Geomorphs: Cone

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Definition of surface, in parametric equations:

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

where:

  • u ranges from 0 to 6ð, scanning three full circles on the XY-plane (this makes the interior appear smooth; if u is from 0 to 2ð, then Mathematica draws lines in the interior).
  • v ranges from 0 to 2, scanning the cone's surface from its tip at the origin to its rim.
  • a is a constant having the value 1.82 in this plot; higher values of a make the cone sharper.

Ancestor: Disc.

Descendants: Amphitheater, Boat, Multi-cone.

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