# Definitions > [!NOTE] Definition (Parametrisation of Surface) > A parametrised surface $S$ is the [[Image of a set under a function|image]] of $U\times V$ under $f$ given by $S=\{ f(u,v)\in \mathbb{R}^{3}: \text{for all } u \in U, v\in V \}$ where $\underline{r}:U\subset \mathbb{R}^{2}\to \mathbb{R}^{3}$ is a [[Function|function]] (known as the **parametrisation** of $S$), $U,V\subset \mathbb{R}$ are [[Real intervals|real intervals]] and $\mathbb{R}^{n}$ denote the [[Real n-Space|real n-space]]. # Properties