#! /usr/bin/python3
# ===================================================================
# draw/plot a bell curve
# ===================================================================
# Formula from:
#
#    statistics.about.com/od/Formulas/ss/
#               The-Normal-Distribution-Or-Bell-Curve.htm
#
# ===================================================================
#
# Notes:
#
# 1. The bell curve formula normalizes the area under the
#    curve to 1.
# 2. All Y values are bell curve formula values and less than 1.
# 3. When plotting, the X values are scaled.
# 4. When plotting, the Y values are scaled.
# 5. Some day re-code to read a data file.
#
# ===================================================================

import numpy as np
import draw_axes as ax
import coordinate_conversion as cc
import user_interface as ui
from graphics import *


# ---- global variables

xscale = 50.0                  # scale bell curve plot 
yscale = 50.0                  # scale bell curve plot
mean   = 0.0                   # plot mean value
sd     = 1.0                   # plot standard deviation


# ---- bell curve x values (standard deviation units)

xdata = [ -3.00,-2.75,-2.50,-2.25,
          -2.00,-1.75,-1.50,-1.25,
          -1.00,-0.75,-0.50,-0.25,
          0.00,
          0.25, 0.50, 0.75, 1.00,
          1.25, 1.50, 1.75, 2.00,
          2.25, 2.50, 2.75, 3.00 ]


# -------------------------------------------------------------------
# ---- return the bell curve y value for a given x value
# ---- x    value (standard deviation units)
# ---- mean (center of distribution)
# ---- sd   standard deviation
# -------------------------------------------------------------------

def BellCurveValue(x,m,sd):

    y = (1.0/sd*np.sqrt(2.0*np.pi)) * \
         pow(np.e,-pow(x-m,2.0)/(2.0*sd*sd))

    return y


# -------------------------------------------------------------------
# ---- plot the bell curve
# ---- xdata   bell curve x points to plot
# ---- xscale  x scale factor
# ---- yscale  y scale factor
# ---- m       mean value (middle of bell curve)
# ---- sd      standard deviation
# -------------------------------------------------------------------

def PlotBellCurve(xdata,xscale,yscale,m,sd):

    win = GraphWin("Bell Curve", 801, 801)
    win.setBackground("white")

    ax.draw_xy_axes(win,True)

    for x in xdata:

        y = BellCurveValue(x,m,sd)

        cy = round(y * yscale)

        cx = round(x * xscale)

        (wx,wy) = cc.center_to_win_coords(cx,cy,win.width,win.height)

        ##l = Line(Point(wx,wy),Point(wx+1,wy+1))
        ##l.setWidth(2)
        ##l.setFill('black')
        ##l.draw(win)

        c = Circle(Point(wx,wy),4)
        c.setFill('black')
        c.draw(win)

    return win


# -------------------------------------------------------------------
# ---- main
# -------------------------------------------------------------------

if __name__ == '__main__':

    # ---- plot bell curve

    win = PlotBellCurve(xdata,xscale,yscale,mean,sd)

    ui.pause()

    win.close()