TY - JOUR
T1 - ON RAY SHOOTING FOR TRIANGLES IN 3-SPACE AND RELATED PROBLEMS
AU - Ezra, Esther
AU - Sharir, Micha
N1 - Publisher Copyright:
© 2022 Society for Industrial and Applied Mathematics Publications. All rights reserved.
PY - 2022
Y1 - 2022
N2 - We consider several problems that involve lines in three dimensions, and present improved algorithms for solving them. The problems include (i) ray shooting amid triangles in R3, (ii) reporting intersections between query lines (segments, or rays) and input triangles, as well as approximately counting the number of such intersections, (iii) computing the intersection of two nonconvex polyhedra, (iv) detecting, counting, or reporting intersections in a set of lines in R3, and (v) output-sensitive construction of an arrangement of triangles in three dimensions. Our approach is based on the polynomial partitioning technique. For example, our ray-shooting algorithm processes a set of n triangles in R3 into a data structure for answering ray shooting queries amid the given triangles, which uses O(n3/2+ε) storage and preprocessing, and answers a query in O(n1/2+ε) time, for any ε>0.
AB - We consider several problems that involve lines in three dimensions, and present improved algorithms for solving them. The problems include (i) ray shooting amid triangles in R3, (ii) reporting intersections between query lines (segments, or rays) and input triangles, as well as approximately counting the number of such intersections, (iii) computing the intersection of two nonconvex polyhedra, (iv) detecting, counting, or reporting intersections in a set of lines in R3, and (v) output-sensitive construction of an arrangement of triangles in three dimensions. Our approach is based on the polynomial partitioning technique. For example, our ray-shooting algorithm processes a set of n triangles in R3 into a data structure for answering ray shooting queries amid the given triangles, which uses O(n3/2+ε) storage and preprocessing, and answers a query in O(n1/2+ε) time, for any ε>0.
KW - Polynomial partitioning
KW - Ray shooting
KW - Three dimensions
KW - Tradeoff
UR - http://www.scopus.com/inward/record.url?scp=85136468888&partnerID=8YFLogxK
U2 - 10.1137/21M1408245
DO - 10.1137/21M1408245
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AN - SCOPUS:85136468888
SN - 0097-5397
VL - 51
SP - 1065
EP - 1095
JO - SIAM Journal on Computing
JF - SIAM Journal on Computing
IS - 4
ER -