Kinetic Voronoi Diagrams and Delaunay Triangulations under Polygonal Distance Functions

Published

Journal Article

© 2015, Springer Science+Business Media New York. Let P be a set of n points and Q a convex k-gon in R2. We analyze in detail the topological (or discrete) changes in the structure of the Voronoi diagram and the Delaunay triangulation of P, under the convex distance function defined by Q, as the points of P move along prespecified continuous trajectories. Assuming that each point of P moves along an algebraic trajectory of bounded degree, we establish an upper bound of O(k4nλr(n)) on the number of topological changes experienced by the diagrams throughout the motion; here λr(n) is the maximum length of an (n, r)-Davenport–Schinzel sequence, and r is a constant depending on the algebraic degree of the motion of the points. Finally, we describe an algorithm for efficiently maintaining the above structures, using the kinetic data structure (KDS) framework.

Full Text

Duke Authors

Cited Authors

  • Agarwal, PK; Kaplan, H; Rubin, N; Sharir, M

Published Date

  • September 8, 2015

Published In

Volume / Issue

  • 54 / 4

Start / End Page

  • 871 - 904

Electronic International Standard Serial Number (EISSN)

  • 1432-0444

International Standard Serial Number (ISSN)

  • 0179-5376

Digital Object Identifier (DOI)

  • 10.1007/s00454-015-9729-3

Citation Source

  • Scopus