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:
```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
The mathematics is necessary :) :) :)
```
 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
> 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).
```
 From: LanuHum Subject: Re: Help to solve a problem: bicubic_patch Date: 22 Feb 2015 19:30:00 Message:
```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.