@ Represents a planar (weakly) $x$-monotone curve.
|
||||
% ===========================
|
||||
\ccRefPageBegin
|
||||
\begin{ccRefConcept}{ArrTraits::ConstructMaxVertex_2}
|
||||
\ccRefines{AdaptableUnaryFunction}
|
||||
\ccRefines{Functor}
|
||||
|
||||
\ccHasModels\ccc{ArrangementBasicTraits_2::Construct_max_vertex_2}
|
||||
|
||||
@@ -227,7 +267,7 @@ Represents a planar (weakly) $x$-monotone curve.
|
||||
% ===================
|
||||
\ccRefPageBegin
|
||||
\begin{ccRefConcept}{ArrTraits::IsVertical_2}
|
||||
\ccRefines{AdaptableUnaryFunction}
|
||||
\ccRefines{Functor}
|
||||
|
||||
\ccHasModels\ccc{ArrangementBasicTraits_2::Is_vertical_2}
|
||||
|
||||
@@ -241,7 +281,7 @@ Represents a planar (weakly) $x$-monotone curve.
|
||||
% ====================
|
||||
\ccRefPageBegin
|
||||
\begin{ccRefConcept}{ArrTraits::CompareYAtX_2}
|
||||
\ccRefines{AdaptableBinaryFunction}
|
||||
\ccRefines{Functor}
|
||||
|
||||
\ccHasModels\ccc{ArrangementBasicTraits_2::Compare_y_at_x_2}
|
||||
|
||||
@@ -258,7 +298,7 @@ Represents a planar (weakly) $x$-monotone curve.
|
||||
% ========================
|
||||
\ccRefPageBegin
|
||||
\begin{ccRefConcept}{ArrTraits::CompareYAtXLeft_2}
|
||||
\ccRefines{AdaptableTernaryFunction}
|
||||
\ccRefines{Functor}
|
||||
|
||||
\ccHasModels\ccc{ArrangementBasicTraits_2::Compare_y_at_x_left_2}
|
||||
|
||||
@@ -279,7 +319,7 @@ Represents a planar (weakly) $x$-monotone curve.
|
||||
% =========================
|
||||
\ccRefPageBegin
|
||||
\begin{ccRefConcept}{ArrTraits::CompareYAtXRight_2}
|
||||
\ccRefines{AdaptableTernaryFunction}
|
||||
\ccRefines{Functor}
|
||||
|
||||
\ccHasModels\ccc{ArrangementBasicTraits_2::Compare_y_at_x_right_2}
|
||||
|
||||
@@ -300,7 +340,7 @@ Represents a planar (weakly) $x$-monotone curve.
|
||||
% ==============
|
||||
\ccRefPageBegin
|
||||
\begin{ccRefConcept}{ArrTraits::Equal_2}
|
||||
\ccRefines{AdaptableBinaryFunction}
|
||||
\ccRefines{Functor}
|
||||
|
||||
\ccHasModels\ccc{ArrangementBasicTraits_2::Equal_2}
|
||||
|
||||
@@ -315,3 +355,91 @@ Represents a planar (weakly) $x$-monotone curve.
|
||||
geometrically equivalent (have the same graph).}
|
||||
\end{ccRefConcept}
|
||||
\ccRefPageEnd
|
||||
|
||||
%%%%%%%% ParameterSpaceInX_2
|
||||
% ==========================
|
||||
\ccRefPageBegin
|
||||
\begin{ccRefConcept}{ArrTraits::ParameterSpaceInX_2}
|
||||
\ccRefines{Functor}
|
||||
|
||||
\ccHasModels\ccc{ArrangementBasicTraits_2::Parameter_space_in_x_2}
|
||||
|
||||
\ccCreationVariable{fo}
|
||||
\ccMethod{Arr_parameter_space operator()(ArrTraits::X_monotone_curve_2 xc,
|
||||
Arr_curve_end ce);}
|
||||
{determines the placement of the $x$-coordinate of the minimal end or
|
||||
maximal end of \ccc{xc} in the parameter space, that is,
|
||||
\ccc{ARR_LEFT_BOUNDARY}, \ccc{ARR_INTERIOR}, or \ccc{ARR_RIGHT_BOUNDARY}.}
|
||||
\end{ccRefConcept}
|
||||
\ccRefPageEnd
|
||||
|
||||
%%%%%%%% ParameterSpaceInY_2
|
||||
% ==========================
|
||||
\ccRefPageBegin
|
||||
\begin{ccRefConcept}{ArrTraits::ParameterSpaceInY_2}
|
||||
\ccRefines{Functor}
|
||||
|
||||
\ccHasModels\ccc{ArrangementBasicTraits_2::Parameter_space_in_y_2}
|
||||
|
||||
\ccCreationVariable{fo}
|
||||
\ccMethod{Arr_parameter_space operator()(ArrTraits::X_monotone_curve_2 xc,
|
||||
Arr_curve_end ce);}
|
||||
{determines the placement of the $y$-coordinate of the minimal end or
|
||||
maximal end of \ccc{xc} in the parameter space, that is,
|
||||
\ccc{ARR_BOTTOM_BOUNDARY}, \ccc{ARR_INTERIOR}, or \ccc{ARR_TOP_BOUNDARY}.}
|
||||
\end{ccRefConcept}
|
||||
\ccRefPageEnd
|
||||
|
||||
%%%%%%%% CompareXNearBoundary_2
|
||||
% =============================
|
||||
\ccRefPageBegin
|
||||
\begin{ccRefConcept}{ArrTraits::CompareXNearBoundary_2}
|
||||
\ccRefines\ccc{ArrTraits::CompareX_2}
|
||||
|
||||
\ccHasModels\ccc{ArrangementBasicTraits_2::Compare_x_near_boundary_2}
|
||||
|
||||
\ccCreationVariable{fo}
|
||||
\ccMethod{Comparison_result operator()(ArrTraits::Point_2 p,
|
||||
ArrTraits::X_monotone_curve_2 xc,
|
||||
Arr_curve_end ce);}
|
||||
{returns \ccc{SMALLER}, \ccc{EQUAL}, or \ccc{LARGER} according
|
||||
to the $x$-ordering of a vertical line passing through the point
|
||||
\ccc{p} and an unbounded end of the curve \ccc{xc}. The relevant end
|
||||
is the minimal end, if \ccc{ce} is \ccc{MIN_END} and the maximal
|
||||
end if \ccc{ce} is \ccc{MAX_END}.
|
||||
\ccPrecond{the curve end has a bounded $x$-coordinate and an
|
||||
unbounded $y$-coordinate. Namely \ccc{xc} is vertical or has a
|
||||
vertical asymptote.}}
|
||||
\ccGlue
|
||||
\ccMethod{Comparison_result operator()(ArrTraits::X_monotone_curve_2 xc1,
|
||||
Arr_curve_end ce1,
|
||||
ArrTraits::X_monotone_curve_2 xc2,
|
||||
Arr_curve_end ce2);}
|
||||
{returns \ccc{SMALLER}, \ccc{EQUAL}, or \ccc{LARGER}
|
||||
according to the $x$-ordering of the unbounded curve ends of
|
||||
\ccc{xc1} and \ccc{xc2}.
|
||||
\ccPrecond{the curve ends have a bounded $x$-coordinate and an
|
||||
unbounded $y$-coordinate. Namely each of \ccc{xc1} and \ccc{xc2} is
|
||||
vertical or has a vertical asymptote.}}
|
||||
\end{ccRefConcept}
|
||||
\ccRefPageEnd
|
||||
|
||||
%%%%%%%% CompareYNearBoundary_2
|
||||
% =============================
|
||||
\ccRefPageBegin
|
||||
\begin{ccRefConcept}{ArrTraits::CompareYNearBoundary_2}
|
||||
\ccRefines\ccc{CompareYAtX_2}
|
||||
|
||||
\ccHasModels\ccc{ArrangementBasicTraits_2::Compare_y_near_boundary_2}
|
||||
|
||||
\ccCreationVariable{fo}
|
||||
\ccMethod{Comparison_result operator()(ArrTraits::X_monotone_curve_2 xc1,
|
||||
ArrTraits::X_monotone_curve_2 xc2,
|
||||
Arr_curve_end ce);}
|
||||
{returns \ccc{SMALLER, EQUAL} or \ccc{LARGER} according to the
|
||||
$y$-ordering of the two curves \ccc{xc1} and \ccc{xc2} at $x = -\infty$
|
||||
(if \ccc{ce} is \ccc{MIN_END}) or at $x = \infty$ (if \ccc{ce} is
|
||||
\ccc{MAX_END}), with the precondition that both curves have unbounded
|
||||
minimal (or maximal) ends that lie at $x = \pm\infty$.}
|
||||
\end{ccRefConcept}
|
||||
\ccRefPageEnd
|
||||
|
||||
@@ -12,7 +12,7 @@
|
||||
\ccDefinition
|
||||
%============
|
||||
|
||||
The class \ccRefName{} is a model of the \ccc{ArrangementTraits_2} concept
|
||||
The class \ccRefName\ is a model of the \ccc{ArrangementTraits_2} concept
|
||||
and can be used to construct and maintain arrangements of bounded segments of
|
||||
algebraic curves of degree $2$ at most, also known as {\sl conic curves}.
|
||||
|
||||
|
||||
@@ -1,17 +1,10 @@
|
||||
\begin{ccRefEnum}{Arr_curve_end}
|
||||
\ccDefinition
|
||||
The enumeration \ccRefName{} is used to indicate one of the two ends
|
||||
of an $x$-monotone curve. It is used by models of the
|
||||
\ccc{ArrangementOpenBoundaryTraits_2} concept.
|
||||
|
||||
\ccInclude{CGAL/Arr_enums.h}
|
||||
\ccInclude{CGAL/Arr_enums.h}
|
||||
|
||||
\ccGlobalEnum{enum Arr_curve_end { ARR_MIN_END, ARR_MAX_END }; }
|
||||
\ccRefLabel{ARR_MIN_END}
|
||||
\ccRefLabel{ARR_MAX_END}
|
||||
\ccHtmlCrossLink{ARR_MIN_END}
|
||||
\ccHtmlCrossLink{ARR_MAX_END}
|
||||
\ccGlobalEnum{enum Arr_curve_end { ARR_MIN_END, ARR_MAX_END }; }
|
||||
\ccRefLabel{ARR_MIN_END}
|
||||
\ccRefLabel{ARR_MAX_END}
|
||||
\ccHtmlCrossLink{ARR_MIN_END}
|
||||
\ccHtmlCrossLink{ARR_MAX_END}
|
||||
|
||||
\ccSeeAlso
|
||||
\ccc{ArrangementOpenBoundaryTraits_2}
|
||||
\end{ccRefEnum}
|
||||
|
||||
+8
-14
@@ -1,19 +1,13 @@
|
||||
\begin{ccRefEnum}{Arr_halfedge_direction}
|
||||
\ccDefinition
|
||||
The enumeration \ccRefName{} is defined by
|
||||
\ccc{CGAL::Arrangement_2<Traits,Dcel>::Halfedge} to specify
|
||||
the direction of the halfedge.
|
||||
\ccInclude{CGAL/Arr_enums.h}
|
||||
|
||||
\ccInclude{CGAL/Arr_enums.h}
|
||||
\ccGlobalEnum{
|
||||
enum Arr_halfedge_direction { ARR_LEFT_TO_RIGHT = -1,
|
||||
ARR_RIGHT_TO_LEFT = 1 }; }
|
||||
|
||||
\ccGlobalEnum{
|
||||
enum Arr_halfedge_direction { ARR_LEFT_TO_RIGHT, ARR_RIGHT_TO_LEFT }; }
|
||||
\ccRefLabel{ARR_LEFT_TO_RIGHT}
|
||||
\ccRefLabel{ARR_RIGHT_TO_LEFT}
|
||||
\ccHtmlCrossLink{ARR_LEFT_TO_RIGHT}
|
||||
\ccHtmlCrossLink{ARR_RIGHT_TO_LEFT}
|
||||
|
||||
\ccRefLabel{ARR_LEFT_TO_RIGHT}
|
||||
\ccRefLabel{ARR_RIGHT_TO_LEFT}
|
||||
\ccHtmlCrossLink{ARR_LEFT_TO_RIGHT}
|
||||
\ccHtmlCrossLink{ARR_RIGHT_TO_LEFT}
|
||||
|
||||
\ccSeeAlso
|
||||
\ccc{CGAL::Arrangement_2<Traits,Dcel>::Halfedge}
|
||||
\end{ccRefEnum}
|
||||
|
||||
+1
-1
@@ -12,7 +12,7 @@
|
||||
|
||||
\ccDefinition
|
||||
|
||||
The traits class \ccRefName{} is a model of the \ccc{ArrangementTraits_2}
|
||||
The traits class \ccRefName\ is a model of the \ccc{ArrangementTraits_2}
|
||||
concept that allow the construction and maintenance of arrangements of
|
||||
sets of pairwise interior-disjoint line segments. It is templated with a
|
||||
\cgal-Kernel model, and it is derived from it. This traits class is a
|
||||
|
||||
+8
-7
@@ -13,17 +13,18 @@
|
||||
\ccDefinition
|
||||
%============
|
||||
|
||||
The categories \ccc{Left_side_category}, \ccc{Right_side_category},
|
||||
\ccc{Bottom_side_category}, and \ccc{Top_side_category},
|
||||
nested in any model of the \ccc{ArrangementBasicTraits_2}, must be
|
||||
convertible to \ccRefName. \ccRefName{} is an empty construct used
|
||||
for dispatching functions based on type of curves that induce the
|
||||
arrangement.
|
||||
\ccRefName{} is an empty construct used for dispatching functions based on
|
||||
type of curves that induce the arrangement. If all curves are expected not
|
||||
to approach the left, right, bottom, or top sides of the boundary of the
|
||||
parameter space, the categories \ccc{Arr_left_side_category},
|
||||
\ccc{Arr_right_side_category}, \ccc{Arr_bottom_side_category}, and
|
||||
\ccc{Arr_top_side_category}, nested in any model of the
|
||||
\ccc{ArrangementBasicTraits_2}, must be defined as \ccRefName{}, respectively.
|
||||
|
||||
\ccInclude{CGAL/Arr_tags.h}
|
||||
|
||||
\ccSeeAlso
|
||||
\ccc{Arr_open_side_tag}\lcTex{(\ccRefPage{CGAL::Arr_open_side_tag})}\\
|
||||
\ccc{Arr_open_side_tag}\lcTex{(\ccRefPage{Arr_open_side_tag})}\\
|
||||
\ccc{ArrangementBasicTraits_2}\lcTex{(\ccRefPage{ArrangementBasicTraits_2})}
|
||||
|
||||
\end{ccRefClass}
|
||||
|
||||
-366
@@ -1,366 +0,0 @@
|
||||
% Reference manual page: ArrangementTraits.tex
|
||||
% Package: Arrangement_2
|
||||
|
||||
\ccRefPageBegin
|
||||
\begin{ccRefConcept}{ArrangementOpenBoundaryTraits_2}
|
||||
|
||||
\ccDefinition
|
||||
% ===========
|
||||
Several predicates are required to handle $x$-monotone curves that
|
||||
approach infinity and thus approach the boundary of the parameter
|
||||
space. These predicates are sufficient to handle not only curves
|
||||
embedded in an unbounded parameter space, but also curves embedded
|
||||
in a bounded parameter space with open boundaries. Models of the
|
||||
concept \ccRefName{} handle curves that approach the boundary of a
|
||||
parameter space. This concept refines the concept
|
||||
\ccc{ArrangementBasicTraits_2}. The arrangement template
|
||||
instantiated with a traits class that models this concept can handle
|
||||
$x$-monotone curves that are unbounded in any direction. The concept
|
||||
\ccRefName{}, nontheless, also supports planar $x$-monotone curves
|
||||
that reach the boundary of an open yet bounded parameter space.
|
||||
|
||||
An $x$-monotone curve may be \emph{closed}, in which case its endpoints
|
||||
are representable as \ccc{Point_2} objects, or \emph{open} at the
|
||||
boundary of the parameter space. It can have one open end and one
|
||||
closed end (e.g., a ray). The nature of the $x$-monotone curves,
|
||||
whether they are expected to be closed or not at any one of the four
|
||||
boundary-sides, is conveyed through the definition of the four nested
|
||||
types \ccc{Left_side_category}, \ccc{Right_side_category},
|
||||
\ccc{Bottom_side_category}, and \ccc{Top_side_category}. If some curves
|
||||
handled by a model of the concept \ccRefName{} are expected to be open
|
||||
on the left, the nested type \ccc{Left_side_category} must be convertible
|
||||
to \ccc{Arr_open_side_tag}. Similarly, if some curves handled by the
|
||||
concept are expected to be open on the right, open at the bottom, or
|
||||
open at the top, the corresponding nested type must be convertible to
|
||||
\ccc{Arr_open_side_tag}. A model of the concept \ccRefName{} must have
|
||||
all the four categories convertible to
|
||||
\ccc{Arr_open_side_tag}.\footnote{We intend to introduce more concepts
|
||||
that require only a subset of the categories to be convertible to
|
||||
\ccc{Arr_open_side_tag}.} In this case the \dcel{} of the arrangement
|
||||
instantiated with the model is initialized with an implicit bounding
|
||||
rectangle. When the parameter space is bounded, it is the exact
|
||||
geometric embedding of the implicit bounding rectangle.
|
||||
|
||||
%% An arrangement that supports unbounded $x$-monotone curves maintains
|
||||
%% an implicit bounding rectangle embedded in the \dcel{} structure.
|
||||
|
||||
\ccRefines
|
||||
\ccc{ArrangementBasicTraits_2}
|
||||
|
||||
%% \ccTypes
|
||||
%% % ======
|
||||
%% \ccNestedType{Curve_2}{models the concept \ccc{ArrTraits::Curve_2}.}
|
||||
|
||||
\ccHeading{Categories}
|
||||
% ==============
|
||||
\ccNestedType{Left_side_category}
|
||||
{Must be convertible to either \ccc{Arr_oblivious_side_tag} or
|
||||
\ccc{Arr_open_side_tag}.}
|
||||
\ccNestedType{Bottom_side_category}
|
||||
{Must be convertible to either \ccc{Arr_oblivious_side_tag} or
|
||||
\ccc{Arr_open_side_tag}.}
|
||||
\ccNestedType{Top_side_category}
|
||||
{Must be convertible to either \ccc{Arr_oblivious_side_tag} or
|
||||
\ccc{Arr_open_side_tag}.}
|
||||
\ccNestedType{Right_side_category}
|
||||
{Must be convertible to either \ccc{Arr_oblivious_side_tag} or
|
||||
\ccc{Arr_open_side_tag}.}
|
||||
|
||||
\ccHeading{Functor Types}
|
||||
% =======================
|
||||
\ccThree{Parameter_space_in_x_2}{}{\hspace*{14cm}}
|
||||
\ccThreeToTwo
|
||||
\ccNestedType{Parameter_space_in_x_2}%
|
||||
{models the concept \ccc{ArrTraits::ParameterSpaceInX_2}.
|
||||
Required only if the traits class supports unbounded curves that
|
||||
approach the left or the right sides (the \ccc{Left_side_category}
|
||||
or the \ccc{Right_side_category} categories are convertible to
|
||||
\ccc{Arr_open_side_tag}).}
|
||||
|
||||
\ccThree{Compare_y_near_boundary_2}{}{\hspace*{14cm}}
|
||||
\ccThreeToTwo
|
||||
\ccNestedType{Compare_y_near_boundary_2}%
|
||||
{models the concept \ccc{ArrTraits::CompareYNearBoundary_2}.
|
||||
Required only if the traits class supports unbounded curves that
|
||||
approach the left or the right sides (the \ccc{Left_side_category}
|
||||
or the \ccc{Right_side_category} categories are convertible to
|
||||
\ccc{Arr_open_side_tag}).}
|
||||
|
||||
\ccThree{Parameter_space_in_y_2}{}{\hspace*{14cm}}
|
||||
\ccThreeToTwo
|
||||
\ccNestedType{Parameter_space_in_y_2}%
|
||||
{models the concept \ccc{ArrTraits::ParameterSpaceInY_2}.
|
||||
Required only if the traits class supports unbounded curves that
|
||||
approach the bottom or the top sides (the \ccc{Bottom_side_category}
|
||||
or the \ccc{Top_side_category} categories are convertible to
|
||||
\ccc{Arr_open_side_tag}).}
|
||||
|
||||
\ccThree{Compare_x_at_limit_2}{}{\hspace*{14cm}}
|
||||
\ccThreeToTwo
|
||||
\ccNestedType{Compare_x_at_limit_2}%
|
||||
{models the concept \ccc{ArrTraits::CompareXAtLimit_2}.
|
||||
Required only if the traits class supports unbounded curves that
|
||||
approach the bottom or the top sides (the \ccc{Bottom_side_category}
|
||||
or the \ccc{Top_side_category} categories are convertible to
|
||||
\ccc{Arr_open_side_tag}).}
|
||||
|
||||
\ccThree{Compare_x_near_limit_2}{}{\hspace*{14cm}}
|
||||
\ccThreeToTwo
|
||||
\ccNestedType{Compare_x_near_limit_2}%
|
||||
{models the concept \ccc{ArrTraits::CompareXNearLimit_2}.
|
||||
Required only if the traits class supports unbounded curves that
|
||||
approach the bottom or the top sides (the \ccc{Bottom_side_category}
|
||||
or the \ccc{Top_side_category} categories are convertible to
|
||||
\ccc{Arr_open_side_tag}).}
|
||||
|
||||
\ccCreationVariable{traits}
|
||||
% \ccCreation
|
||||
% ===========
|
||||
|
||||
\ccHeading{Accessing Functor Objects}
|
||||
% ===================================
|
||||
\ccMethod{Parameter_space_in_x_2 parameter_space_in_x_2_object() const;} {}
|
||||
\ccMethod{Compare_y_near_boundary_2 compare_y_near_boundary_2_object() const;} {}
|
||||
\ccMethod{Parameter_space_in_y_2 parameter_space_in_y_2_object() const;} {}
|
||||
\ccMethod{Compare_x_at_limit_2 compare_x_at_limit_2_object() const;} {}
|
||||
\ccMethod{Compare_x_near_limit_2 compare_x_near_limit_2_object() const;} {}
|
||||
|
||||
\ccHasModels
|
||||
% ==========
|
||||
\ccc{CGAL::Arr_linear_traits_2<Kernel>}\\
|
||||
\ccc{CGAL::Arr_rational_arc_traits_2<AlgKernel,NtTraits>}\\
|
||||
\ccc{CGAL::Arr_algebraic_segment_traits_2<Coefficient>}\\
|
||||
\ccc{CGAL::Arr_curve_data_traits_2<Tr,XData,Mrg,CData,Cnv>}\\
|
||||
\ccc{CGAL::Arr_consolidated_curve_data_traits_2<Traits,Data>}
|
||||
|
||||
\ccSeeAlso
|
||||
% ========
|
||||
\ccc{ArrangementBasicTraits_2}\lcTex{
|
||||
(\ccRefPage{ArrangementBasicTraits_2})}\\
|
||||
\ccc{ArrangementXMonotoneTraits_2}\lcTex{
|
||||
(\ccRefPage{ArrangementXMonotoneTraits_2})}\\
|
||||
\ccc{ArrangementLandmarkTraits_2}\lcTex{
|
||||
(\ccRefPage{ArrangementLandmarkTraits_2})}\\
|
||||
\ccc{ArrangementTraits_2}\lcTex{
|
||||
(\ccRefPage{ArrangementTraits_2})}
|
||||
|
||||
\end{ccRefConcept}
|
||||
\ccRefPageEnd
|
||||
|
||||
%%%%%%%% Functors %%%%%%%%
|
||||
% ========================
|
||||
|
||||
%%%%%%%% ParameterSpaceInX_2
|
||||
% ==========================
|
||||
\ccRefPageBegin
|
||||
\begin{ccRefConcept}{ArrTraits::ParameterSpaceInX_2}
|
||||
\ccRefines{AdaptableBinaryFunction}
|
||||
|
||||
\ccHasModels\ccc{ArrangementOpenBoundaryTraits_2::Parameter_space_in_x_2}
|
||||
|
||||
\ccCreationVariable{fo}
|
||||
|
||||
\ccMethod{Arr_parameter_space operator()(const ArrTraits::X_monotone_curve_2& xcv,
|
||||
Arr_curve_end ce);}{%
|
||||
|
||||
Given an $x$-monotone curve \ccc{xcv} and an enumeration \ccc{ce}
|
||||
that specifies either the minimum or the maximum end of the curve,
|
||||
determines the location of the curve end along the $x$-dimension.
|
||||
The variable \ccc{xcv} identifies the parametric curve
|
||||
$C(t) = (X(t),Y(t))$ defined over an open or half-open interval with
|
||||
endpoints~$0$ and~$1$. The enumeration \ccc{ce} identifies an open
|
||||
end $d \in \{0,1\}$ of $C$. Formally, determines whether
|
||||
$\lim_{t \rightarrow d} X(t)$ evaluates to $b_l$, $b_r$, or a value
|
||||
in between, where $b_l$ and $b_r$ are the $x$-coordinates of the
|
||||
left and right boundaries of the parameter space, respectively.
|
||||
Returns \ccc{ARR_LEFT_BOUNDARY}, \ccc{ARR_RIGHT_BOUNDARY}, or
|
||||
\ccc{ARR_INTERIOR}, accordingly.
|
||||
\ccPrecond{If \ccc{ArrTraits::Left_side_category} is not convertible to
|
||||
\ccc{Arr_open_side_tag} then \ccc{ce} $\neq$ \ccc{ARR_MIN_END}.}
|
||||
\ccPrecond{If \ccc{ArrTraits::Right_side_category} is not convertible to
|
||||
\ccc{Arr_open_side_tag} then \ccc{ce} $\neq$ \ccc{ARR_MAX_END}.}
|
||||
\ccPostcond{If \ccc{ce} = \ccc{ARR_MIN_END} then the result is either
|
||||
\ccc{ARR_LEFT_BOUNDARY} or \ccc{ARR_INTERIOR}.}
|
||||
\ccPostcond{If \ccc{ce} = \ccc{ARR_MAX_END} then the result is either
|
||||
\ccc{ARR_RIGHT_BOUNDARY} or \ccc{ARR_INTERIOR}.}}
|
||||
\end{ccRefConcept}
|
||||
\ccRefPageEnd
|
||||
|
||||
%%%%%%%% CompareYNearBoundary_2
|
||||
% =============================
|
||||
\ccRefPageBegin
|
||||
\begin{ccRefConcept}{ArrTraits::CompareYNearBoundary_2}
|
||||
|
||||
\ccRefines{AdaptableTernaryFunction}
|
||||
|
||||
\ccHasModels\ccc{ArrangementOpenBoundaryTraits_2::Compare_y_near_boundary_2}
|
||||
|
||||
\ccCreationVariable{fo}
|
||||
|
||||
\ccMethod{Comparison_result operator()(const ArrTraits::X_monotone_curve_2& xcv1,
|
||||
const ArrTraits::X_monotone_curve_2& xcv2,
|
||||
Arr_curve_end ce);}{%
|
||||
Given two $x$-monotone curves \ccc{xcv1} and \ccc{xcv2} and an
|
||||
enumeration \ccc{ce} that specifies either the minimum or the maximum
|
||||
ends of the curves, compares the $y$-coordinate of the curves near
|
||||
their respective ends. Returns \ccc{SMALLER}, \ccc{EQUAL}, or
|
||||
\ccc{LARGER} accordingly. More precisely, compares the
|
||||
$y$-coordinates of the vertical projection of a point $p$ onto
|
||||
\ccc{xcv1} and \ccc{xcv2}. If \ccc{ce} is \ccc{ARR_MIN_END}, the
|
||||
predicate \ccc{Parameter_space_in_x_2} evaluates to
|
||||
\ccc{ARR_LEFT_BOUNDARY} when applied to \ccc{xcv1} and \ccc{ce} and
|
||||
when applied to \ccc{xcv2} and \ccc{ce}. In this case $p$ is
|
||||
located far to the left, such that the result is invariant under
|
||||
a translation of $p$ farther to the left. If \ccc{ce} is
|
||||
\ccc{ARR_MAX_END}, the predicate \ccc{Parameter_space_in_x_2}
|
||||
evaluates to \ccc{ARR_RIGHT_BOUNDARY} when applied to \ccc{xcv1} and
|
||||
\ccc{ce} and when applied to \ccc{xcv2} and \ccc{ce}. In that case
|
||||
$p$ is located far to the right in a similar manner.
