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A Fast Point Projection Approach of NURBS surfaces

By Xiangchao Zhang, Xiang Jiang, Paul J. Scott and Philip Cooper

Abstract

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

Topics: TJ, QA75
OAI identifier: oai:eprints.hud.ac.uk:6926
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