Jellby wrote:

> Hi all,
> 
> I'd like to cut a torus off from a sphere or cylinder
> (difference{sphere{}torus{}}). It works ok, but I'd also like it to work
> when the torus intersects itself, i.e., when its "minor" radius is larger
> than the "major" one. If I do as before, I get two cusps shapes joined by
> an elongated shape, and I want to get rid of this last one, keeping only
> the two cusps. Is there some "trick" to get this other than further
> differentiating out this elongated shape or defining an isosurface?
> 
> I'm talking of something like this, but without having to use and calculate
> the box:
> 
> camera { location <0,0,-5> }
> light_source { <10,10,-10>, rgb 1 }
> 
> #declare Rmin=1.1;
> #declare Rmaj=1.0;
> #if(Rmin>Rmaj)
>   #declare X=Rmin*sqrt(1-Rmaj*Rmaj/(Rmin*Rmin));

Why not X=sqrt(Rmin*Rmin-Rmaj*Rmaj) ?

> #else
>   #declare X=0;
> #end
> difference {
>   sphere { 0, 1 pigment { color rgb 1 } }
>   torus  { Rmaj, Rmin  pigment { color rgb <1,0,0> } }
>   box { -X,X }
> }
> 
> I could also use "clipped_by { box { -X,X inverse } }". Would this be more
> efficent than differentiating?

The difference is probably better.

You could also rewrite the difference like this:

difference {
   sphere { 0, 1 pigment { color rgb 1 } }
   torus  { Rmaj, Rmin  pigment { color rgb <1,0,0> } }
   #if(Rmin>Rmaj)
     sphere { 0,sqrt(Rmin*Rmin-Rmaj*Rmaj) }
   #end
}

and then you don't need the earlier block of if-else-end code.

Regards,
John

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