Ray shooting and parametric search
SIAM Journal on Computing
Range searching in low-density environments
Information Processing Letters
Ray Shooting Amidst Spheres in Three Dimensions and Related Problems
SIAM Journal on Computing
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Computational Geometry: Theory and Applications
Handbook of discrete and computational geometry
Ray shooting and lines in space
Handbook of discrete and computational geometry
Ray Shooting, Depth Orders and Hidden Surface Removal
Ray Shooting, Depth Orders and Hidden Surface Removal
Range Searching and Point Location among Fat Objects
ESA '94 Proceedings of the Second Annual European Symposium on Algorithms
Vertical ray shooting for fat objects
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Ray shooting amid balls, farthest point from a line, and range emptiness searching
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Vertical ray shooting and computing depth orders for fat objects
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Approximate range searching using binary space partitions
FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
Linear data structures for fast ray-shooting amidst convex polyhedra
ESA'07 Proceedings of the 15th annual European conference on Algorithms
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We present a data structure for ray-shooting queries in a set of convex fat polyhedra of total complexity n in R3. The data structure uses O(n2+ε) storage and preprocessing time, and queries can be answered in O(log2 n) time. A trade-off between storage and query time is also possible: for any m with n 2, we can construct a structure that uses O(m1+ε) storage and preprocessing time such that queries take O((n/√m)log2 n) time.We also describe a data structure for simplex intersection queries in a set of n convex fat constant-complexity polyhedra in R3. For any m with n 3, we can construct a structure that uses O(m1+ε) storage and preprocessing time such that all polyhedra intersecting a query simplex can be reported in O((n/m1/3)log n+k) time, where k is the number of answers.