Mesh Parameterization Meets Intrinsic Triangulations
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Date
2024
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association and John Wiley & Sons Ltd.
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 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. For minimizing the distortion energy, we suggest alternating between varying the parameter locations of the vertices and intrinsic flipping. We show that this process improves the mapping for different distortion energies at moderate additional 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.
Description
CCS Concepts: Computing methodologies → Computer graphics; Mesh models; Mesh geometry models
@article{10.1111:cgf.15134,
journal = {Computer Graphics Forum},
title = {{Mesh Parameterization Meets Intrinsic Triangulations}},
author = {Akalin, Koray and Finnendahl, Ugo and Sorkine-Hornung, Olga and Alexa, Marc},
year = {2024},
publisher = {The Eurographics Association and John Wiley & Sons Ltd.},
ISSN = {1467-8659},
DOI = {10.1111/cgf.15134}
}