2016/04/12 by Siddharth Pritam, Pritam, Siddharth, Michael Kerber +1
Computer Science · Mathematics · #Computational Geometry (cs.CG) #FOS: Computer and information sciences #Mathematics and Applications #cs.CG
paper · pdf · doi:10.48550/arxiv.1604.03302
This early draft has been published by the first author misinterpreting the purpose of the arxiv server and is by no means in a state for publication. It was uploaded without the consent of the second author and has been withdrawn at his request
openalex publication_date 2016/04/12 · arxiv created 2016/04/18 · arxiv updated 2016/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We trace movements of certain points in space-time along their corresponding continuous path. We partition the space at every moment of time using alpha-Complexes, Voronoi medusa is then the collection or union of restricted Voronoi cells at every moment in time. We can imagine them as a four dimensional structure formed when three dimensional restricted Voronoi cells sweeps continuously through the extra dimension of time. Similarly Delaunay medusa is the collection of the corresponding Delaunay triangulations at each moment in time. In this article we prove that these two structures are homotopic.