Polygon decomposition for efficient construction of Minkowski sums

Pankaj K. Agarwal*, Eyal Flato, Dan Halperin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

94 Scopus citations

Abstract

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 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.

Original languageEnglish
Pages (from-to)39-61
Number of pages23
JournalComputational Geometry: Theory and Applications
Volume21
Issue number1-2
DOIs
StatePublished - 2002

Funding

FundersFunder number
AFIRST/France
Army Research Office MURIDAAH04-96-1-0013
ESPRIT IV LTR28155, 21957
Israeli Ministry of Science
U.S.–Israeli Binational Science Foundation
National Science FoundationCCR-9732787, EIA-9870724, EIA-997287
Directorate for Computer and Information Science and Engineering9870724
Israel Academy of Sciences and Humanities
Israel Science Foundation
Tel Aviv University

    Keywords

    • Convex decomposition
    • Experimental results
    • Minkowski sum
    • Polygon decomposition

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