框架 練習 2.46 2.47

#lang racket

;: 練習 2.46


(define (make-vect x y)
  (cons x y))
(define (xcor-vect vect)
  (car vect))
(define (ycor-vect vect)
  (cdr vect))

(define (add-vect v1 v2)
  (make-vect (+ (xcor-vect v1) (xcor-vect v2))
             (+ (ycor-vect v1) (ycor-vect v2))))

(define (sub-vect v1 v2)
  (make-vect (- (xcor-vect v1) (xcor-vect v2))
             (- (ycor-vect v1) (ycor-vect v2))))
(define (scale-vect s vect)
  (make-vect (* s (xcor-vect vect))
             (* s (ycor-vect vect))))

;: 練習 2.47

(define (make-frame origin edge1 edge2)
  (list origin edge1 edge2))

(define (origin-frame frame)
  (car frame))
(define (edge1-frame frame)
  (cadr frame))
(define (edge2-frame frame)
  (caddr frame))

;: 框架
(define (frame-coord-map frame)
  (lambda (v)
    (add-vect (origin-frame frame)
              (add-vect (scale-vect (xcor-vect v)
                                    (edge1-frame frame))
                        (scale-vect (ycor-vect v)
                                    (edge2-frame frame))))))