(define (make-vect x y) (cons x y))
(define (xcor-vect v) (car v))
(define (ycor-vect v) (cdr v))

(define (add-vect v1 v2)
  (make-vect (+ (xcor-vect v1) (xcor-vect v2))
	     (+ (ycor-vect v1) (ycor-vect v2))))


(define (sub-vect v1 v2)
  (make-vect (- (xcor-vect v1) (xcor-vect v2))
	     (- (ycor-vect v1) (ycor-vect v2))))

(define (scale-vect s v) 
  (make-vect (* (xcor-vect v) s)
	     (* (ycor-vect v) s)))


;; 2.47

(define (make-frame origin edge1 edge2)
  (list origin edge1 edge2))

(define (origin-frame frame)
  (car frame))

(define (edge1-frame frame)
  (cadr frame))

(define (edge2-frame frame)
  (caddr frame))

;(define (make-frame origin edge1 edge2)
  ;(cons origin (cons edge1 edge2)))
;
;(define (origin-frame frame)
;  (car frame))
;
;(define (edge1-frame frame)
;  (cadr frame))
;
;(define (edge2-frame frame)
;  (cddr frame))

;; 2.48

(define (make-segment start end)
  (cons start end))

(define (start-segment segment)
  (car segment))

(define (end-segment segment)
  (cdr segment))


;; 2.49

(define (for-each f l)
  (if (not (null? l))
      (begin (f (car l))
      	     (for-each f (cdr l)))))

(define (frame-coord-map frame)
  (lambda (v)
    (add-vect
     (origin-frame frame)
     (add-vect (scale-vect (xcor-vect v)
                           (edge1-frame frame))
               (scale-vect (ycor-vect v)
                           (edge2-frame frame))))))

(define (draw-line start end)
  (print "(" start " -> "  end ")"))

(define (segments->painter segment-list)
  (lambda (frame)
    (for-each
     (lambda (segment)
       (draw-line
        ((frame-coord-map frame) (start-segment segment))
        ((frame-coord-map frame) (end-segment segment))))
     segment-list)))

(define frame (make-frame (make-vect 1 1) (make-vect 1 0) (make-vect 0 1)))
(define bottom-left (make-vect 0 0))
(define top-left (make-vect 0 1))
(define top-right (make-vect 1 1))
(define bottom-right (make-vect 1 0))
(define top (make-vect 0.5 1))
(define bottom (make-vect 0.5 0))
(define left (make-vect 0 0.5))
(define right (make-vect 1 0.5))

(define outline-painter (segments->painter
  (list
    (make-segment bottom-left bottom-right)
    (make-segment bottom-right top-right)
    (make-segment top-right top-left)
    (make-segment top-left bottom-left))))

(define x-painter
  (segments->painter
    (list
      (make-segment bottom-left top-right)
      (make-segment bottom-right top-left))))

(define diamond-painter
  (segments->painter
    (list
      (make-segment bottom left)
      (make-segment left top)
      (make-segment top right)
      (make-segment right bottom))))


;; 2.50

(define (transform-painter painter origin corner1 corner2)
  (lambda (frame)
    (let ((m (frame-coord-map frame)))
      (let ((new-origin (m origin)))
        (painter
         (make-frame new-origin
                     (sub-vect (m corner1) new-origin)
                     (sub-vect (m corner2) new-origin)))))))

(define (flip-horiz painter)
  (transform-painter 
    painter
    (make-vect 1 0)
    (make-vect 0 0)
    (make-vect 1 1)))

(define (rotate180 painter)
  (transform-painter
    painter
    (make-vect 1 1)
    (make-vect 0 1)
    (make-vect 1 0)))

(define (rotate270 painter)
  (transform-painter
    painter
    (make-vect 0 1)
    (make-vect 0 0)
    (make-vect 1 1)))

(define (rotate90 painter)
  (transform-painter painter
                     (make-vect 1.0 0.0)
                     (make-vect 1.0 1.0)
                     (make-vect 0.0 0.0)))

(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 0.5)))
    (let ((paint-bottom
	   (transform-painter
	      painter1
	      (make-vect 0 0)
	      (make-vect 1 0)
	      split-point))
	  (paint-top
	    (transform-painter
	      painter2
	      split-point
	      (make-vect 1 0.5)
	      (make-vect 0 1))))
      (lambda (frame)
	(paint-bottom frame)
	(paint-top frame)))))

(define (below-rot painter1 painter2)
  (rotate270 
    (beside (rotate90 painter1)
	    (rotate90 painter2))))