Barycentric coordinate system (mathematics)

In geometry, the barycentric coordinate system is a coordinate system in which the location of a point of a simplex (a triangle, tetrahedron, etc.) is specified as the center of mass, or barycenter, of usually unequal masses placed at its vertices. Coordinates also extend outside the simplex, where one or more coordinates become negative. The system was introduced (1827) by August Ferdinand Möbius.

Let ${\displaystyle \mathbf {x} _{1},\ldots ,\mathbf {x} _{n}}$ be the vertices of a simplex in an affine space A. If, for some point ${\displaystyle \mathbf {p} }$ in A,

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