POV-Ray : Newsgroups : povray.general : Bicubic patch with 3 corners ? : Re: Bicubic patch with 3 corners ? Server Time
8 Aug 2024 14:18:57 EDT (-0400)
  Re: Bicubic patch with 3 corners ?  
From: Alexander Enzmann
Date: 7 Dec 2000 14:42:11
Message: <3A2FE895.541040B1@mitre.org>
Rune wrote:
> 
> I have learned myself how to handcode bicubic patches that fits seamlessly
> together. However, I never get the result I want when I try to make a patch
> where two of the corners lie in the same point.

If you have a degenerate edge, you will probably get really nasty
normals out of POV-Ray.  As I recall, there's no code to think about
that case.

> 
> Say I want to make a unit-sphere made of 8 bicubic patches. Could you show
> me what one of those patches would look like in POV-code? It doesn't have to
> be a 100% perfect sphere, but I don't want any "folds" anywhere.

You can't make a sphere out of (non-rational) bicubic Bezier patches. 
It will always have some under or overshoot.

I'd suggest 6 sets of patches.  Think of a cube that's been inflated. 
You don't want to use just 6 patches, since you won't get the tangency
conditions right (well, not and also get something that looks
spherical).  Make each of the 6 faces out of at least 3x3 patches.

For tangency across two patches, remember that the control point on the
edge of the two patches, plus the one that is one step over from the
edge of the two patches have to be in a line.

Xander


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