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

    Robert, Jean Marc ; Toussaint, Godfried. / Linear approximation of simple objects. In: Computational Geometry: Theory and Applications. 1994 ; Vol. 4, No. 1. pp. 27-52.
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