Definition:Surface of Revolution/Definition 2

Definition
Let $H = \set {\tuple {x, y} : y \in \R_{> 0}} \subset \R^2$ be the open upper half-plane.

Let $F \subset H$ be a $1$-dimensional embedded submanifold.

The surface of revolution is the subset $S_F \subseteq \R^3$ such that:


 * $S_F = \set {\tuple {x, y, z} : \tuple {\sqrt{x^2 + y^2}, z} \in F}$

where $F$ is the generating curve of the surface of revolution.