Computing Medial Axis Transform with Feature Preservation via Restricted Power Diagram

Author:

Wang Ningna1,Wang Bin2,Wang Wenping3,Guo Xiaohu1

Affiliation:

1. University of Texas at Dallas

2. Tsinghua University, China

3. Texas A&M University

Abstract

We propose a novel framework for computing the medial axis transform of 3D shapes while preserving their medial features via restricted power diagram (RPD). Medial features, including external features such as the sharp edges and corners of the input mesh surface and internal features such as the seams and junctions of medial axis, are important shape descriptors both topologically and geometrically. However, existing medial axis approximation methods fail to capture and preserve them due to the fundamentally under-sampling in the vicinity of medial features, and the difficulty to build their correct connections. In this paper we use the RPD of medial spheres and its affiliated structures to help solve these challenges. The dual structure of RPD provides the connectivity of medial spheres. The surfacic restricted power cell (RPC) of each medial sphere provides the tangential surface regions that these spheres have contact with. The connected components (CC) of surfacic RPC give us the classification of each sphere, to be on a medial sheet, a seam, or a junction. They allow us to detect insufficient sphere sampling around medial features and develop necessary conditions to preserve them. Using this RPD-based framework, we are able to construct high quality medial meshes with features preserved. Compared with existing sampling-based or voxel-based methods, our method is the first one that can preserve not only external features but also internal features of medial axes.

Funder

National Science Foundation

National Key Research and Development Program of China

Publisher

Association for Computing Machinery (ACM)

Subject

Computer Graphics and Computer-Aided Design

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4. GEM3D: GEnerative Medial Abstractions for 3D Shape Synthesis;Special Interest Group on Computer Graphics and Interactive Techniques Conference Conference Papers '24;2024-07-13

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