;; avg2: num, num --> num
;;
(define (avg2 a b) (/ (+ a b) 2))

;; midpoint: posn, posn --> posn
;;
(define (midpoint p1 p2)
  (make-posn (avg2 (posn-x p1) (posn-x p2))
             (avg2 (posn-y p1) (posn-y p2))))

;; manhattan-distance: posn, posn --> number
;; N.B. The Manhattan distance is the
;;  distance if you can travel n/s or e/w,  but not diagonal.
;;
(define (manhattan-distance p q)
  (+ (abs (- (posn-x p) (posn-x q)))
     (abs (- (posn-y p) (posn-y q)))))

;; too-close?: posn,posn,posn --> boolean
;; Return true if any of p1,p2,p3 near each other.
;;
;; NB You can change the constant close-enough,
;; to tweak too-close?'s threshold.
;;
(define close-enough 2)
(define (too-close? p1 p2 p3)
  (or (<= (manhattan-distance p1 p2) close-enough)
      (<= (manhattan-distance p2 p3) close-enough)
      (<= (manhattan-distance p3 p1) close-enough)))




;;; A polyline is a list of piecewise connected line segments.
;;; We represent a polyline as a list of posns (the vertices).

;; draw-polyline:       list-of-posn --> boolean
;; draw-polyline-color: list-of-posn, color --> boolean
;; 
(define (draw-polyline pts) (draw-polyline-color pts BLACK))

(define (draw-polyline-color pts color)
  (cond [(empty? pts)          false]  ; A polyline of no points? Absurd!
        [(empty? (rest pts))   (draw-solid-line (first pts) (first pts))]
        [else (begin (draw-solid-line (first pts) (second pts) color)
                     (draw-polyline-color (rest pts) color))]))



;; draw-triangle: posn posn posn --> true
;;
(define (draw-triangle a b c) (draw-polyline-color (list a b c a) BLUE))