Efficient r-symmetry detection for triangle meshes

Abstract

In their paper [2012], Kalojanov et al. introduce a theoretical model for shape decomposition into microtiles - building blocks derived by a set of correspondences that define an equivalence relation on the surface points of a given model. The authors also showed that for a specific correspondence functions (rigid r-neighborhood matching) the set of microtiles characterizes all shapes r-similar to a given exemplar. Here, we address the problem of computing a microtile decomposition and show how to efficiently detect r-symmetric of points on triangle meshes. We first demonstrate that a microtile decomposition w.r.t. rigid r-symmetry is computable. Afterwards, we introduce an efficient method for computing microtiles, which permits such involved analysis to be used in variety of geometry processing applications.