Compute barycentric coordinates of a tetrahedron

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

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