Title: Projecting curves onto free-form surfaces

Authors: Xiao-Ping Wang, Wei Wei, Wei-Zhong Zhang

Addresses: Research Centre of CAD/CAM Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, PR China. ' Research Centre of CAD/CAM Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, PR China. ' College of Information Engineering, Qingdao University, Qingdao 266071, PR China

Abstract: This paper presents simple methods of projecting a space curve onto a surface. Here, the parallel projection and the central projection are particularly considered. We derive the differential equations of the projection curve on both parametrically and implicitly defined surface. The projection curve is obtained by numerically solving the initial-value problem for a system of first-order Ordinary Differential Equations (ODEs) in the parametric domain associated with the surface representation for parametric case or in 3D space for implicit case. Some examples are also given to demonstrate that the presented methods are effective and potentially useful in computer-aided design.

Keywords: space curves; curve projection; parametric surface; implicit surface; ODEs; ordinary differential equations; freeform surfaces; parallel projection; central projection; computer-aided design; CAD.

DOI: 10.1504/IJCAT.2010.032204

International Journal of Computer Applications in Technology, 2010 Vol.37 No.2, pp.153 - 159

Published online: 16 Mar 2010 *

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