Large-scale bounded distortion mappings

Shahar Z. Kovalsky, Noam Aigerman, Ronen Basri, Yaron Lipman
2015 ACM Transactions on Graphics  
We propose an efficient algorithm for computing large-scale bounded distortion maps of triangular and tetrahedral meshes. Specifically, given an initial map, we compute a similar map whose differentials are orientation preserving and have bounded condition number. Inspired by alternating optimization and Gauss-Newton approaches, we devise a first order method which combines the advantages of both. On the one hand, its iterations are as computationally efficient as those of alternating
more » ... on. On the other hand, it enjoys preferable convergence properties, associated with Gauss-Newton like approaches. We demonstrate the utility of the proposed approach in efficiently solving geometry processing problems, focusing on challenging large-scale problems.
doi:10.1145/2816795.2818098 fatcat:2ufht2xberci5jg3flt6x7v7by