Isometry‐Aware Preconditioning for Mesh Parameterization Academic Article uri icon

abstract

  • © 2017 The Author(s) Computer Graphics Forum © 2017 The Eurographics Association and John Wiley & Sons Ltd. Published by John Wiley & Sons Ltd. 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.

author list (cited authors)

  • Claici, S., Bessmeltsev, M., Schaefer, S., & Solomon, J.

citation count

  • 26

publication date

  • August 2017

publisher