Definition:Barycentric Coordinates/2 Dimensions

Definition

In the plane, barycentric coordinates are a set of $3$ numbers representing the position of a point as follows:

Let $\mathbf a$, $\mathbf b$ and $\mathbf c$ be the position vectors of the $3$ vertices of a triangle in the plane.

Then the position vector of an arbitrary point $p$ can be expressed uniquely in the form:

$\mathbf p = \alpha \mathbf a + \beta \mathbf b + \gamma \mathbf c$

such that:

$\alpha + \beta + \gamma = 1$

The set $\set {\alpha, \beta, \gamma}$ consists of the barycentric coordinates of $p$.

Also see

• Results about barycentric coordinates can be found here.

Sources

• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): barycentric coordinates