From dc0e8356004b20ead55dfd69caddc766dcb2636a Mon Sep 17 00:00:00 2001
From: Alec Jacobson <alecjacobson@gmail.com>
Date: Tue, 5 Apr 2016 10:23:06 -0400
Subject: [PATCH] facet orientation in tutorial

---
 tutorial/706_FacetOrientation/CMakeLists.txt |    8 +
 tutorial/706_FacetOrientation/main.cpp       |  108 +
 tutorial/CMakeLists.txt                      |    1 +
 tutorial/images/truck-facet-orientation.jpg  |  Bin 0 -> 1142411 bytes
 tutorial/shared/truck.obj                    | 7726 ++++++++++++++++++
 tutorial/tutorial.html                       |   59 +-
 tutorial/tutorial.md                         |   53 +-
 7 files changed, 7953 insertions(+), 2 deletions(-)
 create mode 100644 tutorial/706_FacetOrientation/CMakeLists.txt
 create mode 100755 tutorial/706_FacetOrientation/main.cpp
 create mode 100644 tutorial/images/truck-facet-orientation.jpg
 create mode 100644 tutorial/shared/truck.obj

diff --git a/tutorial/706_FacetOrientation/CMakeLists.txt b/tutorial/706_FacetOrientation/CMakeLists.txt
new file mode 100644
index 000000000..b61c5ba4c
--- /dev/null
+++ b/tutorial/706_FacetOrientation/CMakeLists.txt
@@ -0,0 +1,8 @@
+cmake_minimum_required(VERSION 2.8.12)
+project(706_FacetOrientation)
+
+add_executable(${PROJECT_NAME}_bin
+  main.cpp)
+target_include_directories(${PROJECT_NAME}_bin PRIVATE ${LIBIGL_INCLUDE_DIRS})
+target_compile_definitions(${PROJECT_NAME}_bin PRIVATE ${LIBIGL_DEFINITIONS})
+target_link_libraries(${PROJECT_NAME}_bin ${LIBIGL_LIBRARIES} ${LIBIGL_EXTRA_LIBRARIES})
diff --git a/tutorial/706_FacetOrientation/main.cpp b/tutorial/706_FacetOrientation/main.cpp
new file mode 100755
index 000000000..5a815d1f0
--- /dev/null
+++ b/tutorial/706_FacetOrientation/main.cpp
@@ -0,0 +1,108 @@
+
+#include <igl/read_triangle_mesh.h>
+#include <igl/embree/reorient_facets_raycast.h>
+#include <igl/randperm.h>
+#include <igl/orientable_patches.h>
+#include <igl/slice.h>
+#include <igl/hsv_to_rgb.h>
+#include <igl/viewer/Viewer.h>
+#include <fstream>
+#include <iostream>
+#include <string>
+igl::viewer::Viewer viewer;
+Eigen::MatrixXd V;
+std::vector<Eigen::VectorXi> C(2);
+std::vector<Eigen::MatrixXd> RGB(2);
+Eigen::MatrixXi F;
+std::vector<Eigen::MatrixXi> FF(2);
+bool is_showing_reoriented = false;
+bool facetwise = false;
+
+int main(int argc, char * argv[])
+{
+  using namespace std;
+  cout<<R"(
+Usage:
+
+[space]  Toggle between original and reoriented faces
+F,f      Toggle between patchwise and facetwise reorientation
+S,s      Scramble colors
+)";
+  igl::read_triangle_mesh(TUTORIAL_SHARED_PATH "/truck.obj",V,F);
+
+  const auto & scramble_colors = []()
+  {
+    for(int pass = 0;pass<2;pass++)
+    {
+      Eigen::MatrixXi R;
+      igl::randperm(C[pass].maxCoeff()+1,R);
+      C[pass] = igl::slice(R,Eigen::MatrixXi(C[pass]));
+      Eigen::MatrixXd HSV(C[pass].rows(),3);
