On the union of Jordan regions and collision-free translational motion amidst polygonal obstacles
Discrete & Computational Geometry
Fat Triangles Determine Linearly Many Holes
SIAM Journal on Computing
The complexity of the free space for a robot moving amidst fat obstacles
Computational Geometry: Theory and Applications
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
On the complexity of the union of fat objects in the plane
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
On the union of κ-curved objects
Proceedings of the fourteenth annual symposium on Computational geometry
Computational Geometry: Theory and Applications
Ray shooting and lines in space
Handbook of discrete and computational geometry
On fat partitioning, fat covering and the union size of polygons
Computational Geometry: Theory and Applications
The complexity of the union of (&agr;, &bgr;)-covered objects
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Balanced aspect ratio trees: combining the advantages of k-d trees and octrees
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Ray Shooting, Depth Orders and Hidden Surface Removal
Ray Shooting, Depth Orders and Hidden Surface Removal
On the Boundary Complexity of the Union of Fat Triangles
SIAM Journal on Computing
Balanced aspect ratio trees
Approximate range searching using binary space partitions
FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
Vertical ray shooting and computing depth orders for fat objects
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Ray shooting and intersection searching amidst fat convex polyhedra in 3-space
Proceedings of the twenty-second annual symposium on Computational geometry
Proceedings of the twenty-second annual symposium on Computational geometry
Computational Geometry: Theory and Applications
Ray shooting and intersection searching amidst fat convex polyhedra in 3-space
Computational Geometry: Theory and Applications
Computing the visibility map of fat objects
Computational Geometry: Theory and Applications
Improved bounds on the union complexity of fat objects
FSTTCS '05 Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science
Computing the visibility map of fat objects
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
Triangulating and guarding realistic polygons
Computational Geometry: Theory and Applications
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We describe a data structure for vertical ray shooting in a set of n convex fat polyhedra of constant complexity in 3-space. The structure has O(log2 n) query time, and it uses O(n log3 n(log log n)2) storage. It can also be used for fat objects with curved boundaries, at the cost of a small increase in storage.