DocumentCode
2863269
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
fYear
2004
fDate
2004
Firstpage
49
Lastpage
55
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;
fLanguage
English
Publisher
ieee
Conference_Titel
Geometric Modeling and Processing, 2004. Proceedings
Print_ISBN
0-7695-2078-2
Type
conf
DOI
10.1109/GMAP.2004.1290026
Filename
1290026
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