Dan's Thoughts Thinking somewhat carefully

Exercise 2.3 of SICP

Exercise 2.3: Implement a representation for rectangles in a plane. (Hint: You may want to make use of exercise 2.2.) In terms of your constructors and selectors, create procedures that compute the perimeter and the area of a given rectangle. Now implement a different representation for rectangles. Can you design your system with suitable abstraction barriers, so that the same perimeter and area procedures will work using either representation?

I have decided to use a diagonal segment for representation of make-rectangle and a point with both dimensional magnitudes for make-rectangle2.

(define (make-segment p1 p2)
  (cons p1 p2))
(define (start-segment s)
  (car s))
(define (end-segment s)
  (cdr s))
(define (average a b) (/ (+ a b) 2.0))
(define (make-point x y)
    (cons x y))
(define (x-point p)
  (car p))
(define (y-point p)
  (cdr p))
(define (midpoint-segment s)
  (make-point
    (average
        (x-point (start-segment s))
        (x-point (end-segment s)))
    (average
        (y-point (start-segment s))
        (y-point (end-segment s)))))
 
(define (dimension direction r)
  (- (direction (end-segment r))
     (direction (start-segment r))))
 
(define (width r) (dimension y-point r))
(define (length r) (dimension x-point r))
 
(define (make-rectangle s) s)
 
(define (make-rectangle2 p length width)
  (make-segment p
                (make-point
                  (+ (x-point p) length)
                  (+ (y-point p) width))))
 
(define (area r)
  (* (length r)
     (width r)))
 
(define (perimeter r)
  (* 2 (+ (length r)
          (width r))))

(define R
  (make-rectangle (make-segment
                    (make-point 0 0)
                    (make-point 4 4))))

> (area R)
16
> (perimeter R)
16

(define R2 (make-rectangle2
             (make-point 0 0)
             4 4))

> (area R2)
16
> (perimeter R2)
16

(define R
  (make-rectangle (make-segment
                    (make-point 2 1)
                    (make-point 5 4))))

> (area R)
9
> (perimeter R)
12

(define R2 (make-rectangle2
             (make-point 2 1)
             3 3))

> (area R)
9
> (perimeter R)
12