- "Alexander J. Vincent" <ajvincent@...> writes:

> Okay, now I know that somehow, something in my previous message here was

They can't. As the mathworld page says, only *rational* Bezier curves

> partly incorrect. According to Mathworld @ Wolfram, a Bezier curve can

> represent a conic section exactly.

>

> http://mathworld.wolfram.com/BezierCurve.html

>

> (MathWorld is one of the better math references out there)

>

> But how?

can represent conics exactly. SVG only support non-rational quadratic

and cubic bezier curves which can only approximate them.

--

Bernhard Herzog | Sketch, a drawing program for Unix

herzog@... | http://sketch.sourceforge.net/ - Bernhard Herzog wrote:
>

Correct. If a particular implementation wanted to represent all geometry

> "Alexander J. Vincent" <ajvincent@...> writes:

>

> > Okay, now I know that somehow, something in my previous message here was

> > partly incorrect. According to Mathworld @ Wolfram, a Bezier curve can

> > represent a conic section exactly.

> > http://mathworld.wolfram.com/BezierCurve.html

> They can't. As the mathworld page says, only *rational* Bezier curves

> can represent conics exactly. SVG only support non-rational quadratic

> and cubic bezier curves which can only approximate them.

internally as one type, it could do so by translating them all to rational

beziers, NURBS, or whatever.

Congratulations on the 0.6.8 release of Sketch, by the way!

--

Chris - About 20 years ago I used a fortran program which actually approximated this

extremly well, we used it on a cartogrphic project with considerable

success. But I have misplaced the fortran subroutine. If I find it, I will

post it to the forum. It was not a very difficult formula.

Cheers

Dave Corstorphan