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:

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

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(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.