Explicit representation
\[S(u,v)=(x(u,v),\,y(u,v),\,z(u,v))\]
Parametric map
\[ S(u,v) = \left\{ \begin{array}{l} x(u,v) = R \sin(u)\cos(v) \\ y(u,v) = R \sin(u)\sin(v) \\ z(u,v) = R \cos(u) \end{array} \right. \]
Implicit representation
\[S=\{(x,y,z)\in\mathbb{R}^3 \; |\, F(x,y,z) = 0\}\]
Isosurface of scalar field
\[F(x,y,z) = x^{2}+y^{2}+z^{2}-R^{2} \]