gaussian curvature example in tutorial

Former-commit-id: b887e5239c0b85348aaedf91ce3e7d46ec68a313

include/igl/jet.cpp

@@ -60,7 +60,7 @@ IGL_INLINE void igl::jet(const T x, T * rgb)
 }
 
 template <typename T>
-IGL_INLINE void igl::jet(const T x, T & r, T & g, T & b)
+IGL_INLINE void igl::jet(const T x_in, T & r, T & g, T & b)
 {
   // Only important if the number of colors is small. In which case the rest is
   // still wrong anyway
@@ -69,6 +69,8 @@ IGL_INLINE void igl::jet(const T x, T & r, T & g, T & b)
   const double rone = 0.8;
   const double gone = 1.0;
   const double bone = 1.0;
+  T x = x_in;
+  x = (x_in<0?0:(x>1?1:x));
 
   if(x<1./8.)
   {
@@ -98,6 +100,21 @@ IGL_INLINE void igl::jet(const T x, T & r, T & g, T & b)
   }
 }
 
+template <typename DerivedZ, typename DerivedC>
+IGL_INLINE void igl::jet(
+  const Eigen::PlainObjectBase<DerivedZ> & Z,
+  const bool normalize,
+  Eigen::PlainObjectBase<DerivedC> & C)
+{
+  C.resize(Z.rows(),3);
+  const double min_z = (normalize?Z.minCoeff():0);
+  const double max_z = (normalize?Z.maxCoeff():-1);
+  for(int r = 0;r<Z.rows();r++)
+  {
+    jet((Z(r,0)-min_z)/(max_z-min_z),C(r,0),C(r,1),C(r,2));
+  }
+}
+
 #ifndef IGL_NO_HEADER
 template void igl::jet<double>(double, double*);
 template void igl::jet<double>(double, double&, double&, double&);

include/igl/jet.h

@@ -9,7 +9,7 @@
 #define IGL_JET_H
 #include "igl_inline.h"
 //#ifndef IGL_NO_EIGEN
-//#  include <Eigen/Dense>
+#  include <Eigen/Dense>
 //#endif
 namespace igl
 {
@@ -36,6 +36,16 @@ namespace igl
   IGL_INLINE void jet(const T f, T * rgb);
   template <typename T>
   IGL_INLINE void jet(const T f, T & r, T & g, T & b);
+  // Inputs:
+  //   Z  #Z list of factos 
+  //   normalize  whether to normalize Z to be tightly between [0,1]
+  // Outputs:
+  //   C  #C by 3 list of rgb colors
+  template <typename DerivedZ, typename DerivedC>
+  IGL_INLINE void jet(
+    const Eigen::PlainObjectBase<DerivedZ> & Z,
+    const bool normalize,
+    Eigen::PlainObjectBase<DerivedC> & C);
 };
 
 #ifdef IGL_HEADER_ONLY

include/igl/viewer/Viewer.cpp

@@ -2187,27 +2187,53 @@ namespace igl
   void Viewer::set_colors(const Eigen::MatrixXd &C)
   {
     using namespace std;
+    using namespace Eigen;
+    // Ambient color should be darker color
+    const auto ambient = [](const MatrixXd & C)->MatrixXd
+    {
+      return 0.1*C;
+    };
+    // Specular color should be a less saturated and darker color: dampened
+    // highlights
+    const auto specular = [](const MatrixXd & C)->MatrixXd
+    {
+      const double grey = 0.3;
+      return grey+0.1*(C.array()-grey);
+    };
     if (C.rows() == 1)
     {
       for (unsigned i=0;i<data.V_material_diffuse.rows();++i)
+      {
         data.V_material_diffuse.row(i) = C.row(0);
+      }
+      data.V_material_ambient = ambient(data.V_material_diffuse);
+      data.V_material_specular = specular(data.V_material_diffuse);
 
       for (unsigned i=0;i<data.F_material_diffuse.rows();++i)
+      {
         data.F_material_diffuse.row(i) = C.row(0);
+      }
+      data.F_material_ambient = ambient(data.F_material_diffuse);
+      data.F_material_specular = specular(data.F_material_diffuse);
     }
     else if (C.rows() == data.V.rows())
     {
       options.face_based = false;
       data.V_material_diffuse = C;
+      data.V_material_ambient = ambient(data.V_material_diffuse);
+      data.V_material_specular = specular(data.V_material_diffuse);
     }
     else if (C.rows() == data.F.rows())
     {
       options.face_based = true;
       data.F_material_diffuse = C;
+      data.F_material_ambient = ambient(data.F_material_diffuse);
+      data.F_material_specular = specular(data.F_material_diffuse);
     }
     else
       cerr << "ERROR (set_colors): Please provide a single color, or a color per face or per vertex.";
     data.dirty |= DIRTY_DIFFUSE;
+
   }
 
