Isometry-Aware Preconditioning for Mesh Parameterization
Periodicals(2017)
摘要
AbstractThis 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.
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