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