A general framework for constrained mesh parameterization

Parameterizing or flattening a triangle mesh is necessary for many applications in computer graphics and geometry. While mesh parameterization is a very popular research topic, the vast majority of the literature is focused on minimizing distortion or satisfying constraints related to certain applications such as texturing or quadrilateral remeshing. Certain downstream applications require adherence to more general, geometric constraints -- possibly at the cost of higher distortion. These geometric constraints include requirements such as certain vertices lie on some line or circle, or a planar curve or developable region keeps its shape during parameterization. We present a framework for enforcing such constraints, motivated by the As-Rigid-As-Possible parameterization method, and demonstrate its effectiveness through several examples.