I think the problem with the original approach is the outside of the
object does not form part of a circle.  Even if you get the things to
line up perfectly you will end up with an oval at best.

Give the code I posted a try.  I said it doesn't work but it sure looks
good from one angle.  BTW you don't need to rotate by "R * R * R"
but just "R * R" instead.  I was playing around with higher orders to
see if it smoothed things out... not worth it.

You can replace the cylinders in my code with spheres if you really
like the 3D effect.  Here is the modified code:

#include "colors.inc"
global_settings { assumed_gamma 2.2 }
light_source { < -20, 20, -20 > color White }

camera
{
 location < 0, 0, -10 >
 look_at < 0, 0, 0 >
}

#declare O_Ying =
union
{
    #declare R = 0;
    #while( R < 1 )
        sphere
        {
            < 0, 0, 0 >
            R
            translate < 1.92 - R, 0, 0 >
            rotate R * R * 180 * z
        }
        #declare R = R + 0.01;
    #end
}

object
{
    O_Ying
    pigment { Red }
}

object
{
    O_Ying
    rotate 180 * z
    pigment { Blue }
}

background { White }

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