+      HSV.col(0) = 
+        360.*C[pass].array().cast<double>()/(double)C[pass].maxCoeff();
+      HSV.rightCols(2).setConstant(1.0);
+      igl::hsv_to_rgb(HSV,RGB[pass]);
+    }
+    viewer.data.set_colors(RGB[facetwise]);
+  };
+
+  viewer.callback_key_pressed = 
+    [&scramble_colors]
+    (igl::viewer::Viewer& /*viewer*/, unsigned int key, int mod)->bool
+  {
+    switch(key)
+    {
+    default:
+      return false;
+    case 'F':
+    case 'f':
+    {
+      facetwise = !facetwise;
+      break;
+    }
+    case 'S':
+    case 's':
+    {
+      scramble_colors();
+      return true;
+    }
+    case ' ':
+    {
+      is_showing_reoriented = !is_showing_reoriented;
+      break;
+    }
+    }
+    viewer.data.clear();
+    viewer.data.set_mesh(V,is_showing_reoriented?FF[facetwise]:F);
+    viewer.data.set_colors(RGB[facetwise]);
+    return true;
+  };
+
+
+  // Compute patches
+  for(int pass = 0;pass<2;pass++)
+  {
+    Eigen::VectorXi I;
+    igl::embree::reorient_facets_raycast(
+      V,F,F.rows()*100,10,pass==1,false,false,I,C[pass]);
+    // apply reorientation
+    FF[pass].conservativeResize(F.rows(),F.cols());
+    for(int i = 0;i<I.rows();i++)
+    {
+      if(I(i))
+      {
+        FF[pass].row(i) = (F.row(i).reverse()).eval();
+      }else
+      {
+        FF[pass].row(i) = F.row(i);
+      }
+    }
+  }
+
+  viewer.data.set_mesh(V,is_showing_reoriented?FF[facetwise]:F);
+  viewer.data.set_face_based(true);
+  scramble_colors();
+  viewer.launch();
+}
+
+
diff --git a/tutorial/CMakeLists.txt b/tutorial/CMakeLists.txt
index 8d2d0087c..d09bad47e 100644
--- a/tutorial/CMakeLists.txt
+++ b/tutorial/CMakeLists.txt
@@ -156,6 +156,7 @@ if(TUTORIALS_CHAPTER6)
   if(LIBIGL_WITH_EMBREE)
     add_subdirectory("606_AmbientOcclusion")
     add_subdirectory("607_Picking")
+    add_subdirectory("706_FacetOrientation")
   endif()
   if(LIBIGL_WITH_LIM)
     add_subdirectory("608_LIM")
diff --git a/tutorial/images/truck-facet-orientation.jpg b/tutorial/images/truck-facet-orientation.jpg
new file mode 100644
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diff --git a/tutorial/tutorial.html b/tutorial/tutorial.html
index 2407e0ecd..a12cccc34 100644
--- a/tutorial/tutorial.html
+++ b/tutorial/tutorial.html
@@ -144,6 +144,7 @@ lecture notes links to a cross-platform example application.</p>
 <li><a href="#meshdecimation">703 Mesh Decimation</a></li>
 <li><a href="#signeddistances">704 Signed Distances</a></li>
 <li><a href="#marchingcubes">705 Marching Cubes</a></li>
+<li><a href="#facetorientation">706 Facet Orientation</a></li>
 </ul></li>
 <li><a href="#future">Chapter 8: Outlook for continuing development</a></li>
 </ul>
@@ -3303,6 +3304,55 @@ this signed distance field to an indicator function and contouring reveals
 serious aliasing artifacts.</figcaption>
 </figure>
 
