Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
An optimal algorithm for geometrical congruence
Journal of Algorithms
Point set pattern matching in 3-D
Pattern Recognition Letters
Testing the congruence of d-dimensional point sets
Proceedings of the sixteenth annual symposium on Computational geometry
Crossing Numbers and Hard Erdös Problems in Discrete Geometry
Combinatorics, Probability and Computing
Lenses in arrangements of pseudo-circles and their applications
Journal of the ACM (JACM)
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
Intersection reverse sequences and geometric applications
Journal of Combinatorial Theory Series A
Improved bounds for incidences between points and circles
Proceedings of the twenty-ninth annual symposium on Computational geometry
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We consider the problem of bounding the maximum possible number fk,d(n) of k-simplices that are spanned by a set of n pointsin Rd and are similar to a given simplex. We first show that f2,3(n) = O(n13/6), and then tacklethe general case, and show that fd-2, d(n) = O(nd-8/5) and fd-1,d(n) = O*(nd-72/55), for any d.Our technique extends to derive bounds for other valuesof k and d, and we illustrate this by showing that f2,5(n)=O(n8/3).