A homogeneous transformation combines a three-dimensional linear transformation and a translation in one $4 \times 4$ matrix:

Here, $R$ is a $3 \times 3$ matrix and $t$ is a three-dimensional translation vector. For a point $p = (x, y, z)$, form its homogeneous coordinate:

Apply the transformation:

Return the first three coordinates of every transformed point. A single input point must produce an array of shape $(3,)$, while a batch must produce an array of shape $(N, 3)$.