;;; A Point represents a location in $\Bbb R^2$.

(define (make-Point x y)
  (f64vector x y))

(define (Point-x p)
  (f64vector-ref p 0))

(define (Point-y p)
  (f64vector-ref p 1))

(define (Point-x-set! p val)
  (f64vector-set! p 0 val))

(define (Point-y-set! p val)
  (f64vector-set! p 1 val))

(define (Point? p)
  (declare (fixnum))
  (and (f64vector? p)
       (= (f64vector-length p) 2)))

(define (Point-add p1 p2)
  (declare (flonum))
  (make-Point (+ (Point-x p1) (Point-x p2))
	      (+ (Point-y p1) (Point-y p2))))

(define (Point-subtract p1 p2)
  (declare (flonum))
  (make-Point (- (Point-x p1) (Point-x p2))
	      (- (Point-y p1) (Point-y p2))))

(define (Point-scale x p)
  (declare (flonum))
  (make-Point (* x (Point-x p))
	      (* x (Point-y p))))

(define (Point-dot-product p1 p2)
  (declare (flonum))
  (+ (* (Point-x p1) (Point-x p2))
     (* (Point-y p1) (Point-y p2))))

(define (Point-L2-norm p)
  (declare (flonum))
  (let ((x (Point-x p))
	(y (Point-y p)))
    (sqrt (+ (* x x)
	     (* y y)))))

(define (Point-zero)
  (make-Point 0.0 0.0))