The complexity of cutting convex polytypes

  • Authors:
  • B. Chazelle;H. Edelsbrunner;L. Guibas

  • Affiliations:
  • Princeion University;University of Illinois;Stanford University/DEC-SRC

  • Venue:
  • STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
  • Year:
  • 1987

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Abstract

Throughout this paper, we use the term subdivision as a shorthand for “a subdivision of E2 into convex regions”. A subdivision is said to be of size n if it is made of n convex (open) regions, and it is of degree d if every region is adjacent to at most d other regions. We define the line span of a subdivision as the maximum number of regions which can be intersected by a single line (section 3).