+<h2 id="facetorientation">Facet Orientation</h2>
+
+<p>Models from the web occasionally arrive <em>unorientated</em> in the sense that
+the orderings of each triangles vertices do not consistently agree. Determining
+a consistent facet orientation for a mesh is essential for two-sided lighting
+(e.g., a cloth with red velvet on one side and gold silk on the other side) and
+for inside-outside determination(e.g., using <span class="externalcitation">[generalized winding
+numbers][#generalizedwindingnumber]</span>).</p>
+
+<p>For (open) surfaces representing two-sided sheets, libigl provides a routine to
+force consistent orientations within each orientable patch
+(<code>igl::orientable_patches</code>) of a mesh:</p>
+
+<pre><code class="cpp">igl::bfs_orient(F,FF,C);
+</code></pre>
+
+<p>This simple routine will use breadth-first search on each patch of the mesh to
+enforce a consistent facet orientation in the output faces <code>FF</code>.</p>
+
+<p>For (closed or nearly closed) surfaces representing the boundary of a solid
+object, libigl provides a routine to reorient faces so that the vertex ordering
+corresponds to a counter-clockwise ordering of the vertices with a
+right-hand-rule normal pointing outward. This method <a class="citation" href="#fn:39" title="Jump to citation">[39]<span class="citekey" style="display:none">takayama14</span></a> assumes
+that <a href="https://www.reddit.com/r/askscience/comments/32otgx/which_as_a_is_more_empty_an_atom_or_the_universe/">most of the universe is
+empty</a>.
+That is, most points in space are outside of the solid object than inside.
+Points are sampled over surface patches. For each sample point, rays are shot
+into both hemispheres to compute average of the (distance weighted) ambient
+occlusion on each side. A patch is oriented so that the outward side is <em>less
+occluded</em> (lighter, i.e., facing more void space).</p>
+
+<pre><code class="cpp">igl::embree::reorient_facets_raycast(V,F,FF,I);
+</code></pre>
+
+<p>The boolean vector <code>I</code> reveals which rows of <code>F</code> have been flipped in <code>FF</code>.</p>
+
+<figure>
+<img src="images/truck-facet-orientation.jpg" alt="(Example 706) loads a truck model with
+inconsistent orientations (back facing triangles shown darker). Orientable
+patches are uniquely colored and then oriented to face outward (middle left).
+Alternatively, each individual triangle is considered a patch (middle right)
+and oriented outward independently." />
+<figcaption>(<a href="706_FacetOrientation/main.cpp">Example 706</a>) loads a truck model with
+inconsistent orientations (back facing triangles shown darker). Orientable
+patches are uniquely colored and then oriented to face outward (middle left).
+Alternatively, each individual triangle is considered a &#8220;patch&#8221; (middle right)
+and oriented outward independently.</figcaption>
+</figure>
+
 <h1 id="future">Outlook for continuing development</h1>
 
 <p>Libigl is in active development, and we plan to focus on the following features
@@ -3414,7 +3464,7 @@ repository</a>.</p>
  2008.</p>
 </li>
 
-<li id="fn:15" class="citation"><span class="citekey" style="display:none">sorkine_2007</span><p>Olga Sorkine and Marc Alexa, <a href="https://www.google.com/search?q=As-rigid-as-possible+Surface+Modeling">As-rigid-as-possible Surface
+<li id="fn:15" class="citation"><span class="citekey" style="display:none">sorkine_2007</span><p>Olga Sorkine and Marc Alexa. <a href="https://www.google.com/search?q=As-rigid-as-possible+Surface+Modeling">As-rigid-as-possible Surface
  Modeling</a>, 2007.</p>
 </li>
 
@@ -3546,6 +3596,13 @@ pseudonormal</a>,
  1987.</p>
 </li>
 
+<li id="fn:39" class="citation"><span class="citekey" style="display:none">takayama14</span><p>Kenshi Takayama, Alec Jacobson, Ladislav Kavan, Olga
+ Sorkine-Hornung. <a href="https://www.google.com/search?q=A+Simple+Method+for+Correcting+Facet+Orientations+in+Polygon+Meshes+Based+on+Ray+Casting">A Simple Method for Correcting Facet Orientations in
+ Polygon Meshes Based on Ray
+ Casting</a>,
+ 2014.</p>
+</li>
+
 </ol>
 </div>
 
diff --git a/tutorial/tutorial.md b/tutorial/tutorial.md
index f600032cf..da82267bd 100644
--- a/tutorial/tutorial.md
+++ b/tutorial/tutorial.md
@@ -97,6 +97,7 @@ lecture notes links to a cross-platform example application.
     * [703 Mesh Decimation](#meshdecimation)
     * [704 Signed Distances](#signeddistances)
     * [705 Marching Cubes](#marchingcubes)
+    * [706 Facet Orientation](#facetorientation)
 * [Chapter 8: Outlook for continuing development](#future)
 
