;; Solutions to Picture language project.
;; This project is almost entirely about believing in data abstraction;
;; except for the problems that ask you to write selectors for an
;; abstract data type, there are no CARs or CDRs here.


;; 2.44

(define (up-split painter n)
  (if (= n 0)
      painter
      (let ((smaller (up-split painter (- n 1))))
	(below painter (beside smaller smaller)))))

;; 2.45

(define (split major minor)
  (define (splitter painter n)
    (if (= n 0)
	painter
	(let ((smaller (splitter painter (- n 1))))
	  (major painter (minor smaller smaller)))))
  splitter)

;; 2.46

(define make-vect cons)
(define xcor-vect car)
(define ycor-vect cdr)

(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 (* s (xcor-vect v))
	     (* s (ycor-vect v))))

;; 2.47

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

(define origin-frame car)
(define edge1-frame cadr)
(define edge2-frame caddr)

; or

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

(define origin-frame car)
(define edge1-frame cadr)
(define edge2-frame cddr)       ; this one is different!

;; 2.48

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

;; 2.49

(define frame-painter
  (segments->painter
   (list (make-segment (make-vect 0 0) (make-vect 0 1))
	 (make-segment (make-vect 0 1) (make-vect 1 1))
	 (make-segment (make-vect 1 1) (make-vect 1 0))
	 (make-segment (make-vect 1 0) (make-vect 0 0)))))

(define X-painter
  (segments->painter
   (list (make-segment (make-vect 0 0) (make-vect 1 1))
	 (make-segment (make-vect 1 0) (make-vect 0 1)))))

(define diamond
  (segments->painter
   (list (make-segment (make-vect 0.5 0) (make-vect 1 0.5))
	 (make-segment (make-vect 1 0.5) (make-vect 0.5 1))
	 (make-segment (make-vect 0.5 1) (make-vect 0 0.5))
	 (make-segment (make-vect 0 0.5) (make-vect 0.5 0)))))

(define wave
  (segments->painter
   (list (make-segment (make-vect 0.4 1) (make-vect 0.35 0.85))
	 (make-segment (make-vect 0.35 0.85) (make-vect 0.4 0.65))
	 (make-segment (make-vect 0.4 0.65) (make-vect 0.3 0.65))
	 (make-segment (make-vect 0.3 0.65) (make-vect 0.15 0.6))
	 (make-segment (make-vect 0.15 0.6) (make-vect 0 0.85))
	 (make-segment (make-vect 0 0.65) (make-vect 0.15 0.4))
	 (make-segment (make-vect 0.15 0.4) (make-vect 0.3 0.6))
	 (make-segment (make-vect 0.3 0.6) (make-vect 0.35 0.5))
	 (make-segment (make-vect 0.35 0.5) (make-vect 0.25 0))
	 (make-segment (make-vect 0.4 0) (make-vect 0.5 0.3))
	 (make-segment (make-vect 0.5 0.3) (make-vect 0.6 0))
	 (make-segment (make-vect 0.75 0) (make-vect 0.6 0.45))
	 (make-segment (make-vect 0.6 0.45) (make-vect 1 0.15))
	 (make-segment (make-vect 1 0.35) (make-vect 0.75 0.65))
	 (make-segment (make-vect 0.75 0.65) (make-vect 0.6 0.65))
	 (make-segment (make-vect 0.6 0.65) (make-vect 0.65 0.85))
	 (make-segment (make-vect 0.65 0.85) (make-vect 0.6 1)))))

;; 2.50

(define (flip-horiz painter)
  (transform-painter painter
		     (make-vect 1.0 0.0)
		     (make-vect 0.0 0.0)
		     (make-vect 1.0 1.0)))

(define (rotate180 painter)
  (transform-painter painter
		     (make-vect 1.0 1.0)
		     (make-vect 0.0 1.0)
		     (make-vect 1.0 0.0)))

(define (rotate270 painter)
  (transform-painter painter
		     (make-vect 0.0 1.0)
		     (make-vect 0.0 0.0)
		     (make-vect 1.0 1.0)))

;; 2.51

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

;; or

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

; Don't just glaze over while reading that -- understand and enjoy it!
; Composition of functions makes this problem a lot easier.

;; 2.52 -- changes are in CAPITAL LETTERS below.

;; 2.52a

(define smiley
  (segments->painter
   (list (make-segment (make-vect 0.4 1) (make-vect 0.35 0.85))
	 (make-segment (make-vect 0.35 0.85) (make-vect 0.4 0.65))
	 (make-segment (make-vect 0.4 0.65) (make-vect 0.3 0.65))
	 (make-segment (make-vect 0.3 0.65) (make-vect 0.15 0.6))
	 (make-segment (make-vect 0.15 0.6) (make-vect 0 0.85))
	 (make-segment (make-vect 0 0.65) (make-vect 0.15 0.4))
	 (make-segment (make-vect 0.15 0.4) (make-vect 0.3 0.6))
	 (make-segment (make-vect 0.3 0.6) (make-vect 0.35 0.5))
	 (make-segment (make-vect 0.35 0.5) (make-vect 0.25 0))
	 (make-segment (make-vect 0.4 0) (make-vect 0.5 0.3))
	 (make-segment (make-vect 0.5 0.3) (make-vect 0.6 0))
	 (make-segment (make-vect 0.75 0) (make-vect 0.6 0.45))
	 (make-segment (make-vect 0.6 0.45) (make-vect 1 0.15))
	 (make-segment (make-vect 1 0.35) (make-vect 0.75 0.65))
	 (make-segment (make-vect 0.75 0.65) (make-vect 0.6 0.65))
	 (make-segment (make-vect 0.6 0.65) (make-vect 0.65 0.85))
	 (make-segment (make-vect 0.65 0.85) (make-vect 0.6 1))
	 (MAKE-SEGMENT (MAKE-VECT 0.45 0.75) (MAKE-VECT 0.5 0.7))
	 (MAKE-SEGMENT (MAKE-VECT 0.5 0.7) (MAKE-VECT 0.55 0.75)))))

;; 2.52b

(define (funny-corner-split painter n)
  (if (= n 0)
      painter
      (let ((up (up-split painter (- n 1)))
	    (right (right-split painter (- n 1)))
	    (corner (funny-corner-split painter (- n 1))))
	(beside (below painter UP)
		(below RIGHT corner)))))

;; 2.52c

(define (face-out painter n)
  (let ((combine4 (square-of-four flip-horiz identity
				  rotate180 flip-vert)))
    (combine4 (corner-split (FLIP-HORIZ PAINTER) n))))