期刊
COMPUTER AIDED GEOMETRIC DESIGN
卷 74, 期 -, 页码 -出版社
ELSEVIER
DOI: 10.1016/j.cagd.2019.101767
关键词
Euclidean Distance Degree; Persistent homology; Offset curve; Offset hypersurface; Medial axis; Reach
资金
- National Science Foundation Graduate Research Fellowship Program [DGE 1752814]
- Sapientia Foundation -Institute for Scientific Research
- Max Planck Institute for Mathematics in the Sciences in Leipzig
In this paper, we study the persistent homology of the offset filtration of algebraic varieties. We prove the algebraicity of two quantities central to the computation of persistent homology. Moreover, we connect persistent homology and algebraic optimization. Namely, we express the degree corresponding to the distance variable of the offset hypersurface in terms of the Euclidean Distance Degree of the starting variety, obtaining a new way to compute these degrees. Finally, we describe the non-properness locus of the offset construction and use this to describe the set of points that are topologically interesting (the medial axis and center points of the bounded components of the complement of the variety) and relevant to the computation of persistent homology. (C) 2019 Elsevier B.V. All rights reserved.
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