TY - JOUR
T1 - Ray shooting and stone throwing with near-linear storage
AU - Sharir, Micha
AU - Shaul, Hayim
N1 - Funding Information:
✩ This work was supported by a grant from the Israel Science Fund (for a Center of Excellence in Geometric Computing), and is part of the second author’s Ph.D. dissertation, prepared under the supervision of the first author in Tel Aviv University. Work by Micha Sharir was also supported by NSF Grants CCR-97-32101 and CCR-00-98246, by a grant from the US–Israel Binational Science Foundation, and by the Hermann Minkowski–MINERVA Center for Geometry at Tel Aviv University. * Corresponding author. E-mail addresses: [email protected] (M. Sharir), [email protected] (H. Shaul).
PY - 2005/3
Y1 - 2005/3
N2 - The paper presents two algorithms involving shooting in three dimensions. We first present an algorithm for performing ray shooting amid several special classes of n triangles in three dimensions, including sets of fat triangles, and sets of triangles stabbed by a common line. In all these special cases, our technique requires near-linear preprocessing and storage, and answers a query in O(n2 /3+ε) time. This improves the best known result of O(n3 /4+ε) query time (with near-linear storage) for general triangles. The second algorithm handles stone-throwing amid arbitrary triangles in 3-space, where the curves along which we shoot are vertical parabolic arcs that are trajectories of stones thrown under gravity. We present an algorithm that answers stone-throwing queries in O(n3 /4+ε) time, using near linear storage and preprocessing. As far as we know, this is the first nontrivial solution of this problem. Several extensions of both algorithms are also presented.
AB - The paper presents two algorithms involving shooting in three dimensions. We first present an algorithm for performing ray shooting amid several special classes of n triangles in three dimensions, including sets of fat triangles, and sets of triangles stabbed by a common line. In all these special cases, our technique requires near-linear preprocessing and storage, and answers a query in O(n2 /3+ε) time. This improves the best known result of O(n3 /4+ε) query time (with near-linear storage) for general triangles. The second algorithm handles stone-throwing amid arbitrary triangles in 3-space, where the curves along which we shoot are vertical parabolic arcs that are trajectories of stones thrown under gravity. We present an algorithm that answers stone-throwing queries in O(n3 /4+ε) time, using near linear storage and preprocessing. As far as we know, this is the first nontrivial solution of this problem. Several extensions of both algorithms are also presented.
KW - Data structures
KW - Parametric search
KW - Range searching
KW - Ray shooting
UR - http://www.scopus.com/inward/record.url?scp=84867938200&partnerID=8YFLogxK
U2 - 10.1016/j.comgeo.2004.10.001
DO - 10.1016/j.comgeo.2004.10.001
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:84867938200
SN - 0925-7721
VL - 30
SP - 239
EP - 252
JO - Computational Geometry: Theory and Applications
JF - Computational Geometry: Theory and Applications
IS - 3
ER -