|
||||
\ccPrecond{If \ccc{ArrTraits::Left_side_category} is not convertible to
|
||||
\ccc{Arr_open_side_tag} then \ccc{ce} $\neq$ \ccc{ARR_MIN_END}.}
|
||||
\ccPrecond{If \ccc{ArrTraits::Right_side_category} is not convertible to
|
||||
\ccc{Arr_open_side_tag} then \ccc{ce} $\neq$ \ccc{ARR_MAX_END}.}
|
||||
\ccPrecond{%
|
||||
\ccc{parameter_space_in_x_2}(\ccc{xcv2}, \ccc{ce}) =
|
||||
\ccc{parameter_space_in_x_2}(\ccc{xcv1}, \ccc{ce}).}
|
||||
\ccPrecond{\ccc{parameter_space_in_x_2}(\ccc{xcv1}, \ccc{ce}) $\neq$
|
||||
\ccc{ARR_INTERIOR}.}
|
||||
\ccPrecond{If \ccc{parameter_space_in_x_2}(\ccc{xcv1}, \ccc{ce}) =
|
||||
\ccc{ARR_LEFT_BOUNDARY} then \ccc{ce} = \ccc{ARR_MIN_END}.}
|
||||
\ccPrecond{If \ccc{parameter_space_in_x_2}(\ccc{xcv1}, \ccc{ce}) =
|
||||
\ccc{ARR_RIGHT_BOUNDARY} then \ccc{ce} = \ccc{ARR_MAX_END}.}}
|
||||
\end{ccRefConcept}
|
||||
\ccRefPageEnd
|
||||
|
||||
%%%%%%%% ParameterSpaceInY_2
|
||||
% ==========================
|
||||
\ccRefPageBegin
|
||||
\begin{ccRefConcept}{ArrTraits::ParameterSpaceInY_2}
|
||||
\ccRefines{AdaptableBinaryFunction}
|
||||
|
||||
\ccHasModels\ccc{ArrangementOpenBoundaryTraits_2::Parameter_space_in_y_2}
|
||||
|
||||
\ccCreationVariable{fo}
|
||||
|
||||
\ccMethod{Arr_parameter_space operator()(const ArrTraits::X_monotone_curve_2& xcv,
|
||||
Arr_curve_end ce);}{%
|
||||
Given an $x$-monotone curve \ccc{xcv} and an enumeration \ccc{ce}
|
||||
that specifies either the minimum or the maximum end of the curve,
|
||||
determines the location of the curve end along the $y$-dimension.
|
||||
The variable \ccc{xcv} identifies the parametric curve
|
||||
$C(t) = (X(t),Y(t))$ defined over an open or half-open interval with
|
||||
endpoints~$0$ and~$1$. The enumeration \ccc{ce} identifies an open
|
||||
end $d \in \{0,1\}$ of $C$. Formally, determines whether
|
||||
$\lim_{t \rightarrow d} Y(t)$ evaluates to $b_b$, $b_t$, or a value
|
||||
in between, where $b_b$ and $b_t$ are the $y$-coordinates of the
|
||||
bottom and top boundaries of the parameter space, respectively.
|
||||
Returns \ccc{ARR_BOTTOM_BOUNDARY}, \ccc{ARR_TOP_BOUNDARY}, or
|
||||
\ccc{ARR_INTERIOR}, accordingly.
|
||||
\ccPostcond{If \ccc{ArrTraits::Bottom_side_category} is not convertible to
|
||||
\ccc{Arr_open_side_tag} then the result is not \ccc{ARR_BOTTOM_BOUNDARY}.}
|
||||
\ccPostcond{If \ccc{ArrTraits::Top_side_category} is not convertible to
|
||||
\ccc{Arr_open_side_tag} then the result is not \ccc{ARR_TOP_BOUNDARY}.}}
|
||||
\end{ccRefConcept}
|
||||
\ccRefPageEnd
|
||||
|
||||
%%%%%%%% CompareXAtLimit_2
|
||||
% ================================
|
||||
\ccRefPageBegin
|
||||
\begin{ccRefConcept}{ArrTraits::CompareXAtLimit_2}
|
||||
\ccRefines{AdaptableFunctor}
|
||||
|
||||
\ccHasModels\ccc{ArrangementOpenBoundaryTraits_2::Compare_x_at_limit_2}
|
||||
|
||||
\ccCreationVariable{fo}
|
||||
|
||||
\ccMethod{Comparison_result operator()(const ArrTraits::Point_2& p,
|
||||
const ArrTraits::X_monotone_curve_2& xcv,
|
||||
Arr_curve_end ce);}{%
|
||||
Given a point \ccc{p}, an $x$-monotone curve \ccc{xcv}, and an
|
||||
enumeration \ccc{ce} that specifies either the minimum or the
|
||||
maximum end of the curve where the curve has a vertical asymptote,
|
||||
compares the $x$-coordinate of \ccc{p} and the $x$-coordinate of the
|
||||
limit of the curve at its specificed end. The variable \ccc{xcv}
|
||||
identifies the parametric curve $C(t) = (X(t),Y(t))$ defined over an
|
||||
open or half-open interval with endpoints~$0$ and~$1$. The
|
||||
enumeration \ccc{ce} identifies an open end $d \in \{0,1\}$ of $C$.
|
||||
Formally, compares the $x$-coordinate of \ccc{p} and
|
||||
$\lim_{t \rightarrow d} X(t)$. Returns \ccc{SMALLER}, \ccc{EQUAL}, or
|
||||
\ccc{LARGER} accordingly.
|
||||
\ccPrecond{\ccc{parameter_space_in_y_2}(\ccc{xcv}, \ccc{ce}) $\neq$
|
||||
\ccc{ARR_INTERIOR}.}
|
||||
\ccPrecond{If the parameter space is unbounded, $C$ has a vertical
|
||||
asymptote at its $d$-end; that is,
|
||||
\ccc{parameter_space_in_x_2}(\ccc{xcv}, \ccc{ce}) = \ccc{ARR_INTERIOR}.}}
|
||||
%
|
||||
\ccMethod{Comparison_result operator()(const ArrTraits::X_monotone_curve_2& xcv1,
|
||||
Arr_curve_end ce1,
|
||||
const ArrTraits::X_monotone_curve_2& xcv2,
|
||||
Arr_curve_end ce2);}{%
|
||||
Given two $x$-monotone curves \ccc{xcv1} and \ccc{xcv2} and two
|
||||
indices \ccc{ce1} and \ccc{ce2} that specify either the minimum
|
||||
or the maximum ends of \ccc{xcv1} and \ccc{xcv2}, respectively,
|
||||
where the curves have vertical asymptotes, compares the
|
||||
$x$-coordinates of the limits of the curves at their specificed
|
||||
ends. The variables \ccc{xcv1} and \ccc{xcv2} identify the
|
||||
parametric curves $C_1(t) = (X_1(t),Y_1(t))$ and
|
||||
$C_2(t) = (X_2(t),Y_2(t))$, respectively, defined over open or
|
||||
half-open intervals with endpoints~$0$ and~$1$. The indices
|
||||
\ccc{ce1} and \ccc{ce2} identify open ends $d_1 \in \{0,1\}$ and
|
||||
$d_2 \in \{0,1\}$ of $C_1$ and $C_2$, respectively. Formally,
|
||||
compares $\lim_{t \rightarrow d_1} X_1(t)$ and
|
||||
$\lim_{t \rightarrow d_2} X_2(t)$. Returns \ccc{SMALLER}, \ccc{EQUAL},
|
||||
or \ccc{LARGER} accordingly.
|
||||
\ccPrecond{%
|
||||
\ccc{parameter_space_in_y_2}(\ccc{xcv1}, \ccc{ce1}) $\neq$
|
||||
\ccc{ARR_INTERIOR}.}
|
||||
\ccPrecond{%
|
||||
\ccc{parameter_space_in_y_2}(\ccc{xcv2}, \ccc{ce2}) $\neq$
|
||||
\ccc{ARR_INTERIOR}.}
|
||||
\ccPrecond{If the parameter space is unbounded, $C_1$ has a vertical
|
||||
asymptote at its respective end; that is,\\
|
||||
\ccc{parameter_space_in_x_2}(\ccc{xcv1}, \ccc{ce1}) =
|
||||
\ccc{ARR_INTERIOR}.}
|
||||
\ccPrecond{If the parameter space is unbounded, $C_2$ has a vertical
|
||||
asymptote at its respective end; that is,\\
|
||||
\ccc{parameter_space_in_x_2}(\ccc{xcv2}, \ccc{ce2}) =
|
||||
\ccc{ARR_INTERIOR}.}}
|
||||
\end{ccRefConcept}
|
||||
\ccRefPageEnd
|
||||
|
||||
%%%%%%%% CompareXNearLimit_2
|
||||
% =============================
|
||||
\ccRefPageBegin
|
||||
\begin{ccRefConcept}{ArrTraits::CompareXNearLimit_2}
|
||||
\ccRefines{AdaptableTernaryFunction}
|
||||
|
||||
\ccHasModels\ccc{ArrangementOpenBoundaryTraits_2::Compare_x_near_limit_2}
|
||||
|
||||
\ccCreationVariable{fo}
|
||||
|
||||
\ccMethod{Comparison_result operator()(const ArrTraits::X_monotone_curve_2& xcv1,
|
||||
const ArrTraits::X_monotone_curve_2& xcv2,
|
||||
Arr_curve_end ce);}{%
|
||||
Given two $x$-monotone curves \ccc{xcv1} and \ccc{xcv2} and an
|
||||
enumeration \ccc{ce} that specifies either the minimum ends or the
|
||||
maximum ends of the curves where the curves have a vertical
|
||||
asymptote, compares the $x$-coordinate of the curves near their
|
||||
respective ends. Returns \ccc{SMALLER}, \ccc{EQUAL}, or \ccc{LARGER}
|
||||
accordingly. More precisely, compares the $x$-coordinates of the
|
||||
horizontal projection of a point $p$ onto \ccc{xcv1} and \ccc{xcv2}.
|
||||
If \ccc{xcv1} and \ccc{xcv2} approach the bottom boundary-side, $p$
|
||||
is located far to the bottom, such that the result is invariant
|
||||
under a translation of $p$ farther to the bottom. If \ccc{xcv1}
|
||||
and \ccc{xcv2} approach the top boundary-side, $p$ is located far
|
||||
to the top in a similar manner.
|
||||
\ccPrecond{The $x$-coordinates of the limits of the curves at their
|
||||
respective ends are equal. That is,\\
|
||||
\ccc{compare_x_at_limit_2}(\ccc{xcv1}, \ccc{xcv2}, \ccc{ce}) =
|
||||
\ccc{EQUAL}.}
|
||||
\ccPrecond{%
|
||||
\ccc{parameter_space_in_y_2}(\ccc{xcv1}, \ccc{ce}) =
|
||||
\ccc{parameter_space_in_y_2}(\ccc{xcv2}, \ccc{ce}).}
|
||||
\ccPrecond{\ccc{parameter_space_in_y_2}(\ccc{xcv1}, \ccc{ce}) $\neq$
|
||||
\ccc{ARR_INTERIOR}.}}
|
||||
\end{ccRefConcept}
|
||||
\ccRefPageEnd
|
||||
+10
-13
@@ -13,23 +13,20 @@
|
||||
\ccDefinition
|
||||
%============
|
||||
|
||||
All the four types \ccc{Left_side_category},
|
||||
\ccc{Right_side_category}, \ccc{Bottom_side_category},
|
||||
and \ccc{Top_side_category} nested in any model of the
|
||||
concept \ccc{ArrangementOpenBoundaryTraits} must be convertible
|
||||
to \ccRefName, which derives from \ccc{Arr_oblivious_side_tag}. It
|
||||
implies that some curves are expected to approach the left, right,
|
||||
bottom, or top sides of the open boundary of the parameter
|
||||
space. \ccRefName{} is an empty construct used for dispatching
|
||||
functions based on type of curves that induce the arrangement.
|
||||
\ccRefName{} is an empty construct used for dispatching functions based on
|
||||
type of curves that induce the arrangement. If some curves are expected to
|
||||
approach the left, right, bottom, or top sides of the boundary of the
|
||||
parameter space, the categories \ccc{Arr_left_side_category},
|
||||
\ccc{Arr_right_side_category}, \ccc{Arr_bottom_side_category}, and
|
||||
\ccc{Arr_top_side_category}, nested in any model of the
|
||||
\ccc{ArrangementBasicTraits_2}, must be defined as \ccRefName{}, respectively.
|
||||
|
||||
\ccInclude{CGAL/Arr_tags.h}
|
||||
|
||||
\ccSeeAlso
|
||||
\ccc{Arr_oblivious_side_tag}\lcTex{(\ccRefPage{CGAL::Arr_oblivious_side_tag})}\\
|
||||
\ccc{ArrangementOpenBoundaryTraits_2}%
|
||||
\lcTex{(\ccRefPage{ArrangementOpenBoundaryTraits_2})}
|
||||
|
||||
\ccc{Arr_oblivious_side_tag}\lcTex{(\ccRefPage{Arr_oblivious_side_tag})}\\
|
||||
\ccc{ArrangementBasicTraits_2}\lcTex{(\ccRefPage{ArrangementBasicTraits_2})}
|
||||
|
||||
\end{ccRefClass}
|
||||
|
||||
\ccRefPageEnd
|
||||
|
||||
+232
@@ -0,0 +1,232 @@
|
||||
% +------------------------------------------------------------------------+
|
||||
% | Reference manual page: Arr_rational_arc_traits.tex
|
||||
% +------------------------------------------------------------------------+
|
||||
% |
|
||||
% | Package: Arrangement_2
|
||||
% |
|
||||
% +------------------------------------------------------------------------+
|
||||
|
||||
\ccRefPageBegin
|
||||
\begin{ccRefClass}{Arr_rational_arc_traits_2<AlgKernel,NtTraits>}
|
||||
|
||||
\ccDefinition
|
||||
%============
|
||||
|
||||
The traits class \ccRefName\ is a model of the \ccc{ArrangementTraits_2}
|
||||
concept. It handles bounded or unbounded segments of rational functions,
|
||||
referred to as {\sl rational arcs} (in particular, a rational arc may
|
||||
correspond to the entire graph of a rational function), and enables the
|
||||
construction and maintenance of arrangements of such arcs. Rational
|
||||
functions, and polynomial functions in particular, are not only interesting
|
||||
in their own right, they are also very useful for approximating or
|
||||
interpolating more complicated curves.
|
||||
|
||||
A rational function $y = \frac{P(x)}{Q(x)}$
|
||||
is defined by two polynomials $P$ and $Q$ of arbitrary degrees. In
|
||||
particular, if $Q(x) = 1$ then the function is a simple polynomial
|
||||
function. A bounded rational arc is defined by the graph of a rational
|
||||
function over some internal $[x_{\rm min}, x_{\rm max}]$, where $Q$
|
||||
does not have any real roots in this interval (thus the arc does not
|
||||
contain any poles). However, our traits class is also capable of
|
||||
representing functions defined over an unbounded $x$-range, namely
|
||||
a ``ray'' defined on $(-\infty, x_{\rm max}]$ or on $[x_{\rm min}, \infty)$,
|
||||
or an entire function defined for all real $x$ values. Note that a
|
||||
rational arc is unbounded even if it is defined over some bounded interval,
|
||||
yet $Q$ has zeros in this interval.
|
||||
|
||||
In our representation, all polynomial coefficients (the coefficients of $P$
|
||||
and $Q$) must be rational numbers. This guarantees that the
|
||||
$x$-coordinates of all arrangement vertices (in particular, those
|
||||
representing intersection points) can be represented as roots of
|
||||
polynomials with integer coefficients --- namely, algebraic numbers.
|
||||
The $y$-coordinates can be obtained by simple arithmetic operations on
|
||||
the $x$-coordinates, hence they are also algebraic numbers.
|
||||
|
||||
We therefore require separate representations of the curve coefficients and
|
||||
the point coordinates. The \ccc{NtTraits} should be instantiated with a class
|
||||
that defines nested \ccc{Integer}, \ccc{Rational} and \ccc{Algebraic} number
|
||||
types and supports various operations on them, yielding certified computation
|
||||
results (for example, in can convert rational numbers to algebraic numbers
|
||||
and can compute roots of polynomials with integer coefficients).
|
||||
The \ccc{AlgKernel} template-parameter should be a geometric kernel templated
|
||||
with the \ccc{NtTraits::Algebraic} number-type. It is recommended to
|
||||
instantiate the \ccc{CORE_algebraic_number_traits} class as the \ccc{NtTraits}
|
||||
parameter, with \ccc{Cartesian<NtTraits::Algebraic>} instantiating the kernel.
|
||||
The number types in this case are provided by the {\sc core} library, with its
|
||||
ability to exactly represent simple algebraic numbers.
|
||||
|
||||
The traits class defined its point type to be \ccc{AlgKernel::Point_2},
|
||||
and defines a curve type (and an identical $x$-monotone curve type, as
|
||||
a rational arc is always $x$-monotone by definition) as detailed below.
|
||||
|
||||
\ccInclude{CGAL/Arr_rational_arc_traits_2.h}
|
||||
|
||||
\ccIsModel
|
||||
\ccc{ArrangementTraits_2}
|
||||
|
||||
\subsection*{Class
|
||||
Arr\_rational\_arc\_traits\_2$<$AlgKernel,NtTraits$>$::Curve\_2}
|
||||
%========================================================================
|
||||
|
||||
The \ccc{Curve_2} class nested within the rational-arc traits is used
|
||||
to represent rational arcs and support their construction from a
|
||||
single polynomial and an $x$-definition range or from a pair of polynomials
|
||||
and an $x$-definition range. The copy and default constructor as well as the
|
||||
assignment operator are provided for rational arcs. In addition, an
|
||||
\ccc{operator<<} for the arcs is defined for standard output streams.
|
||||
|
||||
\begin{ccClass}{Arr_rational_arc_traits_2<AlgKernel,NtTraits>::Curve_2}
|
||||
%======================================================================
|
||||
|
||||
\ccTypes
|
||||
%-------
|
||||
|
||||
\ccNestedType{Rat_vector}{A vector of rational numbers (equivalent to
|
||||
\ccc{std::vector<typename NtTraits::Rational}).}
|
||||
|
||||
\ccNestedType{Polynomial}{the \ccc{NtTraits::Polynomial} type
|
||||
(a polynomial with integer coefficients).}
|
||||
|
||||
\ccCreation
|
||||
\ccCreationVariable{a}
|
||||
%---------------------
|
||||
|
||||
\ccConstructor{Curve_2 ();}
|
||||
{default constructor.}
|
||||
|
||||
\ccConstructor{Curve_2 (const Rat_vector& p_coeffs);}
|
||||
{constructs an arc that corresponds to the polynomial $y = P(x)$, defined
|
||||
for every real $x$. The vector \ccc{p_coeffs} specifies the coefficients
|
||||
of $P(x)$, where the polynomial degree is \ccc{p_coeffs.size() - 1} and
|
||||
\ccc{p[k]} is the coefficient of $x^k$ in $P$.}
|
||||
|
||||
\ccConstructor{Curve_2 (const Rat_vector& p_coeffs,
|
||||
const typename NtTraits::Algebraic& s_x,
|
||||
bool dir_right);}
|
||||
{constructs an arc supported by the polynomial $y = P(x)$. If
|
||||
\ccc{dir_right} is \ccc{true}, the arc is defined over the interval
|
||||
$[s_x, \infty)$, otherwise it is defined over $(-\infty, s_x]$.
|
||||
The vector \ccc{p_coeffs} specifies the coefficients of $P(x)$ as above.
|
||||
\ccPrecond{\ccc{s_x != t_x}.}}
|
||||
|
||||
\ccConstructor{Curve_2 (const Rat_vector& p_coeffs,
|
||||
const typename NtTraits::Algebraic& s_x,
|
||||
const typename NtTraits::Algebraic& t_x);}
|
||||
{constructs an arc supported by the polynomial $y = P(x)$, defined over
|
||||
the interval $[s_x, t_x]$, given by the $x$-coordinates of the arc's
|
||||
source and target. The vector \ccc{p_coeffs} specifies the coefficients
|
||||
of $P(x)$ as above.
|
||||
\ccPrecond{\ccc{s_x != t_x}.}}
|
||||
|
||||
\ccConstructor{Curve_2 (const Rat_vector& p_coeffs,
|
||||
const Rat_vector& q_coeffs);}
|
||||
{constructs an arc supported by the rational function
|
||||
$y = \frac{P(x)}{Q(x)}$, defined for every real $x$.
|
||||
The vectors \ccc{p_coeffs} and \ccc{q_coeffs} specify the coefficients
|
||||
of $P(x)$ and $Q(x)$, respectively (see above).}
|
||||
|
||||
|
||||
\ccConstructor{Curve_2 (const Rat_vector& p_coeffs,
|
||||
const Rat_vector& q_coeffs,
|
||||
const typename NtTraits::Algebraic& s_x,
|
||||
bool dir_right);}
|
||||
{constructs an arc supported by the rational function
|
||||
$y = \frac{P(x)}{Q(x)}$. If \ccc{dir_right} is \ccc{true}, the arc is
|
||||
defined over the interval $[s_x, \infty)$, otherwise it is defined
|
||||
over $(-\infty, s_x]$.
|
||||
The vectors \ccc{p_coeffs} and \ccc{q_coeffs} specify the coefficients
|
||||
of $P(x)$ and $Q(x)$, respectively (see above).}
|
||||
|
||||
\ccConstructor{Curve_2 (const Rat_vector& p_coeffs,
|
||||
const Rat_vector& q_coeffs,
|
||||
const typename NtTraits::Algebraic& s_x,
|
||||
const typename NtTraits::Algebraic& t_x);}
|
||||
{constructs an arc supported by the rational function
|
||||
$y = \frac{P(x)}{Q(x)}$, defined over the internal $[s_x, t_x]$,
|
||||
given by the $x$-coordinates of the arc's source and target.
|
||||
The vectors \ccc{p_coeffs} and \ccc{q_coeffs} specify the coefficients
|
||||
of $P(x)$ and $Q(x)$, respectively (see above).
|
||||
\ccPrecond{\ccc{s_x != t_x}.}}
|
||||
|
||||
\ccAccessFunctions
|
||||
%-----------------
|
||||
|
||||
\ccMethod{bool is_continuous() const;}
|
||||
{returns whether \ccVar\ is continuous, namely whether it does not
|
||||
contain any poles in its interior. $x$-monotone curves are always
|
||||
continuous.}
|
||||
|
||||
\ccMethod{const Polynomial& numerator () const;}
|
||||
{returns a polynomial with integer coefficients equivalent to $P(x)$.}
|
||||
|
||||
\ccMethod{const Polynomial& denominator () const;}
|
||||
{returns a polynomial with integer coefficients equivalent to $Q(x)$.}
|
||||
|
||||
\ccMethod{Arr_parameter_space source_boundary_in_x () const;}
|
||||
{returns whether the $x$-coordinate of the source is finite or
|
||||
whether it is $\pm\infty$.}
|
||||
\ccGlue
|
||||
\ccMethod{Arr_parameter_space source_boundary_in_y () const;}
|
||||
{returns whether the $y$-coordinate of the source is finite or
|
||||
whether it is $\pm\infty$.}
|
||||
\ccGlue
|
||||
\ccMethod{const Point_2& source() const;}
|
||||
{returns the source point of the arc.
|
||||
\ccPrecond{The source is finite in both $x$ and $y$.}}
|
||||
\ccGlue
|
||||
\ccMethod{typename NtTraits::Algebraic source_x() const;}
|
||||
{Get the $x$-coordinate of the source point.
|
||||
\ccPrecond{The source point is finite in $x$.}}
|
||||
\ccGlue
|
||||
\ccMethod{typename NtTraits::Algebraic source_y() const;}
|
||||
{Get the $y$-coordinate of the source point.
|
||||
\ccPrecond{The source point is finite in $y$.}}
|
||||
|
||||
\ccMethod{Arr_parameter_space target_boundary_in_x () const;}
|
||||
{returns whether the $x$-coordinate of the target is finite or
|
||||
whether it is $\pm\infty$.}
|
||||
\ccGlue
|
||||
\ccMethod{Arr_parameter_space target_boundary_in_y () const;}
|
||||
{returns whether the $y$-coordinate of the target is finite or
|
||||
whether it is $\pm\infty$.}
|
||||
\ccGlue
|
||||
\ccMethod{const Point_2& target() const;}
|
||||
{returns the target point of the arc.
|
||||
\ccPrecond{The target is finite in both $x$ and $y$.}}
|
||||
\ccGlue
|
||||
\ccMethod{typename NtTraits::Algebraic target_x() const;}
|
||||
{Get the $x$-coordinate of the target point.
|
||||
\ccPrecond{The target point is finite in $x$.}}
|
||||
\ccGlue
|
||||
\ccMethod{typename NtTraits::Algebraic target_y() const;}
|
||||
{Get the $y$-coordinate of the target point.
|
||||
\ccPrecond{The target point is finite in $y$.}}
|
||||
|
||||
\ccMethod{Arr_parameter_space left_boundary_in_x () const;}
|
||||
{returns whether the $x$-coordinate of \ccVar's left end is finite or
|
||||
whether it is $\pm\infty$.}
|
||||
\ccGlue
|
||||
\ccMethod{Arr_parameter_space left_boundary_in_y () const;}
|
||||
{returns whether the $y$-coordinate of \ccVar's left end is finite or
|
||||
whether it is $\pm\infty$.}
|
||||
\ccGlue
|
||||
\ccMethod{const Point_2& left() const;}
|
||||
{returns the left (lexicographically smaller) endpoint of \ccVar{}.
|
||||
\ccPrecond{The left end is finite in both $x$ and $y$.}}
|
||||
|
||||
\ccMethod{Arr_parameter_space right_boundary_in_x () const;}
|
||||
{returns whether the $x$-coordinate of \ccVar's right end is finite or
|
||||
whether it is $\pm\infty$.}
|
||||
\ccGlue
|
||||
\ccMethod{Arr_parameter_space right_boundary_in_y () const;}
|
||||
{returns whether the $y$-coordinate of \ccVar's right end is finite or
|
||||
whether it is $\pm\infty$.}
|
||||
\ccGlue
|
||||
\ccMethod{const Point_2& right() const;}
|
||||
{returns the right (lexicographically larger) endpoint of \ccVar{}.
