M. Pellegrini, Ray-shooting and isotopy classes of lines in 3-dimensional space, in Proc. 2nd Workshop on Algorithms and Data Structures, Ottawa, 1991, pp. 20-- 31.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... Delta of n triangles in R 3 into a data structure, so that the first triangle of Delta hit by a query ray can be reported quickly. In the last few years, the ray shooting has received a considerable attention due to its applications in computer graphics and other geometric problems, e.g. see [1, 4, 3, 8, 14, 20, 28]. The best known algorithm for ray shooting in 3D is due to Agawral and Sharir [4] that can answer a query in O(n 4=5 ) time using O(n 1 ) space and preprocessing. If O(n 4 ffi ) space and preprocessing are allowed, a query can be answered in O(log n) time [4, 8, 28] In this subsection we ....

....e.g. see [1, 4, 3, 8, 14, 20, 28] The best known algorithm for ray shooting in 3D is due to Agawral and Sharir [4] that can answer a query in O(n 4=5 ) time using O(n 1 ) space and preprocessing. If O(n 4 ffi ) space and preprocessing are allowed, a query can be answered in O(log n) time [4, 8, 28]. In this subsection we show that the query time can be improved to close to O(n 3=4 ) using almost linear space and preprocessing. A result by Agarwal and Matousek [3] suggests that it suffices to construct a data structure for detecting an intersection between Delta and a query segment. ....

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M. Pellegrini. Ray shooting and isotopy classes of lines in 3-dimensional spaces. Proc. 2nd Workshop on Algorithms and Data Structures, 1991, pp. 20--31.

....p) 2e then k d(i Gamma 2) 2e di=2e and again the Dehn Sommerville relations extend the bound for all 0 k i. This completes the proof of the Extended Zone Theorem. 2 8 3 Discussion The following immediate application of the Extended Zone Theorem is obtained from an observation of Pellegrini [13, 14], as also discussed in [4] so that for a query ray ae, we can compute the first triangle met by ae in time O(log n) This result improves the preprocessing and space complexity of the best previous solution, given in [4] by a factor of roughly n 1=2 . A related application of the ....

M. Pellegrini, Ray-shooting and isotopy classes of lines in 3-dimensional space, in Proc. 2nd Workshop on Algorithms and Data Structures, Ottawa, 1991, pp. 20-- 31.

....ray tracing) is a central problem in graphics. Given the internal representation of a polygonal 3 dimensional scene and 1 Research supported by NSF grant CCR 8901484, and by Eni and Enidata within the AXL project. Results presented in this paper have appeared in preliminary form in [Pel90] and [Pel91b] 2 New York University, Courant Institute. Present address: King s College, Dept. of Computing, Strand, London WC2R 2LS, U.K. e mail: m.pellegrini oak.cc.kcl.ac.uk 1 some light sources, a good image rendering requires that the amount of light received by every pixel is computed. If the scene ....

....and n the total input size, for any ffl 0. 1. 3 Summary of results For the most general version of the problem involving any polygonal scene and any set of rays only the trivial O(mn) bound were known before the results presented in this paper and appeared in preliminary form in [Pel90] and [Pel91b] We give off line ray shooting algorithms with a substantially sublinear cost per ray, for any set of triangles and rays (Section 5) The size of the data structure used in this paper to answer ray shooting queries in logarithmic time depends on the total complexity of all cells of a ....

M. Pellegrini. Ray shooting and isotopy classes of lines in 3dimensional space. In Proceedings of the 1991 Workshop on Algorithms and Data Structures, number 519 in Lecture Notes in Computer Science, pages 20--31. Springer Verlag, 1991.

....point in a 1dimensional space. Thus from Lemma 1 we can count efficiently how many c oriented facets meet a query segment, and thus also decide if the query segment is empty of intersections. As a matter of fact, by extending a slightly different approach to this ray shooting problem developed in [33] for axis oriented polyhedra (a special case of c oriented polyhedra) it is possible to avoid using parametric search and to reduce the query time to O(log n) We choose to present this weaker result since it is more similar to the solution for the other queries used by the HSRA Algorithm. Using ....

M. Pellegrini. Ray shooting and isotopy classes of lines in 3-dimensional space. To appear in Algorithmica. Preliminary version in Proceedings of the 1991 Workshop on Algorithms and Data Structures, number 519 in Lecture Notes in Computer Science, pages 20--31. Springer Verlag, 1991.

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