# Barycentric coordinates

Main Article
Discussion
Related Articles  [?]
Bibliography  [?]
In an affine space or vector space of dimension n we take n+1 points ${\displaystyle s_{0},s_{1},\ldots ,s_{n}}$ in general position (no k+1 of them lie in an affine subspace of dimension less than k) as a simplex of reference. The barycentric coordinates of a point x are an (n+1)-tuple ${\displaystyle x_{0},x_{1},\ldots ,x_{n}}$ such that
${\displaystyle (x_{0}+\cdots +x_{n})x=x_{0}s_{0}+\cdots +x_{n}s_{n}\,}$
and at least one of ${\displaystyle x_{0},x_{1},\ldots ,x_{n}}$ does not vanish. The coordinates are not affected by scaling, and it may be convenient to take ${\displaystyle x_{0}+\cdots +x_{n}=1}$, in which case they are called areal coordinates.