The Distance between a Point and a Bezier Curveon a Bezier Surface
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.
[1] S.-G. Chen, Geodesic-like curves on parametric surfaces, Computer
Aided Geometric Design 27(1) (2010), pp106-117.
[2] 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.
[3] K.-J. Kim, Minimum distance between a canal surface and a simple
surface, Computer-Aided Design 35 (2003), pp. 871-879
[4] 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
[5] Lin, M. and Manocha, D., 1995. Fast interference detection between
geometric models. The Visual Computer, pp. 541-561.
[6] T. Maekawa, Computation of shortest paths on free-form parametric
surfaces, Journal of Mechanical Design, Transcation of the ASME,
118(4), 1996, pp499-508.
[7] 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
[8] I. Selimovic, Improved algorithms for the projection of points on nurbs
curves and surfaces, Computer Aided Geometric Design 23 (5) (2006),
pp. 439-445.
[9] 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.
[1] S.-G. Chen, Geodesic-like curves on parametric surfaces, Computer
Aided Geometric Design 27(1) (2010), pp106-117.
[2] 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.
[3] K.-J. Kim, Minimum distance between a canal surface and a simple
surface, Computer-Aided Design 35 (2003), pp. 871-879
[4] 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
[5] Lin, M. and Manocha, D., 1995. Fast interference detection between
geometric models. The Visual Computer, pp. 541-561.
[6] T. Maekawa, Computation of shortest paths on free-form parametric
surfaces, Journal of Mechanical Design, Transcation of the ASME,
118(4), 1996, pp499-508.
[7] 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
[8] I. Selimovic, Improved algorithms for the projection of points on nurbs
curves and surfaces, Computer Aided Geometric Design 23 (5) (2006),
pp. 439-445.
[9] 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.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:63844", author = "Wen-Haw Chen and Sheng-Gwo Chen", title = "The Distance between a Point and a Bezier Curveon a Bezier Surface", abstract = "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.", keywords = "Geodesic-like curve, distance, projection, Bezier.", volume = "4", number = "5", pages = "637-4", }
