POV-Ray : Newsgroups : povray.tools.general : Help to solve a problem: bicubic_patch Server Time: 19 Dec 2018 14:29:15 GMT
  Help to solve a problem: bicubic_patch (Message 1 to 3 of 3)  
From: LanuHum
Subject: Help to solve a problem: bicubic_patch
Date: 22 Feb 2015 13:10:01
Message: <web.54e9d43835fbd8f37a3e03fe0@news.povray.org>
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 :) :) :)


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From: clipka
Subject: Re: Help to solve a problem: bicubic_patch
Date: 22 Feb 2015 14:11:03
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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From: LanuHum
Subject: Re: Help to solve a problem: bicubic_patch
Date: 22 Feb 2015 19:30:00
Message: <web.54ea2ddc2ac21f197a3e03fe0@news.povray.org>
clipka <ano### [at] anonymousorg> wrote:
> 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).

Not necessarily. Approximate.
I am going to use rectangular triangles for calculation
But, I don't know how it is effective.
Therefore asked masters.


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