|
||||
\ccPrecond{The right end is finite in both $x$ and $y$.}}
|
||||
|
||||
\end{ccClass}
|
||||
|
||||
\end{ccRefClass}
|
||||
\ccRefPageEnd
|
||||
-631
@@ -1,631 +0,0 @@
|
||||
% +------------------------------------------------------------------------+
|
||||
% | Reference manual page: Arr_rational_function_traits.tex
|
||||
% +------------------------------------------------------------------------+
|
||||
% |
|
||||
% | Package: Arrangement_2
|
||||
% |
|
||||
% +------------------------------------------------------------------------+
|
||||
|
||||
\ccRefPageBegin
|
||||
\begin{ccRefClass}{Arr_rational_function_traits_2<AlgebraicKernel_d_1>}
|
||||
\ccCreationVariable{traits}
|
||||
|
||||
\ccDefinition
|
||||
%============
|
||||
|
||||
The traits class \ccRefName{} is a model of the \ccc{ArrangementTraits_2}
|
||||
concept. It handles bounded and unbounded arcs of rational functions,
|
||||
referred to as {\sl rational arcs} (in particular, such an arc may
|
||||
correspond to the entire graph of a rational function), and enables the
|
||||
construction and maintenance of arrangements of such arcs.
|
||||
%Rational functions, and polynomial functions in particular, are not only
|
||||
%interesting in their own right, they are also very useful for approximating or
|
||||
%interpolating more complex curves.
|
||||
|
||||
A rational function $y = \frac{P(x)}{Q(x)}$ is defined by two polynomials
|
||||
$P$ and $Q$ of arbitrary degrees.
|
||||
If $Q(x) = 1$ then the function is a simple polynomial function.
|
||||
Usually the domain is $\R$ but the function may also be
|
||||
restricted to a bounded interval $[x_{\rm min}, x_{\rm max}]$
|
||||
or defined over a ray $(-\infty, x_{\rm max}]$ or over $[x_{\rm min}, \infty)$.
|
||||
Rational functions are represented by the nested type \ccc{Curve_2}.
|
||||
Note that a rational function may be not continuous since roots of $Q$ induce
|
||||
vertical asymptotes, which would contradict the notion of an $x$-monotone curve
|
||||
as it is introduced by the \ccc{ArrangementTraits_2} concept.
|
||||
Thus, continuous portions of rational functions are represented by the nested
|
||||
type \ccc{X_monotone_curve_2}, which is different from \ccc{Curve_2}.
|
||||
Constructors for both classes are provided by the traits.
|
||||
A \ccc{Curve_2} may be split up into several \ccc{X_monotone_curve_2}
|
||||
using \ccc{Make_x_monotone_2}.
|
||||
|
||||
%If $Q(x) = 1$ then the function is a simple polynomial
|
||||
%function. A bounded rational arc is defined by the graph of a rational
|
||||
%function over some internal $[x_{\rm min}, x_{\rm max}]$, where $Q$
|
||||
%does not have any real roots in this interval (thus the arc does not
|
||||
%contain any vertical asymptotes). Our traits class is also capable of
|
||||
%representing functions defined over an unbounded $x$-range, namely
|
||||
%a ``ray'' defined over $(-\infty, x_{\rm max}]$ or over $[x_{\rm min}, \infty)$,
|
||||
%or a function defined over the entire real $x$-range. Note that a
|
||||
%rational arc may be unbounded even if it is defined over some bounded interval.
|
||||
%In these cases $Q$ has zeros in this interval. That is, the user is able to construct
|
||||
%rational arcs of type \ccc{Curve_2}, which may contain vertical asymptotes.
|
||||
%These may be split up further into \ccc{X_monotone_curve_2} using
|
||||
%\ccc{Make_x_monotone_2}.
|
||||
|
||||
The template parameter of the traits must be a model of the
|
||||
concept \ccc{AlgebraicKernel_d_1}.
|
||||
A rational function is then represented by two polynomials $P$ and $Q$ of type
|
||||
\ccc{AlgebraicKernel_d_1::Polynomial_1}.
|
||||
A point is represented by a rational function and its $x$-coordinate, which is
|
||||
of type \ccc{AlgebraicKernel_d_1::Algebraic_real_1}.
|
||||
Note that an explicit representation of the $y$-coordinate is only computed upon
|
||||
request, which can be a rather costly operation.
|
||||
|
||||
|
||||
The constructed rational functions are cached by the traits class.
|
||||
The cache is local to each traits class object.
|
||||
It is therefore necessary to construct the curves using the constructor
|
||||
objects provided by member functions of the traits class.
|
||||
%This is also the reason why IO is not handled via the usual stream operators.
|
||||
Moreover, a curve must only be used with its own traits.
|
||||
The cache is automatically cleaned up from time to time.
|
||||
The amortized clean up costs are constant. However, there is also a
|
||||
separate member function that cleans up the cache on demand.
|
||||
|
||||
\ccInclude{CGAL/Arr_rational_function_traits_2.h}
|
||||
|
||||
\ccIsModel
|
||||
\ccc{ArrangementTraits_2}\\
|
||||
% \ccc{ArrangementLandmarkTraits_2}\\ %% not a model of this concept since construction of segment is not easy
|
||||
\ccc{ArrangementDirectionalXMonotoneTraits_2}\\
|
||||
\ccc{ArrangementOpenBoundaryTraits_2}
|
||||
|
||||
\ccTypes
|
||||
\ccThree{}{xxxxxxxxxxxxxxxxxxxxxx}{x}
|
||||
\ccTypedef{typedef AlgebraicKernel_d_1 Algebraic_kernel_d_1;}{}\ccGlue
|
||||
\ccTypedef{typedef AlgebraicKernel_d_1::Coefficient Coefficient;}{}\ccGlue
|
||||
\ccTypedef{typedef AlgebraicKernel_d_1::Polynomial_1 Polynomial_1;}{}\ccGlue
|
||||
\ccTypedef{typedef AlgebraicKernel_d_1::Algebraic_real_1 Algebraic_real_1;}{}\ccGlue
|
||||
\ccTypedef{typedef AlgebraicKernel_d_1::Bound Bound;}{}
|
||||
|
||||
%\ccTypedef{typedef AlgebraicKernel_d_1::Bound Approximate_number_type;}{}\ccGlue
|
||||
%\ccNestedType{Approximate_2}{
|
||||
%A model of \ccc{ArrangementLandmarkTraits_2::Approximate_2}}\ccGlue
|
||||
%\ccMethod{Approximate_2 approximate_2_object() const;}{Returns an instance of \ccc{Construct_curve_2}.}
|
||||
|
||||
\ccCreation
|
||||
% =========
|
||||
\ccConstructor{Arr_rational_function_traits_2<AlgebraicKernel_d_1>(const Algebraic_kernel_d_1* kernel);}
|
||||
{constructs an empty traits that uses the kernel pointed by \ccc{kernel}
|
||||
for performing algebraic operations.}
|
||||
|
||||
\ccOperations
|
||||
% ===========
|
||||
\ccThree{xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx}{xxxxxxx}{}
|
||||
\ccMethod{Construct_curve_2 construct_curve_2_object() const;}
|
||||
{Returns an instance of \ccc{Construct_curve_2}.}\ccGlue
|
||||
%\ccMethod{Curve_importer_2 curve_importer_2_object() const;}{Returns an instance of \ccc{Curve_importer_2}.}\ccGlue
|
||||
%\ccMethod{Curve_exporter_2 curve_exporter_2_object() const;}{Returns an instance of \ccc{Curve_exporter_2}.}\ccGlue
|
||||
\ccMethod{Construct_x_monotone_curve_2 construct_x_monotone_curve_2_object() const;}
|
||||
{Returns an instance of \ccc{Construct_x_monotone_curve_2}.}\ccGlue
|
||||
%\ccMethod{X_monotone_curve_importer_2 x_monotone_curve_importer_2_object() const;}{Returns an instance of \ccc{X_monotone_curve_importer_2}.}\ccGlue
|
||||
%\ccMethod{X_monotone_curve_exporter_2 x_monotone_curve_exporter_2_object() const;}{Returns an instance of \ccc{X_monotone_curve_exporter_2}.}\ccGlue
|
||||
|
||||
\ccMethod{void cleanup_cache() const;}
|
||||
{Deletes all curves from the cache that exist only there.}
|
||||
\ccMethod{const Algebraic_kernel_d_1* algebraic_kernel_d_1() const;}
|
||||
{Returns a pointer to the used algerbaic kernel object.}
|
||||
|
||||
\subsection*{Class Arr\_rational\_function\_traits\_2$<$AlgebraicKernel\_d\_1$>$::Curve\_2}
|
||||
\begin{ccClass}{Arr_rational_function_traits_2<AlgebraicKernel_d_1>::Curve_2}
|
||||
\ccCreationVariable{curve}
|
||||
|
||||
The \ccc{Curve_2} class nested within the traits is used
|
||||
to represent rational functions which may be restricted to a certain x-range.
|
||||
|
||||
\ccIsModel
|
||||
|
||||
\ccc{ArrTraits::Curve_2}
|
||||
|
||||
\ccTypes \ccThree{}{xxxxxxxxxxxxxxxxxxxxxx}{x}
|
||||
\ccTypedef{typedef AlgebraicKernel_d_1::Polynomial_1 Polynomial_1;}{}\ccGlue
|
||||
\ccTypedef{typedef AlgebraicKernel_d_1::Algebraic_real_1 Algebraic_real_1;}{}
|
||||
|
||||
\ccOperations
|
||||
\ccThree{xxxxxxxxxxxxxxxxxxxx}{xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx}{}
|
||||
\ccTwo {xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx}{}
|
||||
|
||||
|
||||
\ccMethod{const Polynomial_1& numerator () const;}
|
||||
{returns the numerator of the supporting rational function.}
|
||||
|
||||
\ccMethod{const Polynomial_1& denominator () const;}
|
||||
{returns the denominator of the supporting rational function.}
|
||||
|
||||
\ccMethod{bool is_continuous() const;}
|
||||
{returns whether \ccVar\ is continuous, namely whether it does not
|
||||
contains any vertical asymptotes in its interior.}
|
||||
|
||||
\ccMethod{Arr_parameter_space left_parameter_space_in_x () const;}
|
||||
{returns whether the $x$-coordinate of \ccVar's left end is finite or
|
||||
whether it is $\pm\infty$.}
|
||||
\ccGlue
|
||||
\ccMethod{Arr_parameter_space right_parameter_space_in_x () const;}
|
||||
{returns whether the $x$-coordinate of \ccVar's right end is finite or
|
||||
whether it is $\pm\infty$.}
|
||||
\ccGlue
|
||||
\ccMethod{Algebraic_real_1 left_x() const;}
|
||||
{returns the $x$-coordinate of the left end.
|
||||
\ccPrecond{left\_boundary\_in\_x()==ARR\_INTERIOR}}
|
||||
\ccGlue
|
||||
\ccMethod{Algebraic_real_1 right_x() const;}
|
||||
{returns the $x$-coordinate of the right end.
|
||||
\ccPrecond{right\_boundary\_in\_x()==ARR\_INTERIOR}}
|
||||
\end{ccClass}
|
||||
|
||||
\subsection*{Class Arr\_rational\_function\_traits\_2$<$AlgebraicKernel\_d\_1$>$::X\_monotone\_curve\_2}
|
||||
|
||||
The \ccc{X_monotone_curve_2} class nested within the traits is used
|
||||
to represent $x$-monotone parts of rational functions. In particular, such an $x$-monotone curve
|
||||
may not contain a vertical asymptote in its interior $x$-range.
|
||||
|
||||
\begin{ccClass}{Arr_rational_function_traits_2<AlgebraicKernel_d_1>::X_monotone_curve_2}
|
||||
\ccCreationVariable{xcurve}
|
||||
|
||||
\ccIsModel
|
||||
\ccc{ArrTraits::XMonotoneCurve_2}
|
||||
|
||||
\ccTypes \ccThree{}{xxxxxxxxxxxxxxxxxxxxxx}{x}
|
||||
\ccTypedef{typedef AlgebraicKernel_d_1::Polynomial_1 Polynomial_1;}{}\ccGlue
|
||||
\ccTypedef{typedef AlgebraicKernel_d_1::Algebraic_real_1 Algebraic_real_1;}{}\ccGlue
|
||||
\ccTypedef{typedef Arr_rational_function_traits_2<AlgebraicKernel_d_1>::Point_2 Point_2;}{}
|
||||
|
||||
\ccOperations
|
||||
\ccThree{xxxxxxxxxxxxxxxxxxxx}{xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx}{}
|
||||
\ccTwo {xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx}{}
|
||||
|
||||
|
||||
\ccMethod{const Polynomial_1& numerator () const;}
|
||||
{returns the numerator of the supporting rational function.}
|
||||
|
||||
\ccMethod{const Polynomial_1& denominator () const;}
|
||||
{returns the denominator of the supporting rational function.}
|
||||
|
||||
|
||||
% ======== source
|
||||
\ccMethod{Arr_parameter_space source_parameter_space_in_x () const;}
|
||||
{returns whether the $x$-coordinate of the source is finite or
|
||||
whether it is $\pm\infty$.}
|
||||
\ccGlue
|
||||
\ccMethod{Arr_parameter_space source_parameter_space_in_y () const;}
|
||||
{returns whether the $y$-coordinate of the source is finite or
|
||||
whether it is $\pm\infty$.}
|
||||
\ccGlue
|
||||
\ccMethod{const Point_2& source() const;}
|
||||
{returns the source point of the arc.
|
||||
\ccPrecond{Both the $x$- and $y$-coordinates of the source point is
|
||||
finite.}}
|
||||
\ccGlue
|
||||
\ccMethod{Algebraic_real_1 source_x() const;}
|
||||
{returns the $x$-coordinate of the source point.
|
||||
\ccPrecond{The $x$-coordinate of the source point is finite.}}
|
||||
%\ccGlue
|
||||
%\ccMethod{Algebraic_real_1 source_y() const;}
|
||||
% {returns the $y$-coordinate of the source point.
|
||||
% \ccPrecond{The $y$-coordinate of the source point is finite.}}
|
||||
|
||||
|
||||
% ======== target
|
||||
\ccMethod{Arr_parameter_space target_parameter_space_in_x () const;}
|
||||
{returns whether the $x$-coordinate of the target is finite or
|
||||
whether it is $\pm\infty$.}
|
||||
\ccGlue
|
||||
\ccMethod{Arr_parameter_space target_parameter_space_in_y () const;}
|
||||
{returns whether the $y$-coordinate of the target is finite or
|
||||
whether it is $\pm\infty$.}
|
||||
\ccGlue
|
||||
\ccMethod{const Point_2& target() const;}
|
||||
{returns the target point of the arc.
|
||||
\ccPrecond{Both the $x$- and $y$-coordinates of the target point is
|
||||
finite.}}
|
||||
\ccGlue
|
||||
\ccMethod{Algebraic_real_1 target_x() const;}
|
||||
{returns the $x$-coordinate of the target point.
|
||||
\ccPrecond{The $x$-coordinate of the target point is finite.}}
|
||||
%\ccGlue
|
||||
%\ccMethod{Algebraic_real_1 target_y() const;}
|
||||
% {returns the $y$-coordinate of the target point.
|
||||
% \ccPrecond{The $y$-coordinate of the target point is finite.}}
|
||||
|
||||
|
||||
% ======== left
|
||||
\ccMethod{Arr_parameter_space left_parameter_space_in_x () const;}
|
||||
{returns whether the $x$-coordinate of the left curve end is finite or
|
||||
whether it is $\pm\infty$.}
|
||||
\ccGlue
|
||||
\ccMethod{Arr_parameter_space left_parameter_space_in_y () const;}
|
||||
{returns whether the $y$-coordinate of the left curve end is finite or
|
||||
whether it is $\pm\infty$.}
|
||||
\ccGlue
|
||||
\ccMethod{const Point_2& left() const;}
|
||||
{returns the left point of the arc.
|
||||
\ccPrecond{Both the $x$- and $y$-coordinates of the left point is finite.}}
|
||||
\ccGlue
|
||||
\ccMethod{Algebraic_real_1 left_x() const;}
|
||||
{returns the $x$-coordinate of the left point.
|
||||
\ccPrecond{The $x$-coordinate of the left point is finite.}}
|
||||
%\ccGlue
|
||||
%\ccMethod{Algebraic_real_1 left_y() const;}
|
||||
% {returns the $y$-coordinate of the left point.
|
||||
% \ccPrecond{The $y$-coordinate of the left point is finite.}}
|
||||
|
||||
|
||||
% ======== right
|
||||
\ccMethod{Arr_parameter_space right_parameter_space_in_x () const;}
|
||||
{returns whether the $x$-coordinate of the right curve end is finite or
|
||||
whether it is $\pm\infty$.}
|
||||
\ccGlue
|
||||
\ccMethod{Arr_parameter_space right_parameter_space_in_y () const;}
|
||||
{returns whether the $y$-coordinate of the right curve end is finite or
|
||||
whether it is $\pm\infty$.}
|
||||
\ccGlue
|
||||
\ccMethod{const Point_2& right() const;}
|
||||
{returns the right point of the arc.
|
||||
\ccPrecond{Both the $x$- and $y$-coordinates of The right point is
|
||||
finite.}}
|
||||
\ccGlue
|
||||
\ccMethod{Algebraic_real_1 right_x() const;}
|
||||
{returns the $x$-coordinate of the right point.
|
||||
\ccPrecond{The $x$-coordinate of the right point is finite.}}
|
||||
%\ccGlue
|
||||
%\ccMethod{Algebraic_real_1 right_y() const;}
|
||||
% {returns the $y$-coordinate of the right point.
|
||||
% \ccPrecond{The right point is finite in $y$.}}
|
||||
|
||||
\ccMethod{bool is_left_to_right () const;}
|
||||
{returns whether the curve is oriented from left to right.}
|
||||
\end{ccClass}
|
||||
|
||||
\subsection*{Class Arr\_rational\_function\_traits\_2$<$AlgebraicKernel\_d\_1$>$::Point\_2}
|
||||
\begin{ccClass}{Arr_rational_function_traits_2<AlgebraicKernel_d_1>::Point_2}
|
||||
\ccCreationVariable{point}
|
||||
|
||||
\ccIsModel
|
||||
\ccc{ArrTraits::Point_2}
|
||||
|
||||
\ccTypes \ccThree{}{xxxxxxxxxxxxxxxxxxxxxx}{x}
|
||||
\ccTypedef{typedef AlgebraicKernel_d_1::Polynomial_1 Polynomial_1;}{}\ccGlue
|
||||
\ccTypedef{typedef AlgebraicKernel_d_1::Algebraic_real_1 Algebraic_real_1;}{}\ccGlue
|
||||
\ccTypedef{typedef AlgebraicKernel_d_1::Bound Bound;}{}
|
||||
|
||||
\ccOperations
|
||||
\ccThree{xxxxxxxxxxxxxxxxxxxxxxxxx}{xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx}{}
|
||||
\ccTwo {xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx}{}
|
||||
|
||||
\ccMethod{Polynomial_1 numerator () const;}
|
||||
{returns the numerator of the supporting rational function.}
|
||||
|
||||
\ccMethod{Polynomial_1 denominator () const;}
|
||||
{returns the denominator of the supporting rational function.}
|
||||
|
||||
\ccMethod{std::pair<double,double> to_double() const;}
|
||||
{returns double-approximations of the x- and y-coordinates.}
|
||||
|
||||
\ccMethod{Algebraic_real_1 x() const;}
|
||||
{returns the $x$-coordinate of the point.}
|
||||
\ccThree{xxxxxxxxxxxxxxxxxxxxxxxx}{xxxxx}{}
|
||||
|
||||
\ccMethod{Algebraic_real_1 y() const;}
|
||||
{obtains the y-coordinates of the point. {\bf Attention:} As described above,
|
||||
points are not stored by their y-coordinate in \ccc{Algebraic_real_1}
|
||||
representation. In fact, this representation must be computed on demand, and
|
||||
might become quite costly for points defined by high-degree polynomials.
|
||||
Therefore, it is recommended to avoid calls to this function as much as
|
||||
possible.}
|
||||
|
||||
\ccMethod{std::pair<Bound,Bound> approximate_absolute_x(int a) const;}
|
||||
{Computes a pair $p$ approximating the $x$-coordinate with
|
||||
respect to the given absolute precision $a$.
|
||||
\ccPostcond{$p.first \leq x \leq p.second $}
|
||||
\ccPostcond{$p.second - p.first \leq 2^{-a} $}}
|
||||
|
||||
\ccMethod{std::pair<Bound,Bound> approximate_absolute_y(int a) const;}
|
||||
{Computes a pair $p$ approximating the $y$-coordinate with
|
||||
respect to the given absolute precision $a$.
|
||||
\ccPostcond{$p.first \leq y \leq p.second $}
|
||||
\ccPostcond{$p.second - p.first \leq 2^{-a} $}}
|
||||
|
||||
\ccMethod{std::pair<Bound,Bound> approximate_relative_x(int r) const;}
|
||||
{Computes a pair $p$ approximating the $x$-coordinate with
|
||||
respect to the given relative precision $r$.
|
||||
\ccPostcond{$p.first \leq x \leq p.second $}
|
||||
\ccPostcond{$p.second - p.first \leq 2^{-r}|x| $}}
|
||||
|
||||
\ccMethod{std::pair<Bound,Bound> approximate_relative_y(int r) const;}
|
||||
{Computes a pair $p$ approximating the $y$-coordinate with
|
||||
respect to the given relative precision $r$.
|
||||
\ccPostcond{$p.first \leq y \leq p.second $}
|
||||
\ccPostcond{$p.second - p.first \leq 2^{-r}|y| $}}
|
||||
|
||||
\end{ccClass}
|
||||
\subsection*{Class Arr\_rational\_function\_traits\_2$<$AlgebraicKernel\_d\_1$>$::Construct\_curve\_2}
|
||||
\begin{ccClass}{Arr_rational_function_traits_2<AlgebraicKernel_d_1>::Construct_curve_2}
|
||||
\ccCreationVariable{construct}
|
||||
|
||||
Functor to construct a \ccc{Curve_2}. To enable caching the class is not
|
||||
default constructible and must be obtained via the function
|
||||
\ccc{construct_curve_2_object()}, which is a member of the traits.
|
||||
|
||||
\ccIsModel
|
||||
\ccc{Assignable}\\
|
||||
\ccc{CopyConstructible}\\
|
||||
\ccc{AdaptableBinaryFunction}\\
|
||||
\ccc{AdaptableUnaryFunction}
|
||||
|
||||
\ccTypes \ccThree{}{xxxxxxxxxxxxxxxxxxxxxx}{x}
|
||||
\ccTypedef{typedef AlgebraicKernel_d_1::Polynomial_1 Polynomial_1;}{}\ccGlue
|
||||
\ccTypedef{typedef AlgebraicKernel_d_1::Algebraic_real_1 Algebraic_real_1;}{}\ccGlue
|
||||
\ccTypedef{typedef Arr_rational_function_traits_2<AlgebraicKernel_d_1>::Curve_2 result_type;}{}
|
||||
|
||||
\ccTypedef{typedef Polynomial_1 argument_type;}{}\ccGlue
|
||||
\ccTypedef{typedef Polynomial_1 first_argument_type;}{}\ccGlue
|
||||
\ccTypedef{typedef Polynomial_1 second_argument_type;}{}
|
||||
|
||||
\ccOperations
|
||||
\ccThree{xxxxxxxxxxx}{xxxxx}{}
|
||||
\ccTwo {xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx}{}
|
||||
|
||||
% Operators that accept polynomials:
|
||||
\ccMethod{Curve_2 operator()(Polynomial_1 P) const;}
|
||||
{Constructs a curve representing the polynomial function $y = P(x)$.}\ccGlue
|
||||
\ccMethod{Curve_2 operator()(Polynomial_1 P, const Algebraic_real_1& x, bool right) const;}
|
||||
{Constructs a curve representing the polynomial function $y = P(x)$.
|
||||
The function is defined over the interval $[x,+\infty)$ if $right$ is true
|
||||
and $(-\infty,x]$ otherwise.}\ccGlue
|
||||
\ccMethod{Curve_2 operator()(Polynomial_1 P, const Algebraic_real_1& lower, const Algebraic_real_1& upper) const;}
|
||||
{Constructs a curve representing the polynomial function $y = P(x)$.
|
||||
The function is defined over the interval $[lower,upper]$.}\ccGlue
|
||||
\ccMethod{Curve_2 operator()(Polynomial_1 P, Polynomial_1 Q) const;}
|
||||
{Constructs a curve representing the rational function $y = P(x)/Q(x)$.}\ccGlue
|
||||
\ccMethod{Curve_2 operator()(Polynomial_1 P, Polynomial_1 Q, const Algebraic_real_1& x, bool right) const;}
|
||||
{Constructs a curve representing the rational function $y = P(x)/Q(x)$.
|
||||
The function is defined over the interval $I=[x,+\infty)$ if $right$ is
|
||||
true and $I=(-\infty,x]$ otherwise.}\ccGlue
|
||||
\ccMethod{Curve_2 operator()(Polynomial_1 P, Polynomial_1 Q, const Algebraic_real_1& lower, const Algebraic_real_1& upper) const;}
|
||||
{Constructs a curve representing the rational function $y = P(x)/Q(x)$.
|
||||
The function is defined over the interval $I=[lower,upper]$.}
|
||||
|
||||
% Operators that accept polynomial coefficients:
|
||||
\ccMethod{template <typename InputIterator>
|
||||
Curve_2 operator()(InputIterator begin, InputIterator end) const;}
|
||||
{Constructs a curve representing the polynomial function $y = P(x)$, where
|
||||
the coefficients of $P$ are given in the range \ccc{[begin,end)}.}\ccGlue
|
||||
\ccMethod{template <typename InputIterator>
|
||||
Curve_2 operator()(InputIterator begin, InputIterator end,
|
||||
const Algebraic_real_1& x, bool right) const;}
|
||||
{Constructs a curve representing the polynomial function $y = P(x)$, where
|
||||
the coefficients of $P$ are given in the range \ccc{[begin,end)}. The
|
||||
function is defined over the interval $[x,+\infty)$ if $right$ is true
|
||||
and $(-\infty,x]$ otherwise.}\ccGlue
|
||||
\ccMethod{template <typename InputIterator>
|
||||
Curve_2 operator()(InputIterator begin, InputIterator end,
|
||||
const Algebraic_real_1& lower,
|
||||
const Algebraic_real_1& upper) const;}
|
||||
{Constructs a curve representing the polynomial function $y = P(x)$, where
|
||||
the coefficients of $P$ are given in the range \ccc{[begin,end)}. The
|
||||
function is defined over the interval $[lower,upper]$.}\ccGlue
|
||||
\ccMethod{template <typename InputIterator>
|
||||
Curve_2 operator()(InputIterator begin_numer, InputIterator end_numer,
|
||||
InputIterator begin_denom, InputIterator end_denom) const;}
|
||||
{Constructs a curve representing the rational function $y = P(x)/Q(x)$,
|
||||
where the coefficients of $P$ and $Q$ are given in the ranges
|
||||
\ccc{[begin_numer,end_numer)} and \ccc{[begin_denom,end_denom)},
|
||||
respectively.}\ccGlue
|
||||
\ccMethod{template <typename InputIterator>
|
||||
Curve_2 operator()(InputIterator begin_numer, InputIterator end_numer,
|
||||
InputIterator begin_denom, InputIterator end_denom,
|
||||
const Algebraic_real_1& x, bool right) const;}
|
||||
{Constructs a curve representing the rational function $y = P(x)/Q(x)$,
|
||||
where the coefficients of $P$ and $Q$ are given in the ranges
|
||||
\ccc{[begin_numer,end_numer)} and \ccc{[begin_denom,end_denom)},
|
||||
respectively. The function is defined over the interval $I=[x,+\infty)$
|
||||
if $right$ is true and $I=(-\infty,x]$ otherwise.}\ccGlue
|
||||
\ccMethod{template <typename InputIterator>
|
||||
Curve_2 operator()(InputIterator begin_numer, InputIterator end_numer,
|
||||
InputIterator begin_denom, InputIterator end_denom,
|
||||
const Algebraic_real_1& lower,
|
||||
const Algebraic_real_1& upper) const;}
|
||||
{Constructs a curve representing the rational function $y = P(x)/Q(x)$,
|
||||
where the coefficients of $P$ and $Q$ are given in the ranges
|
||||
\ccc{[begin_numer,end_numer)} and \ccc{[begin_denom,end_denom)},
|
||||
respectively. The function is defined over the interval $I=[lower,upper]$.}
|
||||
|
||||
\end{ccClass}
|
||||
|
||||
\subsection*{Class Arr\_rational\_function\_traits\_2$<$AlgebraicKernel\_d\_1$>$::Construct\_x\_monotone\_curve\_2}
|
||||
\begin{ccClass}{Arr_rational_function_traits_2<AlgebraicKernel_d_1>::Construct_x_monotone_curve_2}
|
||||
|
||||
Functor to construct a \ccc{X_monotone_curve_2}. To enable caching the class
|
||||
is not default constructible and must be obtained via the function
|
||||
\ccc{construct_x_monotone_curve_2_object()}, which is a member of the traits.
