Diskify: a combinatorial approach to the computation of cut networks on surfaces
Published in Computer & Graphics, 2026
Abstract
We present a reliable, fully combinatorial method for UV mapping that leverages a Voronoi-based decomposition of a triangulated surface mesh. Given a sparse set of sample points on the input shape, we construct the corresponding Voronoi partition and iteratively refine it to ensure that all regions are topologically equivalent to disks. From the disk decomposition, we propose two directions. On one side, adjacent regions are merged following a greedy approach that minimizes some objective function, all while preserving disk equivalence. Alternatively, the regions can be used to guide a cut that makes the whole surface topologically equivalent to a disk. In both cases, this topological guarantee enables straightforward and reliable UV parameterization. Our method exhibits an extremely low failure rate, making it suitable for practical use. In quantitative experiments on standard UV mapping benchmarks, we achieve performance comparable to state-of-the-art techniques. Furthermore, we analyze robustness and efficiency across different sampling densities, providing insights into the computational cost of each step of the pipeline.
BibTeX
@article{maggioli2026diskify,
author = {Maggioli, Filippo and Melzi, Simone},
title = {Diskify: a combinatorial approach to the computation of cut networks on surfaces},
journal = {Computer \& Graphics},
pages = {104720},
year = {2026},
issn = {0097-8493},
doi = {https://doi.org/10.1016/j.cag.2026.104720}
}
Resources
Recommended citation: Maggioli Filippo, et al. "Diskify: a combinatorial approach to the computation of cut networks on surfaces." Computer & Graphics. 2026.
