Explicit representation
\[S(u,v)=(x(u,v),\,y(u,v),\,z(u,v))\]
Parametric map
+ Neighborhood information
Implicit representation
\[S=\{(x,y,z)\in\mathbb{R}^3 \; |\, F(x,y,z) = 0\}\]
Isosurface of scalar field
+ Topological modification