MATTopo: Topology-preserving Medial Axis Transform with Restricted Power Diagram

We present a novel topology-preserving 3D medial axis computation frame-work based on volumetric restricted power diagram (RPD), while preservingthe medial features and geometric convergence simultaneously, for both3D CAD and organic shapes. The volumetric RPD discretizes the input 3Dvolume into sub-regions given a set of medial spheres. With this intermedi-ate structure, we convert the homotopy equivalency between the generatedmedial mesh and the input 3D shape into a localized contractibility check-ing for each restricted element (power cell, power face, power edge), bychecking their connected components and Euler characteristics. We furtherpropose a fractional Euler characteristic algorithm for efficient GPU-basedcomputation of Euler characteristic for each restricted element on the fly while computing the volumetric RPD. Compared with existing voxel-basedor point-cloud-based methods, our approach is the first to adaptively anddirectly revise the medial mesh without globally modifying the dependentstructure, such as voxel size or sampling density, while preserving its topol-ogy and medial features. In comparison with the feature preservation methodMATFP [Wang et al.2022], our method provides geometrically comparableresults with fewer spheres and more robustly captures the topology of theinput 3D shape