Parametrization is a key operation for texture mapping and surface coloring (e.g. putting a face picture on mesh). Given a surface mesh with boundary:
- Detect mesh boundary loops
- Perform a flattening of the mesh onto the plane while maintaining a low distortion.
- Visualize the flattened mesh using the normal of the original 3D mesh
Some example meshes are readily available in /samplemeshes for testing
Run main.m in MATLAB to view original mesh, it's intrinsic parameterization, texture in parameterized(uv) space and the mesh after mapping texture
This is a simple implementation of discrete conformal parameterization with boundary constraints as described in the following paper,
Desbrun, Mathieu et al. “Intrinsic Parameterizations of Surface Meshes.” Comput. Graph. Forum 21 (2002): 209-218.
Find the full report here. You can also refer the project page for more information