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nmwsharp / geometry-central

Applied 3D geometry in C++, with a focus on surface meshes.
https://geometry-central.net
MIT License
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Discretization differential forms implementation #48

Open lukkio88 opened 3 years ago

lukkio88 commented 3 years ago

Hi,

A while back I came across this paper : Discrete Differential Forms for Computational Modeling The paper led me to study smooth manifolds and some fundamentals of Riemannian Geometry. Although the paper explains how to implement discrete differential forms I still can't quite match it with the theory.

Can you point in the code where is the implementation of the differential forms, hodge dual etc in the code so I can actually dig into it and see how this is done in practice.

I also would like if formalizing the algorithms in such language actually make it easier the implementation or does it simplify maybe the formalization of the algorithm itself?

nmwsharp commented 3 years ago

Don't mind me responding to a very old issue :)

You can find some implementations here https://github.com/nmwsharp/geometry-central/blob/master/src/surface/intrinsic_geometry_interface.cpp#L586

The terminology and definitions in geometry-central often mirror those in this text: http://www.cs.cmu.edu/~kmcrane/Projects/DDG/paper.pdf