POV-Ray : Newsgroups : povray.advanced-users : Describing a perfect circle with a spline. : Re: Describing a perfect circle with a spline. Server Time
4 Oct 2024 17:01:43 EDT (-0400)
  Re: Describing a perfect circle with a spline.  
From: Charles C
Date: 25 Sep 2007 19:10:00
Message: <web.46f994f2bd0f5648c667cf480@news.povray.org>
andrel <a_l### [at] hotmailcom> wrote:
> I guess that this remark is aimed at my first statement that it is
> essentially not possible. To (hopefully) clarify a bit more: splines are
> polynomials and sin() and cos() require a polynomial with infinite
> length to describe. So you can approximate a circle but never get is
> *exactly* right. That does not mean that for all practical purposes your
> solution below might give a sufficient approximation. You may even tweak
> the Scale a bit, because now all points on the curve are inside the
> circle. Increasing it a bit so that some of the curve is inside and
> another part is outside decreases the error even more.

True. There's always the fact that we're using floats with a finite number
of bits.  I figure <2*pi*cos(Value),2*pi*sin(Value),0> is probably as close
to definition as we can express.  My thinking was just that maybe he could
elminate the added aproximation that comes with using a spline by
retrieving points from the spline that happen to be the very same points
that defined the spline.
Charles


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