;; 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 |27.1|) (read-case-sensitive #t) (teachpacks ((lib "draw.ss" "teachpack" "htdp") (lib "arrow.ss" "teachpack" "htdp") (lib "gui.ss" "teachpack" "htdp"))) (htdp-settings #(#t constructor repeating-decimal #f #t none #f ((lib "draw.ss" "teachpack" "htdp") (lib "arrow.ss" "teachpack" "htdp") (lib "gui.ss" "teachpack" "htdp")))))
;; sierpinski : posn posn posn symbol -> true
;; Given a, b, and c (posns), draw the triangle specified by the 3 posns and color and then use generative recursion to draw the nested triangles.  Return true once the triangles become too small to draw.

(define (sierpinski a b c color)
  (local ((define a-b (midpoint a b))
          (define a-c (midpoint a c))
          (define b-c (midpoint b c)))
    (cond 
      [(too-small? a b c) true]
      [else (and (draw-triangle (round-posn a)
                                (round-posn b)
                                (round-posn c) color)
                 (sierpinski a a-b a-c color)
                 (sierpinski b a-b b-c color)
                 (sierpinski c a-c b-c color))])))

;round-posn : posn -> posn
;Rounds a posn x to the nearest integer

(define (round-posn p)
  (make-posn (inexact->exact (round (posn-x p)))
             (inexact->exact (round (posn-y p)))))

;draw-triangle : posn posn posn -> true
;Draw the triangle that contains a, b, and c as vertices.

(define (draw-triangle a b c color)
  (and (draw-solid-line a b color)
       (draw-solid-line b c color)
       (draw-solid-line c a color)))

;midpoint : posn posn -> posn
;Given a, b, find the midpoint of the two posns.

(define (midpoint a b)
  (make-posn (/ (+ (posn-x a) (posn-x b)) 2)
             (/ (+ (posn-y a) (posn-y b)) 2)))

;too-small? : posn posn posn -> boolean
;Given a, b, c, determine if the triangle is too small.  A triangle is too small if the area of the given triangle is less than MINAREA.

(define MINAREA 5)

(define (too-small? a b c)
  (< (area-of-triangle a b c) MINAREA))

;area-of-triangle : posn posn posn -> number
;Given a, b, c, determine the area of the triangle. (uses Heron's formula)

(define (area-of-triangle a b c)
  (local ((define A (distance b c))
          (define B (distance a c))
          (define C (distance a b))
          (define semiperimeter (/ (+ A B C) 2)))
    (sqrt (* semiperimeter
             (- semiperimeter A)
             (- semiperimeter B)
             (- semiperimeter C)))))

;distance : posn posn -> number
;Given p1, p2, determine the distance between two points.

(define (distance p1 p2)
  (sqrt (+ (sqr (- (posn-x p2) (posn-x p1)))
           (sqr (- (posn-y p2) (posn-y p1))))))

(define CENTER (make-posn 200 200))
(define RADIUS 200)

;;circle-pt : number -> posn
;;Given angle-ratio (ie, 120/360, 240/360, 360/360), find a position on the circle with CENTER and RADIUS as defined above.

(define (circle-pt angle-ratio)
  (local ((define theta (* angle-ratio 2 pi)))
    (make-posn (+ (posn-x CENTER)
                  (* RADIUS (cos theta)))
               (- (posn-y CENTER)
                  (* RADIUS (sin theta))))))

(define A (circle-pt 120/360))
(define B (circle-pt 240/360))
(define C (circle-pt 360/360))

#|
(define WIDTH 400)
(define HEIGHT 400)
(start WIDTH HEIGHT)



(draw-circle CENTER RADIUS 'black)
(draw-solid-disk A 5 'green)
(draw-solid-disk B 5 'blue)
(draw-solid-disk C 5 'purple)
|#

(define WIDTH 1000)
(define HEIGHT 1000)

(define x1 (make-posn 0 (round (inexact->exact HEIGHT))))
(define x2 (make-posn (round (inexact->exact WIDTH))
                      (round (inexact->exact HEIGHT))))
(define x3 (make-posn (round (inexact->exact (/ WIDTH 2)))
                      (round (inexact->exact (* HEIGHT (- 1 (/ (sqrt 3)
                                                               2)))))))

(start WIDTH HEIGHT)
(sierpinski x1 x2 x3 'black)