SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Data structures for mobile data
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Kinetic collision detection between two simple polygons
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Separation-sensitive collision detection for convex objects
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Robot Motion Planning
Voronoi Diagrams of Moving Points in the Plane
WG '91 Proceedings of the 17th International Workshop
Voronoi Diagrams for Moving Disks and Applications
WADS '01 Proceedings of the 7th International Workshop on Algorithms and Data Structures
Separation Sensitive Kinetic Separation Structures for Convex Polygons
JCDCG '00 Revised Papers from the Japanese Conference on Discrete and Computational Geometry
| Hi-index | 0.00 |
We describe a kinetic data structure for maintaining a compact Voronoi-like diagram of convex polygons moving around in the plane. We use a compact diagram for the polygons, dual to the Voronoi, first presented in [MKS96]. A key feature of this diagram is that its size is only a function of the number of polygons and not of their complexity. We demonstrate a local certifying property of that diagram, akin to that of Delaunay triangulations of points. We then obtain a method for maintaining this diagram that is output-sensitive and costs O(log n) per update. Furthermore, we show that for a set of k polygons with a total of n vertices moving along bounded degree algebraic motions, this dual diagram, and thus their compact Voronoi diagram, changes combinatorially Ω(n2) and O(kn2β(k)β(n)) times, where β(ċ) is an extremely slowly growing function. This compact Voronoi diagram can be used for collision detection or retraction motion planning among the moving polygons.