Complexity of projected images of convex subdivisions

Tomio Hirata, Jiří Matoušek, Xue Hou Tan, Takeshi Tokuyama

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

Let S be a subdivision of Rd into n convex regions. We consider the combinatorial complexity of the image of the (k - 1)-skeleton of S orthogonally projected into a k-dimensional subspace. We give an upper bound of the complexity of the projected image by reducing it to the complexity of an arrangement of polytopes. If k = d - 1, we construct a subdivision whose projected image has Ω(n⌊(3d-2)/2⌋) complexity, which is tight when d ≤ 4. We also investigate the number of topological changes of the projected image when a three-dimensional subdivision is rotated about a line parallel to the projection plane.

Original languageEnglish
Pages (from-to)293-308
Number of pages16
JournalComputational Geometry: Theory and Applications
Volume4
Issue number6
DOIs
Publication statusPublished - 1994 Dec

Keywords

  • Algorithms
  • Combinatorial Complexity
  • Computational Geometry
  • Convex Subdivision
  • Projection

ASJC Scopus subject areas

  • Computer Science Applications
  • Geometry and Topology
  • Control and Optimization
  • Computational Theory and Mathematics
  • Computational Mathematics

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