Curves and surfaces represented by polynomial support functions

Z. Sir, Jens Gravesen, B. Juttler

    Research output: Contribution to journalJournal articlepeer-review

    Abstract

    This paper studies shapes (curves and surfaces) which can be described by (piecewise) polynomial support functions. The class of these shapes is closed under convolutions, offsetting, rotations and translations. We give a geometric discussion of these shapes and present methods for the approximation of general curves and surfaces by them. Based on the rich theory of spherical spline functions, this leads to computational techniques for rational curves and surfaces with rational offsets, which can deal with shapes without inflections/parabolic points.
    Original languageEnglish
    JournalTheoretical Computer Science
    Volume392
    Issue number1-3
    Pages (from-to)141-157
    ISSN0304-3975
    DOIs
    Publication statusPublished - 2008

    Keywords

    • approximation by spherical splines
    • convolutions
    • offset surfaces
    • polynomial support function

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