Definition:Barycentric Coordinates/3 Dimensions
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Definition
In $3$ dimensional space, barycentric coordinates are a set of $4$ numbers representing the position of a point as follows:
Let $p_0, p_1, p_2, p_3$ be fixed non-coplanar points, such that $p_i = \tuple {x_i, y_1, z_i}$.
Then an arbitrary point $p$ can be expressed in the form:
- $p = \lambda_0 p_0 + \lambda_1 p_1 + \lambda_2 p_2 + \lambda_3 p_3$
such that:
- $\lambda_0 + \lambda_1 + \lambda_2 + \lambda_3 = 0$
The set $\set {\lambda_0, \lambda_1, \lambda_2, \lambda_3}$ consists of the barycentric coordinates of $p$.
Also see
- Results about barycentric coordinates can be found here.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): barycentric coordinates
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): barycentric coordinates