Rectangular Surface Parametrization

Implementation of the Rectangular Surface Parametrization method by Etienne Corman and Keenan Crane

This implementation is in full python/numba and uses the mouette library for geometry processing.

Dependencies

• Install cyipopt using their installation instructions
• Install all other dependencies using pip install -r requirements.txt

Running the code

python main.py <path/to/mesh> [options]

Mesh formats supported are .obj, .mesh and .geogram_ascii (format from the geogram library)

options:  
  -h, --help            show this help message and exit  
  -o OUTPUT_NAME, --output-name OUTPUT_NAME  
                        Name of the output file. Will be stored in a folder  
                        named '<outname>' as '<outname>.obj'        
  -ff {smooth,curv}, --ff-init-mode {smooth,curv}  
                        which frame field to use as initialization. `smooth`  
                        means smoothing a frame field using diffusion. `curv`  
                        means principal directions of curvature. Defaults to  
                        `smooth`  
  -fb, --free-boundary  Runs the algorithm with no singularities and with a  
                        free boundary. Only works for disk topology meshes.  
  -feat, --detect-features  
                        enables feature detection and alignment  
  -d {none,conformal,iso,area,align}, --disto {none,conformal,iso,area,align}  
                        which distorsion to minimize  
  -optim {LM,cyipopt}, --optimizer {LM,cyipopt}  
                        Which optimizer to use. LM = Levenberg-Marquardt from  
                        mouette.  
  -n N_ITER_MAX, --n-iter-max N_ITER_MAX  
                        maximum number of iterations in optimization  
  -silent, --silent     disables output in terminal  

Visualize the results

We provide a visualize_in_polyscope.py script to visualize the full output in... polyscope. Simply run:

python visualize_in_polyscope.py output/<folder>

where <folder> is a folder generated by the main script. Make sure you ran the --full_output option of the main script to visualize all relevant quantities.

References and useful links

• Link to the original article : https://www.cs.cmu.edu/~kmcrane/Projects/RectangularSurfaceParameterization/RectangularSurfaceParameterization.pdf
• Link to the official code by the authors : https://github.com/etcorman/RectangularSurfaceParameterization/tree/main