Constructing higher-dimensional convex hulls at logarithmic cost per face
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Constructing arrangements of lines and hyperplanes with applications
SIAM Journal on Computing
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Fast ray tracing by ray classification
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Algorithms for line transversals in space
SCG '87 Proceedings of the third annual symposium on Computational geometry
Lines in space-combinators, algorithms and applications
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
The complexity of many faces in arrangements of lines of segments
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Skewed projections with an application to line stabbing in R3
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Arrangements of lines in 3-space: a data structure with applications
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
A deterministic algorithm for partitioning arrangements of lines and its application
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Ray shooting and other applications of spanning trees with low stabbing number
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Visibility with a moving point of view
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Finding stabbing lines in 3-dimensional space
SODA '91 Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms
Computing the antipenumbra of an area light source
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Finding a line transversal of axial objects in three dimensions
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Incidence and nearest-neighbor problems for lines in 3-space
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
On lines missing polyhedral sets in 3-space
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
The visibility skeleton: a powerful and efficient multi-purpose global visibility tool
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
3D visibility made visibly simple: an introduction to the visibility skeleton
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Line transversals of balls and smallest enclosing cylinders in three dimensions
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
3-D to 2-D Pose Determination with Regions
International Journal of Computer Vision - Special issue on computer vision research at NEC Research Institute
Exact from-region visibility culling
EGRW '02 Proceedings of the 13th Eurographics workshop on Rendering
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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 &rgr;, which is the first triangle in T hit by &rgr;?The following results are shown.There is an &OHgr;(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 &Ogr;(g2n2 log n) time (Theorem 2). The query problem is solvable in quasiquadratic &Ogr;(n2+&egr;) preprocessing and storage and logarithmic &Ogr;(log n) query time (Theorem 4).If we are given m rays we can answer ray shooting queries in &Ogr;(m5/6-&dgr; n5/6+5&dgr; log2 n + m log2 n + n log n log m) randomized expected time and &Ogr;(m + n) space (Theorem 5).In time &Ogr;((n+m)5/3+4&dgr;) 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 &Ogr;(m3/4-&dgr; n3/4+3&dgr; log4 n + m log4 n + n log n log m) and &Ogr;(m + n) space (Theorem 6).