sicp每日一题[2.52]

Exercise 2.52

Make changes to the square limit of wave shown in Figure 2.9 by working at each of the levels described above. In particular:

a. Add some segments to the primitive wave painter of Exercise 2.49 (to add a smile, for example).
b. Change the paern constructed by corner-split (for example, by using only one copy of the up-split and right-split images instead of two).
c. Modify the version of square-limit that uses square-of-four so as to assemble the corners in a different pateern. (For example, you might make the big Mr.Rogers look outward from each corner of the square.)

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对于我来说，这道题最大的难度在于理解题意，我根据自己的理解修改之后想：就这么简单？然后去查了其他人的答案，发现还真就这么简单 ：）

(#%require sicp-pict)


(define wave 
  (segments->painter (list 
                      (segment (vect .25 0) (vect .35 .5)) 
                      (segment (vect .35 .5) (vect .3 .6)) 
                      (segment (vect .3 .6) (vect .15 .4)) 
                      (segment (vect .15 .4) (vect 0 .65)) 
                      (segment (vect 0 .65) (vect 0 .85)) 
                      (segment (vect 0 .85) (vect .15 .6)) 
                      (segment (vect .15 .6) (vect .3 .65)) 
                      (segment (vect .3 .65) (vect .4 .65)) 
                      (segment (vect .4 .65) (vect .35 .85)) 
                      (segment (vect .35 .85) (vect .4 1)) 
                      (segment (vect .4 1) (vect .6 1)) 
                      (segment (vect .6 1) (vect .65 .85)) 
                      (segment (vect .65 .85) (vect .6 .65)) 
                      (segment (vect .6 .65) (vect .75 .65)) 
                      (segment (vect .75 .65) (vect 1 .35)) 
                      (segment (vect 1 .35) (vect 1 .15)) 
                      (segment (vect 1 .15) (vect .6 .45)) 
                      (segment (vect .6 .45) (vect .75 0)) 
                      (segment (vect .75 0) (vect .6 0)) 
                      (segment (vect .6 0) (vect .5 .3)) 
                      (segment (vect .5 .3) (vect .4 0)) 
                      (segment (vect .4 0) (vect .25 0)) 
                      )))

(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))))
        (beside painter (below smaller smaller)))))

; a
(define wave-with-smile
  (segments->painter (list 
                      (segment (vect .25 0) (vect .35 .5)) 
                      (segment (vect .35 .5) (vect .3 .6)) 
                      (segment (vect .3 .6) (vect .15 .4)) 
                      (segment (vect .15 .4) (vect 0 .65)) 
                      (segment (vect 0 .65) (vect 0 .85)) 
                      (segment (vect 0 .85) (vect .15 .6)) 
                      (segment (vect .15 .6) (vect .3 .65)) 
                      (segment (vect .3 .65) (vect .4 .65)) 
                      (segment (vect .4 .65) (vect .35 .85))
                      (segment (vect .35 .85) (vect .4 1))
                      (segment (vect .4 1) (vect .6 1)) 
                      (segment (vect .6 1) (vect .65 .85))
                      (segment (vect .65 .85) (vect .6 .65)) 
                      (segment (vect .6 .65) (vect .75 .65)) 
                      (segment (vect .75 .65) (vect 1 .35)) 
                      (segment (vect 1 .35) (vect 1 .15)) 
                      (segment (vect 1 .15) (vect .6 .45)) 
                      (segment (vect .6 .45) (vect .75 0)) 
                      (segment (vect .75 0) (vect .6 0)) 
                      (segment (vect .6 0) (vect .5 .3)) 
                      (segment (vect .5 .3) (vect .4 0)) 
                      (segment (vect .4 0) (vect .25 0))
                      (segment (vect .45 .76) (vect .5 0.72))
                      (segment (vect .5 0.72) (vect .55 .76))
                      )))

(paint wave-with-smile)


(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 up)
              (bottom-right (below right right))
              (corner (corner-split painter (- n 1))))
          (beside (below painter top-left)
                  (below bottom-right corner))))))

(paint (corner-split wave-with-smile 1))

(define (square-of-four tl tr bl br)
  (lambda (painter)
    (let ((top (beside (tl painter) (tr painter)))
          (bottom (beside (bl painter) (br painter))))
      (below bottom top))))

(define (square-limit painter n)
  (let ((combine4 (square-of-four flip-vert rotate180
                                  identity flip-horiz)))
    (combine4 (corner-split painter n))))

(paint (square-limit wave-with-smile 1))

执行结果如下图所示：