;; The first three lines of this file were inserted by DrScheme. They record metadata
;; about the language level of this file in a form that our tools can easily process.
#reader(lib "htdp-intermediate-lambda-reader.ss" "lang")((modname sierpinski) (read-case-sensitive #t) (teachpacks ((lib "draw.ss" "teachpack" "htdp") (lib "gui.ss" "teachpack" "htdp"))) (htdp-settings #(#t constructor repeating-decimal #f #t none #f ((lib "draw.ss" "teachpack" "htdp") (lib "gui.ss" "teachpack" "htdp")))))
;; sierpinski : posn posn posn  ->  true
;; to draw a Sierpinski triangle down at a, b, and c,
;; assuming it is large enough
(define (sierpinski a b c)
  (cond
    [(too-small? a b c) true]
    [else 
      (local ((define a-b (mid-point a b))
	      (define b-c (mid-point b c))
	      (define c-a (mid-point a c)))
	(and
	  (draw-triangle a b c)	    
	  (sierpinski a a-b c-a)
	  (sierpinski b a-b b-c)
	  (sierpinski c c-a b-c)))]))

;; mid-point : posn posn  ->  posn
;; to compute the mid-point between a-posn and b-posn
(define (mid-point a-posn b-posn)
  (make-posn
    (mid (posn-x a-posn) (posn-x b-posn))
    (mid (posn-y a-posn) (posn-y b-posn))))

;; mid : number number  ->  number
;; to compute the average of x and y
(define (mid x y)
  (/ (+ x y) 2))

;; distance: posn posn -> number
;; to compute the distance between two positions
(define (distance posn1 posn2)
  (sqrt  (+ (* (- (posn-x posn1) (posn-x posn2)) (- (posn-x posn1) (posn-x posn2)))
            (* (- (posn-y posn1) (posn-y posn2)) (- (posn-y posn1) (posn-y posn2)))))
)





(define A (make-posn 200 0))
(define B (make-posn 27 300))
(define C (make-posn 373 300))

(start 400 400)
  
;(sierpinski A B C)