|
||||
|
||||
\ccCreationVariable{construct}
|
||||
\ccIsModel
|
||||
\ccc{Assignable}\\
|
||||
\ccc{CopyConstructible}\\
|
||||
\ccc{AdaptableBinaryFunction}\\
|
||||
\ccc{AdaptableUnaryFunction}
|
||||
|
||||
\ccTypes \ccThree{}{xxxxxxxxxxxxxxxxxxxxxx}{x}
|
||||
\ccTypedef{typedef AlgebraicKernel_d_1::Polynomial_1 Polynomial_1;}{}\ccGlue
|
||||
\ccTypedef{typedef AlgebraicKernel_d_1::Algebraic_real_1 Algebraic_real_1;}{}\ccGlue
|
||||
\ccTypedef{typedef Arr_rational_function_traits_2<AlgebraicKernel_d_1>::X_monotone_curve_2 result_type;}{}\ccGlue
|
||||
\ccTypedef{typedef Polynomial_1 argument_type;}{}\ccGlue
|
||||
\ccTypedef{typedef Polynomial_1 first_argument_type;}{}\ccGlue
|
||||
\ccTypedef{typedef Polynomial_1 second_argument_type;}{}
|
||||
|
||||
\ccOperations
|
||||
\ccThree{xxxxxxxxxxxxxxxxxxxx}{xx}{}
|
||||
\ccTwo {xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx}{}
|
||||
|
||||
% Operators that accept polynomials:
|
||||
\ccMethod{X_monotone_curve_2 operator()(Polynomial_1 P) const;}
|
||||
{Constructs an $x$-monotone curve supported by the polynomial function
|
||||
$y = P(x)$.}\ccGlue
|
||||
\ccMethod{X_monotone_curve_2 operator()(Polynomial_1 P,
|
||||
const Algebraic_real_1& x,
|
||||
bool right) const;}
|
||||
{Constructs an $x$-monotone curve supported by the polynomial function
|
||||
$y = P(x)$. The function is defined over the interval $[x,+\infty)$ if
|
||||
$right$ is true and $(-\infty,x]$ otherwise.}\ccGlue
|
||||
\ccMethod{X_monotone_curve_2 operator()(Polynomial_1 P,
|
||||
const Algebraic_real_1& lower,
|
||||
const Algebraic_real_1& upper); const}
|
||||
{Constructs an $x$-monotone curve supported by the polynomial function
|
||||
$y = P(x)$. The function is defined over the interval $[lower,upper]$.}\ccGlue
|
||||
\ccMethod{X_monotone_curve_2 operator()(Polynomial_1 P, Polynomial_1 Q); const}
|
||||
{Constructs an $x$-monotone curve supported by the rational function
|
||||
$y = P(x)/Q(x)$.
|
||||
\ccPrecond{$Q$ has no real roots.}}\ccGlue
|
||||
\ccMethod{X_monotone_curve_2 operator()(Polynomial_1 P, Polynomial_1 Q,
|
||||
const Algebraic_real_1& x,
|
||||
bool right); const}
|
||||
{Constructs an $x$-monotone curve supported by the rational function
|
||||
$y = P(x)/Q(x)$. The function is defined over the interval $I=[x,+\infty)$
|
||||
if $right$ is true and $I=(-\infty,x]$ otherwise.
|
||||
\ccPrecond{$Q$ has no real roots in the interior of $I$.}}\ccGlue
|
||||
\ccMethod{X_monotone_curve_2 operator()(Polynomial_1 P, Polynomial_1 Q,
|
||||
const Algebraic_real_1& lower,
|
||||
const Algebraic_real_1& upper); const
|
||||
}
|
||||
{Constructs an $x$-monotone curve supported by the rational function
|
||||
$y = P(x)/Q(x)$. The function is defined over the interval $I=[lower,upper]$.
|
||||
\ccPrecond{$Q$ has no real roots in the interior of $I$.}}
|
||||
|
||||
% Operators that accept polynomial coefficients:
|
||||
\ccMethod{template <typename InputIterator>
|
||||
X_monotone_curve_2 operator()(InputIterator begin, InputIterator end) const;}
|
||||
{Constructs an $x$-monotone curve supported by the polynomial function
|
||||
$y = P(x)$, where the coefficients of $P$ are given in the range
|
||||
\ccc{[begin,end)}.}\ccGlue
|
||||
\ccMethod{template <typename InputIterator>
|
||||
X_monotone_curve_2 operator()(InputIterator begin, InputIterator end,
|
||||
const Algebraic_real_1& x, bool right) const;}
|
||||
{Constructs an $x$-monotone curve supported by the polynomial function
|
||||
$y = P(x)$, where the coefficients of $P$ are given in the range
|
||||
\ccc{[begin,end)}. The function is defined over the interval $[x,+\infty)$
|
||||
if $right$ is true and $(-\infty,x]$ otherwise.}\ccGlue
|
||||
\ccMethod{template <typename InputIterator>
|
||||
X_monotone_curve_2 operator()(InputIterator begin, InputIterator end
|
||||
const Algebraic_real_1& lower,
|
||||
const Algebraic_real_1& upper); const}
|
||||
{Constructs an $x$-monotone curve supported by the polynomial function
|
||||
$y = P(x)$, where the coefficients of $P$ are given in the range
|
||||
\ccc{[begin,end)}. The function is defined over the interval
|
||||
$[lower,upper]$.}\ccGlue
|
||||
\ccMethod{template <typename InputIterator>
|
||||
X_monotone_curve_2 operator()(InputIterator begin_numer, InputIterator end_numer,
|
||||
InputIterator begin_denom, InputIterator end_denom); const}
|
||||
{Constructs an $x$-monotone curve supported by the rational function
|
||||
$y = P(x)/Q(x)$, where the coefficients of $P$ and $Q$ are given in the
|
||||
ranges \ccc{[begin_numer,end_numer)} and \ccc{[begin_denom,end_denom)},
|
||||
respectively.
|
||||
\ccPrecond{$Q$ has no real roots.}}\ccGlue
|
||||
\ccMethod{template <typename InputIterator>
|
||||
X_monotone_curve_2 operator()(InputIterator begin_numer, InputIterator end_numer,
|
||||
InputIterator begin_denom, InputIterator end_denom,
|
||||
const Algebraic_real_1& x, bool right); const}
|
||||
{Constructs an $x$-monotone curve supported by the rational function
|
||||
$y = P(x)/Q(x)$, where the coefficients of $P$ and $Q$ are given in the
|
||||
ranges \ccc{[begin_numer,end_numer)} and \ccc{[begin_denom,end_denom)},
|
||||
respectively. The function is defined over the interval $I=[x,+\infty)$
|
||||
if $right$ is true and $I=(-\infty,x]$ otherwise.
|
||||
\ccPrecond{$Q$ has no real roots in the interior of $I$.}}\ccGlue
|
||||
\ccMethod{template <typename InputIterator>
|
||||
X_monotone_curve_2 operator()(InputIterator begin_numer, InputIterator end_numer,
|
||||
InputIterator begin_denom, InputIterator end_denom,
|
||||
const Algebraic_real_1& lower, const Algebraic_real_1& upper); const
|
||||
}
|
||||
{Constructs an $x$-monotone curve supported by the rational function
|
||||
$y = P(x)/Q(x)$, where the coefficients of $P$ and $Q$ are given in the
|
||||
ranges \ccc{[begin_numer,end_numer)} and \ccc{[begin_denom,end_denom)},
|
||||
respectively. The function is defined over the interval $I=[lower,upper]$.
|
||||
\ccPrecond{$Q$ has no real roots in the interior of $I$.}}
|
||||
|
||||
\end{ccClass}
|
||||
|
||||
%\subsection*{Class Arr\_rational\_function\_traits\_2$<$AlgebraicKernel\_d\_1$>$::Importer}
|
||||
%\begin{ccClass}{Arr_rational_function_traits_2<AlgebraicKernel_d_1>::Importer}
|
||||
%\ccCreationVariable{import}
|
||||
|
||||
%Functor to import a \ccc{Curve_2} or \ccc{X_monotone_curve_2} from a stream.
|
||||
%To enable caching the class is not default constructible and must be obtained
|
||||
%via the function \ccc{Importer_object()}, which is a member of the traits.
|
||||
|
||||
%\ccIsModel
|
||||
%\ccc{Assignable}\\
|
||||
%\ccc{CopyConstructible}
|
||||
|
||||
%\ccTypes
|
||||
%\ccThree{}{xxxxxxxxxxxxxxxx}{x}
|
||||
%\ccTypedef{typedef Arr_rational_function_traits_2<AlgebraicKernel_d_1>::Curve_2 Curve_2;}{}\ccGlue
|
||||
%\ccTypedef{typedef Arr_rational_function_traits_2<AlgebraicKernel_d_1>::X_monotone_curve_2 X_monotone_curve_2;}{}
|
||||
|
||||
%\ccOperations
|
||||
%\ccThree{xxxxxxxxxxxxx}{}{xxxxxxxxxxxxxxxxxxxxxxxxxxx}
|
||||
%\ccMethod{
|
||||
% std::istream& operator() (
|
||||
% std::istream& is, const Curve_2& curve);}
|
||||
%{
|
||||
% Imports a \ccc{Curve_2} from the given input stream.
|
||||
%}
|
||||
%\ccMethod{
|
||||
% std::istream& operator() (
|
||||
% std::istream& is, const X_monotone_curve_2& curve);}
|
||||
%{
|
||||
% Imports an \ccc{X_monotone_curve_2} from the given input stream.
|
||||
%}
|
||||
|
||||
%\end{ccClass}
|
||||
|
||||
%\subsection*{Class Arr\_rational\_function\_traits\_2$<$AlgebraicKernel\_d\_1$>$::Exporter}
|
||||
%\begin{ccClass}{Arr_rational_function_traits_2<AlgebraicKernel_d_1>::Exporter}
|
||||
%\ccCreationVariable{export}
|
||||
|
||||
%Functor to export a \ccc{Curve_2} or \ccc{X_monotone_curve_2} to a stream.
|
||||
|
||||
%\ccIsModel
|
||||
%\ccc{Assignable}\\
|
||||
%\ccc{CopyConstructible}
|
||||
|
||||
%\ccTypes
|
||||
%\ccThree{}{xxxxxxxxxxxxxxxx}{x}
|
||||
%\ccTypedef{typedef Arr_rational_function_traits_2<AlgebraicKernel_d_1>::Curve_2 Curve_2;}{}\ccGlue
|
||||
%\ccTypedef{typedef Arr_rational_function_traits_2<AlgebraicKernel_d_1>::X_monotone_curve_2 X_monotone_curve_2;}{}
|
||||
|
||||
%\ccOperations
|
||||
%\ccThree{xxxxxxxxxxxxx}{}{xxxxxxxxxxxxxxxxxxxxxxxxxxx}
|
||||
%\ccMethod{
|
||||
% std::ostream& operator() (
|
||||
% std::ostream& os,
|
||||
% const Curve_2& curve);}
|
||||
%{
|
||||
% Exports a \ccc{Curve_2}
|
||||
% into the given output stream.
|
||||
%}
|
||||
|
||||
%\ccMethod{
|
||||
% std::ostream& operator() (
|
||||
% std::ostream& os,
|
||||
% const X_monotone_curve_2& curve);}
|
||||
%{
|
||||
% Exports an \ccc{X_monotone_curve_2}
|
||||
% into the given output stream.
|
||||
%}
|
||||
%
|
||||
%\end{ccClass}
|
||||
|
||||
\end{ccRefClass}
|
||||
\ccRefPageEnd
|
||||
|
||||
|
||||
@@ -2,7 +2,7 @@
|
||||
\RCSdefDate{\ArrangementOnSurfaceRefDate}{$Date$}
|
||||
\ccRefChapter{2D Arrangements\label{chapterArrangement_on_surface_2_ref}}
|
||||
\ccChapterRelease{\ArrangementOnSurfaceRefRev. \ \ArrangementOnSurfaceRefDate}
|
||||
\ccChapterAuthor{Ron Wein, Efi Fogel, Baruch Zukerman, Dan Halperin, Eric Berberich, and Oren Zalzman}
|
||||
\ccChapterAuthor{Ron Wein, Efi Fogel, Baruch Zukerman, Dan Halperin, and Eric Berberich}
|
||||
|
||||
% ===============================================================
|
||||
%\section*{Introduction}
|
||||
@@ -25,6 +25,7 @@ implemented as peripheral classes or as free (global) functions.
|
||||
\subsection*{Enumerations}
|
||||
|
||||
\ccRefIdfierPage{CGAL::Arr_parameter_space}\\
|
||||
\ccRefIdfierPage{CGAL::Arr_boundary_type}\\
|
||||
\ccRefIdfierPage{CGAL::Arr_curve_end}\\
|
||||
\ccRefIdfierPage{CGAL::Arr_halfedge_direction}
|
||||
|
||||
@@ -47,7 +48,6 @@ implemented as peripheral classes or as free (global) functions.
|
||||
\ccRefConceptPage{ArrangementLandmarkTraits_2}\\
|
||||
\ccRefConceptPage{ArrangementXMonotoneTraits_2}\\
|
||||
\ccRefConceptPage{ArrangementTraits_2}\\
|
||||
\ccRefConceptPage{ArrangementOpenBoundaryTraits_2}\\
|
||||
~\\
|
||||
\ccRefConceptPage{ArrangementInputFormatter}\\
|
||||
\ccRefConceptPage{ArrangementOutputFormatter} \\
|
||||
@@ -76,8 +76,7 @@ implemented as peripheral classes or as free (global) functions.
|
||||
\ccRefConceptPage{ArrTraits::Equal_2}\\
|
||||
\ccRefConceptPage{ArrTraits::ParameterSpaceInX_2}\\
|
||||
\ccRefConceptPage{ArrTraits::ParameterSpaceInY_2}\\
|
||||
\ccRefConceptPage{ArrTraits::CompareXAtLimit_2}\\
|
||||
\ccRefConceptPage{ArrTraits::CompareXNearLimit_2}\\
|
||||
\ccRefConceptPage{ArrTraits::CompareXNearBoundary_2}\\
|
||||
\ccRefConceptPage{ArrTraits::CompareYNearBoundary_2}\\
|
||||
% \ccRefConceptPage{ArrTraits::IsOnXIdentification_2}\\
|
||||
% \ccRefConceptPage{ArrTraits::IsOnYIdentification_2}\\
|
||||
@@ -116,7 +115,7 @@ implemented as peripheral classes or as free (global) functions.
|
||||
\ccRefIdfierPage{CGAL::Arr_circular_arc_traits_2<CircularKernel>}\\
|
||||
\ccRefIdfierPage{CGAL::Arr_circular_line_arc_traits_2<CircularKernel>}\\
|
||||
\ccRefIdfierPage{CGAL::Arr_conic_traits_2<RatKernel,AlgKernel,NtTraits>}\\
|
||||
\ccRefIdfierPage{CGAL::Arr_rational_function_traits_2<AlgebraicKernel_d_1>}\\
|
||||
\ccRefIdfierPage{CGAL::Arr_rational_arc_traits_2<AlgKernel,NtTraits>}\\
|
||||
\ccRefIdfierPage{CGAL::Arr_Bezier_curve_traits_2<RatKernel,AlgKernel,NtTraits>}\\
|
||||
\ccRefIdfierPage{CGAL::Arr_algebraic_segment_traits_2<Coefficient>}\\
|
||||
\ccRefIdfierPage{CGAL::Arr_curve_data_traits_2<Tr,XData,Mrg,CData,Cnv>}\\
|
||||
@@ -132,14 +131,6 @@ implemented as peripheral classes or as free (global) functions.
|
||||
\ccRefIdfierPage{CGAL::Arr_trapezoid_ric_point_location<Arrangement>}\\
|
||||
\ccRefIdfierPage{CGAL::Arr_landmarks_point_location<Arrangement,Generator>}
|
||||
|
||||
\subsection*{Tags}
|
||||
|
||||
\ccRefIdfierPage{CGAL::Arr_oblivious_side_tag}\\
|
||||
\ccRefIdfierPage{CGAL::Arr_open_side_tag}
|
||||
% \ccRefIdfierPage{CGAL::Arr_closed_side_tag}\\
|
||||
% \ccRefIdfierPage{CGAL::Arr_contracted_side_tag}\\
|
||||
% \ccRefIdfierPage{CGAL::Arr_identified_side_tag}
|
||||
|
||||
\subsection*{Functions}
|
||||
|
||||
\ccRefIdfierPage{CGAL::is_valid}\\
|
||||
|
||||
@@ -43,6 +43,7 @@
|
||||
\input{Arrangement_on_surface_2_ref/Arr_extended_vertex.tex}
|
||||
\input{Arrangement_on_surface_2_ref/Arr_extended_halfedge.tex}
|
||||
\input{Arrangement_on_surface_2_ref/Arr_extended_face.tex}
|
||||
\input{Arrangement_on_surface_2_ref/Arr_boundary_type.tex}
|
||||
\input{Arrangement_on_surface_2_ref/Arr_curve_end.tex}
|
||||
\input{Arrangement_on_surface_2_ref/Arr_halfedge_direction.tex}
|
||||
\input{Arrangement_on_surface_2_ref/Arr_basic_traits.tex}
|
||||
@@ -57,7 +58,7 @@
|
||||
\input{Arrangement_on_surface_2_ref/Arr_circle_segment_traits.tex}
|
||||
\input{Arrangement_on_surface_2_ref/Arr_circular_arc_traits.tex}
|
||||
\input{Arrangement_on_surface_2_ref/Arr_conic_traits.tex}
|
||||
\input{Arrangement_on_surface_2_ref/Arr_rational_function_traits.tex}
|
||||
\input{Arrangement_on_surface_2_ref/Arr_rational_arc_traits.tex}
|
||||
\input{Arrangement_on_surface_2_ref/Arr_Bezier_traits.tex}
|
||||
\input{Arrangement_on_surface_2_ref/Arr_algebraic_segment_traits.tex}
|
||||
\input{Arrangement_on_surface_2_ref/Arr_mrg_data_traits.tex}
|
||||
@@ -76,7 +77,6 @@
|
||||
\input{Arrangement_on_surface_2_ref/arr_locate.tex}
|
||||
\input{Arrangement_on_surface_2_ref/arr_vert_decomp.tex}
|
||||
\input{Arrangement_on_surface_2_ref/Arr_observer.tex}
|
||||
\input{Arrangement_on_surface_2_ref/Arr_open_boundary_traits.tex}
|
||||
\input{Arrangement_on_surface_2_ref/Arr_with_history_2.tex}
|
||||
\input{Arrangement_on_surface_2_ref/Arr_parameter_space.tex}
|
||||
\input{Arrangement_on_surface_2_ref/arr_with_hist_remove.tex}
|
||||
|
||||
@@ -9,7 +9,11 @@
|
||||
#include <list>
|
||||
#include <fstream>
|
||||
|
||||
typedef CGAL::Exact_predicates_exact_constructions_kernel Kernel;
|
||||
// instead of
|
||||
//typedef CGAL::Exact_predicates_exact_constructions_kernel Kernel;
|
||||
// workaround for VC++
|
||||
struct Kernel : public CGAL::Exact_predicates_exact_constructions_kernel {};
|
||||
|
||||
typedef Kernel::FT Number_type;
|
||||
typedef CGAL::Arr_segment_traits_2<Kernel> Traits_2;
|
||||
typedef Traits_2::Point_2 Point_2;
|
||||
|
||||
@@ -1,80 +1,75 @@
|
||||
//! \file examples/Arrangement_2/ex_rational_functions.cpp
|
||||
// Constructing an arrangement of arcs of rational functions.
|
||||
|
||||
#include <CGAL/basic.h>
|
||||
|
||||
#ifndef CGAL_USE_CORE
|
||||
#include <iostream>
|
||||
int main ()
|
||||
{
|
||||
std::cout << "Sorry, this example needs CORE ..." << std::endl;
|
||||
return 0;
|
||||
std::cout << "Sorry, this example needs CORE ..." << std::endl;
|
||||
return (0);
|
||||
}
|
||||
|
||||
#else
|
||||
|
||||
#include <CGAL/CORE_BigInt.h> // NT
|
||||
#include <CGAL/Algebraic_kernel_d_1.h> // Algebraic Kernel
|
||||
#include <CGAL/Arr_rational_function_traits_2.h> // Traits
|
||||
#include <CGAL/Arrangement_2.h> // Arrangement
|
||||
#include <CGAL/Cartesian.h>
|
||||
#include <CGAL/CORE_algebraic_number_traits.h>
|
||||
#include <CGAL/Arr_rational_arc_traits_2.h>
|
||||
#include <CGAL/Arrangement_2.h>
|
||||
|
||||
typedef CORE::BigInt Number_type;
|
||||
typedef CGAL::Algebraic_kernel_d_1<Number_type> AK1;
|
||||
typedef CGAL::Arr_rational_function_traits_2<AK1> Traits_2;
|
||||
|
||||
typedef Traits_2::Polynomial_1 Polynomial_1;
|
||||
typedef Traits_2::Algebraic_real_1 Alg_real_1;
|
||||
|
||||
typedef CGAL::Arrangement_2<Traits_2> Arrangement_2;
|
||||
typedef CGAL::CORE_algebraic_number_traits Nt_traits;
|
||||
typedef Nt_traits::Rational Rational;
|
||||
typedef Nt_traits::Algebraic Algebraic;
|
||||
typedef CGAL::Cartesian<Algebraic> Alg_kernel;
|
||||
typedef CGAL::Arr_rational_arc_traits_2<Alg_kernel,
|
||||
Nt_traits> Traits_2;
|
||||
typedef Traits_2::Point_2 Point_2;
|
||||
typedef Traits_2::Curve_2 Rational_arc_2;
|
||||
typedef Traits_2::Rat_vector Rat_vector;
|
||||
typedef std::list<Rational_arc_2> Rat_arcs_list;
|
||||
typedef CGAL::Arrangement_2<Traits_2> Arrangement_2;
|
||||
|
||||
int main ()
|
||||
{
|
||||
CGAL::set_pretty_mode(std::cout); // for nice printouts.
|
||||
|
||||
// create a polynomial representing x .-)
|
||||
Polynomial_1 x = CGAL::shift(Polynomial_1(1),1);
|
||||
|
||||
// Traits class object
|
||||
Traits_2 traits;
|
||||
Traits_2::Construct_x_monotone_curve_2 construct_arc
|
||||
= traits.construct_x_monotone_curve_2_object();
|
||||
|
||||
// container storing all arcs
|
||||
std::vector<Traits_2::X_monotone_curve_2> arcs;
|
||||
|
||||
// Create an arc supported by the polynomial y = x^4 - 6x^2 + 8,
|
||||
// defined over the interval [-2.1, 2.1]:
|
||||
Polynomial_1 P1 = x*x*x*x - 6*x*x + 8;
|
||||
Alg_real_1 l(Traits_2::Algebraic_kernel_d_1::Bound(-2.1));
|
||||
Alg_real_1 r(Traits_2::Algebraic_kernel_d_1::Bound(2.1));
|
||||
arcs.push_back(construct_arc(P1, l, r));
|
||||
Rat_vector P1(5);
|
||||
P1[4] = 1; P1[3] = 0; P1[2] = -6; P1[1] = 0; P1[0] = 8;
|
||||
|
||||
Rational_arc_2 a1 (P1, Algebraic(-2.1), Algebraic(2.1));
|
||||
|
||||
// Create an arc supported by the function y = x / (1 + x^2),
|
||||
// defined over the interval [-3, 3]:
|
||||
Polynomial_1 P2 = x;
|
||||
Polynomial_1 Q2 = 1+x*x;
|
||||
|
||||
arcs.push_back(construct_arc(P2, Q2, Alg_real_1(-3), Alg_real_1(3)));
|
||||
|
||||
Rat_vector P2(2);
|
||||
P2[1] = 1; P2[0] = 0;
|
||||
|
||||
Rat_vector Q2(3);
|
||||
Q2[2] = 1; Q2[1] = 0; Q2[0] = 1;
|
||||
|
||||
Rational_arc_2 a2 (P2, Q2, Algebraic(-3), Algebraic(3));
|
||||
|
||||
// Create an arc supported by the parbola y = 8 - x^2,
|
||||
// defined over the interval [-2, 3]:
|
||||
Polynomial_1 P3 = 8 - x*x;
|
||||
arcs.push_back(construct_arc(P3, Alg_real_1(-2), Alg_real_1(3)));
|
||||
|
||||
Rat_vector P3(5);
|
||||
P3[2] = -1; P3[1] = 0; P3[0] = 8;
|
||||
|
||||
Rational_arc_2 a3 (P3, Algebraic(-2), Algebraic(3));
|
||||
|
||||
// Create an arc supported by the line y = -2x,
|
||||
// defined over the interval [-3, 0]:
|
||||
Polynomial_1 P4 = -2*x;
|
||||
arcs.push_back(construct_arc(P4, Alg_real_1(-3), Alg_real_1(0)));
|
||||
|
||||
Rat_vector P4(2);
|
||||
P4[1] = -2; P4[0] = 0;
|
||||
|
||||
Rational_arc_2 a4 (P4, Algebraic(-3), Algebraic(0));
|
||||
|
||||
// Construct the arrangement of the four arcs.
|
||||
Arrangement_2 arr;
|
||||
std::list<Rational_arc_2> arcs;
|
||||
|
||||
// Print the arcs.
|
||||
for (unsigned int i(0); i < arcs.size(); ++i)
|
||||
std::cout << arcs[i]<<std::endl;
|
||||
|
||||
|
||||
Arrangement_2 arr(&traits);
|
||||
insert(arr, arcs.begin(), arcs.end());
|
||||
arcs.push_back (a1);
|
||||
arcs.push_back (a2);
|
||||
arcs.push_back (a3);
|
||||
arcs.push_back (a4);
|
||||
insert (arr, arcs.begin(), arcs.end());
|
||||
|
||||
// Print the arrangement size.
|
||||
std::cout << "The arrangement size:" << std::endl
|
||||
|
||||
-110
@@ -1,110 +0,0 @@
|
||||
//! \file examples/Arrangement_2/ex_rational_functions.cpp
|
||||
// Constructing an arrangement of arcs of rational functions.
|
||||
|
||||
#include <CGAL/basic.h>
|
||||
|
||||
#ifndef CGAL_USE_CORE
|
||||
#include <iostream>
|
||||
int main ()
|
||||
{
|
||||
std::cout << "Sorry, this example needs CORE ..." << std::endl;
|
||||
return 0;
|
||||
}
|
||||
|
||||
#else
|
||||
|
||||
#include <CGAL/CORE_BigInt.h> // Integer
|
||||
#include <CGAL/CORE_BigRat.h> // Rational
|
||||
#include <CGAL/Algebraic_kernel_d_1.h> // Algebraic Kernel
|
||||
#include <CGAL/Arr_rational_function_traits_2.h> // Traits
|
||||
#include <CGAL/Arrangement_2.h> // Arrangement
|
||||
|
||||
typedef CORE::BigInt Integer;
|
||||
typedef CORE::BigRat Rational;
|
||||
typedef CGAL::Algebraic_kernel_d_1<Integer> AK1;
|
||||
typedef CGAL::Arr_rational_function_traits_2<AK1> Traits_2;
|
||||
|
||||
typedef std::vector<Rational> Rat_vec;
|
||||
typedef Traits_2::Algebraic_real_1 Alg_real_1;
|
||||
|
||||
typedef CGAL::Arrangement_2<Traits_2> Arrangement_2;
|
||||
|
||||
int main ()
|
||||
{
|
||||
CGAL::set_pretty_mode(std::cout); // for nice printouts.
