Projecting curves onto free-form surfaces.pdf

Int. J. Computer Applications in Technology, Vol. 37, No. 2, 2010 153 Copyright ? 2010 Inderscience Enterprises Ltd. Projecting curves onto free-form surfaces Xiao-Ping Wang* and Wei Wei Research Centre of CAD/CAM Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, PR China E-mail: harayano@ *Corresponding author Wei-Zhong Zhang College of Information Engineering, Qingdao University, Qingdao 266071, PR China E-mail: zhangwz_01@ 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 curve; projection; parametric surface; implicit surface; ODEs; ordinary differential equations. Reference to this paper should be made as follows: Wang, X-P., Wei, W. and Zhang, W-Z. (2010) ‘Projecting curves onto free-form surfaces’, Int. J. Computer Applications in Technology, Vol. 37, No. 2, pp.153–159. Biographical notes: Xiao-Ping Wang received his PhD in Aerospace Manufacture Engineering from Northwestern Polytechnical University, Xi’an, China, in 2002. He is currently Associate Professor in the Research Centre of CAD/CAM Engineering, Nanjing University of Aeronautics and Astronautics (NUAA), Nanjing, China. He is also a senior member of Chinese Mechanical Engineering Society. His research interests include CAD/CAM, digital design, computer graphics, etc. Wei Wei recei