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
Cited by
10 articles.
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