POV-Ray : Newsgroups : povray.object-collection : Sphere Sweep 1.2 Quadratic spline question : Re: Sphere Sweep 1.2 Quadratic spline question - STOP THE PRESS! Server Time: 24 Oct 2020 19:59:59 GMT
  Re: Sphere Sweep 1.2 Quadratic spline question - STOP THE PRESS!  
From: Bald Eagle
Date: 8 Sep 2020 23:20:00
Cousin Ricky <ric### [at] yahoocom> wrote:

> The end points are the same for both methods, right?  So why would they
> need any influence from the other points?

See below.

> https://commons.wikimedia.org/wiki/File:Quadratic_to_cubic_Bezier_curve.svg

> You can see that the 2nd point
> is on the line between P1 and P2, which needs no input from P3; and the
> 3rd point is on the line between P2 and P3, which needs no input from P1.
>
> Each point on the cubic Bézier curve is computed as:
>    P(t) = (1-t)³*P1 + 3*(1-t)²*t*P2 + 3*(1-t)*t²*P3 + t³*P4

Yeah - I got it now, it "clicked".
The fatigue was like a brick wall and any information was just bouncing off like
ping pong balls.

My tired brain was comingling the Bernstein polynomial terms for the control
points with your calculation of the coordinates OF the control points for the
array.

Thanks, Richard - all is clear now.
It works just fine in the SVG conversion too.  Doesn't look materially different
from the wrong way - likely because the control points are all so close together
and there's not much overall "curve" to the spline.


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