Boy Surface #1

Written by Paul Bourke
January 2004

Projective plane without singularities.

x = A (cos(u) cos(2v) + B sin(u) cos(v)) cos(u) / (B - sin(2u) sin(3v))
y = A (cos(u) sin(2v) - B sin(u) sin(v)) cos(u) / (B - sin(2u) sin(3v))
z = B cos(u) cos(u) / (B - sin(2u) sin(3v))
where A = 2/3 and B = sqrt(2)
and 0 <= u,v <= pi

Animation of a transition from a
Steiner (Roman) surface into the boy surface.