Elsevier

Computational Geometry

Volume 39, Issue 3, April 2008, Pages 143-162
Computational Geometry

Covering points with a polygon

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Abstract

We consider problems in which we try to cover a given set of points (or a maximum number of them) with a given polygon. To solve these problems we use a new type of diagram that captures point-containment information for scalable, rotated, and/or translated versions of convex polygons. For a given polygon P and a contact point q in a point set S, the diagram parameterizes possible translations, rotations, and scales of P in order to represent containment regions for every other point vS. We present geometric and combinatorial properties of this diagram, and describe how it can be computed and used in the solution of several geometric matching problems. The latter have direct applications to object recognition and tolerancing problems in manufacturing.

Keywords

Tolerancing
Optimization

Cited by (0)

Work on this paper by the first author has been supported in part by an Abraham and Jennie Fialkow Academic Lectureship. Work by the first and third authors has been supported in part by the European FP6 Network of Excellence Grant 506766 (AIM@SHAPE). Work by the second author has been supported by the National Science Foundation under Grant CCR-99-02032.