|
||||
|
||||
// Traits class object
|
||||
Traits_2 traits;
|
||||
Traits_2::Construct_x_monotone_curve_2 construct_arc
|
||||
= traits.construct_x_monotone_curve_2_object();
|
||||
|
||||
// container storing all arcs
|
||||
std::vector<Traits_2::X_monotone_curve_2> arcs;
|
||||
|
||||
// Create an arc supported by the function y = 0.1x^4 - 0.6x^2 + 0.8 / 0.1,
|
||||
// defined over the interval [-2.1, 2.1]:
|
||||
Rat_vec P1,Q1;
|
||||
P1.push_back(Rational(8,10));
|
||||
P1.push_back(Rational(0));
|
||||
P1.push_back(Rational(-6,10));
|
||||
P1.push_back(Rational(0));
|
||||
P1.push_back(Rational(1,10));
|
||||
|
||||
Q1.push_back(Rational(1,10));
|
||||
|
||||
Alg_real_1 l(Traits_2::Algebraic_kernel_d_1::Bound(-2.1));
|
||||
Alg_real_1 r(Traits_2::Algebraic_kernel_d_1::Bound(2.1));
|
||||
arcs.push_back(construct_arc(P1.begin(), P1.end(), Q1.begin(), Q1.end(), l, r));
|
||||
|
||||
// Create an arc supported by the function y = 0.1x / (0.1 + 0.1x^2),
|
||||
// defined over the interval [-3, 3]:
|
||||
Rat_vec P2,Q2;
|
||||
P2.push_back(Rational(0));
|
||||
P2.push_back(Rational(1,10));
|
||||
|
||||
Q2.push_back(Rational(1,10));
|
||||
Q2.push_back(Rational(0));
|
||||
Q2.push_back(Rational(1,10));
|
||||
|
||||
arcs.push_back(construct_arc(P2.begin(), P2.end(), Q2.begin(), Q2.end(),
|
||||
Alg_real_1(-3), Alg_real_1(3)));
|
||||
|
||||
// Create an arc supported by the parbola y = 0.8 - 0.1x^2 / 0.1,
|
||||
// defined over the interval [-2, 3]:
|
||||
Rat_vec P3,Q3;
|
||||
P3.push_back(Rational(4,5));
|
||||
P3.push_back(Rational(0));
|
||||
P3.push_back(Rational(-1,10));
|
||||
|
||||
Q3.push_back(Rational(1,10));
|
||||
|
||||
arcs.push_back(construct_arc(P3.begin(), P3.end(), Q3.begin(), Q3.end(),
|
||||
Alg_real_1(-2), Alg_real_1(3)));
|
||||
|
||||
// Create an arc supported by the line y = -0.2x / 0.1,
|
||||
// defined over the interval [-3, 0]:
|
||||
Rat_vec P4,Q4;
|
||||
P4.push_back(Rational(0));
|
||||
P4.push_back(Rational(-1,5));
|
||||
Q4.push_back(Rational(1,10));
|
||||
arcs.push_back(construct_arc(P4.begin(), P4.end(), Q4.begin(), Q4.end(),
|
||||
Alg_real_1(-3), Alg_real_1(0)));
|
||||
|
||||
// Print the arcs.
|
||||
for (unsigned int i(0); i < arcs.size(); ++i)
|
||||
std::cout << arcs[i]<<std::endl;
|
||||
|
||||
// Construct the arrangement of the four arcs.
|
||||
Arrangement_2 arr(&traits);
|
||||
insert(arr, arcs.begin(), arcs.end());
|
||||
|
||||
// Print the arrangement size.
|
||||
std::cout << "The arrangement size:" << std::endl
|
||||
<< " V = " << arr.number_of_vertices()
|
||||
<< ", E = " << arr.number_of_edges()
|
||||
<< ", F = " << arr.number_of_faces() << std::endl;
|
||||
|
||||
return 0;
|
||||
}
|
||||
|
||||
#endif
|
||||
@@ -10,7 +10,8 @@
|
||||
|
||||
typedef CGAL::Gmpq Number_type;
|
||||
typedef CGAL::Cartesian<Number_type> Kernel;
|
||||
typedef CGAL::Arr_geodesic_arc_on_sphere_traits_2<Kernel> Geom_traits_2;
|
||||
typedef CGAL::Arr_geodesic_arc_on_sphere_traits_2<Kernel>
|
||||
Geom_traits_2;
|
||||
typedef Geom_traits_2::Point_2 Point_2;
|
||||
typedef Geom_traits_2::X_monotone_curve_2 X_monotone_curve_2;
|
||||
typedef CGAL::Arr_spherical_topology_traits_2<Geom_traits_2> Topol_traits_2;
|
||||
|
||||
+54
-57
@@ -1,6 +1,5 @@
|
||||
//! \file examples/Arrangement_2/unbounded_rational_functions.cpp
|
||||
// Constructing an arrangement of unbounded portions of rational functions.
|
||||
|
||||
#include <CGAL/basic.h>
|
||||
|
||||
#ifndef CGAL_USE_CORE
|
||||
@@ -8,83 +7,81 @@
|
||||
int main ()
|
||||
{
|
||||
std::cout << "Sorry, this example needs CORE ..." << std::endl;
|
||||
return 0;
|
||||
return (0);
|
||||
}
|
||||
|
||||
#else
|
||||
|
||||
#include <CGAL/CORE_BigInt.h> // NT
|
||||
#include <CGAL/Algebraic_kernel_d_1.h> // Algebraic Kernel
|
||||
#include <CGAL/Arr_rational_function_traits_2.h> // Traits
|
||||
#include <CGAL/Arrangement_2.h> // Arrangement
|
||||
#include <CGAL/Cartesian.h>
|
||||
#include <CGAL/CORE_algebraic_number_traits.h>
|
||||
#include <CGAL/Arr_rational_arc_traits_2.h>
|
||||
#include <CGAL/Arrangement_2.h>
|
||||
|
||||
typedef CORE::BigInt Number_type;
|
||||
typedef CGAL::Algebraic_kernel_d_1<Number_type> AK1;
|
||||
typedef CGAL::Arr_rational_function_traits_2<AK1> Traits_2;
|
||||
|
||||
typedef Traits_2::Polynomial_1 Polynomial_1;
|
||||
typedef Traits_2::Algebraic_real_1 Alg_real_1;
|
||||
|
||||
typedef CGAL::Arrangement_2<Traits_2> Arrangement_2;
|
||||
typedef CGAL::CORE_algebraic_number_traits Nt_traits;
|
||||
typedef Nt_traits::Rational Rational;
|
||||
typedef Nt_traits::Algebraic Algebraic;
|
||||
typedef CGAL::Cartesian<Algebraic> Alg_kernel;
|
||||
typedef CGAL::Arr_rational_arc_traits_2<Alg_kernel,
|
||||
Nt_traits> Traits_2;
|
||||
typedef Traits_2::Point_2 Point_2;
|
||||
typedef Traits_2::Curve_2 Rational_arc_2;
|
||||
typedef Traits_2::Rat_vector Rat_vector;
|
||||
typedef std::list<Rational_arc_2> Rat_arcs_list;
|
||||
typedef CGAL::Arrangement_2<Traits_2> Arrangement_2;
|
||||
|
||||
int main ()
|
||||
{
|
||||
CGAL::set_pretty_mode(std::cout); // for nice printouts.
|
||||
|
||||
// Traits class object
|
||||
AK1 ak1;
|
||||
Traits_2 traits(&ak1);
|
||||
|
||||
// constructor for rational functions
|
||||
Traits_2::Construct_curve_2 construct = traits.construct_curve_2_object();
|
||||
|
||||
// a polynomial representing x .-)
|
||||
Polynomial_1 x = CGAL::shift(Polynomial_1(1),1);
|
||||
|
||||
// container storing all arcs
|
||||
std::vector<Traits_2::Curve_2> arcs;
|
||||
std::list<Rational_arc_2> arcs;
|
||||
|
||||
|
||||
// Create the rational functions (y = 1 / x), and (y = -1 / x).
|
||||
Polynomial_1 P1(1);
|
||||
Polynomial_1 minusP1(-P1);
|
||||
Polynomial_1 Q1 = x;
|
||||
arcs.push_back(construct(P1, Q1));
|
||||
arcs.push_back(construct(minusP1, Q1));
|
||||
Rat_vector P1(1);
|
||||
P1[0] = 1;
|
||||
|
||||
Rat_vector Q1(2);
|
||||
Q1[1] = 1; Q1[0] = 0;
|
||||
|
||||
arcs.push_back (Rational_arc_2 (P1, Q1));
|
||||
|
||||
P1[0] = -1;
|
||||
arcs.push_back (Rational_arc_2 (P1, Q1));
|
||||
|
||||
// Create a bounded segments of the parabolas (y = -4*x^2 + 3) and
|
||||
// (y = 4*x^2 - 3), defined over [-sqrt(3)/2, sqrt(3)/2].
|
||||
Polynomial_1 P2 = -4*x*x+3;
|
||||
Polynomial_1 minusP2 = -P2;
|
||||
std::vector<std::pair<Alg_real_1,int> > roots;
|
||||
const Algebraic half_sqrt3 = CORE::sqrt(Algebraic(3)) / 2;
|
||||
Rat_vector P2(3);
|
||||
P2[2] = -4; P2[1] = 0; P2[0] = 3;
|
||||
|
||||
// [-sqrt(3)/2, sqrt(3)/2]
|
||||
traits.algebraic_kernel_d_1()->solve_1_object()(P2, std::back_inserter(roots));
|
||||
arcs.push_back(construct(P2, roots[0].first, roots[1].first));
|
||||
arcs.push_back(construct(minusP2, roots[0].first, roots[1].first));
|
||||
arcs.push_back (Rational_arc_2 (P2, -half_sqrt3, half_sqrt3));
|
||||
|
||||
P2[2] = 4; P2[0] = -3;
|
||||
arcs.push_back (Rational_arc_2 (P2, -half_sqrt3, half_sqrt3));
|
||||
|
||||
// Create the rational function (y = 1 / 2*x) for x > 0, and the
|
||||
// rational function (y = -1 / 2*x) for x < 0.
|
||||
Polynomial_1 P3(1);
|
||||
Polynomial_1 minusP3(-P3);
|
||||
Polynomial_1 Q3 = 2*x;
|
||||
arcs.push_back(construct(P3, Q3, Alg_real_1(0), true));
|
||||
arcs.push_back(construct(minusP3, Q3, Alg_real_1(0), false));
|
||||
Rat_vector P3(1);
|
||||
P3[0] = 1;
|
||||
|
||||
Rat_vector Q3(2);
|
||||
Q3[1] = 2; Q3[0] = 0;
|
||||
|
||||
arcs.push_back (Rational_arc_2 (P3, Q3, Algebraic(0), true));
|
||||
|
||||
P3[0] = -1;
|
||||
arcs.push_back (Rational_arc_2 (P3, Q3, Algebraic(0), false));
|
||||
|
||||
// Construct the arrangement of the six arcs.
|
||||
//Arrangement_2 arr(&traits);
|
||||
Arrangement_2 arr;
|
||||
insert(arr, arcs.begin(), arcs.end());
|
||||
Arrangement_2 arr;
|
||||
|
||||
insert (arr, arcs.begin(), arcs.end());
|
||||
|
||||
// Print the arrangement size.
|
||||
std::cout << "The arrangement size:" << std::endl
|
||||
<< " V = " << arr.number_of_vertices()
|
||||
<< " (plus " << arr.number_of_vertices_at_infinity()
|
||||
<< " at infinity)"
|
||||
<< ", E = " << arr.number_of_edges()
|
||||
<< ", F = " << arr.number_of_faces()
|
||||
<< " (" << arr.number_of_unbounded_faces() << " unbounded)"
|
||||
<< std::endl << std::endl;
|
||||
<< " V = " << arr.number_of_vertices()
|
||||
<< " (plus " << arr.number_of_vertices_at_infinity()
|
||||
<< " at infinity)"
|
||||
<< ", E = " << arr.number_of_edges()
|
||||
<< ", F = " << arr.number_of_faces()
|
||||
<< " (" << arr.number_of_unbounded_faces() << " unbounded)"
|
||||
<< std::endl << std::endl;
|
||||
|
||||
return 0;
|
||||
}
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2006,2007,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2006 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
@@ -78,10 +78,10 @@ public:
|
||||
typedef Tag_true Has_merge_category;
|
||||
typedef Tag_false Has_do_intersect_category;
|
||||
|
||||
typedef Arr_oblivious_side_tag Left_side_category;
|
||||
typedef Arr_oblivious_side_tag Bottom_side_category;
|
||||
typedef Arr_oblivious_side_tag Top_side_category;
|
||||
typedef Arr_oblivious_side_tag Right_side_category;
|
||||
typedef Arr_oblivious_side_tag Arr_left_side_category;
|
||||
typedef Arr_oblivious_side_tag Arr_bottom_side_category;
|
||||
typedef Arr_oblivious_side_tag Arr_top_side_category;
|
||||
typedef Arr_oblivious_side_tag Arr_right_side_category;
|
||||
|
||||
// Traits-class types:
|
||||
typedef _Bezier_curve_2<Rat_kernel,
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2006,2007,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2005 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2006,2007,2008,2009,2010,2011 Max-Planck-Institute Saarbruecken (Germany).
|
||||
// Copyright (c) 2006-2009 Max-Planck-Institute Saarbruecken (Germany).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you can redistribute it and/or
|
||||
@@ -92,10 +92,10 @@ public:
|
||||
typedef typename CKvA_2::Has_do_intersect_category
|
||||
Has_do_intersect_category;
|
||||
|
||||
typedef typename CKvA_2::Left_side_category Left_side_category;
|
||||
typedef typename CKvA_2::Bottom_side_category Bottom_side_category;
|
||||
typedef typename CKvA_2::Top_side_category Top_side_category;
|
||||
typedef typename CKvA_2::Right_side_category Right_side_category;
|
||||
typedef typename CKvA_2::Arr_left_side_category Arr_left_side_category;
|
||||
typedef typename CKvA_2::Arr_bottom_side_category Arr_bottom_side_category;
|
||||
typedef typename CKvA_2::Arr_top_side_category Arr_top_side_category;
|
||||
typedef typename CKvA_2::Arr_right_side_category Arr_right_side_category;
|
||||
|
||||
typedef typename CKvA_2::Multiplicity Multiplicity;
|
||||
|
||||
@@ -119,31 +119,31 @@ public:
|
||||
return CKvA_2::instance().equal_2_object();
|
||||
}
|
||||
|
||||
|
||||
|
||||
typedef typename CKvA_2::Parameter_space_in_x_2 Parameter_space_in_x_2;
|
||||
Parameter_space_in_x_2 parameter_space_in_x_2_object() const {
|
||||
return CKvA_2::instance().parameter_space_in_x_2_object();
|
||||
}
|
||||
|
||||
typedef typename CKvA_2::Parameter_space_in_y_2 Parameter_space_in_y_2;
|
||||
Parameter_space_in_y_2 parameter_space_in_y_2_object() const {
|
||||
return CKvA_2::instance().parameter_space_in_y_2_object();
|
||||
}
|
||||
|
||||
|
||||
typedef typename CKvA_2::Compare_x_near_boundary_2
|
||||
Compare_x_near_boundary_2;
|
||||
Compare_x_near_boundary_2 compare_x_near_boundary_2_object() const {
|
||||
return CKvA_2::instance().compare_x_near_boundary_2_object();
|
||||
}
|
||||
|
||||
typedef typename CKvA_2::Compare_y_near_boundary_2
|
||||
Compare_y_near_boundary_2;
|
||||
Compare_y_near_boundary_2 compare_y_near_boundary_2_object() const {
|
||||
return CKvA_2::instance().compare_y_near_boundary_2_object();
|
||||
}
|
||||
|
||||
typedef typename CKvA_2::Parameter_space_in_x_2 Parameter_space_in_x_2;
|
||||
Parameter_space_in_x_2 parameter_space_in_x_2_object() const {
|
||||
return CKvA_2::instance().parameter_space_in_x_2_object();
|
||||
}
|
||||
|
||||
typedef typename CKvA_2::Compare_x_at_limit_2 Compare_x_at_limit_2;
|
||||
Compare_x_at_limit_2 compare_x_at_limit_2_object() const {
|
||||
return CKvA_2::instance().compare_x_at_limit_2_object();
|
||||
}
|
||||
|
||||
typedef typename CKvA_2::Compare_x_near_limit_2 Compare_x_near_limit_2;
|
||||
Compare_x_near_limit_2 compare_x_near_limit_2_object() const {
|
||||
return CKvA_2::instance().compare_x_near_limit_2_object();
|
||||
}
|
||||
|
||||
typedef typename CKvA_2::Construct_min_vertex_2 Construct_min_vertex_2;
|
||||
Construct_min_vertex_2 construct_min_vertex_2_object() const {
|
||||
@@ -200,7 +200,13 @@ public:
|
||||
return CKvA_2::instance().merge_2_object();
|
||||
}
|
||||
|
||||
typedef typename CKvA_2::Make_x_monotone_2 Make_x_monotone_2;
|
||||
// TODO typedef ArrangementDirectionalXMonotoneTraits_2 functors +
|
||||
/// check Intersect_2 & Split return order
|
||||
|
||||
|
||||
typedef typename CKvA_2::Make_x_monotone_2 Make_x_monotone_2;
|
||||
|
||||
|
||||
Make_x_monotone_2 make_x_monotone_2_object() const {
|
||||
return Make_x_monotone_2(&CKvA_2::instance());
|
||||
}
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2006,2007,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2005 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2006,2007,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2006 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
@@ -75,27 +75,32 @@ public:
|
||||
typedef typename Base::Isolated_vertex Isolated_vertex;
|
||||
//@}
|
||||
|
||||
//! \name Arrangement types
|
||||
//!@{
|
||||
typedef Arr_bounded_planar_topology_traits_2<Geometry_traits_2, Dcel> Self;
|
||||
// TODO remove adaptor as top-traits might be instantiated by Aos_2 itself
|
||||
typedef Arr_traits_basic_adaptor_2<Geometry_traits_2> Traits_adaptor_2;
|
||||
//!@}
|
||||
|
||||
typedef Arr_bounded_planar_topology_traits_2<Geometry_traits_2, Dcel>
|
||||
Self;
|
||||
|
||||
///! \name The side tags
|
||||
//@{
|
||||
typedef typename Traits_adaptor_2::Left_side_category Left_side_category;
|
||||
typedef typename Traits_adaptor_2::Bottom_side_category Bottom_side_category;
|
||||
typedef typename Traits_adaptor_2::Top_side_category Top_side_category;
|
||||
typedef typename Traits_adaptor_2::Right_side_category Right_side_category;
|
||||
// are inherited from the geometry traits
|
||||
typedef typename Traits_adaptor_2::Arr_left_side_category
|
||||
Arr_left_side_category;
|
||||
typedef typename Traits_adaptor_2::Arr_bottom_side_category
|
||||
Arr_bottom_side_category;
|
||||
typedef typename Traits_adaptor_2::Arr_top_side_category
|
||||
Arr_top_side_category;
|
||||
typedef typename Traits_adaptor_2::Arr_right_side_category
|
||||
Arr_right_side_category;
|
||||
|
||||
BOOST_MPL_ASSERT
|
||||
((boost::is_same< Left_side_category, Arr_oblivious_side_tag >));
|
||||
((boost::is_same< Arr_left_side_category, Arr_oblivious_side_tag >));
|
||||
BOOST_MPL_ASSERT
|
||||
((boost::is_same< Bottom_side_category, Arr_oblivious_side_tag >));
|
||||
((boost::is_same< Arr_bottom_side_category, Arr_oblivious_side_tag >));
|
||||
BOOST_MPL_ASSERT
|
||||
((boost::is_same< Top_side_category, Arr_oblivious_side_tag >));
|
||||
((boost::is_same< Arr_top_side_category, Arr_oblivious_side_tag >));
|
||||
BOOST_MPL_ASSERT
|
||||
((boost::is_same< Right_side_category, Arr_oblivious_side_tag >));
|
||||
((boost::is_same< Arr_right_side_category, Arr_oblivious_side_tag >));
|
||||
//@}
|
||||
|
||||
/*! \struct
|
||||
@@ -206,7 +211,7 @@ private:
|
||||
|
||||
/// \name Auxiliary type definitions.
|
||||
//@{
|
||||
typedef Arrangement_on_surface_2<Geometry_traits_2, Self> Arr;
|
||||
typedef Arrangement_on_surface_2<Geometry_traits_2, Self> Arr;
|
||||
|
||||
// Type definition for the constuction sweep-line visitor.
|
||||
typedef Arr_construction_subcurve<Geometry_traits_2> CSubcurve;
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2005,2006,2007,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2005 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
@@ -58,10 +58,10 @@ public:
|
||||
typedef Tag_true Has_merge_category;
|
||||
typedef Tag_false Has_do_intersect_category;
|
||||
|
||||
typedef Arr_oblivious_side_tag Left_side_category;
|
||||
typedef Arr_oblivious_side_tag Bottom_side_category;
|
||||
typedef Arr_oblivious_side_tag Top_side_category;
|
||||
typedef Arr_oblivious_side_tag Right_side_category;
|
||||
typedef Arr_oblivious_side_tag Arr_left_side_category;
|
||||
typedef Arr_oblivious_side_tag Arr_bottom_side_category;
|
||||
typedef Arr_oblivious_side_tag Arr_top_side_category;
|
||||
typedef Arr_oblivious_side_tag Arr_right_side_category;
|
||||
|
||||
protected:
|
||||
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2003,2004,2005,2006,2007,2008,2009,2010,2011 INRIA Sophia-Antipolis (France).
|
||||
// Copyright (c) 2003-2006 INRIA Sophia-Antipolis (France).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
@@ -113,10 +113,10 @@ public:
|
||||
typedef CGAL::Tag_false Has_merge_category;
|
||||
typedef CGAL::Tag_false Has_do_intersect_category;
|
||||
|
||||
typedef Arr_oblivious_side_tag Left_side_category;
|
||||
typedef Arr_oblivious_side_tag Bottom_side_category;
|
||||
typedef Arr_oblivious_side_tag Top_side_category;
|
||||
typedef Arr_oblivious_side_tag Right_side_category;
|
||||
typedef Arr_oblivious_side_tag Arr_left_side_category;
|
||||
typedef Arr_oblivious_side_tag Arr_bottom_side_category;
|
||||
typedef Arr_oblivious_side_tag Arr_top_side_category;
|
||||
typedef Arr_oblivious_side_tag Arr_right_side_category;
|
||||
|
||||
Arr_circular_arc_traits_2(const CircularKernel &k = CircularKernel())
|
||||
: ck(k) {}
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2003,2004,2005,2006,2007,2008,2009,2010,2011 INRIA Sophia-Antipolis (France).
