peterzhousz / correctednormalcurrent

Interpolated corrected curvature measures for polygonal surfaces

Interpolated corrected curvature measures for polygonal surfaces

This repository is a demo of the paper:

Interpolated corrected curvature measures for polygonal surfaces, Jacques-Olivier Lachaud, Pascal Romon, Boris Thibert, David Coeurjolly, Symposium on Geometry Processing, Computer Graphics Forum, 2020.

@article{cnc2020,
  author  =    {Jacques-Olivier Lachaud, Pascal Romon, Boris Thibert and David
Coeurjolly},
  title   =    {Interpolated corrected curvature measures for polygonal surfaces},
  journal =    {Computer Graphics Forum (Proceedings of Symposium on Geometry Processing 2020)},
  year    =    {2020},
  volume  =    {39},
  number  =    {5},
}

In this project, we compare our stable curvature measure with existing approaches (Normal Cycles, Rusinkiewicz's formula, polynomial fitting via Jet Fitting). Our closed form formulas are given in the CorrectedNormalCurrentFormula.h file. We rely on CGAL for the Monge form via Jet Fitting approach. This project also relies on the DGtal library for basic linear algebra. The project heavily uses polyscope for the visualization and UI.

If you would like to include our CNC estimators in your project, you would just need to copy the CorrectedNormalCurrentFormula.h header and provide your own RealVector and 3x3 matrix operation implementations.

As an example, we also provide a stand-alone implementation (BSD License 2.0) of some formulas using eigen in CorrectedNormalCurrentFormulaEigen.h.

To use this project, just clone it (with submodule):

git clone --recursive https://github.com/dcoeurjo/CorrectedNormalCurrent.git

Then you can compile the example file using:

mkdir build
cd build
cmake ..  -DCMAKE_BUILD_TYPE=Release
make

Note: to compile DGtal, you would need boost (only headers) and zlib.

Once the code has been built, just run simpleTest on a triangulated OBJ file:

simpleTest ../spot.obj

Authors

• Jacques-Olivier Lachaud
• Boris Thibert
• Pascal Romon
• David Coeurjolly

License

GNU LGPL (see header files)