>>   r=sqrt(pow(x-center_x,2)+pow(y-center_y,2)+pow(r_0,2))
> 
> What is r_0?

1. Technically we have a 3D-wave that is centered at
    (center_x, center_y, r_0). Of this wave we take only
    the slice with z=0.

2. Before the correction, amplitude has been the height (or half
    of the height) of the wave. Now the height varies, being
    maximal at (center_x, center_y). Its value there is
    amplitude/r_0.
    On the other hand r_0 determines how fast the wave diminishes.
    Let us say you want to specify the height of the wave (at the
    center) and the distance from the center at which the height
    is halfed. Then choose

    r_0 = distance/sqrt(3)
    amplitude = height*r_0

Hope i got it right

-- 
merge{#local i=-11;#while(i<11)#local
i=i+.1;sphere{<i*(i*i*(.05-i*i*(4e-7*i*i+3e-4))-3)10*sin(i)30>.5}#end
pigment{rgbt 1}interior{media{emission x}}hollow}//  Mark Weyer

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