sicp每日一题[2.50]

Exercise 2.50

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

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这道题挺有意思的，搞明白这道题就明白了 frame 的3个点的位置。如上图所示，为了更好区分，特意用了长方形而不是正方形，第一幅图是原图，O 表示 origin, A 表示 edge1，B 表示 edge2。无论进行何种变换，左下坐标都是 (0, 0)，左上都是(0, 1)， 右下都是(1, 0)， 右上都是(1, 1)，我们只要把变换后的图形中 O, A, B 的新位置作为参数传进去就行。

#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 (flip-horiz painter)
  (transform-painter painter
                     (make-vect 1.0 0.0) ; new origin
                     (make-vect 0.0 0.0) ; new end of edge1
                     (make-vect 1.0 1.0))) ; new end of edge2

(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

(paint einstein)
(paint (flip-horiz einstein))
(paint (rotate90 einstein))
(paint (rotate180 einstein))
(paint (rotate270 einstein))

效果如下图所示，为了跟水平翻转对比，特意把原图加上了：