Up: The Roman Surface

Equations for the Roman Surface

The restriction to the unit sphere of the following function

f(x, y, z) = ( xy, yz, zx ),
defines a map from RP^2 to R^3. Parametrically, the Roman Surface is given by
[ sin(2*u)*cos(v)^2, sin(u)*sin(2*v), cos(u)*sin(2*v) ]
0 <= u <= Pi, -Pi/2 <= v <= Pi/2

source: Gerd Fischer, ed. Mathematical Models from the Collections of Universities and Museums, Vol. 1 & 2.

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