Exercise 2.2. Consider the problem of representing line segments in a plane. Each segment is represented as a pair of points: a starting point and an ending point. Define a constructor make-segment and selectors start-segment and end-segment that define the representation of segments in terms of points. Furthermore, a point can be represented as a pair of numbers: the x coordinate and the y coordinate. Accordingly, specify a constructor make-point and selectors x-point and y-point that define this representation. Finally, using your selectors and constructors, define a procedure midpoint-segment that takes a line segment as argument and returns its midpoint (the point whose coordinates are the average of the coordinates of the endpoints). To try your procedures, you’ll need a way to print points:
(define (print-point p)
(newline)
(display "(")
(display (x-point p))
(display ",")
(display (y-point p))
(display ")"))
定义过程 midpoint-segment 所需要的选择函数和构造函数：
;;; point
(define (make-point x y)
(cons x y))
(define (x-point point)
(car point))
(define (y-point point)
(cdr point))
;;; segment
(define (make-segment start end)
(cons start end))
(define (start-segment segment)
(car segment))
(define (end-segment segment)
(cdr segment))
;;; operation on segment
(define (print-point p)
(newline)
(display "(")
(display (x-point p))
(display ",")
(display (y-point p))
(display ")"))
(define (midpoint-segment segment)
(make-point (/ (+ (x-point (start-segment segment))
(x-point (end-segment segment)))
2)
(/ (+ (y-point (start-segment segment))
(y-point (end-segment segment)))
2)))
测试：
(load "../testframe.scm")
;;; the midpoint of points (1, 3) and (4, 5) is (5/2, 4)
(assert-output-equal
"\n(5/2,4)"
(print-point (midpoint-segment (make-segment (make-point 1 3) (make-point 4 5)))))