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Least Squares Affine Transitions for Global Parameterization

Abstract : This paper presents an efficient algorithm for a global parameterization of triangular surface meshes. In contrast to previous techniques which achieve global parameterization through the optimization of non-linear systems of equations, our algorithm is solely based on solving at most two linear equation systems, in the least square sense. Therefore, in terms of running time the unfolding procedure is highly efficient. Our approach is direct – it solves for the planar UV coordinates of each vertex directly – hence avoiding any numerically challenging planar reconstruction in a post-process. This results in a robust unfolding algorithm. Curvature prescription for user-provided cone singularities can either be specified manually, or suggested automatically by our approach. Experiments on a variety of surface meshes demonstrate the runtime efficiency of our algorithm and the quality of its unfolding. To demonstrate the utility and versatility of our approach, we apply it to seamless texturing. The proposed algorithm is computationally efficient, robust and results in a parameterization with acceptable metric distortion.
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https://hal.archives-ouvertes.fr/hal-01547522
Contributor : Julien Tierny <>
Submitted on : Monday, June 26, 2017 - 8:05:43 PM
Last modification on : Friday, December 20, 2019 - 1:22:01 AM
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Ana Vintescu, Florent Dupont, Guillaume Lavoué, Pooran Memari, Julien Tierny. Least Squares Affine Transitions for Global Parameterization. WSCG 2017 5th International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision 2017, May 2017, Plzen, Czech Republic. ⟨hal-01547522⟩

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