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Given finite sets P and T of points in the Euclidean space R d ,t he point pattern matching problem studied in this paper is to find all translations f ∈ R d such that P + f ⊆ T. A fast search algorithm with some variants is presented for point patterns P that have regular grid-like geometric shape. The algorithm is analogous to the Knuth-Morris-Pratt algorithm of string matching. The time requirement of the search is O(r|T | )w herer is the grid dimension of P. Pattern P has grid dimension r = 1 if it consists of evenly spaced points on a line. In general, a pattern P is an r-dimensional grid if it has for some p ∈ P and e1,...,er ∈ R d and positive integers m1,...,mr ar epresentationP = {p +i1e1 + ·· ·+irer | 0 ≤ ij ≤ mj } where the ij 's are integers. Both P and T are given to the search algorithm in the lexicographic order.

Geometric Point Pattern Matching in the Knuth-Morris-Pratt Way