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 21:19:56 GMT
  Re: Sphere Sweep 1.2 Quadratic spline question - STOP THE PRESS!  
From: Cousin Ricky
Date: 8 Sep 2020 07:07:11
On 2020-08-31 1:22 PM (-4), Cousin Ricky wrote:
> 
> To get an SVG style quadratic curve, you would need to use 
> SSWP_BEZIER_SPLINE, and clone the middle control point:
> 
>    SphereSweep_Approx
>    ( SSWP_BEZIER_SPLINE,
>      array { P1, P2, P2, P3 },
>      array { Line, Line, Line, Line}, 100, 0
>    )

That is wrong!  Something didn't look right about the curve, so I went 
back and double-checked the Bézier theory.  The correct solution is this:

   SphereSweep_Approx
   ( SSWP_BEZIER_SPLINE,
     array { P1, P2 * 2/3 + P1 / 3, P2 * 2/3 + P3 / 3, P3 },
     array { Line, Line, Line, Line}, 100, 0
   )

I will post an example illustration in p.b.i.


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