Bezier and polynomial methods of making curves

Mohamed Imine; Hiroshi Nagahashi; Takeshi Agui

doi:10.1117/12.235533

22 March 1996 Bezier and polynomial methods of making curves

Mohamed Imine, Hiroshi Nagahashi, Takeshi Agui

Proceedings Volume 2644, Fourth International Conference on Computer-Aided Design and Computer Graphics; (1996) https://doi.org/10.1117/12.235533
Event: Fourth International Conference on Computer-Aided Design and Computer Graphics, 1995, Wuhan, China

Abstract

The researches for Bezier and polynomial curves and surfaces, and their applications to curve- fitting have been reported in many papers. However the relation between control points and polynomial coefficients, because of the complexity of computation, have rarely been studied. In this paper, we propose a new method to transform the Bezier to the polynomial representation and vice-versa. An equation is given, for generating an (m + 1) polygonal Bezier control points to approximate an (n + 1) ones. This method, unlike previous works, is more transparent because it is given in form of one equation. With this method, the curve goes through the two endpoints of the polygonal, and we do not need to perform any transformation such as Chebyshev polynomial in order to obtain good approximation. A criterion of reduction is given in order to known if a polygonal Bezier is reducible without error or not. An error estimation is also given only in terms of control points. All equations are given explicitly and in matrix form, for Bezier curves. Finally, we discuss some applications of this method to curve-fitting, order increasing and decreasing, and also its extension to rational Bezier and polynomial.

Citation Download Citation

Mohamed Imine, Hiroshi Nagahashi, and Takeshi Agui "Bezier and polynomial methods of making curves", Proc. SPIE 2644, Fourth International Conference on Computer-Aided Design and Computer Graphics, (22 March 1996); https://doi.org/10.1117/12.235533

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available