期刊
COMPUTER GRAPHICS FORUM
卷 36, 期 5, 页码 37-47出版社
WILEY
DOI: 10.1111/cgf.13243
关键词
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资金
- NSF [IIS 1148976]
- MIT Skoltech Seed Fund
- MIT Research Support Committee
- Army Research Office [W911NF-12-R-0011]
- Div Of Information & Intelligent Systems
- Direct For Computer & Info Scie & Enginr [1148976] Funding Source: National Science Foundation
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 R-2 or of a tetrahedral mesh in R-3, 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.
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