World Academy of Science, Engineering and Technology
Published May 26, 2010 | Version 14845
Journal article Open

The Distance between a Point and a Bezier Curveon a Bezier Surface

Description

The distance between two objects is an important problem in CAGD, CAD and CG etc. It will be presented in this paper that a simple and quick method to estimate the distance between a point and a Bezier curve on a Bezier surface.

Files

14845.pdf

Files (107.4 kB)

Name Size
md5:8111bd38b5700bd6047070c5abe6626b
107.4 kB Preview Download

Additional details

References

  • S.-G. Chen, Geodesic-like curves on parametric surfaces, Computer Aided Geometric Design 27(1) (2010), pp106-117.
  • S.M. Hu and J. Wallner, A second order algorithm for orthogonal projection onto curves and surfaces, Computer Aided Geometric Design 22 (3) (2005), pp. 251-260.
  • K.-J. Kim, Minimum distance between a canal surface and a simple surface, Computer-Aided Design 35 (2003), pp. 871-879
  • Y.L. Ma and W.T. Hewitt, Point inversion and projection for nurbs curve and surface: control polygon approach, Computer Aided Geometric Design 20 (2) (2003), pp. 79-99
  • Lin, M. and Manocha, D., 1995. Fast interference detection between geometric models. The Visual Computer, pp. 541-561.
  • T. Maekawa, Computation of shortest paths on free-form parametric surfaces, Journal of Mechanical Design, Transcation of the ASME, 118(4), 1996, pp499-508.
  • M. Reuter, T. Mikkelsen, E. Sherbrooke, T. Maekawa, N. Patrikalakis: Solving Nonlinear Polynomial Systems in the Barycentric Bernstein Basis. In: The Visual Computer 24 (3). 2007, p. 187 - 200
  • I. Selimovic, Improved algorithms for the projection of points on nurbs curves and surfaces, Computer Aided Geometric Design 23 (5) (2006), pp. 439-445.
  • F. Thomas, C. Turnbull, L. Ros and S. Cameron, Computing signed distances between free-form objects, Proceedings of the IEEE conference on robotics and automation 2000 vol. 4 (2000), pp. 3713-3718 [10] J.M. Zhou, E.C. Sherbrooke and N. Patrikalakis, Computation of stationary points of distance functions, Engineering with Computers 9 (1993), pp. 231-246.