期刊
ACM TRANSACTIONS ON GRAPHICS
卷 37, 期 4, 页码 -出版社
ASSOC COMPUTING MACHINERY
DOI: 10.1145/3197517.3201337
关键词
generalized winding number; inside-outside segmentation; tree-based algorithm; robust geometry processing
资金
- NSERC Discovery Grants [RGPIN2017-05235, RGPAS-2017-507938, RGPIN-2017-05524]
- NSERC DAS [RGPAS-2017-507909]
- Connaught Funds [NR2016-17]
- Canada Research Chairs Program
Inside-outside determination is a basic building block for higher-level geometry processing operations. Generalized winding numbers provide a robust answer for triangle meshes, regardless of defects such as self-intersections, holes or degeneracies. In this paper, we further generalize the winding number to point clouds. Previous methods for evaluating the winding number are slow for completely disconnected surfaces, such as triangle soups or-in the extreme case-point clouds. We propose a tree-based algorithm to reduce the asymptotic complexity of generalized winding number computation, while closely approximating the exact value. Armed with a fast evaluation, we demonstrate the winding number in a variety of new applications: voxelization, signing distances, generating 3D printer paths, defect-tolerant mesh booleans and point set surfaces.
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