sicp每日一题[2.51]

Exercise2.51

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).

这道题目难度不大，理解了 2.50 那张图后，再仿照 beside 的代码，只要把3个坐标的位置调整一下就可以了; 至于利用 beside 和旋转来实现 below，就更简单了，先把2幅图向右旋转90°，然后 beside 排到一起，
最后再把排到一起的图形向左旋转90°即可。

#lang racket


(require (planet "sicp.ss" ("soegaard" "sicp.plt" 2 1)))


(define sub-vect vector-sub)

; Transforming and combining painters
(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)))))

; analogous to beside
(define (below painter1 painter2)
  (let ((split-point (make-vect 0.0 0.5)))
    (let ((paint-up
           (transform-painter
            painter2
            split-point
            (make-vect 1.0 0.5)
            (make-vect 0.0 1.0)))
          (paint-low
           (transform-painter
            painter1
            (make-vect 0.0 0.0)
            (make-vect 1.0 0.0)
            split-point)))
      (lambda (frame)
        (paint-up frame)
        (paint-low frame)))))

(paint (below einstein (beside einstein einstein)))

(define (rotate90 painter)
  (transform-painter painter
                     (make-vect 1.0 0.0) ; new origin
                     (make-vect 1.0 1.0) ; new end of edge1
                     (make-vect 0.0 0.0))) ; new end of edge2

(define (rotate180 painter)
  (transform-painter painter
                     (make-vect 0.0 1.0) ; new origin
                     (make-vect 1.0 1.0) ; new end of edge1
                     (make-vect 0.0 0.0))) ; new end of edge2

(define (rotate270 painter)
  (transform-painter painter
                     (make-vect 0.0 1.0) ; new origin
                     (make-vect 0.0 0.0) ; new end of edge1
                     (make-vect 1.0 1.0))) ; new end of edge2

; in terms of beside and suittable rotation
(define (below- painter1 painter2)
  (rotate90 (beside (rotate270 painter1) (rotate270 painter2))))

(paint (below- einstein (beside einstein einstein)))

结果如下所示：