(define-module interpolation
  :exports (lerp lerper stepped-lerper
            point-lerp point-lerper
            bezier2 bezierer2)

  (define-typed (lerp a :number b :number t :number)
    (+ (* t (- b a)) a))

  (define-typed (lerper a :number b :number)
    (define-typed (ret t :number)
      (lerp a b t))
    ret)

  (define-typed (stepped-lerper a :number b :number #steps :number)
    (let ((t 0)
          (dt (/ 1 #steps)))
      (lambda ()
        (let ((res (lerp a b t)))
          (mutate! t (+ t dt))
          res))))

  (define make-point pair)
  (define point->x first)
  (define point->y rest)

  (define (point-lerp p1 p2 t)
    (make-point (lerp (point->x p1) (point->x p2) t)
                (lerp (point->y p1) (point->y p2) t)))

  (define (point-lerper p1 p2)
    (lambda (t) (point-lerp p1 p2 t)))

  (define (bezier2 p1 p2 p3 t)
    (point-lerp (point-lerp p1 p2 t)
                (point-lerp p2 p3 t)
                t))

  (define (bezierer2 p1 p2 p3)
    (let ((lerper1 (point-lerper p1 p2))
          (lerper2 (point-lerper p2 p3)))
      (lambda (t)
        (point-lerp (lerper1 t)
                    (lerper2 t) t))))
  )