   void Viewer::set_UV(const Eigen::MatrixXd& UV)

tutorial/202_GaussianCurvature/CMakeLists.txt

@@ -0,0 +1,11 @@
+cmake_minimum_required(VERSION 2.6)
+project(202_GaussianCurvature)
+
+include("../CMakeLists.shared")
+
+set(SOURCES
+${PROJECT_SOURCE_DIR}/main.cpp
+)
+
+add_executable(${CMAKE_PROJECT_NAME} ${SOURCES} ${SHARED_SOURCES})
+target_link_libraries(${CMAKE_PROJECT_NAME} ${SHARED_LIBRARIES})

tutorial/202_GaussianCurvature/main.cpp

@@ -0,0 +1,27 @@
+#include <igl/readOFF.h>
+#include <igl/viewer/Viewer.h>
+#include <igl/gaussian_curvature.h>
+#include <igl/jet.h>
+
+int main(int argc, char *argv[])
+{
+  using namespace Eigen;
+  using namespace igl;
+  using namespace std;
+  MatrixXd V;
+  MatrixXi F;
+  igl::readOFF("../shared/bumpy.off",V,F);
+
+  VectorXd K;
+  gaussian_curvature(V,F,K);
+
+  // Compute pseudocolor
+  MatrixXd C;
+  jet(K,true,C);
+
+  // Plot the mesh with pseudocolors
+  igl::Viewer viewer;
+  viewer.set_mesh(V, F);
+  viewer.set_colors(C);
+  viewer.launch();
+}

tutorial/images/bumpy-gaussian-curvature.jpg.REMOVED.git-id

@@ -0,0 +1 @@
+bd2c02b7b891c2fae7344caad4108f45e0511ad2

tutorial/readme.md

@@ -1,5 +1,5 @@
 xhtml header:   <script type="text/javascript" src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>
-css: default.css
+css: style.css
 
 # Introduction
 
@@ -10,6 +10,7 @@ TODO
 * **100_FileIO**: Example of reading/writing mesh files
 * **101_Serialization**: Example of using the XML serialization framework
 * **102_DrawMesh**: Example of plotting a mesh
+* [202 Gaussian Curvature](#gaus)
 
 # Compilation Instructions
 
@@ -26,5 +27,36 @@ On Linux and MacOSX, you can use the provided bash script:
 
     sh ../compile_example.sh
 
-This is an equation
- $a = bx$ 
+# Chapter 2: Discrete Geometric Quantities and Operators
+This chapter illustrates a few discrete quantities that libigl can compute on a
+mesh. This also provides an introduction to basic drawing and coloring routines
+in our example viewer. Finally, we construct popular discrete differential
+geometry operators.
+
+## <a id=gaus></a> Gaussian Curvature
+Gaussian curvature on a continuous surface is defined as the product of the
+principal curvatures:
+
+ $k_G = k_1 k_2.$
+
+As an _intrinsic_ measure, it depends on the metric and
+not the surface's embedding.
+
+Intuitively, Gaussian curvature tells how locally spherical or _elliptic_ the
+surface is ( $k_G>0$ ), how locally saddle-shaped or _hyperbolic_ the surface
+is ( $k_G<0$ ), or how locally cylindrical or _parabolic_ ( $k_G=0$ ) the
+surface is.
+
+In the discrete setting, one definition for a ``discrete Gaussian curvature''
+on a triangle mesh is via a vertex's _angular deficit_:
+
+ $k_G(v_i) = 2π - \sum\limits_{j\in N(i)}θ_{ij},$
+
+where $N(i)$ are the triangles incident on vertex $i$ and $θ_{ij}$ is the angle
+at vertex $i$ in triangle $j$.
+
+Just like the continuous analog, our discrete Gaussian curvature reveals
+elliptic, hyperbolic and parabolic vertices on the domain.
+
+![The `GaussianCurvature` example computes discrete Gaussian curvature and visualizes it in
+pseudocolor.](images/bumpy-gaussian-curvature.jpg)

tutorial/shared/cheburashka.off.REMOVED.git-id

@@ -0,0 +1 @@
+7e7666a89c45b2de12f43db62209b6fafa6cbd62

tutorial/shared/decimated-knight.off

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+OFF
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tutorial/style.css

