On the union of Jordan regions and collision-free translational motion amidst polygonal obstacles
Discrete & Computational Geometry
Optimal point location in a monotone subdivision
SIAM Journal on Computing
On the general motion planning problem with two degrees of freedom
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
SCG '85 Proceedings of the first annual symposium on Computational geometry
An algorithm for planning collision-free paths among polyhedral obstacles
Communications of the ACM
On simultaneous inner and outer approximation of shapes
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Gross motion planning—a survey
ACM Computing Surveys (CSUR)
Exact and approximation algorithms for computing optimal fat decompositions
Computational Geometry: Theory and Applications - Special issue on the 14th Canadian conference on computational geometry — CCCG02
| Hi-index | 0.00 |
We study rigid motions of a rectangle amidst polygonal obstacles. The best known algorithms for this problem have running time &OHgr;(n2) where n is the number of obstacle corners. We introduce the tightness of a motion planning problem as a measure of the difficulty of a planning problem in an intuitive sense and describe an algorithm with running time &ogr;((a/b · 1/&egr; crit + 1)n(log n)2), where a ≥ b are the lengths of the sides of a rectangle and &egr;crit is the tightness of the problem. We show further that the complexity (= number of vertices) of the boundary of n bow-ties (c.f. Figure 1.1) is &Ogr;(n). Similar results for the union of other simple geometric figures such as triangles and wedges are also presented.