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A Fast Point Projection Approach of NURBS surfaces

Zhang, Xiangchao, Jiang, Xiang, Scott, Paul J. and Cooper, Philip (2009) A Fast Point Projection Approach of NURBS surfaces. In: A4A6 - Algorithms for Approximation VI 2009, 31st August - 4th September 2009, Ambleside, UK. (Unpublished)

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    Abstract

    In precision metrology, point projection is required when matching mea-
    surement data with the reference NURBS template. In this paper we present a fast
    approach to calculate the foot-point parameters of the orthogonal projection point.
    The entire NURBS surface is rstly divided into 'simple' Bezier patches. The cor-
    rect parameter spans can be determined according to the convex-hull property of
    NURBS. A 'jumping mechanism' is established to help determine the correct switch-
    ing direction between parameter intervals. To improve the reliability of the rene-
    ment result, a second-order approximation approach is adopted. It approximates the
    local curve on the NURBS surface along the optimal incremental direction using an
    arc. The normal curvature of this arc is calculated based on the theory of dieren-
    tial geometry. In this way, point projection becomes a single variable optimisation
    problem. This method is insensitive to the initial guess and can achieve a quadratic
    convergence rate. Finally numerical examples are given to demonstrate the validity
    and eciency of this method.

    Item Type: Conference or Workshop Item (Paper)
    Subjects: T Technology > TJ Mechanical engineering and machinery
    Q Science > QA Mathematics > QA75 Electronic computers. Computer science
    Schools: School of Computing and Engineering
    School of Computing and Engineering > Centre for Precision Technologies
    School of Computing and Engineering > Centre for Precision Technologies > Surface Metrology Group
    Related URLs:
    Depositing User: Xianchao Zhang
    Date Deposited: 31 Mar 2010 08:44
    Last Modified: 07 Sep 2011 12:37
    URI: http://eprints.hud.ac.uk/id/eprint/6926

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