On the union of Jordan regions and collision-free translational motion amidst polygonal obstacles
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
Polynomial/rational approximation of Minkowski sum boundary curves
Graphical Models and Image Processing
LEDA: a platform for combinatorial and geometric computing
LEDA: a platform for combinatorial and geometric computing
On the design of CGAL a computational geometry algorithms library
Software—Practice & Experience - Special issue on discrete algorithm engineering
The design and implementation of panar maps in CGAL
Journal of Experimental Algorithmics (JEA)
Robot Motion Planning
Triangulating Planar Graphs While Minimizing the Maximum Degree
SWAT '92 Proceedings of the Third Scandinavian Workshop on Algorithm Theory
Exact minkowski sums and applications
Proceedings of the eighteenth annual symposium on Computational geometry
Improved construction of vertical decompositions of three-dimensional arrangements
Proceedings of the eighteenth annual symposium on Computational geometry
High-Level Filtering for Arrangements of Conic Arcs
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Managing uncertainty in moving objects databases
ACM Transactions on Database Systems (TODS)
Mission-critical management of mobile sensors: or, how to guide a flock of sensors
DMSN '04 Proceeedings of the 1st international workshop on Data management for sensor networks: in conjunction with VLDB 2004
The visibility--voronoi complex and its applications
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Pianos are not flat: rigid motion planning in three dimensions
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Dynamic topological predicates and notifications in moving objects databases
Proceedings of the 6th international conference on Mobile data management
The visibility-Voronoi complex and its applications
Computational Geometry: Theory and Applications - Special issue on the 21st European workshop on computational geometry (EWCG 2005)
Exact and approximate construction of offset polygons
Computer-Aided Design
On the exact maximum complexity of Minkowski sums of convex polyhedra
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Advanced programming techniques applied to Cgal's arrangement package
Computational Geometry: Theory and Applications
A comprehensive and robust procedure for obtaining the nofit polygon using Minkowski sums
Computers and Operations Research
Exact and efficient construction of planar Minkowski sums using the convolution method
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Journal of Computational and Applied Mathematics
Exact and efficient construction of Minkowski sums of convex polyhedra with applications
Computer-Aided Design
Mathematical model and efficient algorithms for object packing problem
Computational Geometry: Theory and Applications
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Minkowski sum based octree generation for triangular meshes
ISCIS'06 Proceedings of the 21st international conference on Computer and Information Sciences
International Journal of Computer Applications in Technology
Collision free region determination by modified polygonal Boolean operations
Computer-Aided Design
| Hi-index | 0.00 |
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.