POV-Ray : Newsgroups : povray.tools.general : Help to solve a problem: bicubic_patch : Re: Help to solve a problem: bicubic_patch Server Time
29 Nov 2022 12:52:49 EST (-0500)
  Re: Help to solve a problem: bicubic_patch  
From: clipka
Date: 22 Feb 2015 09:11:03
Message: <54e9e377$1@news.povray.org>
Am 22.02.2015 um 14:07 schrieb LanuHum:
> Hi!
> There is nurbs-curve with four control points.
> For an example: (1,1.5,0.5),(0.5,0.5,1.2),(-0.8,-1,0.3),(-2,0.1,0.8)
> It is necessary to create a tube along a curve, using two bicubic patches
> Radius tube = R
> The mathematics is necessary :) :) :)

Note that the mathematics say that strictly speaking this is impossible: 
With bicubic patches you can neither create a tube with perfectly 
circular cross-section (because a cubic spline in 2d space never forms a 
perfect circular arc), nor can you use them for any curved tubular 
structure with constant cross-section (because the parallel curve of a 
cubic spline in 2d space is never another cubic spline unless they both 
are linear).

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