> 
> So, I've been trying half a dozen ways to make a shape, and I managed to work
> out the equations to do it with an isosurface.
> (because OMG are parametrics SLOOOOOOW)
> 
> 
> Only the frequency of the sine wave for the serrated, lemon-juicer top doesn't
> look right, and it's hard to really see what's going wrong with all of the
> unexpected noise.
> 
> #declare ISphereR = 24;
> #declare I_Phi = function {tan(z/x)}
> #declare F_Sphere = function {pow(x,2)+pow(y,2)+pow(z,2) - pow(ISphereR,2)}


you are working with a scale of 1 unit = 1mm, that's still a radius of 
57.6 cm, or a diameter of 1.15m.

> 
> // a sine wave 80% of full size, with 3 peaks
> #declare F_Wave = function {ISphereR*0.8 * sin(3*I_Phi(x, y, z))}
> // only generate a spherical isosurface for the parts where the height
> //  is less than the sine wave function
> #declare I = function {select(F_Wave(x,y,z)-y, 0, 0, 1)}
> 
> //----------------For debugging---------------------------
> //#declare S_Wave = function {I(x,y,z)*F_Sphere(x,y,z)}
> //--------------------------------------------------------
> #declare S_Wave = function {select(y, F_Sphere (x, y, z),
> I(x,y,z)*F_Sphere(x,y,z))}
> 
> 
>   #declare Gradient = 5500;
>   #declare Min_factor= 0.7;
>   #declare I_Surface = isosurface {
>     //function {Pattern(x, y, z).red - 0.5}
>     function {S_Wave (x, y, z)}
>     open
>     threshold 0
>     max_gradient 5500
>     //evaluate Gradient*Min_factor,  sqrt(Gradient/(Gradient*Min_factor)),  min
> (0.7, 1.0)
>     accuracy     0.1
>     contained_by {box {<-1, -1, -1>*ISphereR*1.1, <1, 1, 1>*ISphereR*1.1}}
>      }
> 

Do you realize that
sqrt(Gradient/(Gradient*Min_factor)) = sqrt(1/Min_factorf) ?

For the base sphere, you can use the internal one.

#include "function.inc"

then, use f_sphere(x,y,z, Radius)

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