@@ -0,0 +1,190 @@
+/*
+ * NOTE:
+ * - The use of browser-specific styles (-moz-, -webkit-) should be avoided.
+ *   If used, they may not render correctly for people reading the email in
+ *   a different browser than the one from which the email was sent.
+ * - The use of state-dependent styles (like a:hover) don't work because they
+ *   don't match at the time the styles are made explicit. (In email, styles
+ *   must be explicitly applied to all elements -- stylesheets get stripped.)
+ */
+
+/* This is the overall wrapper, it should be treated as the `body` section. */
+.markdown-here-wrapper {
+}
+
+/* To add site specific rules, you can use the `data-md-url` attribute that we
+   add to the wrapper element. Note that rules like this are used depending
+   on the URL you're *sending* from, not the URL where the recipient views it.
+*/
+/* .markdown-here-wrapper[data-md-url*="mail.yahoo."] ul { color: red; } */
+
+pre, code {
+  font-size: 0.85em;
+  font-family: Consolas, Inconsolata, Courier, monospace;
+}
+
+code {
+  margin: 0 0.15em;
+  padding: 0 0.3em;
+  white-space: pre-wrap;
+  border: 1px solid #EAEAEA;
+  background-color: #F8F8F8;
+  border-radius: 3px;
+  display: inline; /* added to fix Yahoo block display of inline code */
+}
+
+pre {
+  font-size: 1em;
+  line-height: 1.2em;
+}
+
+pre code {
+  white-space: pre;
+  overflow: auto; /* fixes issue #70: Firefox/Thunderbird: Code blocks with horizontal scroll would have bad background colour */
+  border-radius: 3px;
+  border: 1px solid #CCC;
+  padding: 0.5em 0.7em;
+  display: block !important; /* added to counteract the Yahoo-specific `code` rule; without this, code blocks in Blogger are broken */
+}
+
+/* In edit mode, Wordpress uses a `* { font: ...;} rule+style that makes highlighted
+code look non-monospace. This rule will override it. */
+.markdown-here-wrapper[data-md-url*="wordpress."] code span {
+  font: inherit;
+}
+
+/* Wordpress adds a grey background to `pre` elements that doesn't go well with
+our syntax highlighting. */
+.markdown-here-wrapper[data-md-url*="wordpress."] pre {
+  background-color: transparent;
+}
+
+/* This spacing has been tweaked to closely match Gmail+Chrome "paragraph" (two line breaks) spacing. */
+p {
+  /* !important is needed here because Hotmail/Outlook.com uses !important to
+     kill the margin in <p>. We need this to win. */
+  margin: 1.2em 0 !important;
+}
+
+table, pre, dl, blockquote, q, ul, ol {
+  margin: 1.2em 0;
+}
+
+ul, ol {
+  padding-left: 2em;
+}
+
+li {
+  margin: 0.5em 0;
+}
+
+/* Space paragraphs in a list the same as the list itself. */
+li p {
+  /* Needs !important to override rule above. */
+  margin: 0.5em 0 !important;
+}
+
+/* Smaller spacing for sub-lists */
+ul ul, ul ol, ol ul, ol ol {
+  margin: 0;
+  padding-left: 1em;
+}
+
+dl {
+  padding: 0;
+}
+
+dl dt {
+  font-size: 1em;
+  font-weight: bold;
+  font-style: italic;
+}
+
+dl dd {
+  margin: 0 0 1em;
+  padding: 0 1em;
+}
+
+blockquote, q {
+  border-left: 4px solid #DDD;
+  padding: 0 1em;
+  color: #777;
+  quotes: none;
+}
+
+blockquote::before, blockquote::after, q::before, q::after {
+  content: none;
+}
+
+h1, h2, h3, h4, h5, h6 {
+  margin: 1.3em 0 1em;
+  padding: 0;
+  font-weight: bold;
+  font-family: "HelveticaNeue-Light", "Helvetica Neue Light", "Helvetica Neue", Helvetica, Arial, "Lucida Grande", sans-serif; 
+}
+
+h1 {
+  font-size: 1.6em;
+  border-bottom: 1px solid #ddd;
+}
+
+h2 {
+  font-size: 1.4em;
+  border-bottom: 1px solid #eee;
+}
+
+h3 {
+  font-size: 1.3em;
+}
+
+h4 {
+  font-size: 1.2em;
+}
+
+h5 {
+  font-size: 1em;
+}
+
+h6 {
+  font-size: 1em;
+  color: #777;
+}
+
+table {
+  padding: 0;
+  border-collapse: collapse;
+  border-spacing: 0;
+  font-size: 1em;
+  font: inherit;
+  border: 0;
+}
+
+tbody {
+  margin: 0;
+  padding: 0;
+  border: 0;
+}
+
+table tr {
+  border: 0;
+  border-top: 1px solid #CCC;
+  background-color: white;
+  margin: 0;
+  padding: 0;
+}
+
+table tr:nth-child(2n) {
+  background-color: #F8F8F8;
+}
+
+table tr th, table tr td {
+  font-size: 1em;
+  border: 1px solid #CCC;
+  margin: 0;
+  padding: 0.5em 1em;
+}
+
+table tr th {
+ font-weight: bold;
+  background-color: #F0F0F0;
+}