Title :
On convergence of the control polygons series of C-Bezier curves
Author :
Dong, Chenshi ; Wang, Guozhao
Author_Institution :
Dept. of Math., Zhejiang Univ., Hangzhou, China
Abstract :
The C-Bezier curve is introduced to CAD/CAM to deal with circular arcs, cylinders, and cones. It can precisely represent these conic curves in a Bezier-like way. A conjecture of Q.Y. Chen and G.Z. Wang (2003) is that the sequence of control polygons associated with the C-Bezier representation of a curve converges to the curve itself as the curve degree n goes to infinity. In this paper we prove this conjecture.
Keywords :
CAD/CAM; computational geometry; curve fitting; engineering graphics; C-Bezier curves; CAD; CAM; circular arcs; cones; conic curves; control polygons series; convergence; cylinders; CADCAM; Chebyshev approximation; Computer aided manufacturing; Convergence; Costs; H infinity control; Mathematics; Polynomials; Solid modeling;
Conference_Titel :
Geometric Modeling and Processing, 2004. Proceedings
Print_ISBN :
0-7695-2078-2
DOI :
10.1109/GMAP.2004.1290026
