- publication
- Eurographics Symposium on Geometry Processing 2024
- authors
- Koray Akalin, Ugo Finnendahl, Olga Sorkine-Hornung, Marc Alexa
abstract
A parameterization of a triangle mesh is a realization in the plane so that all triangles have positive signed area. Triangle mesh parameterizations are commonly computed by minimizing a distortion energy, measuring the distortions of the triangles as they are mapped into the parameter domain. It is commonly assumed that the triangulation is fixed and the triangles are mapped affinely. We consider a more general setup and additionally optimize among the intrinsic triangulations of the piecewise linear input geometry. This means the distortion energy is computed for the same geometry, yet the space of possible parameterizations is enlarged nonetheless. We suggest to alternate between varying the parameter locations of the vertices and intrinsic flipping to minimize the distortion energy. We show that this process improves the mapping for several common distortion energies at moderate additional computational cost. We also find intrinsic triangulations that are better starting points for the optimization of positions, offering a compromise between the full optimization approach and exploiting the additional freedom of intrinsic triangulations.