The "flower power" thread on povray-general wandered into the area of 
"Starr Roses"

http://news.povray.org/povray.general/33515/

Mike Williams came up with a very nice "dahlia" based on one method of 
extending this object to 3-D:

http://news.povray.org/povray.general/33515/?mtop=235716&moff=18

But I'm still fixated on "spherical products" as a method of extending 
2D parametric equations (see 
http://news.povray.org/povray.binaries.images/32476/ ).

So, here is a spherical product of the quasi-polar Starr rose (with A = 
10, B = 30, C = 30) and the polar function R = sin (10 T ).

(That is, in Ingo's param.inc ready form:

F1 = function(u,v) {(2 + sin(A*u)/2)*cos(u + sin(B*u)/C)*sin(10*v)*cos(v) }

F2 = function(u,v){sin(10*v)*sin(v)}

F3 = function(u,v) {(2 + sin(A*u)/2)*sin(u + sin(B*u)/C)*sin(10*v)*cos(v) }

object { Parametric(
       F1, F2, F3,
       <-0.0001, -0.0001>, <2*pi + 0.0001, 2*pi + 0.0001>,
       200,200,"SomeFile.inc"
    )
[insert object characteristics] } )

Other spherical products make likewise interesting flowers.

Dave Matthews

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Attachments:
Download 'starrrosesphereproduct01.jpg' (45 KB)

Preview of image 'starrrosesphereproduct01.jpg'

Awesome image!

A pity that I understand nothing of the math involved.

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Now if Only a person could stagger the petals or something similar, so that
they wouldn't line up like that, it would be pretty close to what I needed.

A.D.B

Dave Matthews wrote:

> The "flower power" thread on povray-general wandered into the area of
> "Starr Roses"
>
> http://news.povray.org/povray.general/33515/
>
> Mike Williams came up with a very nice "dahlia" based on one method of
> extending this object to 3-D:
>
> http://news.povray.org/povray.general/33515/?mtop=235716&moff=18
>
> But I'm still fixated on "spherical products" as a method of extending
> 2D parametric equations (see
> http://news.povray.org/povray.binaries.images/32476/ ).
>
> So, here is a spherical product of the quasi-polar Starr rose (with A =
> 10, B = 30, C = 30) and the polar function R = sin (10 T ).
>
> (That is, in Ingo's param.inc ready form:
>
> F1 = function(u,v) {(2 + sin(A*u)/2)*cos(u + sin(B*u)/C)*sin(10*v)*cos(v) }
>
> F2 = function(u,v){sin(10*v)*sin(v)}
>
> F3 = function(u,v) {(2 + sin(A*u)/2)*sin(u + sin(B*u)/C)*sin(10*v)*cos(v) }
>
> object { Parametric(
>        F1, F2, F3,
>        <-0.0001, -0.0001>, <2*pi + 0.0001, 2*pi + 0.0001>,
>        200,200,"SomeFile.inc"
>     )
> [insert object characteristics] } )
>
> Other spherical products make likewise interesting flowers.
>
> Dave Matthews
>
>   ------------------------------------------------------------------------
>  [Image]

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Anthony D. Baye wrote:
>Now if Only a person could stagger the petals or something similar, so that
>they wouldn't line up like that, it would be pretty close to what I needed.
>
>A.D.B

I've been puzzling over that, myself.  I'll let you know if I come up with
something.

Dave Matthews

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I spent a few hours this morning playing with this, even though I understand
zero about the math I had fun.

Thanks for another technique to add to the collection.

Results attached

Cheers

"Dave Matthews" <dma### [at] wrmnwestmnscuedu> wrote in message
news:web.3fa10c8de5932df88062416c0@news.povray.org...
> Anthony D. Baye wrote:
> >Now if Only a person could stagger the petals or something similar, so
that
> >they wouldn't line up like that, it would be pretty close to what I
needed.
> >
> >A.D.B
>
> I've been puzzling over that, myself.  I'll let you know if I come up with
> something.
>
> Dave Matthews
>

Post a reply to this message

Attachments:
Download 'Flower.jpg' (108 KB)

Preview of image 'Flower.jpg'

Darren Hewson wrote:
>I spent a few hours this morning playing with this, even though I understand
>zero about the math I had fun.
>
>Thanks for another technique to add to the collection.
>
>Results attached
>
>Cheers
>

Wow.  Those are better than anything I could come up with!  Details, please!

Dave Matthews

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Well, I cheated a little, three of them are multiple copies of the mesh just
rotated and scaled to give extra petals (the red flower top right is three
copies of your original each rotated and scaled slightly), one of them is
two different meshes csg'd together. I did use different values of A, B and
C for three of the flowers, though there is probably a lot more exploring to
be done (like I said I know diddly about the math) and maybe you can get a
lot of different flowers this way.

I can post the surce if you want it.

Cheers

"Dave Matthews" <dma### [at] wrmnwestmnscuedu> wrote in message
news:web.3fa25ea75cfd491e8062416c0@news.povray.org...
> Darren Hewson wrote:
> >I spent a few hours this morning playing with this, even though I
understand
> >zero about the math I had fun.
> >
> >Thanks for another technique to add to the collection.
> >
> >Results attached
> >
> >Cheers
> >
>
> Wow.  Those are better than anything I could come up with!  Details,
please!
>
> Dave Matthews
>
>
>

Post a reply to this message

Darren Hewson wrote:

> Well, I cheated a little, three of them are multiple copies of the mesh just
> rotated and scaled to give extra petals (the red flower top right is three
> copies of your original each rotated and scaled slightly), one of them is
> two different meshes csg'd together. I did use different values of A, B and
> C for three of the flowers, though there is probably a lot more exploring to
> be done (like I said I know diddly about the math) and maybe you can get a
> lot of different flowers this way.
> 
> I can post the surce if you want it.
> 

Of course, now I see it.  Thanks.  I've been going crazy trying to do 
this by changing A, B, and C, and adding a "+sin(D*v)/E" or whatever in 
just about every conceivable place and combination.  (Mike Williams has 
some great pointers on how to modify and combine functions in his 
isosurface tutorial, but none of them were quite getting what you had.) 
  As you say, I did come up with some interesting other "flowers," but 
nothing very realistic.  Simple solutions usually elude me (as do 
difficult ones, but I don't mind those so much.)

Thanks again

Dave Matthews

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