Fast Injective Mesh Parameterization via Beltrami Coefficient Prolongation
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Date
2026
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association and John Wiley & Sons Ltd.
Abstract
We present a highly efficient and robust method for free boundary injective parameterization of disk-like triangle meshes with low isometric distortion. Harmonic function–based approaches, grounded in a strong mathematical framework, are widely employed. In particular, harmonic maps are valuable for guaranteeing injectivity under suitable boundary conditions. They are also computationally efficient, as they operate within a linear subspace [FW22]. However, this restriction to a limited subspace often introduces substantial isometric distortion, especially on highly curved surfaces. In contrast, methods that explore the full space of piecewise linear maps [SPSH∗17] achieve much lower isometric distortion, but at the expense of increased computational cost. We propose a hybrid method that combines the speed and robustness of harmonic maps with the generality of full-space methods to produce injective maps with low isometric distortion up to 50 times faster than state-of-theart methods. The core concept is simple but powerful. Instead of searching for the optimal parameterization over the original mesh via a full-space method, we simplify the input fine mesh and parameterize the coarse mesh. We then prolong the Beltrami coefficients from the coarse mesh parameterization to the fine mesh, resulting in a customized Laplacian matrix that gives rise to a harmonic map in a modified metric [WGS23,FW25]. Our method ensures injectivity, offers great computational efficiency, and produces significantly lower isometric distortion compared to harmonic maps.
Description
@article{10.1111:cgf.70341,
journal = {Computer Graphics Forum},
title = {{Fast Injective Mesh Parameterization via Beltrami Coefficient Prolongation}},
author = {Fargion, Guy and Weber, Ofir},
year = {2026},
publisher = {The Eurographics Association and John Wiley & Sons Ltd.},
ISSN = {1467-8659},
DOI = {10.1111/cgf.70341}
}