## Arcs to Bezier curves.

### Arcs to Bezier curves.

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

### Arcs to Bezier curves.

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

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Some 2D graphics systems do not allow you to draw arcs. Instead they
want you to approximate the arcs using Bezier curves. An example is