Whitney Umbrella

By Paul Bourke
November 2002

There is a singularity at (0,0,0)
and a self intersection along the line x=y=0.

x = 0.5 sin2(u) cos(2 v)

y = 0.5 sin2(u) sin(2 v)

z = sin(u) sin(v)

0 <= u <= pi, 0 <= v <= 2 pi


Implicit form

x2 y - z2 = 0