|
||||
// Copyright (c) 2003-2006 INRIA Sophia-Antipolis (France).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
@@ -533,10 +533,10 @@ namespace CGAL {
|
||||
typedef CGAL::Tag_false Has_merge_category;
|
||||
typedef CGAL::Tag_false Has_do_intersect_category;
|
||||
|
||||
typedef Arr_oblivious_side_tag Left_side_category;
|
||||
typedef Arr_oblivious_side_tag Bottom_side_category;
|
||||
typedef Arr_oblivious_side_tag Top_side_category;
|
||||
typedef Arr_oblivious_side_tag Right_side_category;
|
||||
typedef Arr_oblivious_side_tag Arr_left_side_category;
|
||||
typedef Arr_oblivious_side_tag Arr_bottom_side_category;
|
||||
typedef Arr_oblivious_side_tag Arr_top_side_category;
|
||||
typedef Arr_oblivious_side_tag Arr_right_side_category;
|
||||
|
||||
typedef internal_Argt_traits::Not_X_Monotone Not_X_Monotone;
|
||||
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2006,2007,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2005 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
@@ -73,10 +73,10 @@ public:
|
||||
typedef Tag_true Has_merge_category;
|
||||
typedef Tag_false Has_do_intersect_category;
|
||||
|
||||
typedef Arr_oblivious_side_tag Left_side_category;
|
||||
typedef Arr_oblivious_side_tag Bottom_side_category;
|
||||
typedef Arr_oblivious_side_tag Top_side_category;
|
||||
typedef Arr_oblivious_side_tag Right_side_category;
|
||||
typedef Arr_oblivious_side_tag Arr_left_side_category;
|
||||
typedef Arr_oblivious_side_tag Arr_bottom_side_category;
|
||||
typedef Arr_oblivious_side_tag Arr_top_side_category;
|
||||
typedef Arr_oblivious_side_tag Arr_right_side_category;
|
||||
|
||||
// Traits objects:
|
||||
typedef _Conic_arc_2<Rat_kernel, Alg_kernel, Nt_traits> Curve_2;
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2006,2007,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2005, 2009 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
@@ -82,14 +82,14 @@ public:
|
||||
|
||||
// Base_traits_2 is Arr_curve_data_traits that already completes
|
||||
// incomplete tags
|
||||
typedef typename Base_traits_2::Left_side_category
|
||||
Left_side_category;
|
||||
typedef typename Base_traits_2::Bottom_side_category
|
||||
Bottom_side_category;
|
||||
typedef typename Base_traits_2::Top_side_category
|
||||
Top_side_category;
|
||||
typedef typename Base_traits_2::Right_side_category
|
||||
Right_side_category;
|
||||
typedef typename Base_traits_2::Arr_left_side_category
|
||||
Arr_left_side_category;
|
||||
typedef typename Base_traits_2::Arr_bottom_side_category
|
||||
Arr_bottom_side_category;
|
||||
typedef typename Base_traits_2::Arr_top_side_category
|
||||
Arr_top_side_category;
|
||||
typedef typename Base_traits_2::Arr_right_side_category
|
||||
Arr_right_side_category;
|
||||
};
|
||||
|
||||
} //namespace CGAL
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2005,2007,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2005 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
@@ -31,7 +31,6 @@
|
||||
|
||||
#include <CGAL/basic.h>
|
||||
#include <CGAL/Arr_enums.h>
|
||||
#include <CGAL/Arr_tags.h>
|
||||
|
||||
namespace CGAL {
|
||||
|
||||
@@ -63,23 +62,19 @@ public:
|
||||
PARAMETER_SPACE_IN_X_CURVE_END_OP,
|
||||
PARAMETER_SPACE_IN_X_POINT_OP,
|
||||
PARAMETER_SPACE_IN_X_CURVE_OP,
|
||||
COMPARE_Y_NEAR_BOUNDARY_OP,
|
||||
COMPARE_Y_ON_BOUNDARY_OP,
|
||||
IS_ON_X_IDENTIFICATION_POINT_OP,
|
||||
IS_ON_X_IDENTIFICATION_CURVE_OP,
|
||||
COMPARE_Y_ON_BOUNDARY_OP,
|
||||
COMPARE_Y_NEAR_BOUNDARY_OP,
|
||||
|
||||
PARAMETER_SPACE_IN_Y_CURVE_END_OP,
|
||||
PARAMETER_SPACE_IN_Y_POINT_OP,
|
||||
PARAMETER_SPACE_IN_Y_CURVE_OP,
|
||||
COMPARE_X_NEAR_BOUNDARY_POINT_CURVE_END_OP,
|
||||
COMPARE_X_NEAR_BOUNDARY_CURVE_ENDS_OP,
|
||||
COMPARE_X_ON_BOUNDARY_OP,
|
||||
IS_ON_Y_IDENTIFICATION_POINT_OP,
|
||||
IS_ON_Y_IDENTIFICATION_CURVE_OP,
|
||||
COMPARE_X_AT_LIMIT_POINT_CURVE_END_OP,
|
||||
COMPARE_X_AT_LIMIT_CURVE_ENDS_OP,
|
||||
COMPARE_X_NEAR_LIMIT_OP,
|
||||
COMPARE_X_ON_BOUNDARY_POINTS_OP,
|
||||
COMPARE_X_ON_BOUNDARY_POINT_CURVE_END_OP,
|
||||
COMPARE_X_ON_BOUNDARY_CURVE_ENDS_OP,
|
||||
COMPARE_X_NEAR_BOUNDARY_OP,
|
||||
|
||||
NUMBER_OF_OPERATIONS
|
||||
};
|
||||
@@ -167,18 +162,11 @@ public:
|
||||
unsigned int count_parameter_space_in_x_point() const
|
||||
{ return m_counters[PARAMETER_SPACE_IN_X_POINT_OP]; }
|
||||
|
||||
unsigned int count_is_on_x_identification_point() const
|
||||
{ return m_counters[IS_ON_X_IDENTIFICATION_POINT_OP]; }
|
||||
|
||||
unsigned int count_is_on_x_identification_curve() const
|
||||
{ return m_counters[IS_ON_X_IDENTIFICATION_CURVE_OP]; }
|
||||
|
||||
unsigned int count_compare_y_on_boundary() const
|
||||
{ return m_counters[COMPARE_Y_ON_BOUNDARY_OP]; }
|
||||
|
||||
unsigned int count_compare_y_near_boundary() const
|
||||
{ return m_counters[COMPARE_Y_NEAR_BOUNDARY_OP]; }
|
||||
|
||||
unsigned int count_compare_y_on_boundary() const
|
||||
{ return m_counters[COMPARE_Y_ON_BOUNDARY_OP]; }
|
||||
|
||||
// bottom-top
|
||||
|
||||
@@ -191,32 +179,14 @@ public:
|
||||
unsigned int count_parameter_space_in_y_point() const
|
||||
{ return m_counters[PARAMETER_SPACE_IN_Y_POINT_OP]; }
|
||||
|
||||
unsigned int count_is_on_y_identification_point() const
|
||||
{ return m_counters[IS_ON_Y_IDENTIFICATION_POINT_OP]; }
|
||||
unsigned int count_compare_x_near_boundary_point_curve_end() const
|
||||
{ return m_counters[COMPARE_X_NEAR_BOUNDARY_POINT_CURVE_END_OP]; }
|
||||
|
||||
unsigned int count_is_on_y_identification_curve() const
|
||||
{ return m_counters[IS_ON_Y_IDENTIFICATION_CURVE_OP]; }
|
||||
|
||||
unsigned int count_compare_x_at_limit_point_curve_end() const
|
||||
{ return m_counters[COMPARE_X_AT_LIMIT_POINT_CURVE_END_OP]; }
|
||||
|
||||
unsigned int count_compare_x_at_limit_curve_ends() const
|
||||
{ return m_counters[COMPARE_X_AT_LIMIT_CURVE_ENDS_OP]; }
|
||||
|
||||
unsigned int count_compare_x_near_limit() const
|
||||
{ return m_counters[COMPARE_X_NEAR_LIMIT_OP]; }
|
||||
|
||||
unsigned int count_compare_x_on_boundary_points() const
|
||||
{ return m_counters[COMPARE_X_ON_BOUNDARY_POINTS_OP]; }
|
||||
|
||||
unsigned int count_compare_x_on_boundary_point_curve_end() const
|
||||
{ return m_counters[COMPARE_X_ON_BOUNDARY_POINT_CURVE_END_OP]; }
|
||||
|
||||
unsigned int count_compare_x_on_boundary_curve_ends() const
|
||||
{ return m_counters[COMPARE_X_ON_BOUNDARY_CURVE_ENDS_OP]; }
|
||||
|
||||
unsigned int count_compare_x_near_boundary() const
|
||||
{ return m_counters[COMPARE_X_NEAR_BOUNDARY_OP]; }
|
||||
unsigned int count_compare_x_near_boundary_curve_ends() const
|
||||
{ return m_counters[COMPARE_X_NEAR_BOUNDARY_CURVE_ENDS_OP]; }
|
||||
|
||||
unsigned int count_compare_x_on_boundary() const
|
||||
{ return m_counters[COMPARE_X_ON_BOUNDARY_OP]; }
|
||||
|
||||
/// \name Types and functors inherited from the base
|
||||
//@{
|
||||
@@ -226,14 +196,14 @@ public:
|
||||
typedef typename Base::Has_merge_category Has_merge_category;
|
||||
typedef typename Base::Has_do_intersect_category Has_do_intersect_category;
|
||||
|
||||
typedef typename internal::Arr_complete_left_side_category< Base >::Category
|
||||
Left_side_category;
|
||||
typedef typename internal::Arr_complete_bottom_side_category< Base >::Category
|
||||
Bottom_side_category;
|
||||
typedef typename internal::Arr_complete_top_side_category< Base >::Category
|
||||
Top_side_category;
|
||||
typedef typename internal::Arr_complete_right_side_category< Base >::Category
|
||||
Right_side_category;
|
||||
typedef typename internal::Arr_complete_left_side_tag< Base >::Tag
|
||||
Arr_left_side_category;
|
||||
typedef typename internal::Arr_complete_bottom_side_tag< Base >::Tag
|
||||
Arr_bottom_side_category;
|
||||
typedef typename internal::Arr_complete_top_side_tag< Base >::Tag
|
||||
Arr_top_side_category;
|
||||
typedef typename internal::Arr_complete_right_side_tag< Base >::Tag
|
||||
Arr_right_side_category;
|
||||
|
||||
typedef typename Base::Point_2 Point_2;
|
||||
typedef typename Base::X_monotone_curve_2 X_monotone_curve_2;
|
||||
@@ -567,32 +537,24 @@ public:
|
||||
|
||||
};
|
||||
|
||||
/*! A functor that determines whether a point or a curve lies on an identification in x.
|
||||
/*! A functor that compares the y-coordinates of curve ends near the
|
||||
* boundary of the parameter space.
|
||||
*/
|
||||
class Is_on_x_identification_2 {
|
||||
class Compare_y_near_boundary_2 {
|
||||
private:
|
||||
typename Base::Is_on_x_identificiation_2 m_object;
|
||||
mutable unsigned int & m_counter1;
|
||||
mutable unsigned int & m_counter2;
|
||||
typename Base::Compare_y_near_boundary_2 m_object;
|
||||
unsigned int & m_counter;
|
||||
|
||||
public:
|
||||
/*! Construct */
|
||||
Is_on_x_identification_2(const Base * base,
|
||||
unsigned int & counter1,
|
||||
unsigned int & counter2) :
|
||||
m_object(base->is_on_x_identificiation_2_object()),
|
||||
m_counter1(counter1),
|
||||
m_counter2(counter2) {}
|
||||
Compare_y_near_boundary_2(const Base * base, unsigned int & counter) :
|
||||
m_object(base->compare_y_near_boundary_2_object()), m_counter(counter) {}
|
||||
|
||||
/*! Operate */
|
||||
Arr_parameter_space operator()(const Point_2 & p) const
|
||||
{ ++m_counter1; return m_object(p); }
|
||||
|
||||
|
||||
/*! Operate */
|
||||
Arr_parameter_space operator()(const X_monotone_curve_2 & xc) const
|
||||
{ ++m_counter2; return m_object(xc); }
|
||||
|
||||
Comparison_result operator()(const X_monotone_curve_2 & xc1,
|
||||
const X_monotone_curve_2 & xc2,
|
||||
Arr_curve_end ce) const
|
||||
{ ++m_counter; return m_object(xc1, xc2, ce); }
|
||||
};
|
||||
|
||||
/*! A functor that compares the y-coordinate of two given points
|
||||
@@ -616,28 +578,11 @@ public:
|
||||
{ ++m_counter; return m_object(p1, p2); }
|
||||
};
|
||||
|
||||
/*! A functor that compares the y-coordinates of curve ends near the
|
||||
* boundary of the parameter space.
|
||||
*/
|
||||
class Compare_y_near_boundary_2 {
|
||||
private:
|
||||
typename Base::Compare_y_near_boundary_2 m_object;
|
||||
unsigned int & m_counter;
|
||||
|
||||
public:
|
||||
/*! Construct */
|
||||
Compare_y_near_boundary_2(const Base * base, unsigned int & counter) :
|
||||
m_object(base->compare_y_near_boundary_2_object()), m_counter(counter) {}
|
||||
|
||||
/*! Operate */
|
||||
Comparison_result operator()(const X_monotone_curve_2 & xc1,
|
||||
const X_monotone_curve_2 & xc2,
|
||||
Arr_curve_end ce) const
|
||||
{ ++m_counter; return m_object(xc1, xc2, ce); }
|
||||
};
|
||||
|
||||
// TODO Is_on_x_identification_2
|
||||
|
||||
// bottom-top
|
||||
|
||||
|
||||
/*! A functor that determines whether an endpoint of an x-monotone arc lies
|
||||
* on a boundary of the parameter space along the y axis.
|
||||
*/
|
||||
@@ -674,49 +619,21 @@ public:
|
||||
|
||||
};
|
||||
|
||||
/*! A functor that determines whether a point or a curve lies on an identification in x.
|
||||
*/
|
||||
class Is_on_y_identification_2 {
|
||||
private:
|
||||
typename Base::Is_on_y_identificiation_2 m_object;
|
||||
mutable unsigned int & m_counter1;
|
||||
mutable unsigned int & m_counter2;
|
||||
|
||||
public:
|
||||
/*! Construct */
|
||||
Is_on_y_identification_2(const Base * base,
|
||||
unsigned int & counter1,
|
||||
unsigned int & counter2) :
|
||||
m_object(base->is_on_y_identificiation_2_object()),
|
||||
m_counter1(counter1),
|
||||
m_counter2(counter2) {}
|
||||
|
||||
/*! Operate */
|
||||
Arr_parameter_space operator()(const Point_2 & p) const
|
||||
{ ++m_counter1; return m_object(p); }
|
||||
|
||||
|
||||
/*! Operate */
|
||||
Arr_parameter_space operator()(const X_monotone_curve_2 & xc) const
|
||||
{ ++m_counter2; return m_object(xc); }
|
||||
|
||||
};
|
||||
|
||||
/*! A functor that compares the x-limits of curve ends on the
|
||||
/*! A functor that compares the x-coordinates of curve ends near the
|
||||
* boundary of the parameter space.
|
||||
*/
|
||||
class Compare_x_at_limit_2 {
|
||||
class Compare_x_near_boundary_2 {
|
||||
private:
|
||||
typename Base::Compare_x_at_limit_2 m_object;
|
||||
typename Base::Compare_x_near_boundary_2 m_object;
|
||||
unsigned int & m_counter1;
|
||||
unsigned int & m_counter2;
|
||||
|
||||
public:
|
||||
/*! Construct */
|
||||
Compare_x_at_limit_2(const Base * base,
|
||||
Compare_x_near_boundary_2(const Base * base,
|
||||
unsigned int & counter1,
|
||||
unsigned int & counter2) :
|
||||
m_object(base->compare_x_at_limit_2_object()),
|
||||
m_object(base->compare_x_near_boundary_2_object()),
|
||||
m_counter1(counter1),
|
||||
m_counter2(counter2) {}
|
||||
|
||||
@@ -735,88 +652,29 @@ public:
|
||||
};
|
||||
|
||||
|
||||
/*! A functor that compares the x-coordinates of curve ends near the
|
||||
* boundary of the parameter space.
|
||||
*/
|
||||
class Compare_x_near_limit_2 {
|
||||
private:
|
||||
typename Base::Compare_x_near_limit_2 m_object;
|
||||
unsigned int & m_counter;
|
||||
|
||||
public:
|
||||
/*! Construct */
|
||||
Compare_x_near_limit_2(const Base * base,
|
||||
unsigned int & counter) :
|
||||
m_object(base->compare_x_near_limit_2_object()),
|
||||
m_counter(counter) {}
|
||||
|
||||
|
||||
/*! Operate */
|
||||
Comparison_result operator()(const X_monotone_curve_2 & xc1,
|
||||
const X_monotone_curve_2 & xc2,
|
||||
Arr_curve_end ce) const
|
||||
{ ++m_counter; return m_object(xc1, xc2, ce); }
|
||||
};
|
||||
|
||||
/*! A functor that compares the x-coordinate of two given points
|
||||
* that lie on horizontal boundaries.
|
||||
*/
|
||||
class Compare_x_on_boundary_2 {
|
||||
private:
|
||||
typename Base::Compare_x_on_boundary_2 m_object;
|
||||
unsigned int & m_counter1;
|
||||
unsigned int & m_counter2;
|
||||
unsigned int & m_counter3;
|
||||
unsigned int & m_counter;
|
||||
|
||||
public:
|
||||
/*! Construct */
|
||||
Compare_x_on_boundary_2(const Base * base,
|
||||
unsigned int & counter1, unsigned int & counter2, unsigned int & counter3 ) :
|
||||
Compare_x_on_boundary_2(const Base * base, unsigned int & counter) :
|
||||
m_object(base->compare_x_on_boundary_2_object()),
|
||||
m_counter1(counter1),
|
||||
m_counter2(counter2),
|
||||
m_counter3(counter3)
|
||||
m_counter(counter)
|
||||
{}
|
||||
|
||||
/*! Operate */
|
||||
Comparison_result operator()(const Point_2 & p1,
|
||||
const Point_2 & p2) const
|
||||
{ ++m_counter1; return m_object(p1, p2); }
|
||||
|
||||
/*! Operate */
|
||||
Comparison_result operator()(const Point_2 & pt,
|
||||
const X_monotone_curve_2 & xcv, Arr_curve_end ce) const
|
||||
{ ++m_counter2; return m_object(pt, xcv, ce); }
|
||||
|
||||
/*! Operate */
|
||||
Comparison_result operator()(const X_monotone_curve_2 & xcv1, Arr_curve_end ce1,
|
||||
const X_monotone_curve_2 & xcv2, Arr_curve_end ce2) const
|
||||
{ ++m_counter3; return m_object(xcv1, ce1, xcv2, ce2); }
|
||||
|
||||
{ ++m_counter; return m_object(p1, p2); }
|
||||
};
|
||||
|
||||
/*! A functor that compares the x-coordinates of curve ends near the
|
||||
* boundary of the parameter space.
|
||||
*/
|
||||
class Compare_x_near_boundary_2 {
|
||||
private:
|
||||
typename Base::Compare_x_near_boundary_2 m_object;
|
||||
unsigned int & m_counter;
|
||||
|
||||
public:
|
||||
/*! Construct */
|
||||
Compare_x_near_boundary_2(const Base * base,
|
||||
unsigned int & counter) :
|
||||
m_object(base->compare_x_near_boundary_2_object()),
|
||||
m_counter(counter) {}
|
||||
|
||||
|
||||
/*! Operate */
|
||||
Comparison_result operator()(const X_monotone_curve_2 & xc1,
|
||||
const X_monotone_curve_2 & xc2,
|
||||
Arr_curve_end ce) const
|
||||
{ ++m_counter; return m_object(xc1, xc2, ce); }
|
||||
};
|
||||
// TODO Is_on_y_identification_2
|
||||
|
||||
//@}
|
||||
|
||||
@@ -886,20 +744,6 @@ public:
|
||||
);
|
||||
}
|
||||
|
||||
Is_on_x_identification_2 is_on_x_identification_2_object() const
|
||||
{ return Is_on_x_identification_2(
|
||||
this,
|
||||
m_counters[IS_ON_X_IDENTIFICATION_POINT_OP],
|
||||
m_counters[IS_ON_X_IDENTIFICATION_CURVE_OP]
|
||||
);
|
||||
}
|
||||
|
||||
Compare_y_on_boundary_2 compare_on_boundary_2_object() const
|
||||
{ return Compare_y_on_boundary_2(this, m_counters[COMPARE_Y_ON_BOUNDARY_OP]); }
|
||||
|
||||
Compare_y_near_boundary_2 compare_near_boundary_2_object() const
|
||||
{ return Compare_y_near_boundary_2(this, m_counters[COMPARE_Y_NEAR_BOUNDARY_OP]); }
|
||||
|
||||
// bottom-top
|
||||
Parameter_space_in_y_2 parameter_space_in_y_2_object() const
|
||||
{ return Parameter_space_in_y_2(
|
||||
@@ -910,30 +754,6 @@ public:
|
||||
);
|
||||
}
|
||||
|
||||
Is_on_y_identification_2 is_on_y_identification_2_object() const
|
||||
{ return Is_on_y_identification_2(
|
||||
this,
|
||||
m_counters[IS_ON_Y_IDENTIFICATION_POINT_OP],
|
||||
m_counters[IS_ON_Y_IDENTIFICATION_CURVE_OP]
|
||||
);
|
||||
}
|
||||
|
||||
Compare_x_at_limit_2 compare_x_at_limit_2_object() const
|
||||
{ return Compare_x_at_limit_2(this,
|
||||
m_counters[COMPARE_X_AT_LIMIT_POINT_CURVE_END_OP],
|
||||
m_counters[COMPARE_X_AT_LIMIT_CURVE_ENDS_OP]); }
|
||||
|
||||
Compare_x_near_limit_2 compare_x_near_limit_2_object() const
|
||||
{ return Compare_x_near_limit_2(this, m_counters[COMPARE_X_NEAR_LIMIT_OP]); }
|
||||
|
||||
Compare_x_on_boundary_2 compare_x_on_boundary_2_object() const
|
||||
{ return Compare_x_on_boundary_2(this,
|
||||
m_counters[COMPARE_X_ON_BOUNDARY_POINTS_OP],
|
||||
m_counters[COMPARE_X_ON_BOUNDARY_POINT_CURVE_END_OP],
|
||||
m_counters[COMPARE_X_ON_BOUNDARY_CURVE_ENDS_OP]); }
|
||||
|
||||
Compare_x_near_boundary_2 compare_x_near_boundary_2_object() const
|
||||
{ return Compare_x_near_boundary_2(this, m_counters[COMPARE_X_NEAR_BOUNDARY_OP]); }
|
||||
|
||||
//@}
|
||||
|
||||
@@ -1008,14 +828,10 @@ Out_stream & operator<<(Out_stream & os,
|
||||
<< traits.count_parameter_space_in_x_point() << std::endl
|
||||
<< "# of PARAMETER_SPACE_IN_X curve operation = "
|
||||
<< traits.count_parameter_space_in_x_curve() << std::endl
|
||||
<< "# of IS_ON_X_IDENTIFICIATION point operation = "
|
||||
<< traits.count_is_on_x_identification_point() << std::endl
|
||||
<< "# of IS_ON_X_IDENTIFICATION curve operation = "
|
||||
<< traits.count_is_on_x_identification_curve() << std::endl
|
||||
<< "# of COMPARE_Y_ON_BOUNDARY operation = "
|
||||
<< traits.count_compare_y_on_boundary() << std::endl
|
||||
<< "# of COMPARE_Y_NEAR_BOUNDARY operation = "
|
||||
<< traits.count_compare_y_near_boundary() << std::endl
|
||||
<< "# of COMPARE_Y_ON_BOUNDARY operation = "
|
||||
<< traits.count_compare_y_on_boundary() << std::endl
|
||||
// bottom-top
|
||||
<< "# of PARAMETER_SPACE_IN_Y curve-end operation = "
|
||||
<< traits.count_parameter_space_in_y_curve_end() << std::endl
|
||||
@@ -1023,24 +839,12 @@ Out_stream & operator<<(Out_stream & os,
|
||||
<< traits.count_parameter_space_in_y_point() << std::endl
|
||||
<< "# of PARAMETER_SPACE_IN_Y curve operation = "
|
||||
<< traits.count_parameter_space_in_y_curve() << std::endl
|
||||
<< "# of IS_ON_Y_IDENTIFICIATION point operation = "
|
||||
<< traits.count_is_on_y_identification_point() << std::endl
|
||||
<< "# of IS_ON_Y_IDENTIFICATION curve operation = "
|
||||
<< traits.count_is_on_y_identification_curve() << std::endl
|
||||
<< "# of COMPARE_X_AT_LIMIT point/curve-end operation = "
|
||||
<< traits.count_compare_x_at_limit_point_curve_end() << std::endl
|
||||
<< "# of COMPARE_X_AT_LIMIT curve-ends operation = "
|
||||
<< traits.count_compare_x_at_limit_curve_ends() << std::endl
|
||||
<< "# of COMPARE_X_NEAR_LIMIT operation = "
|
||||
<< traits.count_compare_x_near_limit() << std::endl
|
||||
<< "# of COMPARE_X_ON_BOUNDARY points operation = "
|
||||
<< traits.count_compare_x_on_boundary_points() << std::endl
|
||||
<< "# of COMPARE_X_ON_BOUNDARY point/curve-end operation = "
|
||||
<< traits.count_compare_x_on_boundary_point_curve_end() << std::endl
|
||||
<< "# of COMPARE_X_ON_BOUNDARY curve-ends operation = "
|
||||
<< traits.count_compare_x_on_boundary_curve_ends() << std::endl
|
||||
<< "# of COMPARE_X_NEAR_BOUNDARY operation = "
|
||||
<< traits.count_compare_x_near_boundary() << std::endl
|
||||
<< "# of COMPARE_X_NEAR_BOUNDARY point/curve-end operation = "
|
||||
<< traits.count_compare_x_near_boundary_point_curve_end() << std::endl
|
||||
<< "# of COMPARE_X_NEAR_BOUNDARY curve-ends operation = "
|
||||
<< traits.count_compare_x_near_boundary_curve_ends() << std::endl
|
||||
<< "# of COMPARE_X_ON_BOUNDARY operation = "
|
||||
<< traits.count_compare_x_on_boundary() << std::endl
|
||||
|
||||
<< "total # = " << sum << std::endl
|
||||
<< "# of traits constructed = " << Traits::increment(false)
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2006,2007,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2005 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
@@ -68,14 +68,14 @@ public:
|
||||
typedef typename Base_traits_2::Has_do_intersect_category
|
||||
Has_do_intersect_category;
|
||||
|
||||
typedef typename internal::Arr_complete_left_side_category< Base_traits_2 >::Category
|
||||
Left_side_category;
|
||||
typedef typename internal::Arr_complete_bottom_side_category< Base_traits_2 >::Category
|
||||
Bottom_side_category;
|
||||
typedef typename internal::Arr_complete_top_side_category< Base_traits_2 >::Category
|
||||
Top_side_category;
|
||||
typedef typename internal::Arr_complete_right_side_category< Base_traits_2 >::Category
|
||||
Right_side_category;
|
||||
typedef typename internal::Arr_complete_left_side_tag< Base_traits_2 >::Tag
|
||||
Arr_left_side_category;
|
||||
typedef typename internal::Arr_complete_bottom_side_tag< Base_traits_2 >::Tag
|
||||
Arr_bottom_side_category;
|
||||
typedef typename internal::Arr_complete_top_side_tag< Base_traits_2 >::Tag
|
||||
Arr_top_side_category;
|
||||
typedef typename internal::Arr_complete_right_side_tag< Base_traits_2 >::Tag
|
||||
Arr_right_side_category;
|
||||
|
||||
// Representation of a curve with an addtional data field:
|
||||
typedef _Curve_data_ex<Base_curve_2, Curve_data> Curve_2;
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2005,2006,2007,2008,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2006 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2005,2006,2007,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2005 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2005,2006,2007,2008,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2005 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2006,2007,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2006 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2006,2007,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2005 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
|
||||
File diff suppressed because it is too large
Load Diff
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2005 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2005,2007,2008,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2005 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
|
||||
+2
-2
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2006 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
@@ -312,7 +312,7 @@ public:
|
||||
#endif // CGAL_ARR_GEODESIC_ARC_ON_SPHERE_PARTITION_TRAITS_2_H
|
||||
|
||||
|
||||
// Copyright (c) 2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2006 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
|
||||
File diff suppressed because it is too large
Load Diff
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2006,2007,2008,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2006 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
|
||||
+1
-1
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2006,2007,2008,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2006 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2006,2007,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2006 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2006,2007,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2006 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
@@ -151,6 +151,11 @@ public:
|
||||
p_polyY(NULL),
|
||||
p_normY(NULL)
|
||||
{
|
||||
CGAL_precondition_code (
|
||||
Rat_kernel ker;
|
||||
typename Rat_kernel::Equal_2 equal = ker.equal_2_object();
|
||||
);
|
||||
|
||||
// Copy the control points and compute their bounding box.
|
||||
const int pts_size = std::distance (pts_begin, pts_end);
|
||||
double x, y;
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2006,2007,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2006 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2006,2007,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2006 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
@@ -1345,29 +1345,26 @@ bool _Bezier_x_monotone_2<RatKer, AlgKer, NtTrt, BndTrt>::equals
|
||||
// Split the subcurve into two at a given split point.
|
||||
//
|
||||
template <class RatKer, class AlgKer, class NtTrt, class BndTrt>
|
||||
void _Bezier_x_monotone_2<RatKer, AlgKer, NtTrt, BndTrt>::
|
||||
split(const Point_2& p, Self& c1, Self& c2) const
|
||||
void _Bezier_x_monotone_2<RatKer, AlgKer, NtTrt, BndTrt>::split
|
||||
(const Point_2& p,
|
||||
Self& c1, Self& c2) const
|
||||
{
|
||||
//this was added to handle the case where p is the endpoint of another
|
||||
//Bezier curve and the curve is vertical
|
||||
//this was added to handle the case where p is the endpoint of another Bezier curve
|
||||
//and the curve is vertical
|
||||
if ( p.is_rational() && is_vertical() ){
|
||||
Nt_traits nt_traits;
|
||||
Rat_point_2 rp = (Rat_point_2) p;
|
||||
Rat_point_2 rp=(Rat_point_2) p;
|
||||
std::list<Algebraic> sols;
|
||||
|
||||
// typename std::list<Algebraic>::iterator sol = sols.begin();
|
||||
Integer rpyn = nt_traits.numerator(rp.y());
|
||||
Polynomial poly_y =
|
||||
nt_traits.scale(_curve.y_polynomial(),
|
||||
nt_traits.denominator(rp.y())) -
|
||||
nt_traits.construct_polynomial(&rpyn, 0);
|
||||
nt_traits.compute_polynomial_roots(poly_y, 0, 1, std::back_inserter(sols));
|
||||
CGAL_assertion(sols.size() == 1);
|
||||
p.add_originator(Originator(_curve, _xid,*sols.begin()) );
|
||||
typename std::list<Algebraic>::iterator sol=sols.begin();
|
||||
Integer rpyn=nt_traits.numerator(rp.y());
|
||||
Polynomial poly_y=nt_traits.scale(_curve.y_polynomial(),nt_traits.denominator(rp.y())) - nt_traits.construct_polynomial(&rpyn,0);
|
||||
nt_traits.compute_polynomial_roots (poly_y,0,1,std::back_inserter(sols));
|
||||
CGAL_assertion(sols.size()==1);
|
||||
p.add_originator (Originator(_curve, _xid,*sols.begin()) );
|
||||
}
|
||||
|
||||
CGAL_precondition(p.get_originator(_curve, _xid) != p.originators_end() ||
|
||||
p.is_rational());
|
||||
CGAL_precondition (p.get_originator (_curve, _xid) != p.originators_end() || p.is_rational());
|
||||
|
||||
// Duplicate the curve.
