An involute spiral that matches G2 Hermite data in the plane

T.N.T. Goodman, D.S. Meek, D.J. Walton

    Research output: Contribution to journalArticle

    13 Citations (Scopus)

    Abstract

    A construction is given for a planar rational Pythagorean hodograph spiral, which interpolates any two-point G Hermite data that a spiral can match. When the curvature at one of the points is zero, the construction gives the unique interpolant that is an involute of a rational Pythagorean hodograph curve of the form cubic over linear. Otherwise, the spiral comprises an involute of a Tschirnhausen cubic together with at most two circular arcs. The construction is by explicit formulas in the first case, and requires the solution of a quadratic equation in the second case.
    Original languageEnglish
    Pages (from-to)733-756
    Number of pages24
    JournalComputer Aided Geometric Design
    Volume26
    Issue number7
    DOIs
    Publication statusPublished - Oct 2009

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