Surface Command

Surface[ <Expression>, <Expression>, <Expression>, <Parameter Variable 1>, <Start Value>, <End Value>, <Parameter Variable 2>, <Start Value>, <End Value> ]

Yields the Cartesian parametric 3D surface for the given x-expression (first <Expression>), y-expression (second <Expression>) and z-expression (third <Expression>), using two <Parameter Variables> within the given intervals [<Start Value>, <End Value>].

Example: Let r and R be two positive real numbers: Surface[(R + r cos( u)) cos(v) , (R + r cos( u)) sin(v) , r sin(u ), u, 0, 2 π , v, 0, 2 π] creates the torus generated by a circle of radius r whose center rotates about zAxis at a distance R.

Note:

• End Value must be greater than or equal to Start Value and both must be finite.
• x, y and z are not allowed as parameter variables.

Surface[ <Function>, <Angle> ]

Creates a surface of revolution, rotating the given Function from 0 to given Angle around the x-axis.

Surface[<Curve>, <Angle>, <Line>]

Creates a surface of revolution, rotating the Curve from 0 to given Angle around the Line.