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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