Practical construction of globally injective parameterizations with positional constraints

Abstract

We propose a novel method to compute globally injective parameterizations with arbitrary positional constraints on disk topology meshes. Central to this method is the use of a scaffold mesh that reduces the globally injective constraint to a locally flipfree condition. Hence, given an initial parameterized mesh containing flipped triangles and satisfying the positional constraints, we only need to remove the flips of a overall mesh consisting of the parameterized mesh and the scaffold mesh while always meeting positional constraints. To successfully apply this idea, we develop two key techniques.