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;; Sierp Types

;; A Sierp is a self-similar struture that is either 
;; -- SierpBase 
;; -- list-of-Sierp

;; The base-case Sierpinski structure that has
;; has 3 posns in clockwise order from the top:
;; top, lower right, lower left
(define-struct SierpBase (top lr ll))


;; A list-of-Sierp is a list and is either
;; -- empty
;; -- (cons Sierp list-of-Sierp)


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;; Functions for creating Sierpinski gaskets.

;; Makes an equilateral triangle with a base of width.
;; This is a base case Sierpinski gasket.
(define (make-FullSizeSierp width)
  (local 
      [(define width_2 (/ width 2))
       (define root3 (sqrt 3))]
  (make-SierpBase (make-posn width_2 0)
                  (make-posn 0 (* width_2 root3))
                  (make-posn width (* width_2 root3)))))

;; getMidPt:  posn posn --> posn
;; Returns the mid-point between two posns.
(define (getMidPt p1 p2)
  (make-posn (/ (+ (posn-x p1) (posn-x p2)) 2)
             (/ (+ (posn-y p1) (posn-y p2)) 2)))

;; make-nextSierp:  SierpBase --> list-of-Sierp
;; Takes a SierpBase and returns a list-of-Sierp filled with 3 SierpBases
;; where the SierpBases are formed from the vertices of the input
;; SierpBase and the mid-points of its sides.
;; The 3 SierpBases are in clockwise order from the top of the input SierpBase.
(define (make-nextSierp sierpBase)
  (local
      [(define midTopLr (getMidPt (SierpBase-top sierpBase)
                                  (SierpBase-lr sierpBase)))
       (define midLrLl  (getMidPt (SierpBase-lr sierpBase) 
                                  (SierpBase-ll sierpBase)))
       (define midLlTop (getMidPt (SierpBase-ll sierpBase) 
                                  (SierpBase-top sierpBase)))]
    (list (make-SierpBase (SierpBase-top sierpBase) midTopLr midLlTop)
          (make-SierpBase midTopLr (SierpBase-lr sierpBase) midLrLl)     
          (make-SierpBase midLlTop midLrLl (SierpBase-ll sierpBase)))))


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;; Functions for drawing Sierpinski gaskets.
;; Incomplete -- How to draw inductive case?

;; draw-sierpBase:  SierpBase --> boolean
;; Draws a SierpBase on the output canvas.
(define (draw-sierpBase sierpBase)
  (and (draw-solid-line (SierpBase-top sierpBase) 
                        (SierpBase-lr sierpBase))
       (draw-solid-line (SierpBase-lr sierpBase)
                        (SierpBase-ll sierpBase))
       (draw-solid-line (SierpBase-ll sierpBase)
                        (SierpBase-top sierpBase))))


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"Sierp test cases:"
(define width 500)

(define s1 (make-FullSizeSierp width))
(define s1_next (make-nextSierp s1))


(start width width)

(draw-sierpBase s1)