> > You know how a cone can be
> > used to connect two spheres to make a shape like you'd get with a
> > linear sphere_sweep.  I'm trying to connect these two spheres with a
> > similar shape.
> >
> > sphere {<0,0,0>,a1 scale <1,1,b1/a1>}
> > sphere {<x0,0,0>a2 scale <1,1,b2/a2>}
> >
> > Does that make it any clearer what I'm trying to do?
>
> It sounds like you are looking for a supercone shape. Look in shapes.inc
> for a macro for creating these..though you may have a hard time fitting
> it to the capping ellipsoids. This transformation can not be done
> directly in POV, you have to use either an isosurface, process a mesh,
> or do it with CSG and existing primitives.

Thanks everyone.  After spending most of a day with this.  Thanks to
the help from Mike, I was able to create the isosurface I asked for,
which as Christopher points out above is (I believe) the same shape
you can get using a supercone.  Where most of the time was spent
however was tring to make the shape join smoothly with the capping
ellipsoids.  In the end I gave up and opted to move away from using
ellipsoids to using a torus filled in with a cylinder.  Two of these shapes
I could easily join smoothly with two cylinders and a prism.

By the way... thanks to pointing me to the shapes.inc file.  I see its
got this:

 Connect_Spheres(PtA, RadiusA, PtB, RadiusB).

It makes the work I spent to write this macro now look a little
silly:

  #macro sphere2fill(V1,R1,V2,R2)
    #local V2a = V2-V1;
    #local angle_z1 = VRotationD(<V2a.x, V2a.y, 0>, x, z);
    #local V2b = vaxis_rotate(V2a, z, angle_z1);
    #local angle_y2 = VRotationD(<V2b.x, 0, V2b.z>, x, y);
    #local V2c = vaxis_rotate(V2b, y, angle_y2);
    #local theta = asin((R1-R2)/V2c.x);

    cone {
      <R1*sin(theta), 0, 0>, R1*cos(theta)
      <V2c.x+R2*sin(theta), 0, 0>, R2*cos(theta)
      rotate -y*angle_y2
      rotate -z*angle_z1
      translate V1
    }
  #end

As a way to say thank you here is another macro that I wrote that
smoothy fills in the space between 3 spheres when used with 3
sphere and 3 sphere2fill calls.  In other words it doesn't draw the
cones or the spheres.

  #macro sphere3fill(V1,R1,V2,R2,V3,R3)
    #local V2a = V2-V1;
    #local V3a = V3-V1;
    #local angle_z1 = VRotationD(<V2a.x, V2a.y, 0>, x, z);
    #local V2b = vaxis_rotate(V2a, z, angle_z1);
    #local V3b = vaxis_rotate(V3a, z, angle_z1);
    #local angle_y2 = VRotationD(<V2b.x, 0, V2b.z>, x, y);
    #local V2c = vaxis_rotate(V2b, y, angle_y2);
    #local V3c = vaxis_rotate(V3b, y, angle_y2);
    #local angle_x3 = VRotationD(<0, V3c.y, V3c.z>, -z, x);
    #local angle_x3p = VRotationD(<0, V3c.y, V3c.z>, z, x);
    #local V2d = vaxis_rotate(V2c, x, angle_x3);
    #local V3d = vaxis_rotate(V3c, x, angle_x3);
    #local V2dp = vaxis_rotate(V2c, x, angle_x3p);
    #local V3dp = vaxis_rotate(V3c, x, angle_x3p);
    #local angle_z5 = degrees(asin((R1-R2)/V2c.x));
    #local angle_x4 = degrees(asin(((((R2-R1)/(V2d.x))*V3d.x+R1)
        -(R3))/(V3d.z*cos(radians(angle_z5)))));
    #local V2e = vaxis_rotate(V2d, x, angle_x4);
    #local V3e = vaxis_rotate(V3d, x, angle_x4);
    #local V2ep = vaxis_rotate(V2dp, -x, angle_x4);
    #local V3ep = vaxis_rotate(V3dp, -x, angle_x4);
    #local V2f = vaxis_rotate(V2e, -z, angle_z5);
    #local V3f = vaxis_rotate(V3e, -z, angle_z5);
    #local V2fp = vaxis_rotate(V2ep, -z, angle_z5);
    #local V3fp = vaxis_rotate(V3ep, -z, angle_z5);
    #local minD = 2*min(R1,R2,R3);

    #local fill1 = prism {
      linear_spline linear_sweep -R1,-R1+minD,4
      <0,0>, <V2f.x,V2f.z>, <V3f.x,V3f.z>, <0,0>
    }

    #local fill2 = prism {
      linear_spline linear_sweep -R1,-R1+minD,4
      <0,0>, <V2fp.x,V2fp.z>, <V3fp.x,V3fp.z>, <0,0>
    }

    merge {
      object {fill1
        rotate z*angle_z5
        rotate -x*angle_x4
        rotate -x*angle_x3
      }
      object {fill2
        rotate z*angle_z5
        rotate x*angle_x4
        rotate -x*angle_x3p
      }
      rotate -y*angle_y2
      rotate -z*angle_z1
      translate V1
    }
  #end

Note the walls are as only as thick as the diameter of the
smallest sphere so this shape might be hollow.  Does anyone
know how to do the above without the hollow space?

And one last question about the ellipsoids problem.  I'm
convinced that the shape that smoothly joins two ellipsoids
is NOT a supercone as the shape doesn't intersect the
ellipsoids in a plane.  And even if I cut the super cone so
that it touches the ellipsoid at <0,0,0> in the x-y plane at
some non-zero x value smoothly and it also touches the
ellipsoid in the x-z plane smoothly at x=0 if both ellipsoids
have the same z extent, then those turned out to be the
only points of contact between the two surfaces.  So...
knowing that I have no idea how to find the isosurface that
would meet my needs.  Does anyone know how the
sphere_sweep call works?  Would it be possible to write
something like an ellipsoid_sweep?  If so I'm sure its way
over my head but maybe its something someone here will
want to play with.

Thanks again everyone,
Carl

Post a reply to this message