sicp exercise 2.51

;; Exercise 2.51.  Define the below operation for painters. Below takes two painters as arguments. The resulting painter, given a frame, draws with the first painter in the bottom of the frame and with the second painter in the top. Define below in two different ways -- first by writing a procedure that is analogous to the beside procedure given above, and again in terms of beside and suitable rotation operations (from exercise 2.50).

(define (beside painter1 painter2)
  (let ((split-point (make-vect 0.5 0.0)))
    (let ((paint-left
           (transform-painter painter1
                              (make-vect 0.0 0.0)
                              split-point
                              (make-vect 0.0 1.0)))
          (paint-right
           (transform-painter painter2
                              split-point
                              (make-vect 1.0 0.0)
                              (make-vect 0.5 1.0))))
      (lambda (frame)
        (paint-left frame)
        (paint-right frame)))))


(define (below painter1 painter2)
  (let ((split-point (make-vect 0.0 0.5)))
    (let ((paint-above
           (transform-painter painter1
                              split-point
                              (make-vect 0.1 0.5)
                              (make-vect 0.0 1.0)))
          (paint-below
           (transform-painter painter2
                              (make-vect 0.0 0.0)
                              (make-vect 1.0 0.0)
                              split-point)))
  (lambda (frame)
    (paint-above frame)
    (paint-below frame)))))



;; below can be expressed in terma of besides as
;; (rotate-270 (besides (rotate-90 painter) (rotate-90 painter)))

(define (below1 painter1 painter2)
  (rotate-270-deg-counterclockwise (besides (rotate-90-deg-cc painter1))
                                   (besided (rotate-90-deg-cc painter2))))