SICP 习题参考答案 2.2

win_hate

1. 
   
2. (define (make-vect x y)
   
3.   (list x y))
   
4. 
   
5. (define (xcor-vect v)
   
6.   (car v))
   
7. 
   
8. (define (ycor-vect v)
   
9.   (cadr v))
   
10. 
    
11. (define (add-vect w v)
    
12.   (map + w v))
    
13. 
    
14. (define (sub-vect w v)
    
15.   (map - w v))
    
16. 
    
17. (define (scale-vect k v)
    
18.   (map (lambda (x) (* k x)) v))
    

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win_hate

Exercise 2.47.  Here are two possible constructors for frames:

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

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

For each constructor supply the appropriate selectors to produce an implementation for frames.

[ 本帖最后由 win_hate 于 2008-10-18 11:59 编辑 ]

win_hate

1. 
   
2. (define (make-frame origin edge1 edge2)
   
3.   (list origin edge1 edge2))
   
4. 
   
5. (define (origin-frame frame)
   
6.   (car frame))
   
7. 
   
8. (define (edge1-frame frame)
   
9.   (cadr frame))
   
10. 
    
11. (define (edge2-frame frame)
    
12.   (caddr frame))
    

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这里只实现了用 list 的，用 cons 的就算了吧。

[ 本帖最后由 win_hate 于 2008-10-18 11:59 编辑 ]

win_hate

Exercise 2.48.  A directed line segment in the plane can be represented as a pair of vectors -- the vector running from the origin to the start-point of the segment, and the vector running from the origin to the end-point of the segment. Use your vector representation from exercise 2.46 to define a representation for segments with a constructor make-segment and selectors start-segment and end-segment.

win_hate

1. 
   
2. (define (make-segment v1 v2)
   
3.   (cons v1 v2))
   
4. 
   
5. (define (start-segment s)
   
6.   (car s))
   
7. 
   
8. (define (end-segment s)
   
9.   (cdr s))
   

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用一下 cons，算是对上一题的补偿。

win_hate

Exercise 2.49.  Use segments->painter to define the following primitive painters:

a.  The painter that draws the outline of the designated frame.

b.  The painter that draws an ``X'' by connecting opposite corners of the frame.

c.  The painter that draws a diamond shape by connecting the midpoints of the sides of the frame.

d.  The wave painter.

win_hate

这些图有个共同的模式－－－将若干个点连起来。所以我写了一个辅助函数，list->segment。应该叫 points->segments 才对，不过已经这样写了，不改了。

1. 
   
2. (define (list->segment xs)
   
3.   (define (f r x xs)
   
4.     (if (null? xs) r
   
5.         (f (cons (make-segment x (car xs)) r) (car xs) (cdr xs))))
   
6.   (f '() (car xs) (cdr xs)))
   

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• draw-frame
  
  1. 
     
  2. (define draw-frame
     
  3.   (let ((v (list (make-vect 0 0)
     
  4.                  (make-vect 0 1)
     
  5.                  (make-vect 1 1)
     
  6.                  (make-vect 1 0)
     
  7.                  (make-vect 0 0))))
     
  8.     (segments->painter (list->segment v))))
     

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• "X"
  
  
  1. 
     
  2. (define X
     
  3.   (let ((s1 (list->segment (list (make-vect 0 0)
     
  4.                                  (make-vect 1 1))))
     
  5.         (s2 (list->segment (list (make-vect 0 1)
     
  6.                                  (make-vect 1 0)))))
     
  7.     (segments->painter (append s1 s2))))
     

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• diamond
  
  1. 
     
  2. (define diamond
     
  3.   (let ((v (list (make-vect 0 0.5)
     
  4.                  (make-vect 0.5 1)
     
  5.                  (make-vect 1 0.5)
     
  6.                  (make-vect 0.5 0)
     
  7.                  (make-vect 0 0.5))))
     
  8.     (segments->painter (list->segment v))))
     

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• wave
  
  1. 
     
  2. (define wave
     
  3.   (let ((v1 (list (make-vect 0 26)
     
  4.                   (make-vect 6 17)
     
  5.                   (make-vect 12 25)
     
  6.                   (make-vect 14 21)
     
  7.                   (make-vect 10 0)))
     
  8.         (v2 (list (make-vect 16 0)
     
  9.                   (make-vect 21 13)
     
  10.                   (make-vect 25 0)))
      
  11.         (v3 (list (make-vect 31 0)
      
  12.                   (make-vect 25 19)
      
  13.                   (make-vect 41 6)))
      
  14.         (v4 (list (make-vect 41 15)
      
  15.                   (make-vect 31 27)
      
  16.                   (make-vect 25 27)
      
  17.                   (make-vect 27 35)
      
  18.                   (make-vect 25 41)))
      
  19.         (v5 (list (make-vect 16 41)
      
  20.                   (make-vect 14 35)
      
  21.                   (make-vect 16 27)
      
  22.                   (make-vect 12 27)
      
  23.                   (make-vect 6 25)
      
  24.                   (make-vect 0 35))))                  
      
  25.     (let ((segments (map (lambda (z) (list->segment
      
  26.                                      (map (lambda (x) (map (lambda (y) (/ y 41.0)) x)) z)))
      
  27.                         (list v1 v2 v3 v4 v5))))
      
  28.       (segments->painter (foldr append '() segments)))))
      

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[ 本帖最后由 win_hate 于 2008-10-18 14:31 编辑 ]

win_hate

Exercise 2.50.  Define the transformation flip-horiz, which flips painters horizontally, and transformations that rotate painters counterclockwise by 180 degrees and 270 degrees.

win_hate

1. 
   
2. (define (flip-horiz painter)
   
3.   (transform-painter painter
   
4.                      (make-vect 1 0)
   
5.                      (make-vect 0 0)
   
6.                      (make-vect 1 1)))
   
7. 
   
8. (define (rotate180 painter)
   
9.   (transform-painter painter
   
10.                      (make-vect 1 1)
    
11.                      (make-vect 0 1)
    
12.                      (make-vect 1 0)))
    
13. 
    
14. (define (rotate270 painter)
    
15.   (transform-painter painter
    
16.                      (make-vect 0 1)
    
17.                      (make-vect 0 0)
    
18.                      (make-vect 1 1)))
    

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win_hate

Exercise 2.51.  Define the below operation for painters. Below takes two painters as arguments. The resulting painter, given a frame, draws with the first painter in the bottom of the frame and with the second painter in the top. Define below in two different ways -- first by writing a procedure that is analogous to the beside procedure given above, and again in terms of beside and suitable rotation operations (from exercise 2.50).