On the union of Jordan regions and collision-free translational motion amidst polygonal obstacles
Discrete & Computational Geometry
Separating two simple polygons by a sequence of translations
Discrete & Computational Geometry
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Handbook of discrete and computational geometry
Handbook of discrete and computational geometry
LEDA: a platform for combinatorial and geometric computing
LEDA: a platform for combinatorial and geometric computing
Robot Motion Planning
Triangulating Planar Graphs While Minimizing the Maximum Degree
SWAT '92 Proceedings of the Third Scandinavian Workshop on Algorithm Theory
The Design and Implementation of Planar Maps in CGAL
WAE '99 Proceedings of the 3rd International Workshop on Algorithm Engineering
Dynamic Minkowski sums under scaling
Computer-Aided Design
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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.