Isometry-Aware Preconditioning for Mesh Parameterization
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Date
2017
Journal Title
Journal ISSN
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Publisher
The Eurographics Association and John Wiley & Sons Ltd.
Abstract
This paper presents a new preconditioning technique for large-scale geometric optimization problems, inspired by applications in mesh parameterization. Our positive (semi-)definite preconditioner acts on the gradients of optimization problems whose variables are positions of the vertices of a triangle mesh in R2 or of a tetrahedral mesh in R3, converting localized distortion gradients into the velocity of a globally near-rigid motion via a linear solve. We pose our preconditioning tool in terms of the Killing energy of a deformation field and provide new efficient formulas for constructing Killing operators on triangle and tetrahedral meshes. We demonstrate that our method is competitive with state-of-the-art algorithms for locally injective parameterization using a variety of optimization objectives and show applications to two- and three-dimensional mesh deformation.
Description
@article{10.1111:cgf.13243,
journal = {Computer Graphics Forum},
title = {{Isometry-Aware Preconditioning for Mesh Parameterization}},
author = {Claici, Sebastian and Bessmeltsev, Mikhail and Schaefer, Scott and Solomon, Justin},
year = {2017},
publisher = {The Eurographics Association and John Wiley & Sons Ltd.},
ISSN = {1467-8659},
DOI = {10.1111/cgf.13243}
}