  We present a novel topology-preserving 3D medial axis computation framework
based on volumetric restricted power diagram (RPD), while preserving the medial
features and geometric convergence simultaneously, for both 3D CAD and organic
shapes. The volumetric RPD discretizes the input 3D volume into sub-regions
given a set of medial spheres. With this intermediate structure, we convert the
homotopy equivalency between the generated medial mesh and the input 3D shape
into a localized contractibility checking for each restricted element (power
cell, power face, power edge), by checking their connected components and Euler
characteristics. We further propose a fractional Euler characteristic algorithm
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 point-cloud-based methods, our approach is the first to
adaptively and directly revise the medial mesh without globally modifying the
dependent structure, such as voxel size or sampling density, while preserving
its topology and medial features. In comparison with the feature preservation
method MATFP, our method provides geometrically comparable results with fewer
spheres and more robustly captures the topology of the input 3D shape.
