Non Euclidean Sliced Optimal Transport Sampling

Source code of the article:

Genest, Baptiste, Nicolas Courty, and David Coeurjolly. "Non-Euclidean Sliced Optimal Transport Sampling", Computer Graphics Forum (Proceedings of Eurographics), April, 2024

Here are the instructions to generate blue noise samples on the sphere and hyperbolic spaces in any dimensions or to sample meshes of genus 0 (see spherical sampling) or genus >= 2 (see local hyperbolic sampling)

Note that we use CLI11 to provide a clear command line API, you can use --help on any executable to see all available options.

Ref : https://github.com/CLIUtils/CLI11

Building (Linux/macOS)

We use CMake, hence the usual building commands are required

from root folder :

mkdir build 
cd build
cmake ..
make -j7

Visualization

If you want to see the effects of each parameter or simply to see the algorithm in action you can use the option :

--viz 

to enable visualization with polyscope : https://polyscope.run/

Blue Noise on the sphere or on the hyperbolic plane

To generate blue noise points on the sphere in dimension 3, a classical use-case would be

./spherical_bluenoise --dim 3 --sample_size 1000 --viz 

The process is the same for the hyperbolic case with the executable.

Note that you can sample any distribution by providing samples with the option --target_measure nu.pts

Spherical Mesh Sampling

CEPS Modification

We use CEPS (https://github.com/MarkGillespie/CEPS) to maps a genus zero mesh to the sphere, To generate and output the spherical mesh, you must replace the file CEPS/src/SphericalUniformization/SphericalUniformization.cpp by this_folder/SphericalUniformization.cpp before compiling and then launch :

CEPS_BUILD_FILE/bin/spherical_uniformize input_mesh.obj

to generate the mesh.

To then sample a mesh, use

./spherical_mesh_sampling --input_mesh ../data/spot.obj --sphere_mesh ../data/spherical-spot.obj --sample_size 1000

The command above would reproduce the top row of the figure 6.

Local Hyperbolic Mesh Sampling

./local_hyperbolic_mesh_sampling --input_mesh ../data/macaca.obj --sample_size 1000

The command above would reproduce the bottom row of the figure 6.

Visualizing results

./vizu_pc --input_mesh ../data/macaca.obj --input_points /tmp/out.pts

Projective Plane Sampling

The code here only illustrates visually its use but one could export points clouds in the same way as illustrated in the code of spherical_bluenoise.cpp for instance.