Affiliations: College of Mechanical Engineering and Automation, Huaqiao University, Xiamen, Fujian, China
Correspondence:
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Corresponding author: Bin Liu, College of Mechanical Engineering and Automation, Huaqiao University, Xiamen, Fujian, China. Tel.: +86 592 6162597; Fax: +86 592 6162599; E-mail: [email protected], [email protected].
Abstract: Computation of the distance between two objects is an important problem in computer aided geometric design. To make up the deficiencies in the existing algorithm, a calculation method of the closet distance between point and curve on mesh surfaces is proposed. The curves on surfaces are represented by geodesic B-spline, and the knot insertion algorithm in classic B-spline curve is expand to curved space, so that the geodesic B-spline curve can be decomposed into combination of sub-Bézier curves; using the intermediate results of the expand De Casteljau's algorithm, derivative of curve can be calculated. On this basis, the orthogonal projection point calculation algorithm, which is the projection point from point to curve, in Euclidean space is extended to curved space, and the point calculation method of the orthogonal projection on curved space is given, that is to say, the geodesic distance between point and its orthogonal projection point is the shortest distance from point to curve. Experimental results show that, the proposed method is robust, effective, and with a good adaptability to the shape variation of surface.
Keywords: Distance, orthogonal projection, geodesic B-spline, curves on surfaces, mesh
