Polygon decomposition for efficient construction of Minkowski sums


Conference Paper

© Springer-Verlag Berlin Heidelberg 2000. Several algorithms for computing the Minkowski sum of two polygons in the plane begin by decomposing each polygon into convex subpolygons. We examine different methods for decomposing polygons by their suitability for efficient construction of Minkowski sums. We study and experiment with various well-known decompositions as well as with several new decomposition schemes. We report on our experiments with the various decompositions and different input polygons. Among our findings are that in general: (i) triangulations are too costly (ii) what constitutes a good decomposition for one of the input polygons depends on the other input polygon-consequently, we develop a procedure for simultaneously decomposing the two polygons such that a “mixed” objective function is minimized, (iii) there are optimal decomposition algorithms that significantly expedite the Minkowski-sum computation, but the decomposition itself is expensive to compute - in such cases simple heuristics that approximate the optimal decomposition perform very well.

Full Text

Duke Authors

Cited Authors

  • Agarwal, PK; Flato, E; Halperin, D

Published Date

  • January 1, 2000

Published In

Volume / Issue

  • 1879 /

Start / End Page

  • 20 - 31

Electronic International Standard Serial Number (EISSN)

  • 1611-3349

International Standard Serial Number (ISSN)

  • 0302-9743

Digital Object Identifier (DOI)

  • 10.1007/3-540-45253-2_3

Citation Source

  • Scopus