Boy Surface #1Written by Paul BourkeJanuary 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.
Boy-Like SurfaceWritten by Paul BourkeOctober 1992 Projective plane without singularities.
Boy Surface, #2Written by Paul BourkeJanuary 2004 Projective plane without singularities. x = cos(t) sin(s) y = sin(t) sin(s) z = cos(s) x| = A ((2 x2 - y2 - z2) + 2 y z (y2 - z2) + z x (x2 - z2) + x y (y2 - x2)) y| = B ((y2 - z2) + z x (z2 - x2) + x y (y2 - x2)) z| = C (x + y + z) ((x + y + z)3 + 4 (y - x) (z - y) (x - z))
where A = 1/2, B = sqrt(3)/2, and C = 1/8
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