# L-31 MCS 260 Mon 5 Nov 2007 : guisample.py
#
# GUI to sample a user given function.

from Tkinter import *
from math import *

class SampleFun():
   """
   GUI to sample f(x) over [a,b]
   """
   def __init__(self,wdw):
      "defines layout and data of GUI"
      wdw.title("Plot Expressions")
      self.L1 = Label(wdw,text="f(x) =")
      self.L1.grid(row=0)
      self.f = Entry(wdw) # for f(x)
      self.f.grid(row=0,column=1,\
         columnspan=5,sticky=W+E+N+S)
      self.L2 = Label(wdw,text="a =")
      self.L2.grid(row=1,column=0)
      self.a = Entry(wdw) # for a
      self.a.grid(row=1,column=1)
      self.L2 = Label(wdw,text="b =")
      self.L2.grid(row=1,column=2)
      self.b = Entry(wdw) # for b
      self.b.grid(row=1,column=3)
      self.L3 = Label(wdw,text="N =")
      self.L3.grid(row=1,column=4)
      self.n = Entry(wdw) # for N
      self.n.grid(row=1,column=5)
      self.d = 400 # dimension of canvas
      self.c = Canvas(wdw,width=self.d,\
         height=self.d,bg='white')
      self.c.grid(row=3,columnspan=6)
      self.s = Button(wdw,text="sample and plot",\
         command=self.Show)
      self.s.grid(row=2,column=0,\
         columnspan=6,sticky=W+E+N+S)
      self.x = [] # where sampled
      self.y = [] # sampled values
      self.P = [] # scaled points

   def Sample(self):
      "samples the function"
      A = float(self.a.get())
      B = float(self.b.get())
      N = int(self.n.get())
      dx = (B-A)/(N+1)
      x = A
      self.x = []
      self.y = []
      for k in range(0,N):
         y = eval(self.f.get())
         self.x.append(x)
         self.y.append(y)
         x = x + dx

   def ScalePt(self,x,a,b,c,d):
      "maps x from [a,b] into [c,d]"
      return (d-c)/(b-a)*(x-a) + c

   def Scale(self):
      "scales the points"
      A = float(self.a.get())
      B = float(self.b.get())
      m = min(self.y)
      M = max(self.y)
      U = 0.95*self.d
      L = 0.05*self.d
      self.P = []
      for k in range(0,len(self.x)):
         X = self.ScalePt(self.x[k],A,B,L,U)
         Y = self.ScalePt(self.y[k],m,M,L,U)
         Y = U - Y + L # origin is topleft
         self.P.append((X,Y))

   def Show(self):
      "samples, scales, and shows"
      self.Sample()
      self.Scale()
      self.c.delete(ALL) # refresh canvas
      for k in range(0,len(self.P)):
         self.c.create_oval(\
            self.P[k][0]-6,self.P[k][1]-6,\
            self.P[k][0]+6,self.P[k][1]+6,\
            width=1,outline='black',fill='SkyBlue2')

def main():
   top = Tk()
   gui = SampleFun(top)
   top.mainloop()

if __name__ == "__main__": main()