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 language | English |
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Pages (from-to) | 293-308 |
Number of pages | 16 |
Journal | Computational Geometry: Theory and Applications |
Volume | 4 |
Issue number | 6 |
DOIs | |
Publication status | Published - 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