Alec Jacobson 6bbabfb5fb Merge branch 'master' of github.com:libigl/libigl 11 years ago
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101_FileIO 073be51f91 tutorials index starts from 1 11 years ago
103_DrawMesh 073be51f91 tutorials index starts from 1 11 years ago
104_Events abd3989efb - new tutorial example for harmonic parametrization 11 years ago
105_Colors 0aaef7e68f fix in cmake file for glew 11 years ago
106_Overlays f692781ff9 - added tutorial for principal curvature directions 11 years ago
107_Matlab ae03f73648 * added tutorial for ARAP parametrization (broken) 11 years ago
201_Normals 4529821552 - added support for per corner normals 11 years ago
202_GaussianCurvature 643bb356eb gaussian curvature example in tutorial 11 years ago
203_CurvatureDirections f692781ff9 - added tutorial for principal curvature directions 11 years ago
501_HarmonicParam ae03f73648 * added tutorial for ARAP parametrization (broken) 11 years ago
502_LSCMParam 9a0c025dfb - added tutorial example LSCM + helper functions 11 years ago
503_ARAPParam 49dadb340c arap parameterization working, really 11 years ago
cmake 49dadb340c arap parameterization working, really 11 years ago
images 643bb356eb gaussian curvature example in tutorial 11 years ago
shared ae03f73648 * added tutorial for ARAP parametrization (broken) 11 years ago
CMakeLists.shared 49dadb340c arap parameterization working, really 11 years ago
compile_example.sh 49dadb340c arap parameterization working, really 11 years ago
compile_example_xcode.sh ae03f73648 * added tutorial for ARAP parametrization (broken) 11 years ago
compile_macosx.sh 0daa5ce93b cmake/examples working on alecs mac 11 years ago
readme.md 1de0c75000 arap parameterization no longer allowing reflections, using ref triangles 11 years ago
style.css 643bb356eb gaussian curvature example in tutorial 11 years ago

readme.md

css: style.css html header:

Introduction

TODO

Index

  • 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

Compilation Instructions

All examples depends on glfw, glew and anttweakbar. A copy of the sourcecode of each library is provided together with libigl and they can be precompiled using:

Alec: Is this just compiling the dependencies? Then perhaps rename compile_dependencies_*

sh compile_macosx.sh (MACOSX)
sh compile_linux.sh (LINUX)
compile_windows.bat (Visual Studio 2012)

Every example can be compiled by using the cmake file provided in its folder. On Linux and MacOSX, you can use the provided bash script:

sh ../compile_example.sh

(Optional: compilation with libigl as static library)

By default, libigl is a headers only library, thus it does not require compilation. However, one can precompile libigl as a statically linked library. See ../README.md in the main directory for compilations instructions to produce libigl.a and other libraries. Once compiled, these examples can be compiled using the CMAKE flag -DLIBIGL_USE_STATIC_LIBRARY=ON:

../compile_example.sh -DLIBIGL_USE_STATIC_LIBRARY=ON

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.

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:

$k_G(vi) = 2π - \sum\limits{j\in N(i)}θ_{ij},$

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.

This is an example of syntax highlighted code:

#include <foo.html>
int main(int argc, char * argv[])
{
  return 0;
}