 # Chapter 1 [chapter1:introductiontolibigl]
@@ -2967,6 +2968,51 @@ marching cubes to contour the 0-level set (center). For comparison, clamping
 this signed distance field to an indicator function and contouring reveals
 serious aliasing artifacts.](images/armadillo-marching-cubes.jpg)
 
+## Facet Orientation [facetorientation]
+
+Models from the web occasionally arrive _unorientated_ in the sense that
+the orderings of each triangles vertices do not consistently agree. Determining
+a consistent facet orientation for a mesh is essential for two-sided lighting
+(e.g., a cloth with red velvet on one side and gold silk on the other side) and
+for inside-outside determination(e.g., using [generalized winding
+numbers][#generalizedwindingnumber]).
+
+For (open) surfaces representing two-sided sheets, libigl provides a routine to
+force consistent orientations within each orientable patch
+(`igl::orientable_patches`) of a mesh:
+
+```cpp
+igl::bfs_orient(F,FF,C);
+```
+
+This simple routine will use breadth-first search on each patch of the mesh to
+enforce a consistent facet orientation in the output faces `FF`.
+
+For (closed or nearly closed) surfaces representing the boundary of a solid
+object, libigl provides a routine to reorient faces so that the vertex ordering
+corresponds to a counter-clockwise ordering of the vertices with a
+right-hand-rule normal pointing outward. This method [#takayama14][] assumes
+that [most of the universe is
+empty](https://www.reddit.com/r/askscience/comments/32otgx/which_as_a_is_more_empty_an_atom_or_the_universe/).
+That is, most points in space are outside of the solid object than inside.
+Points are sampled over surface patches. For each sample point, rays are shot
+into both hemispheres to compute average of the (distance weighted) ambient
+occlusion on each side. A patch is oriented so that the outward side is _less
+occluded_ (lighter, i.e., facing more void space).
+
+```cpp
+igl::embree::reorient_facets_raycast(V,F,FF,I);
+```
+
+The boolean vector `I` reveals which rows of `F` have been flipped in `FF`.
+
+![([Example 706](706_FacetOrientation/main.cpp)) loads a truck model with
+inconsistent orientations (back facing triangles shown darker). Orientable
+patches are uniquely colored and then oriented to face outward (middle left).
+Alternatively, each individual triangle is considered a "patch" (middle right)
+and oriented outward independently.](images/truck-facet-orientation.jpg)
+
+
 # Outlook for continuing development [future]
 
 Libigl is in active development, and we plan to focus on the following features
@@ -3123,8 +3169,13 @@ pseudonormal](https://www.google.com/search?q=Signed+distance+computation+using+
 [#sorkine_2004]: Olga Sorkine, Yaron Lipman, Daniel Cohen-Or, Marc Alexa,
   Christian Rössl and Hans-Peter Seidel. [Laplacian Surface
   Editing](https://www.google.com/search?q=Laplacian+Surface+Editing), 2004.
-[#sorkine_2007]: Olga Sorkine and Marc Alexa, [As-rigid-as-possible Surface
+[#sorkine_2007]: Olga Sorkine and Marc Alexa. [As-rigid-as-possible Surface
   Modeling](https://www.google.com/search?q=As-rigid-as-possible+Surface+Modeling), 2007.
+[#takayama14]: Kenshi Takayama, Alec Jacobson, Ladislav Kavan, Olga
+  Sorkine-Hornung. [A Simple Method for Correcting Facet Orientations in
+  Polygon Meshes Based on Ray
+  Casting](https://www.google.com/search?q=A+Simple+Method+for+Correcting+Facet+Orientations+in+Polygon+Meshes+Based+on+Ray+Casting),
+  2014.
 [#vallet_2008]: Bruno Vallet and Bruno Lévy. [Spectral Geometry Processing with
   Manifold
   Harmonics](https://www.google.com/search?q=Spectral+Geometry+Processing+with+Manifold+Harmonics),