Linear approximation of simple objects

Jean Marc Robert, Godfried Toussaint

Research output: Contribution to journalArticle

Abstract

Let S be a family of m convex polygons in the plane with a total number of n vertices and let each polygon have a positive weight associated with it. This paper presents algorithms to solve the weighted minmax approximation and the weighted minsum approximation problems. For the first problem, a line minimizing the maximum weighted orthogonal Euclidean distance to the polygons can be found in O(n2logn) time and O(n2) space. The time and space complexities can be reduced to O(n log n) and O(n), respectively, when the weights are equal. For the second problem, a line minimizing the sum of the weighted distances to the polygons can be found in O(nm log m) time and O(n) space. For both problems, we also consider constrained versions of these problems.

Original languageEnglish (US)
Pages (from-to)27-52
Number of pages26
JournalComputational Geometry: Theory and Applications
Volume4
Issue number1
DOIs
StatePublished - Jan 1 1994

Fingerprint

Linear Approximation
Polygon
Weighted Approximation
Line
Convex polygon
Space Complexity
Approximation Problem
Euclidean Distance
Min-max
Time Complexity
Object
Approximation

Keywords

  • Dual transform
  • Line sweep algorithms
  • Linear approximation

ASJC Scopus subject areas

  • Computer Science Applications
  • Geometry and Topology
  • Control and Optimization
  • Computational Theory and Mathematics
  • Computational Mathematics

Cite this

Linear approximation of simple objects. / Robert, Jean Marc; Toussaint, Godfried.

In: Computational Geometry: Theory and Applications, Vol. 4, No. 1, 01.01.1994, p. 27-52.

Research output: Contribution to journalArticle

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