Bounded Distortion Parametrization in the Space of Metrics

摘要

We present a framework for global parametrization that utilizes thernedge lengths (squared) of the mesh as variables. Given a meshrnwith arbitrary topology and prescribed cone singularities, we flattenrnthe original metric of the surface under strict bounds on the metricrndistortion (various types of conformal and isometric measuresrnare supported). Our key observation is that the space of boundedrndistortion metrics (given any particular bounds) is convex, and arnbroad range of useful and well-known distortion energies are convexrnas well. With the addition of nonlinear Gaussian curvature constraints,rnthe parametrization problem is formulated as a constrainedrnoptimization problem, and a solution gives a locally injective map.rnOur method is easy to implement. Sequential convex programmingrn(SCP) is utilized to solve this problem effectively. We demonstraternthe flexibility of the method and its uncompromised robustness andrncompare it to state-of-the-art methods.