Geometric fit of a point set by generalized circles

Mark-Christopher Körner, Jack Brimberg, Henrik Juel, Anita Schöbel

    Research output: Contribution to journalJournal articleResearchpeer-review

    Abstract

    In our paper we approximate a set of given points by a general circle. More precisely, given two norms k 1 and k 2 and a set of points in the plane, we consider the problem of locating and scaling the unit circle of norm k 1 such that the sum of weighted distances between the circumference of the circle and the given points is minimized, where the distance is measured by a norm k 2. We present results for the general case. In the case that k 1 and k 2 are both polyhedral norms, we are able to solve the problem by investigating a finite candidate set.
    Original languageEnglish
    JournalJournal of Global Optimization
    Volume51
    Issue number1
    Pages (from-to)115-132
    ISSN0925-5001
    DOIs
    Publication statusPublished - 2010

    Keywords

    • circle location
    • dimensional facility
    • minisum
    • polyhedral norms

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