|
||||
c1 = c2 = *this;
|
||||
@@ -1383,6 +1380,8 @@ split(const Point_2& p, Self& c1, Self& c2) const
|
||||
c1._ps = p;
|
||||
c2._pt = p;
|
||||
}
|
||||
|
||||
return;
|
||||
}
|
||||
|
||||
// ---------------------------------------------------------------------------
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2006,2007,2008,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2005 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2006,2007,2008,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2005 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2006,2007,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2005 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2006,2007,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2005 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2006,2007,2008,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2005 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
|
||||
+1
-1
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2006,2007,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2005 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2006,2007,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2005 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2006,2007,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2006 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2006,2007,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2005 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2005 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2006,2007,2008,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2005 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2006,2007,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2005 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2006,2007,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 1997 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2006,2007,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2006 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
|
||||
+8
-255
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2006 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
@@ -861,10 +861,10 @@ public:
|
||||
Parameter_space_in_y_2 parameter_space_in_y_2_object() const
|
||||
{ return Parameter_space_in_y_2(); }
|
||||
|
||||
/*! A functor that compares the x-limits of arc ends on the
|
||||
/*! A functor that compares the x-coordinates of arc ends near the
|
||||
* boundary of the parameter space.
|
||||
*/
|
||||
class Compare_x_limit_on_boundary_2 {
|
||||
class Compare_x_near_boundary_2 {
|
||||
protected:
|
||||
typedef Arr_great_circular_arc_on_cylinder_traits_2<Kernel> Traits;
|
||||
|
||||
@@ -874,13 +874,13 @@ public:
|
||||
/*! Constructor
|
||||
* \param traits the traits (in case it has state)
|
||||
*/
|
||||
Compare_x_limit_on_boundary_2(const Traits * traits) : m_traits(traits) {}
|
||||
Compare_x_near_boundary_2(const Traits * traits) : m_traits(traits) {}
|
||||
|
||||
friend class Arr_great_circular_arc_on_cylinder_traits_2<Kernel>;
|
||||
|
||||
public:
|
||||
/*! Compare the x-coordinate of a direction with the x-limit of an
|
||||
* arc end on the boundary.
|
||||
/*! Compare the x-coordinate of a direction with the x-coordinate of an
|
||||
* arc end near the boundary.
|
||||
* \param p the point direction.
|
||||
* \param xcv the arc, the endpoint of which is compared.
|
||||
* \param ce the arc-end indicator -
|
||||
@@ -898,8 +898,6 @@ public:
|
||||
const X_monotone_curve_2 & xcv,
|
||||
Arr_curve_end ce) const
|
||||
{
|
||||
// TODO implement (simplify)
|
||||
|
||||
CGAL_precondition(point.is_no_boundary());
|
||||
CGAL_precondition_code
|
||||
(const Point_2 & p2 = (ce == ARR_MIN_END) ? xcv.left() : xcv.right(););
|
||||
@@ -933,7 +931,7 @@ public:
|
||||
return (ce == ARR_MIN_END) ? LARGER : SMALLER;
|
||||
}
|
||||
|
||||
/*! Compare the x-limits of 2 arc ends on the boundary of the
|
||||
/*! Compare the x-coordinates of 2 arc ends near the boundary of the
|
||||
* parameter space.
|
||||
* \param xcv1 the first arc.
|
||||
* \param ce1 the first arc end indicator -
|
||||
@@ -957,115 +955,6 @@ public:
|
||||
const X_monotone_curve_2 & xcv2,
|
||||
Arr_curve_end ce2) const
|
||||
{
|
||||
// TODO implement (simplify)
|
||||
|
||||
CGAL_precondition_code
|
||||
(const Point_2 & p1 = (ce1 == ARR_MIN_END) ? xcv1.left() : xcv1.right(););
|
||||
CGAL_precondition(!p1.is_no_boundary());
|
||||
CGAL_precondition_code
|
||||
(const Point_2 & p2 = (ce2 == ARR_MIN_END) ? xcv2.left() : xcv2.right(););
|
||||
CGAL_precondition(!p2.is_no_boundary());
|
||||
|
||||
if (xcv1.is_vertical() && xcv2.is_vertical()) {
|
||||
CGAL_precondition(!xcv1.is_on_boundary());
|
||||
CGAL_precondition(!xcv2.is_on_boundary());
|
||||
|
||||
/* The following is replaced by the code above
|
||||
* if (xcv1.is_on_boundary() && xcv2.is_on_boundary()) return EQUAL;
|
||||
* if (xcv1.is_on_boundary()) return SMALLER;
|
||||
* if (xcv2.is_on_boundary()) return LARGER;
|
||||
*/
|
||||
|
||||
// Non of the arcs coincide with the discontinuity arc:
|
||||
// Obtain the directions contained in the underlying planes, which are
|
||||
// also on the xy-plane:
|
||||
Direction_3 normal1 = xcv1.plane().orthogonal_direction();
|
||||
Direction_2 p = (xcv1.is_directed_right()) ?
|
||||
Direction_2(-(normal1.dy()), normal1.dx()) :
|
||||
Direction_2(normal1.dy(), -(normal1.dx()));
|
||||
Direction_3 normal2 = xcv2.plane().orthogonal_direction();
|
||||
Direction_2 q = (xcv2.is_directed_right()) ?
|
||||
Direction_2(-(normal2.dy()), normal2.dx()) :
|
||||
Direction_2(normal2.dy(), -(normal2.dx()));
|
||||
|
||||
const Kernel * kernel = m_traits;
|
||||
if (kernel->equal_2_object()(p, q)) return EQUAL;
|
||||
const Direction_2 & nx = Traits::neg_x_2();
|
||||
return (kernel->counterclockwise_in_between_2_object()(nx, p, q)) ?
|
||||
LARGER : SMALLER;
|
||||
}
|
||||
if (xcv1.is_vertical()) {
|
||||
CGAL_precondition(!xcv1.is_on_boundary());
|
||||
/* The following is replaced by the code above
|
||||
* if (xcv1.is_on_boundary()) return SMALLER;
|
||||
*/
|
||||
return (ce2 == ARR_MAX_END) ? SMALLER : LARGER;
|
||||
}
|
||||
if (xcv2.is_vertical()) {
|
||||
CGAL_precondition(!xcv2.is_on_boundary());
|
||||
/* The following is replaced by the code above
|
||||
* if (xcv2.is_on_boundary()) return LARGER;
|
||||
*/
|
||||
return (ce1 == ARR_MAX_END) ? LARGER : SMALLER;
|
||||
}
|
||||
// Non of the arcs are vertical:
|
||||
if (ce1 == ce2) return EQUAL;
|
||||
if (ce1 == ARR_MIN_END) return SMALLER;
|
||||
return LARGER;
|
||||
}
|
||||
};
|
||||
|
||||
/*! Obtain a Compare_x_limit_on_boundary_2 function object */
|
||||
Compare_x_limit_on_boundary_2 compare_x_limit_on_boundary_2_object() const
|
||||
{ return Compare_x_limit_on_boundary_2(this); }
|
||||
|
||||
|
||||
/*! A functor that compares the x-coordinates of arc ends near the
|
||||
* boundary of the parameter space.
|
||||
*/
|
||||
class Compare_x_near_boundary_2 {
|
||||
protected:
|
||||
typedef Arr_great_circular_arc_on_cylinder_traits_2<Kernel> Traits;
|
||||
|
||||
/*! The traits (in case it has state) */
|
||||
const Traits * m_traits;
|
||||
|
||||
/*! Constructor
|
||||
* \param traits the traits (in case it has state)
|
||||
*/
|
||||
Compare_x_near_boundary_2(const Traits * traits) : m_traits(traits) {}
|
||||
|
||||
friend class Arr_great_circular_arc_on_cylinder_traits_2<Kernel>;
|
||||
|
||||
public:
|
||||
|
||||
/*! Compare the x-coordinates of 2 arc ends near the boundary of the
|
||||
* parameter space.
|
||||
* \param xcv1 the first arc.
|
||||
* \param ce1 the first arc end indicator -
|
||||
* ARR_MIN_END - the minimal end of xcv1 or
|
||||
* ARR_MAX_END - the maximal end of xcv1.
|
||||
* \param xcv2 the second arc.
|
||||
* \param ce2 the second arc end indicator -
|
||||
* ARR_MIN_END - the minimal end of xcv2 or
|
||||
* ARR_MAX_END - the maximal end of xcv2.
|
||||
* \return the second comparison result:
|
||||
* SMALLER - x(xcv1, ce1) < x(xcv2, ce2);
|
||||
* EQUAL - x(xcv1, ce1) = x(xcv2, ce2);
|
||||
* LARGER - x(xcv1, ce1) > x(xcv2, ce2).
|
||||
* \pre the ce1 end of the arc xcv1 lies on a boundary.
|
||||
* \pre the ce2 end of the arc xcv2 lies on a boundary.
|
||||
* \pre xcv1 does not coincide with the vertical identification curve.
|
||||
* \pre xcv2 does not coincide with the vertical identification curve.
|
||||
*/
|
||||
Comparison_result operator()(const X_monotone_curve_2 & xcv1,
|
||||
const X_monotone_curve_2 & xcv2,
|
||||
Arr_curve_end ce) const
|
||||
{
|
||||
// TODO implement (simplify)
|
||||
|
||||
Arr_curve_end ce1 = ce2 = ce;
|
||||
|
||||
CGAL_precondition_code
|
||||
(const Point_2 & p1 = (ce1 == ARR_MIN_END) ? xcv1.left() : xcv1.right(););
|
||||
CGAL_precondition(!p1.is_no_boundary());
|
||||
@@ -1126,143 +1015,7 @@ public:
|
||||
Compare_x_near_boundary_2 compare_x_near_boundary_2_object() const
|
||||
{ return Compare_x_near_boundary_2(this); }
|
||||
|
||||
/*! A functor that compares the y-limits of arc ends on the
|
||||
* boundary of the parameter space.
|
||||
*/
|
||||
class Compare_y_limit_on_boundary_2 {
|
||||
protected:
|
||||
typedef Arr_great_circular_arc_on_cylinder_traits_2<Kernel> Traits;
|
||||
|
||||
/*! The traits (in case it has state) */
|
||||
const Traits * m_traits;
|
||||
|
||||
/*! Constructor
|
||||
* \param traits the traits (in case it has state)
|
||||
*/
|
||||
Compare_y_limit_on_boundary_2(const Traits * traits) : m_traits(traits) {}
|
||||
|
||||
friend class Arr_great_circular_arc_on_cylinder_traits_2<Kernel>;
|
||||
|
||||
public:
|
||||
/*! Compare the y-limits of 2 curves at their ends on the boundary
|
||||
* of the parameter space.
|
||||
* \param xcv1 the first arc.
|
||||
* \param xcv2 the second arc.
|
||||
* \param ce the arc end indicator.
|
||||
* \return the second comparison result.
|
||||
* \pre the ce ends of the arcs xcv1 and xcv2 lie either on the left
|
||||
* boundary or on the right boundary of the parameter space.
|
||||
* There is no horizontal identification curve!
|
||||
*/
|
||||
Comparison_result operator()(const X_monotone_curve_2 & xcv1,
|
||||
const X_monotone_curve_2 & xcv2,
|
||||
Arr_curve_end ce) const
|
||||
{
|
||||
CGAL_precondition(!xcv1.is_degenerate());
|
||||
CGAL_precondition(!xcv2.is_degenerate());
|
||||
|
||||
const Point_2 & l1 = xcv1.left();
|
||||
const Point_2 & r1 = xcv1.right();
|
||||
const Point_2 & l2 = xcv2.left();
|
||||
const Point_2 & r2 = xcv2.right();
|
||||
|
||||
// If xcv1 is vertical, xcv1 coincides with the discontinuity arc:
|
||||
if (xcv1.is_vertical()) {
|
||||
CGAL_precondition(!l1.is_no_boundary());
|
||||
CGAL_precondition(!r1.is_no_boundary());
|
||||
}
|
||||
|
||||
// If xcv2 is vertical, xcv2 coincides with the discontinuity arc:
|
||||
if (xcv2.is_vertical()) {
|
||||
CGAL_precondition(!l2.is_no_boundary());
|
||||
CGAL_precondition(!r2.is_no_boundary());
|
||||
}
|
||||
|
||||
if (ce == ARR_MIN_END) {
|
||||
// Handle the south pole. It has the smallest y coords:
|
||||
if (l1.is_min_boundary())
|
||||
return (l2.is_min_boundary()) ? EQUAL : SMALLER;
|
||||
if (l2.is_min_boundary()) return LARGER;
|
||||
|
||||
// None of xcv1 and xcv2 endpoints coincide with a pole:
|
||||
Comparison_result cr = m_traits->compare_y(l1, l2);
|
||||
if (cr != EQUAL) return cr;
|
||||
|
||||
// If Both arcs are vertical, they overlap:
|
||||
if (xcv1.is_vertical() && xcv2.is_vertical()) return EQUAL;
|
||||
if (xcv1.is_vertical()) return LARGER;
|
||||
if (xcv2.is_vertical()) return SMALLER;
|
||||
|
||||
// Non of the arcs is verticel. Thus, non of the endpoints coincide
|
||||
// with a pole.
|
||||
// Compare the y-coord. at the x-coord of the most left right-endpoint.
|
||||
CGAL_assertion(r1.is_no_boundary());
|
||||
CGAL_assertion(r2.is_no_boundary());
|
||||
|
||||
if (m_traits->compare_xy(r1, r2) == LARGER) {
|
||||
// use r2 and xcv1:
|
||||
Oriented_side os = m_traits->oriented_side(xcv1.plane(), r2);
|
||||
return (os == ON_ORIENTED_BOUNDARY) ? EQUAL :
|
||||
(xcv1.is_directed_right()) ?
|
||||
((os == ON_NEGATIVE_SIDE) ? LARGER : SMALLER) :
|
||||
((os == ON_NEGATIVE_SIDE) ? SMALLER : LARGER);
|
||||
}
|
||||
// use r1 and xcv2:
|
||||
Oriented_side os = m_traits->oriented_side(xcv2.plane(), r1);
|
||||
return (os == ON_ORIENTED_BOUNDARY) ? EQUAL :
|
||||
(xcv2.is_directed_right()) ?
|
||||
((os == ON_NEGATIVE_SIDE) ? SMALLER : LARGER) :
|
||||
((os == ON_NEGATIVE_SIDE) ? LARGER : SMALLER);
|
||||
}
|
||||
|
||||
// ce == ARR_MAX_END
|
||||
|
||||
// Handle the north pole. It has the largest y coords:
|
||||
if (r1.is_max_boundary()) return (r2.is_max_boundary()) ? EQUAL : LARGER;
|
||||
if (r2.is_max_boundary()) return SMALLER;
|
||||
|
||||
// None of xcv1 and xcv2 endpoints coincide with a pole:
|
||||
Direction_2 r1_xy = Traits::project_xy(r1);
|
||||
Comparison_result cr = m_traits->compare_y(r1, r2);
|
||||
if (cr != EQUAL) return cr;
|
||||
|
||||
// If Both arcs are vertical, they overlap:
|
||||
if (xcv1.is_vertical() && xcv2.is_vertical()) return EQUAL;
|
||||
if (xcv1.is_vertical()) return LARGER;
|
||||
if (xcv2.is_vertical()) return SMALLER;
|
||||
|
||||
// Compare to the left:
|
||||
Direction_2 p_r1 = Traits::project_xy(r1);
|
||||
cr = m_traits->compare_y(r1, r2);
|
||||
if (cr != EQUAL) return cr;
|
||||
|
||||
// Non of the arcs is verticel. Thus, non of the endpoints coincide with
|
||||
// a pole.
|
||||
// Compare the y-coord. at the x-coord of the most right left-endpoint.
|
||||
CGAL_assertion(l1.is_no_boundary());
|
||||
CGAL_assertion(l2.is_no_boundary());
|
||||
|
||||
if (m_traits->compare_xy(l1, l2) == SMALLER) {
|
||||
// use l2 and xcv1:
|
||||
Oriented_side os = m_traits->oriented_side(xcv1.plane(), l2);
|
||||
return (os == ON_ORIENTED_BOUNDARY) ? EQUAL :
|
||||
(xcv1.is_directed_right()) ?
|
||||
((os == ON_NEGATIVE_SIDE) ? LARGER : SMALLER) :
|
||||
((os == ON_NEGATIVE_SIDE) ? SMALLER : LARGER);
|
||||
}
|
||||
// use l1 and xcv2:
|
||||
Oriented_side os = m_traits->oriented_side(xcv2.plane(), l1);
|
||||
return (os == ON_ORIENTED_BOUNDARY) ? EQUAL :
|
||||
(xcv2.is_directed_right()) ?
|
||||
((os == ON_NEGATIVE_SIDE) ? SMALLER : LARGER) :
|
||||
((os == ON_NEGATIVE_SIDE) ? LARGER : SMALLER);
|
||||
}
|
||||
};
|
||||
|
||||
/*! Obtain a Compare_y_limit_on_boundary_2 function object */
|
||||
Compare_y_limit_on_boundary_2 compare_y_limit_on_boundary_2_object() const
|
||||
{ return Compare_y_limit_on_boundary_2(this); }
|
||||
|
||||
/*! A functor that compares the y-coordinates of arc ends near the
|
||||
* boundary of the parameter space.
|
||||
*/
|
||||
@@ -1399,7 +1152,7 @@ public:
|
||||
/*! Obtain a Compare_y_near_boundary_2 function object */
|
||||
Compare_y_near_boundary_2 compare_y_near_boundary_2_object() const
|
||||
{ return Compare_y_near_boundary_2(this); }
|
||||
|
||||
|
||||
/*! A functor that indicates whether a geometric object lies on the
|
||||
* horizontal identification arc. Since there is no such thing in the
|
||||
* parameter space, the operators immediately return false.
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2006,2007,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2006 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
@@ -53,10 +53,10 @@ public:
|
||||
typedef Tag_false Has_merge_category;
|
||||
typedef Tag_false Has_do_intersect_category;
|
||||
|
||||
typedef Arr_oblivious_side_tag Left_side_category;
|
||||
typedef Arr_oblivious_side_tag Bottom_side_category;
|
||||
typedef Arr_oblivious_side_tag Top_side_category;
|
||||
typedef Arr_oblivious_side_tag Right_side_category;
|
||||
typedef Arr_oblivious_side_tag Arr_left_side_category;
|
||||
typedef Arr_oblivious_side_tag Arr_bottom_side_category;
|
||||
typedef Arr_oblivious_side_tag Arr_top_side_category;
|
||||
typedef Arr_oblivious_side_tag Arr_right_side_category;
|
||||
|
||||
public:
|
||||
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2007,2008,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2005 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2003,2004,2005,2006,2007,2008,2009,2010,2011 INRIA Sophia-Antipolis (France).
|
||||
// Copyright (c) 2003-2006 INRIA Sophia-Antipolis (France).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
@@ -62,10 +62,10 @@ public:
|
||||
typedef CGAL::Tag_false Has_merge_category;
|
||||
typedef CGAL::Tag_false Has_do_intersect_category;
|
||||
|
||||
typedef Arr_oblivious_side_tag Left_side_category;
|
||||
typedef Arr_oblivious_side_tag Bottom_side_category;
|
||||
typedef Arr_oblivious_side_tag Top_side_category;
|
||||
typedef Arr_oblivious_side_tag Right_side_category;
|
||||
typedef Arr_oblivious_side_tag Arr_left_side_category;
|
||||
typedef Arr_oblivious_side_tag Arr_bottom_side_category;
|
||||
typedef Arr_oblivious_side_tag Arr_top_side_category;
|
||||
typedef Arr_oblivious_side_tag Arr_right_side_category;
|
||||
|
||||
Arr_line_arc_traits_2(const CircularKernel &k = CircularKernel())
|
||||
: ck(k) {}
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2006,2007,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2006 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
@@ -57,10 +57,10 @@ public:
|
||||
typedef Tag_true Has_merge_category;
|
||||
typedef Tag_false Has_do_intersect_category;
|
||||
|
||||
typedef Arr_open_side_tag Left_side_category;
|
||||
typedef Arr_open_side_tag Bottom_side_category;
|
||||
typedef Arr_open_side_tag Top_side_category;
|
||||
typedef Arr_open_side_tag Right_side_category;
|
||||
typedef Arr_open_side_tag Arr_left_side_category;
|
||||
typedef Arr_open_side_tag Arr_bottom_side_category;
|
||||
typedef Arr_open_side_tag Arr_top_side_category;
|
||||
typedef Arr_open_side_tag Arr_right_side_category;
|
||||
|
||||
typedef typename Kernel::Line_2 Line_2;
|
||||
typedef typename Kernel::Ray_2 Ray_2;
|
||||
@@ -747,7 +747,7 @@ public:
|
||||
typedef Arr_linear_traits_2<Kernel> Traits;
|
||||
|
||||
/*! The traits (in case it has state) */
|
||||
const Traits* m_traits;
|
||||
const Traits * m_traits;
|
||||
|
||||
/*! Constructor
|
||||
* \param traits the traits (in case it has state)
|
||||
@@ -1064,30 +1064,13 @@ public:
|
||||
Parameter_space_in_y_2 parameter_space_in_y_2_object() const
|
||||
{ return Parameter_space_in_y_2(); }
|
||||
|
||||
/*! A function object that compares the x-limits of arc ends on the
|
||||
/*! A function object that compares the x-coordinates of arc ends near the
|
||||
* boundary of the parameter space
|
||||
*/
|
||||
class Compare_x_at_limit_2 {
|
||||
protected:
|
||||
typedef Arr_linear_traits_2<Kernel> Traits;
|
||||
|
||||
/*! The traits (in case it has state) */
|
||||
const Traits* m_traits;
|
||||
|
||||
/*! Constructor
|
||||
* \param traits the traits (in case it has state)
|
||||
* The constructor is declared private to allow only the functor
|
||||
* obtaining function, which is a member of the nesting class,
|
||||
* constructing it.
|
||||
*/
|
||||
Compare_x_at_limit_2(const Traits* traits) : m_traits(traits) {}
|
||||
|
||||
//! Allow its functor obtaining function calling the private constructor.
|
||||
friend class Arr_linear_traits_2<Kernel>;
|
||||
|
||||
class Compare_x_near_boundary_2 {
|
||||
public:
|
||||
/*! Compare the x-limit of a vertical line at a point with the x-limit of
|
||||
* a line end on the boundary at y = +/- oo.
|
||||
/*! Compare the x-coordinate of a point with the x-coordinate of
|
||||
* a line end near the boundary at y = +/- oo.
|
||||
* \param p the point direction.
|
||||
* \param xcv the line, the endpoint of which is compared.
|
||||
* \param ce the line-end indicator -
|
||||
@@ -1098,66 +1081,19 @@ public:
|
||||
* EQUAL - x(p) = x(xc, ce);
|
||||
* LARGER - x(p) > x(xc, ce).
|
||||
* \pre p lies in the interior of the parameter space.
|
||||
* \pre the ce end of the line xcv lies on a boundary, implying
|
||||
* that xcv1 is vertical.
|
||||
* \pre the ce end of the line xcv lies on a boundary.
|
||||
*/
|
||||
Comparison_result operator()(const Point_2 & p,
|
||||
const X_monotone_curve_2 & xcv,
|
||||
Arr_curve_end ) const
|
||||
{
|
||||
CGAL_precondition(! xcv.is_degenerate());
|
||||
CGAL_precondition(xcv.is_vertical());
|
||||
CGAL_precondition (! xcv.is_degenerate());
|
||||
CGAL_precondition (xcv.is_vertical());
|
||||
|
||||
const Kernel* kernel = m_traits;
|
||||
return (kernel->compare_x_at_y_2_object()(p, xcv.supp_line()));
|
||||
Kernel kernel;
|
||||
return (kernel.compare_x_at_y_2_object() (p, xcv.supp_line()));
|
||||
}
|
||||
|
||||
/*! Compare the x-limits of 2 arcs ends on the boundary of the
|
||||
* parameter space at y = +/- oo.
|
||||
* \param xcv1 the first arc.
|
||||
* \param ce1 the first arc end indicator -
|
||||
* ARR_MIN_END - the minimal end of xcv1 or
|
||||
* ARR_MAX_END - the maximal end of xcv1.
|
||||
* \param xcv2 the second arc.
|
||||
* \param ce2 the second arc end indicator -
|
||||
* ARR_MIN_END - the minimal end of xcv2 or
|
||||
* ARR_MAX_END - the maximal end of xcv2.
|
||||
* \return the second comparison result:
|
||||
* SMALLER - x(xcv1, ce1) < x(xcv2, ce2);
|
||||
* EQUAL - x(xcv1, ce1) = x(xcv2, ce2);
|
||||
* LARGER - x(xcv1, ce1) > x(xcv2, ce2).
|
||||
* \pre the ce1 end of the line xcv1 lies on a boundary, implying
|
||||
* that xcv1 is vertical.
|
||||
* \pre the ce2 end of the line xcv2 lies on a boundary, implying
|
||||
* that xcv2 is vertical.
|
||||
*/
|
||||
Comparison_result operator()(const X_monotone_curve_2 & xcv1,
|
||||
Arr_curve_end /* ce1 */,
|
||||
const X_monotone_curve_2 & xcv2,
|
||||
Arr_curve_end /*! ce2 */) const
|
||||
{
|
||||
CGAL_precondition(! xcv1.is_degenerate());
|
||||
CGAL_precondition(! xcv2.is_degenerate());
|
||||
CGAL_precondition(xcv1.is_vertical());
|
||||
CGAL_precondition(xcv2.is_vertical());
|
||||
|
||||
const Kernel* kernel = m_traits;
|
||||
const Point_2 p = kernel->construct_point_2_object()(ORIGIN);
|
||||
return (kernel->compare_x_at_y_2_object()(p, xcv1.supp_line(),
|
||||
xcv2.supp_line()));
|
||||
}
|
||||
};
|
||||
|
||||
/*! Obtain a Compare_x_at_limit_2 function object */
|
||||
Compare_x_at_limit_2 compare_x_at_limit_2_object() const
|
||||
{ return Compare_x_at_limit_2(this); }
|
||||
|
||||
/*! A function object that compares the x-coordinates of arc ends near the
|
||||
* boundary of the parameter space
|
||||
*/
|
||||
class Compare_x_near_limit_2 {
|
||||
public:
|
||||
|
||||
/*! Compare the x-coordinates of 2 arcs ends near the boundary of the
|
||||
* parameter space at y = +/- oo.
|
||||
* \param xcv1 the first arc.
|
||||
@@ -1172,54 +1108,38 @@ public:
|
||||
* SMALLER - x(xcv1, ce1) < x(xcv2, ce2);
|
||||
* EQUAL - x(xcv1, ce1) = x(xcv2, ce2);
|
||||
* LARGER - x(xcv1, ce1) > x(xcv2, ce2).
|
||||
* \pre the ce end of the line xcv1 lies on a boundary, implying
|
||||
* that xcv1 is vertical.
|
||||
* \pre the ce end of the line xcv2 lies on a boundary, implying
|
||||
* that xcv2 is vertical.
|
||||
* \pre the the $x$-coordinates of xcv1 and xcv2 at their ce ends are
|
||||
* equal, implying that the curves overlap!
|
||||
* \pre the ce1 end of the line xcv1 lies on a boundary.
|
||||
* \pre the ce2 end of the line xcv2 lies on a boundary.
