Quote:>Probably this is one of the simplest question in Computer Graphics.

>I need to convert Circles and arcs into Bezier Curves for storing them.

>If you know the algorithm just explain me plainly what to do. i don't have

>any books on graphics with me right now but you may site some papers.

>Thanks a lot for your time

>skdutta

>NB -This may not be interesting to many people. Please send e-mail

I don't know enough to go into a lot of detail, but I do know that

you can't use a Bezier curve to exactly duplicate a circle or an

arc -- you will get an _approximation_ to the circle/arc you're

trying to describe, and the accuracy of the approximation changes

as the angle subtended by the arc increases. (Right now, I'm looking

at a book called Geometric Modeling , by Michael E. Mortenson,

Copyright 1985, John Wiley & Sons, Inc., ISBN 0-471-88279-8 .)

However, it is possible to use what's known as a rational polynomial

to exactly duplicate a segment of a circular arc, but not even this

can exactly duplicate a complete circle. (A rational polynomial is

defined as the algebraic ratio of two polynomial functions., i.e.,

(f(x) / g(x)).) So if you were to use this, you'd have to divide a

circle up into at least two pieces, and represent each as a rational

polynomial.

I can't find anything here on the rational polynomial form of

Bezier polynomials (if there is such a thing), but there is a

reference here to rational B-Splines:

Tiller, W. Rational B-splines for curves and surface representation.

IEEE Computer Graphics and Applications 3(6):61-69, Sept. 1983.

Anyway, that's about as much as I know about the subject just off

hand -- hope it helps. Perhaps someone else out there can shed some

more light on the subject?

|~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~|

| David Douglas |

| Graduate Computer Science program |

| University of South Carolina |

| Columbia, S.C. 29208 |

|~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~|

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~