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Finding transversals for sets of simple geometric figures

Authors
Journal
Theoretical Computer Science
0304-3975
Publisher
Elsevier
Publication Date
Volume
35
Identifiers
DOI: 10.1016/0304-3975(85)90005-2
Disciplines
  • Computer Science

Abstract

Abstract A straight line that intersects all members of a set S of objects in the real plane is called a transversal of S. Geometric transforms are described that reduce transversal problems for various types of objects to convex hull problems for points. These reductions lead to efficient algorithms for finding transversals which are also described. Applications of the algorithms are found in computer graphics: “Reproduce the line displayed by a collection of pixels”, and in statistics: “Find the line that minimizes the maximum distance from a collection of (weighted) points in the plane”.

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