discrete total curvature estimation

A universal total curvature estimation method that works for both triangle meshes and point clouds. For details, see the SIGGRAPH 2023 paper by Crane Chen under the supervision of Misha Kazhdan.

This codebase is in libigl-style. We also implemented another version for open3d users, the open3d-style codebase of our paper can be found here.

Comparison with other popular libraries

Dependencies

• STL
• eigen for matrix data structures
• openmp for parallelization
• libigl for mesh data structures and geometry processing tools
• polyscope for 3D visualizations and rendering

OS

The code was developed on MacOS 12.6. We verified the compilation and running of the code on Ubuntu 18.04. We also verifie the compilation and running of the code on Windows 10 with Visual Studio 2022, where we accessed CMake through Visual Studio.

MacOS and Ubuntu

Compile

Fetch the code with dependencies:

git clone https://github.com/HeCraneChen/total-curvature-estimation.git --recursive

Compile this project using the standard cmake routine:

cd total-curvature-estimation
mkdir build
cd build
cmake ..
make

The above commands use FetchContent of CMake to automatically download libigl and its dependencies. If that did not work for you, try to point to the local libigl. In that case, use

cmake -DFETCHCONTENT_SOURCE_DIR_LIBIGL=../libigl ..

to replace

cmake ..

Run

From within the build directory, for triangle mesh, just issue:

./TotalCurvature --in ../example_data/cow.ply --out ../results/cow_mesh.txt --format mesh

For point cloud, just issue:

./TotalCurvature --in ../example_data/cow_points.ply ../example_data/cow_normals.ply --out ../results/cow_cloud.txt --format point_cloud

A glfw app should launch displaying a cow, rendered with color representing total curvature of each point. Results of the calculated curvature will be saved in a txt file. Note that the values in the visualizer has been rescaled for better visual effect. Refer to the output txt file for the calculated total curvature values.

Windows with Visual Studio

Compile

Open the Visual Studio IDE, and click the following

Open a local folder and open the total-curvature-estimation folder cloned from this repo

File Open CMake... and open the CMakeLists.txt

Build Build All

Run

cd total-curvature-estimation

mkdir build

scp ./out/build/x64-Debug/TotalCurvature.exe ./build/TotalCurvature.exe

scp ./out/build/x64-Debug/_deps/gmp-src/lib/libgmp-10.dll ./build/libgmp-10.dll

cd build

TotalCurvature --in ../example_data/cow.ply --out ../results/cow_mesh.txt --format mesh

TotalCurvature --in ../example_data/cow_points.ply ../example_data/cow_normals.ply --out ../results/cow_cloud.txt --format point_cloud

Citation

@inproceedings{10.1145/3587421.3595439,
author = {Chen, Crane He},
title = {Estimating Discrete Total Curvature with Per Triangle Normal Variation},
year = {2023},
isbn = {9798400701436},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
url = {https://doi.org/10.1145/3587421.3595439},
doi = {10.1145/3587421.3595439},
booktitle = {ACM SIGGRAPH 2023 Talks},
articleno = {56},
numpages = {2},
location = {Los Angeles, CA, USA},
series = {SIGGRAPH '23}
}