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
>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
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 |