The power of geometric duality
BIT - Ellis Horwood series in artificial intelligence
Constructing arrangements of lines and hyperplanes with applications
SIAM Journal on Computing
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Topologically sweeping an arrangement
Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
Combinatorial complexity bounds for arrangements of curves and spheres
Discrete & Computational Geometry - Special issue on the complexity of arrangements
Repeated angles in the plane and related problems
Journal of Combinatorial Theory Series A
On the zone theorem for hyperplane arrangements
SIAM Journal on Computing
On counting point-hyperplane incidences
Computational Geometry: Theory and Applications - Special issue: The European workshop on computational geometry -- CG01
Distinct Distances in Three and Higher Dimensions
Combinatorics, Probability and Computing
Improving the crossing lemma by finding more crossings in sparse graphs: [extended abstract]
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Point–Line Incidences in Space
Combinatorics, Probability and Computing
On the number of directions determined by a three-dimensional points set
Journal of Combinatorial Theory Series A
An Improved Bound for Joints in Arrangements of Lines in Space
Discrete & Computational Geometry
Incidences between Points and Circles in Three and Higher Dimensions
Discrete & Computational Geometry
Incidences of not-too-degenerate hyperplanes
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Repeated Angles in Three and Four Dimensions
SIAM Journal on Discrete Mathematics
Distinct Triangle Areas in a Planar Point Set
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
Farthest segments and extremal triangles spanned by points in R3
Information Processing Letters
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We formulate and give partial answers to several combinatorial problems on four-tuples of n points in three-space. (i) The number of minimum (nonzero) volume tetrahedra spanned by n points in R3 is Θ(n3). (ii) The number of unit-volume tetrahedra determined by n points in R3 is O(n7/2), and there are point sets for which this number is ω(n3 log log n). (iii) The tetrahedra determined by n points in R3, not all on a plane, have at least ω(n) distinct volumes, and there are point sets for which this number is O(n); this gives a first partial answer for the three-dimensional case to an old question of Erdős, Purdy, and Straus. We also give an O(n3) time algorithm for reporting all tetrahedra of minimum nonzero volume, and thereby extend an early algorithm of Edelsbrunner, O'Rourke, and Seidel.