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- W1995313500 abstract "In this paper we consider the following problems: given a set T of triangles in 3-space, with |T| = n,answer the query “given a line l, does l stab the set of triangles?” (query problem).find whether a stabbing line exists for the set of triangles (existence problem).Given a ray r, which is the first triangle in T hit by r?The following results are shown.There is an O(n3) lower bound on the descriptive complexity of the set of all stabbers for a set of triangles.The existence problem for triangles on a set of planes with g different plane inclinations can be solved in O(g2n2 log n) time (Theorem 2). The query problem is solvable in quasiquadratic O(n2+e) preprocessing and storage and logarithmic O(log n) query time (Theorem 4).If we are given m rays we can answer ray shooting queries in O(m5/6-δ n5/6+5δ log2 n + m log2 n + n log n log m) randomized expected time and O(m + n) space (Theorem 5).In time O((n+m)5/3+4δ) it is possible to decide whether two non convex polyhedra of complexity m and n intersect (Corollary 1).Given m rays and n axis-oriented boxes we can answer ray shooting queries in randomized expected time O(m3/4-δ n3/4+3δ log4 n + m log4 n + n log n log m) and O(m + n) space (Theorem 6)." @default.
- W1995313500 created "2016-06-24" @default.
- W1995313500 creator A5028551838 @default.
- W1995313500 date "1990-01-01" @default.
- W1995313500 modified "2023-10-18" @default.
- W1995313500 title "Stabbing and ray shooting in 3 dimensional space" @default.
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- W1995313500 doi "https://doi.org/10.1145/98524.98563" @default.
- W1995313500 hasPublicationYear "1990" @default.
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