Fast Harmonic Mappings

Abstract: We present solutions for locally injective low-distortion harmonic mappings between surfaces that are significantly faster than state-of-the-art methods with similar requirements. We focus on two types of harmonic mappings: planar shape deformation and seamless parameterization. For each of these problems, we analyze the optimization problem and construct specific solvers that take advantage of harmonic functions properties to achieve the desired speedup. First, we use an alternating tangential projection method to solve the convex optimization problem defined in [LW16] for planar shape deformations. Then, we efficiently find a basis for the space of solutions to the HGP linear system [BCW17], and use ATP and Newton solvers to quickly find a low-distortion locally injective seamless parametrization in this subspace. We present experiments which demonstrate the speed and quality of our methods, and we show that these are orders of magnitude faster than other algorithms with comparable properties.

* M.Sc. research supervised by Dr. Ofir Weber