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

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arXiv:2403.18761v1 Announce Type: new
Abstract: We present a novel volumetric RPD (restricted power diagram) based framework for approximating the medial axes of 3D CAD shapes adaptively, while preserving topological equivalence, medial features, and geometric convergence. To solve the topology preservation problem, we propose a volumetric RPD based strategy, which discretizes the input volume into sub-regions given a set of medial spheres. With this intermediate structure, we convert the homotopy equivalence between the generated medial mesh and the input 3D shape into a localized problem between each primitive of the medial mesh (vertex, edge, face) and its dual restricted elements (power cell, power face, power edge), by checking their connected components and Euler characteristics. We further proposed a fractional Euler characteristic strategy for efficient GPU-based computation of Euler characteristic for each restricted element on the fly while computing the volumetric RPD. Compared with existing voxel-based or sampling-based methods, our method is the first that can adaptively and directly revise the medial mesh without modifying the dependent structure globally, such as voxel size or sampling density. Compared with the feature preservation method MATFP, our method offers geometrically comparable results with fewer number of spheres, while more robustly captures the topology of the input shape.

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