Bounds on the Moving Control Points of Hybrid Curves

✍ Scribed by Guo-Zhao Wang; Jian-Min Zheng

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 257 KB
• Volume: 59
• Category: Article
• ISSN: 1077-3169
• DOI: 10.1006/gmip.1996.0411

✦ Synopsis

and M n,m (t) is the so called moving control point which is itself a rational Be ´zier curve of same degree and same Hybrid curves provide an attractive method for approximating rational Be ´zier curves by polynomial Be ´zier curves. In this weights as the initial rational curve, i.e., paper, several methods are provided to estimate the error bounds for the approximation to the moving control point of the hybrid curves. When the given rational Be ´zier curves satis-

fies the convergent conditions for moving control point of the hybrid curve, by these methods we can choose a hybrid curve with a certain degree such that the distance between the moving in which P i , M n i are control points that are uniquely detercontrol point and a special point is less than a given error mined by the above three equations [1]. The representation bound . So the polynomial Be ´zier curves to approximate the

(3) leads directly to a polynomial approximation P(t) by rational Be ´zier curve can be obtained by replacing the moving simply replacing the moving control point with a stationary control point with the special point.