We present a novel linear solver for interactive parameterization tasks. Our method is based on the observation that quasi-conformal parameterizations of a triangle mesh are largely determined by boundary conditions. These boundary conditions are typically constructed interactively by users, who have to take several artistic and geometric constraints into account while introducing cuts on the geometry. Commonly, the main computational burden in these methods is solving a linear system every time new boundary conditions are imposed. The core of our solver is a novel approach to efficiently update the Cholesky factorization of the linear system to reflect new boundary conditions, thereby enabling a seamless and interactive workflow even for large meshes consisting of several millions of vertices.
We thank Rohan Shawhney and Noam Aigerman for inspiring discussions. Jacques Lucke helped us tremendously with integrating our solver into Blender. We are grateful to the anonymous reviewers for their constructive comments. This work was partially supported by the Personalized Health and Related Technologies (PHRT) SwissHeart grant.