POV-Ray : Newsgroups : povray.general : Mathematically derived bicubic patches : Re: Mathematically derived bicubic patches Server Time
30 Jul 2024 02:28:54 EDT (-0400)
  Re: Mathematically derived bicubic patches  
From: Jim Charter
Date: 14 Jan 2010 07:18:26
Message: <4b4f0b92$1@news.povray.org>
Jim Holsenback wrote:
> "Jim Charter" <jrc### [at] msncom> wrote in message 
> news:4b4ea3e0$1@news.povray.org...
>> Are you saying the leaves in "Clay Pots" were created in a modeler that 
>> outputs bi-cubic patches such as Hamapatch?
> 
> Yes ... Bishop3D
> 
>> But that you would rather shape their profiles with mathematical curves, 
>> then fill in the surfaces using bicubic patches?
>>
>> Or that you have already done that but would like to do it better?
> 
> Although the pots turned out rather well, the leaves/petals not so much ... 
> I'm just looking for a better way. Maybe I just need to spend more time with 
> a modeller to get the desired results.
> 
>> It would seem that by the time you come up with a method for interrogating 
>> some curve(s), or even just some spline(s) to get corner and control 
>> points for some patch(es), you might just as well use the points to 
>> generate triangles?
> 
> Well now that you mention it triangles DOES sound like a better approach.
> 
> Some of the stuff I have read (unless I misunderstood) seemed to indicate 
> multiple patches "glued" togeather to create the final shape ... I'm into 
> new territory with this so I'm not standing by any of my assumptions at this 
> point. If you think another method would yield better results, I'm open to 
> exploring them ...
> 

The advantage to generating the leaves with SDL lies in the possibility 
of randomizing each individual leaf to subtly change its shape. Or, a 
set of variations could be instanced to save memory.

Splines could be defined for the leaf's basic silhouette in all three 
planes.  Those basic definitions, which would differ for each species of 
leaf, could then be varied slightly from leaf to leaf.  The surface can 
be filled in with either patches or triangles.  I expect there are 
already some grass macros around that would show how to do the basics of 
much of this.  Still, it's an interesting proposal to develop say, a set 
of splines for other species of leaf besides grass blades.

See the SDL I posted in p.b.scene-files to show what I am talking about.
The leaf is profiled in the x-z plane for its basic silhouette
and in the z-y plane to give the curve along it's spine.  The 
cross-section in the x-y plane is omitted.  One side of the leaf is done 
using patches the other using triangles.  The smoothing on the triangles 
is crude, I admit.


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