**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**30184

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

**Authors:**
Wen-Haw Chen,
Sheng-Gwo Chen

**Abstract:**

**Keywords:**
Geodesic-like curve,
distance,
projection,
Bezier.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1083727

**References:**

[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.