Seamless Parametrization in Penner Coordinates

Ryan Capouellez1, Denis Zorin1
1New York University

Abstract

We introduce a conceptually simple and efficient algorithm for seamless parametrization, a key element in constructing quad layouts and texture charts on surfaces. More specifically, we consider the construction of parametrizations with prescribed holonomy signatures i.e., a set of angles at singularities, and rotations along homology loops, preserving which is essential for constructing parametrizations following an input field, as well as for user control of the parametrization structure. Our algorithm performs exceptionally well on a large dataset based on Thingi10k [Zhou and Jacobson 2016], (16156 meshes) as well as on a challenging smaller dataset of [Myles et al. 2014], converging, on average, in 9 iterations. Although the algorithm lacks a formal mathematical guarantee, presented empirical evidence and the connections between convex optimization and closely related algorithms, suggest that a similar formulation can be found for this algorithm in the future.

Paper

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Results

Examples of seamless parametrizations computed with our method.

BibTex

@article{capouellez:2023:seamless,
author = {Capouellez, Ryan and Zorin, Denis},
title = {Seamless Parametrization in Penner Coordinates},
year = {2024},
issue_date = {July 2024},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
volume = {43},
number = {4},
issn = {0730-0301},
url = {https://doi.org/10.1145/3658202},
doi = {10.1145/3658202},
journal = {ACM Trans. Graph.},
month = {jul},
articleno = {61},
numpages = {13},
keywords = {parametrization, seamless, discrete metrics, cone metrics, conformal, intrinsic triangulation, penner coordinates}
}