# comp.graphics.algorithms

## Subject: Re: Estimation of Bezier curve flatness criteria

Kingdom wrote:

> The original problem is building stoke for Bezier curves. In my
> situation stoke have to consists of Bezier curves with the same degree.

It took a while to realize that by "stoke" you meant "stroke", and by
that you meant you want to draw a Bezier curve as a line of a certain
width. So, in more usual terms, you need an offset curve for a
Bezier, und you want to draw that as a Bezier

> (P0,P1,P2) - source curve

Not really. Those are the control points of the center curve.

> (L0,L1,L2) and (P0,P1,P2) - left and right curves
^^^^^^^^^^---- (R0,R1,R2)

> I think, I have found effective flatness criteria for source curve, I
> suppose that distance between source and left/right curves in "good"
> cases is about distance between parametric centers dist(P(0.5),L(0.5)).

Flatness is not really your problem, so I doubt a flatness criterion
will be the best tool to solve it.

The actual problem is that the true offset curve of a Bezier curve is
not itself a bezier curve. And no, de Casteljau in and of itself
won't help. You have to replace the Bezier curve by a Bezier
*spline*, or by a completely different type of curve (a NURBS, maybe).

--
Hans-Bernhard Broeker (broeker@physik.rwth-aachen.de)
Even if all the snow were burnt, ashes would remain.