# L-7 MCS 275 Wed 30 Jan 2008 : flake.py

from Tkinter import *
import math

class KochFlake():
   """
   GUI to draw a Koch flake canvas.
   """
   def __init__(self,wdw):
      "determines the layout of the GUI"
      wdw.title('a regular n Koch flake')
      self.d = 400
      self.n = IntVar()
      self.k = IntVar()
      self.sn = Scale(wdw,orient='horizontal',\
        from_=3,to=20,tickinterval=1,\
        length=self.d,variable=self.n,\
        command=self.DrawFlake)
      self.sn.set(10)
      self.sn.grid(row=0,column=1)
      self.c = Canvas(wdw,width=self.d,\
        height=self.d,bg ='white')
      self.c.grid(row=1,column=1)
      self.sk = Scale(wdw,orient='vertical',\
        from_=0,to=6,tickinterval=1,\
        length=self.d,variable=self.k,\
        command=self.DrawFlake)
      self.sk.set(0)
      self.sk.grid(row=1,column=0)

   def koch(self,A,B,k):
      "recursive drawing of Koch curve"
      if(k==0):
         self.c.create_line(A[0],A[1],B[0],B[1],width=2)
      else:
         L = ((2*A[0]+B[0])/3.0,(2*A[1]+B[1])/3.0)
         R = ((A[0]+2*B[0])/3.0,(A[1]+2*B[1])/3.0)
         M = ((A[0]+B[0])/2.0,(A[1]+B[1])/2.0)
         s = math.sqrt(3)/6
         T = (s*(A[1]-B[1]),s*(B[0]-A[0]))
         P = (M[0]-T[0],M[1]-T[1])
         self.koch(A,L,k-1)
         self.koch(L,P,k-1)
         self.koch(P,R,k-1)
         self.koch(R,B,k-1)

   def DrawFlake(self,v):
      "Draws a regular Koch flake"
      cx = self.d/2
      cy = self.d/2
      radius = 0.4*self.d
      self.c.delete(ALL)
      n = self.n.get()
      k = self.k.get()
      t = '(' + str(n) + ',' + str(k) + ')'
      self.c.create_text(cx,cy,text=t,tags="text")
      L = []
      for i in range(0,n):
         vx = cx + radius*math.cos(2*i*math.pi/n)
         vy = cy + radius*math.sin(2*i*math.pi/n)
         L.append((vx,vy))
      for i in range(0,n-1):
         self.koch(L[i],L[i+1],k)
      self.koch(L[n-1],L[0],k)

def main():
   top = Tk()
   show = KochFlake(top)
   top.mainloop()

if __name__ == "__main__": main()