;;; Scheme Recursive Art Contest Entry
;;;
;;; Please do not include your name or personal info in this file.
;;;
;;; Title: Bell Curves
;;;
;;; Description:
;;;   <O mighty curve
;;;    Thou be kind and generous
;;;    Math is very hard.>



(define (draw)
  ; YOUR CODE HERE
  


	(define (bellcurve) 	
		(define (drawaxis)
			(begin
				(goto -1000 0)
				(pendown)
				(goto 1000 0)
				(penup)
			)
		)
		(define (drawcurve z)
			; Draw from -4 to +4 SD
			(define (normpdf z)
				(define (pdf z mean sd) 
					(* (/ 1 (* (* sd sd) 6.283185307179)) (expt 2.718281828459 (- 0 (/ (expt (- z mean) 2) (* 2 (* sd sd))))))
				)
				(pdf z 0 1)
			)
			(if (< z 4)
				(begin (goto (* z 250) (* 4000 (normpdf z))) (drawcurve (+ z 0.01)))
			)

		)	
		(begin
			(drawaxis)
			(penup)
			(setposition -1000 0)
			(pendown)
			(drawcurve -4)
		)

	)
	
	(define (drawstudents x y)
		(define (student x y  vert)
			(define (face cx cy radius)
				(define (face-helper cx cy radius x)
					(if (<= x radius)
						(begin
							(goto (+ cx x) (- cy (sqrt (- (expt radius 2) (expt x 2)))))
							(face-helper cx cy radius (+ x 1))
						)	
					)
				)
				(face-helper cx cy radius (- 0 radius))
			)
			(if (and (< x 900 ) (> y -800))
				(begin
					; Move painter to starting position
					(penup)
					(setposition (+ 25 x) (- y 10))
					
					; Draw the peasant's head
					(pendown)
					(goto (+ x 5) (- y 30))
					(goto (+ x 45) (- y 30))
					(goto (+ 25 x) (- y 10))
					
					(penup)
					(setposition (+ x 25) (- y 30))
					(pendown)
					(face (+ x 25) (- y 30) 15)
					
					; Move painter to starting position for body
					(penup)
					(setposition (+ x 25) (- y 45))
					
					; Draw the cross that is the body
					(pendown)
					(goto (+ x 25) (- y 75))
					
					(penup)
					(goto (+ x 5) (- y 60))
					(pendown)
					(goto (+ x 45) (- y 60))
					
					; Move to position for legs
					(penup)
					(goto (+ x 25) (- y 75))
					
					; Draw them legs
					(pendown)
					(goto (+ x 10) (- y 90))
					(goto (+ x 25) (- y 75))
					(goto (+ x 40) (- y 90))
					
					(if (= vert 1)
						(student x (- y 100) 1)
						(begin (student x (- y 100) 1) (student (+ x 50) y 0))

					)
					
					
					
				)
			)
		)
		
		(begin
			(student x y 0)
		)
	)
  
    (begin
		(bellcurve)
		(drawstudents -900 0)
		(goto 1100 -11000)
	)
  ; END MY CODE
  
  (exitonclick))

; Please leave this last line alone.  You may add additional procedures above
; this line.
(draw)