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2.2.4.rkt
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#lang scheme
;; test address: http://www.biwascheme.org/demo/pictlang.html
(define (right-split painter n)
(if (= 0 n)
painter
(let ((smaller (right-split painter (- n 1))))
(beside painter (below smaller smaller)))))
(define (corner-split painter n)
(if (= 0 n)
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))))
;; exercise 2.44
(define (up-split painter n)
(if (= 0 n)
painter
(let ((smaller (up-split painter (- n 1))))
(below painter (beside smaller smaller)))))
(define (square-of-four top-left top-right bottom-left bottom-right)
(lambda (painter)
(let ((top (beside (top-left painter) (top-right painter)))
(bottom (beside (bottom-left painter) (bottom-right painter))))
(below bottom top))))
(define (flipped-pairs painter)
(let ((combine4 (square-of-four identity flip-vert
identity flip-vert)))
(combine4 painter)))
(define (square-limit-h painter n)
(let ((combine4 (square-of-four flip-horiz identity
rotate180 flip-vert)))
(combine4 (corner-split painter n))))
;; exercise 2.45
(define (split big-combiner small-combiner)
(lambda (painter n)
(let ((smaller ((split big-combiner small-combiner) painter (- n 1))))
(big-combiner painter (small-combiner smaller)))))
(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-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 vect s)
(make-vect
(* s (xcor-vect vect))
(* s (ycor-vect vect))))
(define (make-frame origin edge1 edge2)
(list origin edge1 edge2))
(define (origin-frame frame)
(car frame))
(define (edge1 frame)
(cadr frame))
(define (edge2 frame)
(caddr frame))
(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)))
;; exercise 2.48
(define (make-segment start end)
(cons start end))
(define (start-segment segment)
(car segment))
(define (end-segment segment)
(cdr segment))
;; exercise 2.49
(define frame-painter
(segments->painter (list (make-segment
(make-vect 0 0)
(make-vect 1 0))
(make-segment
(make-vect 1 0)
(make-vect 1 1))
(make-segment
(make-vect 0 0)
(make-vect 0 1))
(make-segment
(make-vect 0 1)
(make-vect 1 1)))))
(define fork-painter
(segments->painter (list (make-segment
(make-vect 0.0 0.0)
(make-vect 1.0 1.0))
(make-segment
(make-vect 1.0 0.0)
(make-vect 0.0 1.0)))))
(define (transform-painter painter origin edge1 edge2)
(lambda (frame)
(let ((m (frame-coord-map frame)))
(let ((new-origin (m origin)))
(painter (make-frame
new-origin
(sub-vect (m edge1) new-origin)
(sub-vect (m edge2) new-origin)))))))
(define (flip-vect painter)
(transform-painter painter
(make-vect 0.0 1.0)
(make-vect 1.0 1.0)
(make-vect 0.0 0.0)))
(define (shrink-to-upper-right painter)
(tansform-painter painter
(make-vect 0.5 0.5)
(make-vect 0.1 0.5)
(make-vect 0.5 1.0)))
(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 (squash-inwards painter)
(transform-painter painter
(make-vect 0.0 0.0)
(make-vect 0.65 0.35)
(make-vect 0.35 0.65)))
(define (beside painter1 painter2)
(let ((split-pointer (make-vect 0.5 0.0)))
(let ((paint-left
(transform-painter painter1
(make-vect 0.0 0.0)
split-pointer
(0.0 1.0)))
(paint-right
(transform-painter painter2
split-pointer
(make-vect 1.0 0.0)
(make-vect 0.5 1.0))))
(lambda (frame)
(paint-left frame)
(paint-right frame)))))
(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.)))
(define (rotate270 painter)
(transform-painter painter
(make-vect 0.0 1.0)
(make-vect 0.0 0.0)
(make-vect 1.0 1.0)))
;; exercise 2.51
(define (below painter1 painter2)
(let ((split-point (make-vect 0.0 0.5)))
(let ((bottom (transform-painter painter1
(make-vect 0.0 0.0)
(make-vect 1.0 0.0)
split-point))
(top (transform-painter painter2
split-point
(make-vect 1.0 0.5)
(make-vect 0.0 1.0))))
(lambda (frame)
(bottom frame)
(top frame)))))
;; 本解法实质上要搞清楚线性代数的变换规则就可以了，需要一定的线性代数矩阵运算基础
(define (below painter1 painter2)
(lambda (frame)
((flip-horiz
(rotate90
(beside
(rotate270
(flip-horiz painter1))
(rotate270
(flip-horiz painter2)))))
frame)))