Fat triangles determine linearly many holes
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Point location in fat subdivisions
Information Processing Letters
Vertical decompositions for triangles in 3-space
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
The complexity of the free space for a robot moving amidst fat obstacles
Computational Geometry: Theory and Applications
A practical exact motion planning algorithm for polygonal object amidst polygonal obstacles
Proceedings of the Workshop on Geometry and Robotics
On fence design and the complexity of push plans for orienting parts
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Computing optimal &agr;-fat and &agr;-small decompositions
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Efficient and small representation of line arrangements with applications
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Computational Geometry: Theory and Applications
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
Pianos are not flat: rigid motion planning in three dimensions
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
A Simple Algorithm for Complete Motion Planning of Translating Polyhedral Robots
International Journal of Robotics Research
Smoothed analysis of probabilistic roadmaps
Computational Geometry: Theory and Applications
Towards an evolved lower bound for the most circular partition of a square
CEC'09 Proceedings of the Eleventh conference on Congress on Evolutionary Computation
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We present an efficient and simple paradigm for motion planning amidst fat obstacles. The paradigm fits in the cell decomposition approach to motion planning and exploits workspace properties that follow from the fatness of the obstacles. These properties allow us to decompose the workspace, subject to some constraints, rather than to decompose the higher-dimensional free space directly. A sequence of uniform steps transforms the workspace decomposition into a free space decomposition of asymptotically the same (expectedly small) size. The approach applies to robots with any fixed number of degrees of freedom and turns out to be successful in many cases: it leads to nearly optimal O(nlogn) algorithms for motion planning in 2D, and for motion planning in 3D amidst obstacles of comparable size. In addition, we obtain algorithms for planning 3D motions among polyhedral obstacles, running in O(n2logn) time, and among arbitrary obstacles, running in time O(n3).