|
||||
*/
|
||||
Comparison_result
|
||||
operator()(const X_monotone_curve_2& CGAL_precondition_code(xcv1),
|
||||
const X_monotone_curve_2& CGAL_precondition_code(xcv2),
|
||||
Arr_curve_end /*! ce2 */) const
|
||||
Comparison_result operator()(const X_monotone_curve_2 & xcv1,
|
||||
Arr_curve_end /* ce1 */,
|
||||
const X_monotone_curve_2 & xcv2,
|
||||
Arr_curve_end /*! ce2 */) const
|
||||
{
|
||||
CGAL_precondition(! xcv1.is_degenerate());
|
||||
CGAL_precondition(! xcv2.is_degenerate());
|
||||
CGAL_precondition(xcv1.is_vertical());
|
||||
CGAL_precondition(xcv2.is_vertical());
|
||||
return EQUAL;
|
||||
CGAL_precondition (! xcv1.is_degenerate());
|
||||
CGAL_precondition (! xcv2.is_degenerate());
|
||||
CGAL_precondition (xcv1.is_vertical());
|
||||
CGAL_precondition (xcv2.is_vertical());
|
||||
|
||||
Kernel kernel;
|
||||
typename Kernel::Point_2 p = kernel.construct_point_2_object() (ORIGIN);
|
||||
return (kernel.compare_x_at_y_2_object() (p,
|
||||
xcv1.supp_line(),
|
||||
xcv2.supp_line()));
|
||||
}
|
||||
};
|
||||
|
||||
/*! Obtain a Compare_x_near_limit_2 function object */
|
||||
Compare_x_near_limit_2 compare_x_near_limit_2_object() const
|
||||
{ return Compare_x_near_limit_2(); }
|
||||
/*! Obtain a Compare_x_near_boundary_2 function object */
|
||||
Compare_x_near_boundary_2 compare_x_near_boundary_2_object() const
|
||||
{ return Compare_x_near_boundary_2(); }
|
||||
|
||||
|
||||
/*! A function object that compares the y-limits of arc ends on the
|
||||
/*! A function object that compares the y-coordinates of arc ends near the
|
||||
* boundary of the parameter space.
|
||||
*/
|
||||
class Compare_y_near_boundary_2 {
|
||||
protected:
|
||||
typedef Arr_linear_traits_2<Kernel> Traits;
|
||||
|
||||
/*! The traits (in case it has state) */
|
||||
const Traits* m_traits;
|
||||
|
||||
/*! Constructor
|
||||
* \param traits the traits (in case it has state)
|
||||
* The constructor is declared private to allow only the functor
|
||||
* obtaining function, which is a member of the nesting class,
|
||||
* constructing it.
|
||||
*/
|
||||
Compare_y_near_boundary_2(const Traits* traits) : m_traits(traits) {}
|
||||
|
||||
//! Allow its functor obtaining function calling the private constructor.
|
||||
friend class Arr_linear_traits_2<Kernel>;
|
||||
|
||||
public:
|
||||
/*! Compare the y-limits of 2 lines at their ends on the boundary
|
||||
/*! Compare the y-coordinates of 2 lines at their ends near the boundary
|
||||
* of the parameter space at x = +/- oo.
|
||||
* \param xcv1 the first arc.
|
||||
* \param xcv2 the second arc.
|
||||
@@ -1233,38 +1153,42 @@ public:
|
||||
Arr_curve_end ce) const
|
||||
{
|
||||
// Make sure both curves are defined at x = -oo (or at x = +oo).
|
||||
CGAL_precondition(! xcv1.is_degenerate());
|
||||
CGAL_precondition(! xcv2.is_degenerate());
|
||||
CGAL_precondition((ce == ARR_MIN_END &&
|
||||
xcv1.left_infinite_in_x() == ARR_LEFT_BOUNDARY &&
|
||||
xcv2.left_infinite_in_x() == ARR_LEFT_BOUNDARY) ||
|
||||
(ce == ARR_MAX_END &&
|
||||
xcv1.right_infinite_in_x() == ARR_RIGHT_BOUNDARY &&
|
||||
xcv2.right_infinite_in_x() == ARR_RIGHT_BOUNDARY));
|
||||
CGAL_precondition (! xcv1.is_degenerate());
|
||||
CGAL_precondition (! xcv2.is_degenerate());
|
||||
CGAL_precondition ((ce == ARR_MIN_END &&
|
||||
xcv1.left_infinite_in_x() == ARR_LEFT_BOUNDARY &&
|
||||
xcv2.left_infinite_in_x() == ARR_LEFT_BOUNDARY) ||
|
||||
(ce == ARR_MAX_END &&
|
||||
xcv1.right_infinite_in_x() == ARR_RIGHT_BOUNDARY &&
|
||||
xcv2.right_infinite_in_x() == ARR_RIGHT_BOUNDARY));
|
||||
|
||||
// Compare the slopes of the two supporting lines.
|
||||
const Kernel* kernel = m_traits;
|
||||
const Comparison_result res_slopes =
|
||||
kernel->compare_slope_2_object()(xcv1.supp_line(), xcv2.supp_line());
|
||||
Kernel kernel;
|
||||
const Comparison_result res_slopes =
|
||||
kernel.compare_slope_2_object() (xcv1.supp_line(), xcv2.supp_line());
|
||||
|
||||
if (res_slopes == EQUAL) {
|
||||
// In case the two supporting line are parallel, compare their
|
||||
// relative position at x = 0, which is the same as their position
|
||||
// at infinity.
|
||||
const Point_2 p = kernel->construct_point_2_object()(ORIGIN);
|
||||
return (kernel->compare_y_at_x_2_object()(p, xcv1.supp_line(),
|
||||
typename Kernel::Point_2 p = kernel.construct_point_2_object() (ORIGIN);
|
||||
return (kernel.compare_y_at_x_2_object() (p,
|
||||
xcv1.supp_line(),
|
||||
xcv2.supp_line()));
|
||||
}
|
||||
|
||||
// Flip the slope result if we compare at x = -oo:
|
||||
return (ce == ARR_MIN_END) ? CGAL::opposite(res_slopes) : res_slopes;
|
||||
if (ce == ARR_MIN_END)
|
||||
// Flip the slope result if we compare at x = -oo:
|
||||
return ((res_slopes == LARGER) ? SMALLER : LARGER);
|
||||
|
||||
// If we compare at x = +oo, the slope result is what we need:
|
||||
return (res_slopes);
|
||||
}
|
||||
};
|
||||
|
||||
|
||||
/*! Obtain a Compare_y_limit_on_boundary_2 function object */
|
||||
/*! Obtain a Compare_y_near_boundary_2 function object */
|
||||
Compare_y_near_boundary_2 compare_y_near_boundary_2_object() const
|
||||
{ return Compare_y_near_boundary_2(this); }
|
||||
{ return Compare_y_near_boundary_2(); }
|
||||
|
||||
//@}
|
||||
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2006,2007,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2005 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2005,2006,2007,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2005 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
@@ -69,10 +69,10 @@ public:
|
||||
typedef Tag_true Has_left_category;
|
||||
typedef Tag_false Has_do_intersect_category;
|
||||
|
||||
typedef Arr_oblivious_side_tag Left_side_category;
|
||||
typedef Arr_oblivious_side_tag Bottom_side_category;
|
||||
typedef Arr_oblivious_side_tag Top_side_category;
|
||||
typedef Arr_oblivious_side_tag Right_side_category;
|
||||
typedef Arr_oblivious_side_tag Arr_left_side_category;
|
||||
typedef Arr_oblivious_side_tag Arr_bottom_side_category;
|
||||
typedef Arr_oblivious_side_tag Arr_top_side_category;
|
||||
typedef Arr_oblivious_side_tag Arr_right_side_category;
|
||||
|
||||
/*! Default Constructor */
|
||||
Arr_non_caching_segment_basic_traits_2()
|
||||
@@ -136,6 +136,10 @@ public:
|
||||
Kernel kernel;
|
||||
|
||||
// The two segments must be defined at q and also to its left.
|
||||
CGAL_precondition_code(
|
||||
Compare_y_at_x_2 compare_y_at_x = kernel.compare_y_at_x_2_object();
|
||||
);
|
||||
|
||||
CGAL_precondition
|
||||
(Segment_assertions::_assert_is_point_on(p, cv1, Has_exact_division())&&
|
||||
Segment_assertions::_assert_is_point_on(p, cv2, Has_exact_division()));
|
||||
@@ -196,6 +200,10 @@ public:
|
||||
Kernel kernel;
|
||||
|
||||
// The two segments must be defined at q and also to its right.
|
||||
CGAL_precondition_code(
|
||||
Compare_y_at_x_2 compare_y_at_x = kernel.compare_y_at_x_2_object();
|
||||
);
|
||||
|
||||
CGAL_precondition
|
||||
(Segment_assertions::_assert_is_point_on(p, cv1, Has_exact_division())&&
|
||||
Segment_assertions::_assert_is_point_on(p, cv2, Has_exact_division()));
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2006,2007,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2005 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
@@ -62,10 +62,10 @@ public:
|
||||
typedef typename Base::Has_left_category Has_left_category;
|
||||
typedef typename Base::Has_do_intersect_category Has_do_intersect_category;
|
||||
|
||||
typedef typename Base::Left_side_category Left_side_category;
|
||||
typedef typename Base::Bottom_side_category Bottom_side_category;
|
||||
typedef typename Base::Top_side_category Top_side_category;
|
||||
typedef typename Base::Right_side_category Right_side_category;
|
||||
typedef typename Base::Arr_left_side_category Arr_left_side_category;
|
||||
typedef typename Base::Arr_bottom_side_category Arr_bottom_side_category;
|
||||
typedef typename Base::Arr_top_side_category Arr_top_side_category;
|
||||
typedef typename Base::Arr_right_side_category Arr_right_side_category;
|
||||
|
||||
typedef typename Base::Point_2 Point_2;
|
||||
typedef typename Base::X_monotone_curve_2 X_monotone_curve_2;
|
||||
@@ -168,6 +168,7 @@ public:
|
||||
// Make sure that p lies on the interior of the curve.
|
||||
CGAL_precondition_code (
|
||||
Compare_xy_2 compare_xy = base.compare_xy_2_object();
|
||||
Compare_y_at_x_2 compare_y_at_x = base.compare_y_at_x_2_object();
|
||||
);
|
||||
|
||||
Construct_min_vertex_2 min_vertex = base.construct_min_vertex_2_object();
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2006,2007,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2005 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2007,2009,2011 Max-Planck-Institute for Computer Science (Germany).
|
||||
// Copyright (c) 2007 Max-Planck-Institute for Computer Science (Germany).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2005,2006,2007,2008,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2005 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
|
||||
+55
-208
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2006,2007,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2005 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
@@ -62,14 +62,14 @@ public:
|
||||
typedef typename Base_traits_2::Has_do_intersect_category
|
||||
Has_do_intersect_category;
|
||||
|
||||
typedef typename internal::Arr_complete_left_side_category< Base_traits_2 >::Category
|
||||
Left_side_category;
|
||||
typedef typename internal::Arr_complete_bottom_side_category< Base_traits_2 >::Category
|
||||
Bottom_side_category;
|
||||
typedef typename internal::Arr_complete_top_side_category< Base_traits_2 >::Category
|
||||
Top_side_category;
|
||||
typedef typename internal::Arr_complete_right_side_category< Base_traits_2 >::Category
|
||||
Right_side_category;
|
||||
typedef typename internal::Arr_complete_left_side_tag< Base_traits_2 >::Tag
|
||||
Arr_left_side_category;
|
||||
typedef typename internal::Arr_complete_bottom_side_tag< Base_traits_2 >::Tag
|
||||
Arr_bottom_side_category;
|
||||
typedef typename internal::Arr_complete_top_side_tag< Base_traits_2 >::Tag
|
||||
Arr_top_side_category;
|
||||
typedef typename internal::Arr_complete_right_side_tag< Base_traits_2 >::Tag
|
||||
Arr_right_side_category;
|
||||
|
||||
/* Overlay is implemented as sweep-line visitor. The sweep-line algorithm
|
||||
* never uses Compare_y_at_x_left_2, and it never performs merging of curves.
|
||||
@@ -577,86 +577,6 @@ public:
|
||||
return Parameter_space_in_x_2 (m_base_traits);
|
||||
}
|
||||
|
||||
|
||||
/*! A function object that determines whether an x-monotone curve or a
|
||||
* point coincide with the vertical identification curve.
|
||||
*/
|
||||
class Is_on_x_identification_2 {
|
||||
protected:
|
||||
//! The base traits.
|
||||
const Base_traits_2 *m_base;
|
||||
|
||||
/*! Constructor.
|
||||
* The constructor is declared private to allow only the functor
|
||||
* obtaining function, which is a member of the nesting class,
|
||||
* constructing it.
|
||||
*/
|
||||
Is_on_x_identification_2 (const Base_traits_2* tr) : m_base (tr) {}
|
||||
|
||||
//! Allow its functor obtaining function calling the private constructor.
|
||||
friend class Arr_batched_point_location_traits_2<Arrangement_2>;
|
||||
|
||||
public:
|
||||
bool operator() (const Point_2 & p) const
|
||||
{
|
||||
return m_base->is_on_x_identification_2_object() (p.base());
|
||||
}
|
||||
|
||||
bool operator() (const X_monotone_curve_2 & xcv) const
|
||||
{
|
||||
return m_base->is_on_x_identification_2_object() (xcv.base());
|
||||
}
|
||||
};
|
||||
|
||||
/*! Obtain a Is_on_x_identification_2 function object */
|
||||
Is_on_x_identification_2 is_on_x_identification_2_object () const
|
||||
{
|
||||
return Is_on_x_identification_2 (m_base_traits);
|
||||
}
|
||||
|
||||
/*! A functor that compares the y-coordinate of two given points
|
||||
* that lie on the vertical identification curve.
|
||||
*/
|
||||
class Compare_y_on_boundary_2 {
|
||||
protected:
|
||||
//! The base traits.
|
||||
const Base_traits_2 * m_base;
|
||||
|
||||
/*! Constructor.
|
||||
* \param tr The base traits class. It must be passed, to handle
|
||||
* non stateless traits (e.g., it stores data).
|
||||
* The constructor is declared private to allow only the functor
|
||||
* obtaining function, which is a member of the nesting class,
|
||||
* constructing it.
|
||||
*/
|
||||
Compare_y_on_boundary_2(const Base_traits_2 * tr) : m_base(tr) {}
|
||||
|
||||
//! Allow its functor obtaining function calling the private constructor.
|
||||
friend class Arr_batched_point_location_traits_2<Arrangement_2>;
|
||||
|
||||
public:
|
||||
Comparison_result operator()(const Point_2 & p1, const Point_2 & p2) const
|
||||
{
|
||||
return m_base->compare_x_on_boundary_2_object()(p1.base(), p2.base());
|
||||
}
|
||||
Comparison_result operator() (const Point_2 & pt,
|
||||
const X_monotone_curve_2& xcv, Arr_curve_end ce) const
|
||||
{
|
||||
return m_base->compare_x_on_boundary_2_object()(pt.base(), xcv.base(), ce);
|
||||
}
|
||||
Comparison_result operator() (const X_monotone_curve_2& xcv1, Arr_curve_end ce1,
|
||||
const X_monotone_curve_2& xcv2, Arr_curve_end ce2) const
|
||||
{
|
||||
return m_base->compare_x_on_boundary_2_object()(xcv1.base(), ce1, xcv2.base(), ce2);
|
||||
}
|
||||
};
|
||||
|
||||
/*! Obtain a Compare_y_on_boundary_2 functor object. */
|
||||
Compare_y_on_boundary_2 compare_y_on_boundary_2_object () const
|
||||
{
|
||||
return Compare_y_on_boundary_2(m_base_traits);
|
||||
}
|
||||
|
||||
/*! A function object that compares the y-coordinates of curve ends near the
|
||||
* boundary of the parameter space
|
||||
*/
|
||||
@@ -695,6 +615,41 @@ public:
|
||||
return Compare_y_near_boundary_2(m_base_traits);
|
||||
}
|
||||
|
||||
/*! A functor that compares the y-coordinate of two given points
|
||||
* that lie on the vertical identification curve.
|
||||
*/
|
||||
class Compare_y_on_boundary_2 {
|
||||
protected:
|
||||
//! The base traits.
|
||||
const Base_traits_2 * m_base;
|
||||
|
||||
/*! Constructor.
|
||||
* \param tr The base traits class. It must be passed, to handle
|
||||
* non stateless traits (e.g., it stores data).
|
||||
* The constructor is declared private to allow only the functor
|
||||
* obtaining function, which is a member of the nesting class,
|
||||
* constructing it.
|
||||
*/
|
||||
Compare_y_on_boundary_2(const Base_traits_2 * tr) : m_base(tr) {}
|
||||
|
||||
//! Allow its functor obtaining function calling the private constructor.
|
||||
friend class Arr_batched_point_location_traits_2<Arrangement_2>;
|
||||
|
||||
public:
|
||||
Comparison_result operator()(const Point_2 & p1, const Point_2 & p2) const
|
||||
{
|
||||
return m_base->compare_x_on_boundary_2_object()(p1.base(), p2.base());
|
||||
}
|
||||
};
|
||||
|
||||
/*! Obtain a Compare_y_on_boundary_2 functor object. */
|
||||
Compare_y_on_boundary_2 compare_y_on_boundary_2_object () const
|
||||
{
|
||||
return Compare_y_on_boundary_2(m_base_traits);
|
||||
}
|
||||
|
||||
// TODO Is_on_x_identification_2
|
||||
|
||||
// bottom-top
|
||||
|
||||
/*! A functor that determines whether an endpoint of an x-monotone arc lies
|
||||
@@ -740,46 +695,10 @@ public:
|
||||
return Parameter_space_in_y_2 (m_base_traits);
|
||||
}
|
||||
|
||||
/*! A function object that determines whether an x-monotone curve or a
|
||||
* point coincide with the horizontal identification curve.
|
||||
*/
|
||||
class Is_on_y_identification_2 {
|
||||
protected:
|
||||
//! The base traits.
|
||||
const Base_traits_2 *m_base;
|
||||
|
||||
/*! Constructor.
|
||||
* The constructor is declared private to allow only the functor
|
||||
* obtaining function, which is a member of the nesting class,
|
||||
* constructing it.
|
||||
*/
|
||||
Is_on_y_identification_2 (const Base_traits_2* tr) : m_base (tr) {}
|
||||
|
||||
//! Allow its functor obtaining function calling the private constructor.
|
||||
friend class Arr_batched_point_location_traits_2<Arrangement_2>;
|
||||
|
||||
public:
|
||||
bool operator() (const Point_2 & p) const
|
||||
{
|
||||
return m_base->is_on_y_identification_2_object() (p.base());
|
||||
}
|
||||
|
||||
bool operator() (const X_monotone_curve_2 & xcv) const
|
||||
{
|
||||
return m_base->is_on_y_identification_2_object() (xcv.base());
|
||||
}
|
||||
};
|
||||
|
||||
/*! Obtain a Is_on_y_identification_2 function object */
|
||||
Is_on_y_identification_2 is_on_y_identification_2_object () const
|
||||
{
|
||||
return Is_on_y_identification_2 (m_base_traits);
|
||||
}
|
||||
|
||||
/*! A functor that compares the x-limits of curve ends on the
|
||||
/*! A functor that compares the x-coordinates of curve ends near the
|
||||
* boundary of the parameter space.
|
||||
*/
|
||||
class Compare_x_at_limit_2 {
|
||||
class Compare_x_near_boundary_2 {
|
||||
protected:
|
||||
//! The base traits.
|
||||
const Base_traits_2 * m_base;
|
||||
@@ -791,7 +710,7 @@ public:
|
||||
* obtaining function, which is a member of the nesting class,
|
||||
* constructing it.
|
||||
*/
|
||||
Compare_x_at_limit_2(const Base_traits_2 * tr) : m_base(tr) {}
|
||||
Compare_x_near_boundary_2(const Base_traits_2 * tr) : m_base(tr) {}
|
||||
|
||||
//! Allow its functor obtaining function calling the private constructor.
|
||||
friend class Arr_batched_point_location_traits_2<Arrangement_2>;
|
||||
@@ -801,8 +720,8 @@ public:
|
||||
const X_monotone_curve_2 & xcv,
|
||||
Arr_curve_end ce) const
|
||||
{
|
||||
return m_base->compare_x_at_limit_2_object()(p.base(),
|
||||
xcv.base(), ce);
|
||||
return m_base->compare_x_near_boundary_2_object()(p.base(),
|
||||
xcv.base(), ce);
|
||||
}
|
||||
|
||||
Comparison_result operator()(const X_monotone_curve_2 & xcv1,
|
||||
@@ -810,52 +729,15 @@ public:
|
||||
const X_monotone_curve_2 & xcv2,
|
||||
Arr_curve_end ce2) const
|
||||
{
|
||||
return m_base->compare_x_at_limit_2_object()(xcv1.base(), ce1,
|
||||
xcv2.base(), ce2);
|
||||
return m_base->compare_x_near_boundary_2_object()(xcv1.base(), ce1,
|
||||
xcv2.base(), ce2);
|
||||
}
|
||||
};
|
||||
|
||||
/*! Obtain a Compare_x_at_limit_2 function object. */
|
||||
Compare_x_at_limit_2 compare_x_at_limit_2_object () const
|
||||
/*! Obtain a Compare_x_near_boundary_2 function object. */
|
||||
Compare_x_near_boundary_2 compare_x_near_boundary_2_object () const
|
||||
{
|
||||
return Compare_x_at_limit_2(m_base_traits);
|
||||
}
|
||||
|
||||
/*! A functor that compares the x-coordinates of curve ends near the
|
||||
* boundary of the parameter space.
|
||||
*/
|
||||
class Compare_x_near_limit_2 {
|
||||
protected:
|
||||
//! The base traits.
|
||||
const Base_traits_2 * m_base;
|
||||
|
||||
/*! Constructor.
|
||||
* \param tr The base traits class. It must be passed, to handle
|
||||
* non stateless traits (e.g., it stores data).
|
||||
* The constructor is declared private to allow only the functor
|
||||
* obtaining function, which is a member of the nesting class,
|
||||
* constructing it.
|
||||
*/
|
||||
Compare_x_near_limit_2(const Base_traits_2 * tr) : m_base(tr) {}
|
||||
|
||||
//! Allow its functor obtaining function calling the private constructor.
|
||||
friend class Arr_batched_point_location_traits_2<Arrangement_2>;
|
||||
|
||||
public:
|
||||
Comparison_result operator()(const X_monotone_curve_2 & xcv1,
|
||||
const X_monotone_curve_2 & xcv2,
|
||||
Arr_curve_end ce) const
|
||||
{
|
||||
return m_base->compare_x_near_limit_2_object()(xcv1.base(),
|
||||
xcv2.base(),
|
||||
ce);
|
||||
}
|
||||
};
|
||||
|
||||
/*! Obtain a Compare_x_near_limit_2 function object. */
|
||||
Compare_x_near_limit_2 compare_x_near_limit_2_object () const
|
||||
{
|
||||
return Compare_x_near_limit_2(m_base_traits);
|
||||
return Compare_x_near_boundary_2(m_base_traits);
|
||||
}
|
||||
|
||||
/*! A functor that compares the x-coordinate of two given points
|
||||
@@ -891,42 +773,7 @@ public:
|
||||
return Compare_x_on_boundary_2(m_base_traits);
|
||||
}
|
||||
|
||||
/*! A functor that compares the x-coordinates of curve ends near the
|
||||
* boundary of the parameter space.
|
||||
*/
|
||||
class Compare_x_near_boundary_2 {
|
||||
protected:
|
||||
//! The base traits.
|
||||
const Base_traits_2 * m_base;
|
||||
|
||||
/*! Constructor.
|
||||
* \param tr The base traits class. It must be passed, to handle
|
||||
* non stateless traits (e.g., it stores data).
|
||||
* The constructor is declared private to allow only the functor
|
||||
* obtaining function, which is a member of the nesting class,
|
||||
* constructing it.
|
||||
*/
|
||||
Compare_x_near_boundary_2(const Base_traits_2 * tr) : m_base(tr) {}
|
||||
|
||||
//! Allow its functor obtaining function calling the private constructor.
|
||||
friend class Arr_batched_point_location_traits_2<Arrangement_2>;
|
||||
|
||||
public:
|
||||
Comparison_result operator()(const X_monotone_curve_2 & xcv1,
|
||||
const X_monotone_curve_2 & xcv2,
|
||||
Arr_curve_end ce) const
|
||||
{
|
||||
return m_base->compare_x_near_boundary_2_object()(xcv1.base(),
|
||||
xcv2.base(),
|
||||
ce);
|
||||
}
|
||||
};
|
||||
|
||||
/*! Obtain a Compare_x_near_boundary_2 function object. */
|
||||
Compare_x_near_boundary_2 compare_x_near_boundary_2_object () const
|
||||
{
|
||||
return Compare_x_near_boundary_2(m_base_traits);
|
||||
}
|
||||
// TODO Is_on_y_identification_2
|
||||
|
||||
};
|
||||
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2005,2007,2008,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2005 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2007,2008,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2005 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2005,2006,2007,2008,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2005 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2005,2006,2007,2008,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2005 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
|
||||
+1
-1
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2005,2006,2007,2008,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2005 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2007,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2005 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
@@ -131,8 +131,6 @@ public:
|
||||
*/
|
||||
struct Construct_coord_iterator
|
||||
{
|
||||
typedef const ANT* result_type;
|
||||
|
||||
/*! Get an iterator for the approximate coordinates. */
|
||||
const ANT* operator() (const NN_Point_2& nnp) const
|
||||
{
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2005,2006,2007,2008,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2005 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
|
||||
+1
-1
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2005,2008,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2005 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
|
||||
+1
-1
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2005,2006,2007,2008,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2005 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
|
||||
+1
-1
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2006,2007,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2005 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
|
||||
+7
-1
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2006,2007,2008,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2005 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
@@ -122,6 +122,10 @@ Object Arr_simple_point_location<Arrangement>::_base_vertical_ray_shoot
|
||||
const Comparison_result curve_above_under = (shoot_up ? LARGER : SMALLER);
|
||||
|
||||
// Go over all halfedges in the arrangement.
|
||||
typename Traits_adaptor_2::Is_in_x_range_2 is_in_x_range =
|
||||
geom_traits->is_in_x_range_2_object();
|
||||
typename Traits_adaptor_2::Compare_y_at_x_2 compare_y_at_x =
|
||||
geom_traits->compare_y_at_x_2_object();
|
||||
typename Traits_adaptor_2::Is_vertical_2 is_vertical =
|
||||
geom_traits->is_vertical_2_object();
|
||||
typename Traits_adaptor_2::Compare_y_position_2 compare_y_position =
|
||||
@@ -130,6 +134,8 @@ Object Arr_simple_point_location<Arrangement>::_base_vertical_ray_shoot
|
||||
geom_traits->compare_y_at_x_right_2_object();
|
||||
typename Traits_adaptor_2::Compare_y_at_x_left_2 compare_y_at_x_left =
|
||||
geom_traits->compare_y_at_x_left_2_object();
|
||||
typename Traits_adaptor_2::Compare_xy_2 compare_xy =
|
||||
geom_traits->compare_xy_2_object();
|
||||
|
||||
typename Dcel::Edge_const_iterator eit =
|
||||
top_traits->dcel().edges_begin();
|
||||
|
||||
+1
-1
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2005,2006,2007,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2005 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
|
||||
+1
-1
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2005,2006,2008,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2005 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
|
||||
+1
-1
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2005,2006,2007,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2005 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
|
||||
+1
-1
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2006,2007,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 2005 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2005,2006,2007,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 1997 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
// Copyright (c) 2005,2006,2007,2008,2009,2010,2011 Tel-Aviv University (Israel).
|
||||
// Copyright (c) 1997 Tel-Aviv University (Israel).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you may redistribute it under
|
||||
|
||||
Some files were not shown because too many files have changed in this diff Show More
Reference in New Issue
Block a user