# Compute barycentric coordinates of a tetrahedron

A compact computation with matrices - 04/2014 - #Jumble

$$\begin{bmatrix} a \\ b \\ c \end{bmatrix} = \begin{bmatrix} \mathbf P_1 - \mathbf P_4 & \mathbf P_2 - \mathbf P_4 & \mathbf P_3 - \mathbf P_4 \end{bmatrix}^{-1} . \begin{bmatrix} \mathbf P - \mathbf P_4 \end{bmatrix} \\

d = 1 - a - b - c - d

$$

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