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On Wed, 22 Nov 2000 12:44:35 +0200, Peter Popov wrote:
>On 20 Nov 2000 00:43:24 -0500, ron### [at] povray org (Ron Parker)
>wrote:
>
>>Mathematically, it's impossible to do in a general way. Specifically, you
>>can't create a curve that's parallel to an arbitrary cubic or quadratic curve.
>
>Hmm... CorelDraw! seems to do it in one way or the other. The result
>is a non-tesselated curve. How come?
Good question. I do know it's possible to approximate a parallel to
an arbitrary cubic with piecewise cubics; I have a reference to a paper
on that around here somewhere. My source for the statement that you can't
do it with arbitrary cubics is the c.g.algorithms FAQ; I can't support my
statement for quadratics.
From the FAQ:
Subject 4.01: How do I generate a Bezier curve that is parallel to another
Bezier?
You can't. The only case where this is possible is when the
Bezier can be represented by a straight line. And then the
parallel 'Bezier' can also be represented by a straight line.
The situation is different for the broader class of rational
Bezier curves. For example, these can represent circular arcs,
and a parallel offset is just a concentric circular arc, also
representable as a rational Bezier.
--
Ron Parker http://www2.fwi.com/~parkerr/traces.html
My opinions. Mine. Not anyone else's.
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