Sphere-based cut construction for planar parameterizations

Abstract

We present a novel algorithm to compute high-quality cuts for generating low isometric distortion planar parameterizations. Based on the observation that conformal spherical and planar parameterizations have similar distortion distributions at the extrusive areas that lead to high isometric distortions, our method utilizes a spherical parameterization of the input mesh to guide the cut construction. After parameterizing the input mesh onto a sphere as conformal as possible, a hierarchical clustering of the divisive type is conducted on the sphere to find high isometric distortion regions, where high isometric distortion may also be introduced in the planar parameterization and which are connected to define a cut. Compared with previous methods, this approach can generate better cuts, resulting in lower isometric distortions. We demonstrate the efficacy and practical robustness of our method on a data set of over 5000 meshes, which are parameterized with low isometric distortion by two existing parameterization approaches.