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2.44.rkt
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#lang racket/gui
(require graphics/graphics)
(open-graphics)
(define vp (open-viewport "A Picture Language" 500 500))
(define draw (draw-viewport vp))
(define (clear) ((clear-viewport vp)))
(define line (draw-line vp))
(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 (* s (xcor-vect v))
(* s (ycor-vect v))))
(define (make-frame origin edge1 edge2)
(list origin edge1 edge2))
(define (origin-frame f)
(car f))
(define (edge1-frame f)
(cadr f))
(define (edge2-frame f)
(caddr f))
(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 (make-segment start end)
(cons start end))
(define (start-segment segment)
(car segment))
(define (end-segment segment)
(cdr segment))
(define (segments->painter segment-list)
(lambda (frame)
(for-each
(lambda (segment)
(let ((start-coord-map ((frame-coord-map frame) (start-segment segment)))
(end-coord-map ((frame-coord-map frame) (end-segment segment))))
(line
(make-posn (xcor-vect start-coord-map) (ycor-vect start-coord-map))
(make-posn (xcor-vect end-coord-map) (ycor-vect end-coord-map)))))
segment-list)))
(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 (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 (flip-vert painter)
(transform-painter painter
(make-vect 0.0 1.0)
(make-vect 1.0 1.0)
(make-vect 0.0 0.0)))
(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 outline-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 0 1)
(make-vect 1 0)))))
(define diamond-painter
(segments->painter
(list
(make-segment (make-vect 0 0.5)
(make-vect 0.5 0))
(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)))))
(define wave-painter
(segments->painter
(list
(make-segment (make-vect 0.5 0.4) ;;; leg triangle
(make-vect 0.6 0))
(make-segment (make-vect 0.5 0.4)
(make-vect 0.4 0))
(make-segment (make-vect 0.3 0)
(make-vect 0.35 0.4))
(make-segment (make-vect 0.35 0.4)
(make-vect 0.3 0.7))
(make-segment (make-vect 0.3 0.7)
(make-vect 0.2 0.6))
(make-segment (make-vect 0.2 0.6)
(make-vect 0 0.8))
(make-segment (make-vect 0 0.9)
(make-vect 0.2 0.7))
(make-segment (make-vect 0.2 0.7)
(make-vect 0.3 0.75))
(make-segment (make-vect 0.3 0.75)
(make-vect 0.4 0.75))
(make-segment (make-vect 0.4 0.75)
(make-vect 0.35 0.9))
(make-segment (make-vect 0.35 0.9)
(make-vect 0.4 1))
(make-segment (make-vect 0.5 1)
(make-vect 0.55 0.9))
(make-segment (make-vect 0.55 0.9)
(make-vect 0.5 0.75))
(make-segment (make-vect 0.5 0.75)
(make-vect 0.6 0.75))
(make-segment (make-vect 0.6 0.75)
(make-vect 1 0.45))
(make-segment (make-vect 1 0.3)
(make-vect 0.6 0.5))
(make-segment (make-vect 0.6 0.5)
(make-vect 0.7 0)))))
(define (rotate-180 painter)
(flip-vert painter))
(define (rotate-270 painter)
(transform-painter painter
(make-vect 1.0 0.0)
(make-vect 1.0 1.0)
(make-vect 0.0 0.0)))
(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)))))
(define (right-split painter n)
(if (= n 0)
painter
(let ((smaller (right-split painter (- n 1))))
(beside painter (below smaller smaller)))))
(define (up-split painter n)
(if (= n 0)
painter
(let ((smaller (up-split painter (- n 1))))
(below painter (beside smaller smaller)))))
(define (corner-split painter n)
(if (= n 0)
painter
(let ((up (up-split painter (- n 1)))
(right (right-split painter (- n 1))))
(let ((top-left (beside up up))
(bottom-right (below right right))
(corner (corner-split painter (- n 1))))
(beside (below painter top-left)
(below bottom-right corner))))))
(define (square-limit painter n)
(let ((quarter (corner-split painter n)))
(let ((half (beside (flip-horiz quarter) quarter)))
(below (flip-vert half) half))))
(define (below-transformations painter1 painter2)
(flip-horiz (flip-vert (rotate-270 (beside (rotate-270 painter1) (rotate-270 painter2))))))
(define unit-frame (make-frame (make-vect 0 500) (make-vect 500 0) (make-vect 0 -500)))
((corner-split wave-painter 4) unit-frame)