Whitney Umbrella
By Paul Bourke
November 2002

x = 0.5 sin^{2}(u) cos(2 v)
y = 0.5 sin^{2}(u) sin(2 v)
z = sin(u) sin(v)
0 <= u <= pi, 0 <= v <= 2 pi

There is a singularity at (0,0,0)
and a self intersection along the line x=y=0.
Implicit form
x^{2} y  z^{2} = 0
