88 lines
3.1 KiB
Markdown
88 lines
3.1 KiB
Markdown
css: style.css
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html header: <script type="text/javascript" src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>
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<link rel="stylesheet" href="http://yandex.st/highlightjs/7.3/styles/default.min.css">
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<script src="http://yandex.st/highlightjs/7.3/highlight.min.js"></script>
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<script>hljs.initHighlightingOnLoad();</script>
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# Introduction
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TODO
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# Index
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* **100_FileIO**: Example of reading/writing mesh files
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* **101_Serialization**: Example of using the XML serialization framework
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* **102_DrawMesh**: Example of plotting a mesh
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* [202 Gaussian Curvature](#gaus)
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# Compilation Instructions
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All examples depends on glfw, glew and anttweakbar. A copy
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of the sourcecode of each library is provided together with libigl
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and they can be precompiled using:
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**Alec: Is this just compiling the dependencies? Then perhaps rename `compile_dependencies_*`**
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sh compile_macosx.sh (MACOSX)
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sh compile_linux.sh (LINUX)
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compile_windows.bat (Visual Studio 2012)
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Every example can be compiled by using the cmake file provided in its folder.
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On Linux and MacOSX, you can use the provided bash script:
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sh ../compile_example.sh
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## (Optional: compilation with libigl as static library)
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By default, libigl is a _headers only_ library, thus it does not require
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compilation. However, one can precompile libigl as a statically linked library.
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See `../README.md` in the main directory for compilations instructions to
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produce `libigl.a` and other libraries. Once compiled, these examples can be
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compiled using the `CMAKE` flag `-DLIBIGL_USE_STATIC_LIBRARY=ON`:
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../compile_example.sh -DLIBIGL_USE_STATIC_LIBRARY=ON
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# Chapter 2: Discrete Geometric Quantities and Operators
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This chapter illustrates a few discrete quantities that libigl can compute on a
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mesh. This also provides an introduction to basic drawing and coloring routines
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in our example viewer. Finally, we construct popular discrete differential
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geometry operators.
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## <a id=gaus></a> Gaussian Curvature
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Gaussian curvature on a continuous surface is defined as the product of the
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principal curvatures:
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$k_G = k_1 k_2.$
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As an _intrinsic_ measure, it depends on the metric and
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not the surface's embedding.
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Intuitively, Gaussian curvature tells how locally spherical or _elliptic_ the
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surface is ( $k_G>0$ ), how locally saddle-shaped or _hyperbolic_ the surface
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is ( $k_G<0$ ), or how locally cylindrical or _parabolic_ ( $k_G=0$ ) the
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surface is.
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In the discrete setting, one definition for a ``discrete Gaussian curvature''
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on a triangle mesh is via a vertex's _angular deficit_:
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$k_G(v_i) = 2π - \sum\limits_{j\in N(i)}θ_{ij},$
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where $N(i)$ are the triangles incident on vertex $i$ and $θ_{ij}$ is the angle
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at vertex $i$ in triangle $j$.
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Just like the continuous analog, our discrete Gaussian curvature reveals
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elliptic, hyperbolic and parabolic vertices on the domain.
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This is an example of syntax highlighted code:
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```cpp
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#include <foo.html>
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int main(int argc, char * argv[])
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{
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return 0;
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}
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```
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