Geomorphs: Facing Snails

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Definition of surface, in parametric equations:

x(u,v) = cos(v) cos(u)
y(u,v) = sin(v) cos(u)
z(u,v) = (1 - a v) sin(u)


  • u ranges from -/2 to /2, scanning a half circle from the pointed tip at top to the pointed tip at bottom.
  • v ranges from 0 to 6, scanning a full circle on the XY-plane three times, producing the three snails which meet each other face-to-face (each is inside the other).
  • a is a parameter ranging from 0.1 to 0.2 and back again to 0.1, with a step of 0.01, giving the 20 frames shown here. If a = 0 the facing snails is reduced to its ancestor, the sphere.

Ancestor: Sphere.

Descendants: Cocoon, Conch, Onion Slice.

Note: If you do not see Greek characters on this page, it is probably because the font you are currently using with your browser does not include the Greek code-page. In this page, character is pi.

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