期刊
ACM TRANSACTIONS ON GRAPHICS
卷 37, 期 4, 页码 -出版社
ASSOC COMPUTING MACHINERY
DOI: 10.1145/3197517.3201396
关键词
medial axis; shape analysis; voxelization; Voronoi diagrams
资金
- National Science Foundation [IIS-1302200, DBI-1356388, RI-1618685]
- Div Of Biological Infrastructure
- Direct For Biological Sciences [1356388] Funding Source: National Science Foundation
We present a novel algorithm for computing the medial axes of 3D shapes. We make the observation that the medial axis of a voxel shape can be simply yet faithfully approximated by the interior Voronoi diagram of the boundary vertices, which we call the voxel core. We further show that voxel cores can approximate the medial axes of any smooth shape with homotopy equivalence and geometric convergence. These insights motivate an algorithm that is simple, efficient, numerically stable, and equipped with theoretical guarantees. Compared with existing voxel-based methods, our method inherits their simplicity but is more scalable and can process significantly larger inputs. Compared with sampling-based methods that offer similar theoretical guarantees, our method produces visually comparable results but more robustly captures the topology of the input shape.
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