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30 Jul 2024 04:20:33 EDT (-0400)
  Mathematically derived bicubic patches (Message 1 to 7 of 7)  
From: Jim Holsenback
Subject: Mathematically derived bicubic patches
Date: 12 Jan 2010 17:19:35
Message: <4b4cf577@news.povray.org>
Hola,

Since I can barely draw a straght line with a ruler, I've not had much luck 
making bicubic patches that look like leaves and petals (Clay Pots post in 
p.b.i) I was wondering if anyone had done anything along those lines but 
using formula's instead on pushing and pulling on a shape in a modeller. 
I've done some homework and have some links bookmarked, but will save them 
for late night insomnia (some pretty heady reading btw) ... Not looking for 
a short cut, but if anyone has anything they might like to offer up for 
study, that would be nice!

Hasta Bye


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From: Jim Charter
Subject: Re: Mathematically derived bicubic patches
Date: 13 Jan 2010 23:56:00
Message: <4b4ea3e0$1@news.povray.org>
Jim Holsenback wrote:
> Hola,
> 
> Since I can barely draw a straght line with a ruler, I've not had much luck 
> making bicubic patches that look like leaves and petals (Clay Pots post in 
> p.b.i) I was wondering if anyone had done anything along those lines but 
> using formula's instead on pushing and pulling on a shape in a modeller. 
> I've done some homework and have some links bookmarked, but will save them 
> for late night insomnia (some pretty heady reading btw) ... Not looking for 
> a short cut, but if anyone has anything they might like to offer up for 
> study, that would be nice!
> 
> Hasta Bye 
> 
> 

It's not clear to me either:

how you made those leaves in "Clay Pots",

or

how you would rather make them.

Are you saying the leaves in "Clay Pots" were created in a modeler that 
outputs bi-cubic patches such as Hamapatch?

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?

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?


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From: Jim Holsenback
Subject: Re: Mathematically derived bicubic patches
Date: 14 Jan 2010 06:01:25
Message: <4b4ef985@news.povray.org>
"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 ...

Jim


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From: Jim Charter
Subject: Re: Mathematically derived bicubic patches
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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From: Stephen
Subject: Re: Mathematically derived bicubic patches
Date: 14 Jan 2010 09:25:31
Message: <4b4f295b$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.
> 

You would probably get some help at the Bishop3D forums, if you ask.
Miri is quite good at making these forms free hand. She created some 
grass leaves as I remember. There is also a method of uploading control 
points from a file if you can get a way of calculating them. Or you can 
use your own SDL code with the raw script plugin.


-- 

Best Regards,
	Stephen


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From: Jim Holsenback
Subject: Re: Mathematically derived bicubic patches
Date: 14 Jan 2010 12:21:35
Message: <4b4f529f@news.povray.org>
"Stephen" <mca### [at] aolDOTcom> wrote in message 
news:4b4f295b$1@news.povray.org...
> You would probably get some help at the Bishop3D forums, if you ask.
> Miri is quite good at making these forms free hand. She created some grass 
> leaves as I remember. There is also a method of uploading control points 
> from a file if you can get a way of calculating them. Or you can use your 
> own SDL code with the raw script plugin.

JimC's approach shows promise, and it also off loads my guilt about using 
Bishop after the trial period. I MUST find money in my budget if I'm going 
to continue using it.

Jim


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From: Stephen
Subject: Re: Mathematically derived bicubic patches
Date: 14 Jan 2010 13:55:29
Message: <4b4f68a1$1@news.povray.org>
Jim Holsenback wrote:
> "Stephen" <mca### [at] aolDOTcom> wrote in message 
> news:4b4f295b$1@news.povray.org...
>> You would probably get some help at the Bishop3D forums, if you ask.
>> Miri is quite good at making these forms free hand. She created some grass 
>> leaves as I remember. There is also a method of uploading control points 
>> from a file if you can get a way of calculating them. Or you can use your 
>> own SDL code with the raw script plugin.
> 
> JimC's approach shows promise, and it also off loads my guilt about using 
> Bishop after the trial period. I MUST find money in my budget if I'm going 
> to continue using it.
> 

There is that, personally I think it is a bit overpriced. One of the 
benefits of testing is getting a free copy :D




-- 

Best Regards,
	Stephen


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