{"title":"The Distance between a Point and a Bezier Curveon a Bezier Surface","authors":"Wen-Haw Chen, Sheng-Gwo Chen","volume":41,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":540,"pagesEnd":544,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/14845","abstract":"The distance between two objects is an important\r\nproblem in CAGD, CAD and CG etc. It will be presented in this paper\r\nthat a simple and quick method to estimate the distance between a\r\npoint and a Bezier curve on a Bezier surface.","references":"[1] S.-G. Chen, Geodesic-like curves on parametric surfaces, Computer\r\nAided Geometric Design 27(1) (2010), pp106-117.\r\n[2] S.M. Hu and J. Wallner, A second order algorithm for orthogonal\r\nprojection onto curves and surfaces, Computer Aided Geometric Design\r\n22 (3) (2005), pp. 251-260.\r\n[3] K.-J. Kim, Minimum distance between a canal surface and a simple\r\nsurface, Computer-Aided Design 35 (2003), pp. 871-879\r\n[4] Y.L. Ma and W.T. Hewitt, Point inversion and projection for nurbs curve\r\nand surface: control polygon approach, Computer Aided Geometric\r\nDesign 20 (2) (2003), pp. 79-99\r\n[5] Lin, M. and Manocha, D., 1995. Fast interference detection between\r\ngeometric models. The Visual Computer, pp. 541-561.\r\n[6] T. Maekawa, Computation of shortest paths on free-form parametric\r\nsurfaces, Journal of Mechanical Design, Transcation of the ASME,\r\n118(4), 1996, pp499-508.\r\n[7] M. Reuter, T. Mikkelsen, E. Sherbrooke, T. Maekawa, N. Patrikalakis:\r\nSolving Nonlinear Polynomial Systems in the Barycentric Bernstein\r\nBasis. In: The Visual Computer 24 (3). 2007, p. 187 - 200\r\n[8] I. Selimovic, Improved algorithms for the projection of points on nurbs\r\ncurves and surfaces, Computer Aided Geometric Design 23 (5) (2006),\r\npp. 439-445.\r\n[9] F. Thomas, C. Turnbull, L. Ros and S. Cameron, Computing signed\r\ndistances between free-form objects, Proceedings of the IEEE conference\r\non robotics and automation 2000 vol. 4 (2000), pp. 3713-3718\r\n[10] J.M. Zhou, E.C. Sherbrooke and N. Patrikalakis, Computation of\r\nstationary points of distance functions, Engineering with Computers 9\r\n(1993), pp. 231-246.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 41, 2010"}