2.3
练习 2.3 请实现一种平面矩形的表示（提示：你有可能借用练习2.2的结果）。基于你的构造函数和选择函数定义几个过程，计算给定矩形的周长和面积等。现在请再为矩形实现另一种表示方式。你应该怎样设计系统，使之能提供适当的抽象屏障，使同一个周长或者面积过程对两种不同表示都能工作？
这里只给出了简化的两种方式，只支持边与坐标轴平等的矩形
第一种方式
通过定义左上角、右下角两个点，来确定一个矩形。
(define (make-point x y) (cons x y))
(define (x-point p) (car p))
(define (y-point p) (cdr p))
(define (make-segment start end)
(cons start end)
)
(define (start-segment segment) (car segment))
(define (end-segment segment) (cdr segment))
(define (print-point p)
(newline)
(display "(")
(display (x-point p))
(display ", ")
(display (y-point p))
(display ")"))
(define (print-segment segment)
(newline)
(print-point (start-segment segment))
(display " ---- ")
(print-point (end-segment segment))
)
(define (rect left-top-point right-bottom-point) (cons left-top-point right-bottom-point))
(define (print-rect rect)
(newline)
(display "Rectange: ")
(print-segment rect)
)
(define r (rect (make-point 0 0) (make-point 5 10)))
(print-rect r)
(define left-top-point car)
(define right-bottom-point cdr)
(print-point (left-top-point r))
(print-point (right-bottom-point r))
(define (length rectangle) (abs (- (x-point (left-top-point rectangle)) (x-point (right-bottom-point rectangle)))))
(newline)
(display "length of the rectangle is ")
(display (length r))
(define (width rectangle) (abs (- (y-point (left-top-point rectangle)) (y-point (right-bottom-point rectangle)))))
(newline)
(display "width of the rectangle is ")
(display (width r))
(define (area rectangle) (* (length rectangle) (width rectangle)))
(newline)
(display "area of the rectangle is ")
(display (area r))
第二种方式
通过定义一个底边线段，再加上一个高度值，来确定一个矩形：
(define (print-point p)
(newline)
(display "(")
(display (x-point p))
(display ", ")
(display (y-point p))
(display ")"))
(define (print-segment segment)
(newline)
(print-point (start-segment segment))
(display " ---- ")
(print-point (end-segment segment))
)
(define (make-point x y) (cons x y))
(define (x-point p) (car p))
(define (y-point p) (cdr p))
(define (make-segment start end)
(cons start end)
)
(define (start-segment segment) (car segment))
(define (end-segment segment) (cdr segment))
(define (rect2 bottom-segment height) (cons bottom-segment height))
(define r (rect2 (make-segment (make-point 5 10) (make-point 10 10)) 8))
(define (print-rect2 r)
(newline)
(print-segment (car r))
(display "*")
(display (cdr r))
)
(display "The rectangle is ")
(print-rect2 r)
(define side car)
(newline)
(display "The side of the rectangle is ")
(print-segment (side r))
(define (length r) (abs (- (x-point (start-segment (side r))) (x-point (end-segment (side r))))))
(newline)
(display "The length of the rectangle is ")
(display (length r))
(define width cdr)
(define (area r) (* (length r) (width r)))
(newline)
(display "The area of the rectangle is ")
(display (area r))