TY - JOUR
T1 - Ray shooting amidst spheres in three dimensions and related problems
AU - Mohaban, Shai
AU - Sharir, Micha
PY - 1997/6
Y1 - 1997/6
N2 - We consider the problem of ray shooting amidst spheres in 3-space: given n arbitrary (possibly intersecting) spheres in 3-space and any ε > 0, we show how to preprocess the spheres in fme O(n3+ε) into a data structure of size O(n3+ε) so that any ray-shooting query can be answered in time O(nε). Our result improves previous techniques (see [P. K. Agarwal L. Guibas, M. Pellegrini, and M. Sharir, "Ray shooting amidst spheres," unpublished note] and [P. K Agarwal and J. Matoušek, Discrete Comput. Geom., 11 (1994), pp. 393-418]), where roughly O(n4) storage was required to support fast queries. Our result shows that ray shooting amidst spheres has complexity comparable with that of ray shooting amidst planes in 3-space. Our technique applies to more general (convex) objects in 3-space, and we also discuss these extensions.
AB - We consider the problem of ray shooting amidst spheres in 3-space: given n arbitrary (possibly intersecting) spheres in 3-space and any ε > 0, we show how to preprocess the spheres in fme O(n3+ε) into a data structure of size O(n3+ε) so that any ray-shooting query can be answered in time O(nε). Our result improves previous techniques (see [P. K. Agarwal L. Guibas, M. Pellegrini, and M. Sharir, "Ray shooting amidst spheres," unpublished note] and [P. K Agarwal and J. Matoušek, Discrete Comput. Geom., 11 (1994), pp. 393-418]), where roughly O(n4) storage was required to support fast queries. Our result shows that ray shooting amidst spheres has complexity comparable with that of ray shooting amidst planes in 3-space. Our technique applies to more general (convex) objects in 3-space, and we also discuss these extensions.
KW - Computational geometry
KW - Ray shooting
UR - http://www.scopus.com/inward/record.url?scp=0006627263&partnerID=8YFLogxK
U2 - 10.1137/S0097539793252080
DO - 10.1137/S0097539793252080
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AN - SCOPUS:0006627263
SN - 0097-5397
VL - 26
SP - 654
EP - 674
JO - SIAM Journal on Computing
JF - SIAM Journal on Computing
IS - 3
ER -