(defun translate! (out matrix vec)
  "Translate MATRIX by VEC, storing the result in the existing matrix, OUT."
  ;; NOTE: to avoid a cons of a matrix, instead of writing this in the normal
  ;; mathematical manner of: (*! out (set-translation (id) vec) matrix) (which
  ;; applies the translation after the transfomration stored in MATRIX) we
  ;; instead do the dot product by hand (eliding a pile of terms that wipe out
  ;; to zero) to compute the new translation column. This also happens to save
  ;; a lot of operations too.
  (box.math.mat4:with-components ((o out))
    (box.math.mat4:copy! out matrix)
    (box.math.vec4:with-components ((v vec))
      (psetf
       o03 (+ o03 vx)
       o13 (+ o13 vy)
       o23 (+ o23 vz)))
    o))