Holes and dependences in an ordered complex

H. Edelsbrunner, K. Ölsböck, Computer Aided Geometric Design 73 (2019) 1–15.

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Journal Article | Published | English
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Abstract
We use the canonical bases produced by the tri-partition algorithm in (Edelsbrunner and Ölsböck, 2018) to open and close holes in a polyhedral complex, K. In a concrete application, we consider the Delaunay mosaic of a finite set, we let K be an Alpha complex, and we use the persistence diagram of the distance function to guide the hole opening and closing operations. The dependences between the holes define a partial order on the cells in K that characterizes what can and what cannot be constructed using the operations. The relations in this partial order reveal structural information about the underlying filtration of complexes beyond what is expressed by the persistence diagram.
Publishing Year
Date Published
2019-08-01
Journal Title
Computer Aided Geometric Design
Volume
73
Page
1-15
IST-REx-ID

Cite this

Edelsbrunner H, Ölsböck K. Holes and dependences in an ordered complex. Computer Aided Geometric Design. 2019;73:1-15. doi:10.1016/j.cagd.2019.06.003
Edelsbrunner, H., & Ölsböck, K. (2019). Holes and dependences in an ordered complex. Computer Aided Geometric Design, 73, 1–15. https://doi.org/10.1016/j.cagd.2019.06.003
Edelsbrunner, Herbert, and Katharina Ölsböck. “Holes and Dependences in an Ordered Complex.” Computer Aided Geometric Design 73 (2019): 1–15. https://doi.org/10.1016/j.cagd.2019.06.003.
H. Edelsbrunner and K. Ölsböck, “Holes and dependences in an ordered complex,” Computer Aided Geometric Design, vol. 73, pp. 1–15, 2019.
Edelsbrunner H, Ölsböck K. 2019. Holes and dependences in an ordered complex. Computer Aided Geometric Design. 73, 1–15.
Edelsbrunner, Herbert, and Katharina Ölsböck. “Holes and Dependences in an Ordered Complex.” Computer Aided Geometric Design, vol. 73, Elsevier, 2019, pp. 1–15, doi:10.1016/j.cagd.2019.06.003.
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