changed 'well known' to 'well-known'
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@@ -24,7 +24,7 @@ allows an explicit handling of mixed operations.
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\section Algebraic_foundationsAlgebraic Algebraic Structures
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The algebraic structure concepts introduced within this section are
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motivated by their well known counterparts in traditional algebra,
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motivated by their well-known counterparts in traditional algebra,
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but we also had to pay tribute to existing types and their restrictions.
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To keep the interface minimal,
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it was not desirable to cover all known algebraic structures,
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@@ -69,7 +69,7 @@ their existence, the usual arithmetic and comparison operators are required
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to be realized via \cpp operator overloading.
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The division operator is reserved for division in fields.
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All other unary (e.g., sqrt) and binary functions
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(e.g., gcd, div) must be models of the well known \stl-concepts
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(e.g., gcd, div) must be models of the well-known \stl-concepts
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`AdaptableUnaryFunction` or `AdaptableBinaryFunction`
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concept and local to the traits class
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(e.g., \link AlgebraicStructureTraits::Sqrt `Algebraic_structure_traits<AS>::Sqrt()(x)` \endlink).
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@@ -285,7 +285,7 @@ The `Vertex_conflict_2` predicate. The left-most, bottom-most and top-most circl
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What we essentially want to compute when we construct incrementally a
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Voronoi diagram, is whether the object to be inserted destroys an edge
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of the Voronoi diagram or not. In the case of points this is really
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easy and it amounts to the well known <I>incircle</I> test.
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easy and it amounts to the well-known <I>incircle</I> test.
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In the case
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of circles the situation is more complicated. We can have six possible
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outcomes as to what portion of an edge of the Apollonius diagram the
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@@ -146051,7 +146051,7 @@ of geometric optics."
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, year = 1993
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, pages = "37--42"
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, keywords = "travelling salesman problem, heuristic, approximation algorithms, convex hulls"
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, comments = "It is well known that the nearest insertion and cheapest
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, comments = "It is well-known that the nearest insertion and cheapest
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insertion are a factor 2 apx for TSP, and this is tight.
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Interestingly, for pts in the plane, if you start with a tour
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consisting of the convex hull vertices, and continue with nearest or
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@@ -257,7 +257,7 @@ const Face& f);
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/*! \name Modifying Functions (Euler Operators)
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The following Euler operations modify consistently the combinatorial
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structure of the halfedge data structure. The geometry remains unchanged.
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Note that well known graph operations are also captured with these
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Note that well-known graph operations are also captured with these
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Euler operators, for example an edge contraction is equal to a
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`join_vertex()` operation, or an edge removal to `join_face()`.
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@@ -235,7 +235,7 @@ public:
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// The following Euler operations modify consistently the combinatorial
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// structure of the halfedge data structure. The geometry remains
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// unchanged. Note that well known graph operations are also captured with
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// unchanged. Note that well-known graph operations are also captured with
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// these Euler operators, for example an edge contraction is equal to a
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// `join_vertex()' operation, or an edge removal to `join_face()'.
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//
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@@ -5469,7 +5469,7 @@ The following functionality has been added or changed:
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bounding boxes of more complicated geometries. Useful for (self-)
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intersection tests of surfaces etc.
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- 2D Snap Rounding (new package)
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Snap Rounding is a well known method for converting
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Snap Rounding is a well-known method for converting
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arbitrary-precision arrangements of segments into a fixed-precision
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representation. In the study of robust geometric computing, it can
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be classified as a finite precision approximation technique.
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@@ -219,7 +219,7 @@ diagram. The points defining the power diagram are the projections of
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the points in \f$ \mathcal{P}\f$ onto \f$ \mathcal{H}\f$, each point weighted
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with its negative square distance to \f$ \mathcal{H}\f$. Algorithms for the
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computation of power diagrams via the dual regular triangulation are
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well known and for example provided by \cgal in the class
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well-known and for example provided by \cgal in the class
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`Regular_triangulation_2<Gt, Tds>`.
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\subsection InterpolationImplementation_1 Implementation
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@@ -37,7 +37,7 @@ will be `(w,0)`.
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\param number_of_kd_trees The seventh parameter is briefly described later on this page; for a
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detailed description see \cgalCite{cgal:hp-isr-02}.
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Snap Rounding (SR, for short) is a well known method for converting
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Snap Rounding (SR, for short) is a well-known method for converting
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arbitrary-precision arrangements of segments into a fixed-precision
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representation \cgalCite{gght-srlse-97}, \cgalCite{gm-rad-98}, \cgalCite{h-psifp-99}. In
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the study of robust geometric computing, it can be classified as a
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@@ -7,7 +7,7 @@
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\cgalPkgPicture{snap-detail.png}
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\cgalPkgSummaryBegin
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\cgalPkgAuthor{Eli Packer}
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\cgalPkgDesc{Snap Rounding is a well known method for converting arbitrary-precision arrangements of segments into a fixed-precision representation. In the study of robust geometric computing, it can be classified as a finite precision approximation technique. Iterated Snap Rounding is a modification of Snap Rounding in which each vertex is at least half-the-width-of-a-pixel away from any non-incident edge. This package supports both methods.}
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\cgalPkgDesc{Snap Rounding is a well-known method for converting arbitrary-precision arrangements of segments into a fixed-precision representation. In the study of robust geometric computing, it can be classified as a finite precision approximation technique. Iterated Snap Rounding is a modification of Snap Rounding in which each vertex is at least half-the-width-of-a-pixel away from any non-incident edge. This package supports both methods.}
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\cgalPkgManuals{Chapter_2D_Snap_Rounding,PkgSnapRounding2Ref}
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\cgalPkgSummaryEnd
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\cgalPkgShortInfoBegin
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@@ -10,7 +10,7 @@ namespace CGAL {
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\section Snap_rounding_2Introduction Introduction
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Snap Rounding (SR, for short) is a well known method for converting
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Snap Rounding (SR, for short) is a well-known method for converting
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arbitrary-precision arrangements of segments into a fixed-precision
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representation \cgalCite{gght-srlse-97}, \cgalCite{gm-rad-98}, \cgalCite{h-psifp-99}. In
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the study of robust geometric computing, it can be classified
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@@ -1,4 +1,4 @@
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Snap Rounding (SR, for short) is a well known method for converting
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Snap Rounding (SR, for short) is a well-known method for converting
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arbitrary-precision arrangements of segments into a fixed-precision
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representation [Good,Guib,Hobb]. In the study of robust geometric
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computing, it can be classified as a finite precision approximation
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