# function_gui.py
# 
# draw the graph of a user supplied function
# using Zelle's graphics API
#
# Jim M, Sep 2013

from graphics import *
from math import *

def main():

    # define a bunch of parameters
    windowWidth = 400     # in pixels
    windowHeight = 300
    xMin = 0.0
    xMax = 10.0
    yMin = -1.5
    yMax = 1.5
    xBorder = 1.0        # in x,y coordinates
    yBorder = 0.2
    nSteps = 200

    # set up the window
    window = GraphWin("Function Plot", windowWidth, windowHeight)
    window.setCoords(xMin - xBorder, yMin - yBorder,
                     xMax + xBorder, yMax + yBorder)

    plotRectangle = Rectangle(Point(xMin, yMin),
                              Point(xMax, yMax))
    plotRectangle.setOutline("grey")
    plotRectangle.draw(window)

    functionEntry = Entry(Point(xMax - 2.0, yMax - 0.2), 12)
    functionEntry.setText("sin(x)")
    functionEntry.draw(window)

    print "Enter a function, then click the mouse."
    mouse_position = window.getMouse()
    function = functionEntry.getText()

    # draw the function
    # 
    # The basic idea is to draw many tiny line segments,
    # using a very small change in x. Calculus, basically, without the limit.
    #
    # The eval() function can be used to calcuate
    # the value of function, as long as the variable
    # names in the string are given values.
    #
    dx = (xMax - xMin)/nSteps
    x = xMin
    for i in range(nSteps):
        # draw a line from (x, f(x)) to ((x+dx, f(x+dx))
        (x1, y1) = (x, eval(function))
        x = x + dx
        (x2, y2) = (x, eval(function))
        Line(Point(x1, y1), Point(x2, y2)).draw(window)

    # wait for the user to quit
    user_input = raw_input("Type <return> to quit. ")
    window.close()

main()