#pointsXYcircleNormal.py
#standard Normal distribution of randomly generate (x,y) integer points around origin,
# mu=0  distance sigma=1
#Average distance of a point to the origin: ~.79 MAD sqrt(2/pi)

import random
import math

def distance_pair_points(x1,y1, x2,y2):
    return math.sqrt((x2-x1)**2+(y2-y1)**2)


num_points = int(input("Enter the number of normal random points: "))

X = []  #x-coordinates
Y = []  #y-coordinates

for p in range(num_points):
    alpha = random.random()*2*math.pi   #random angle in radians
    dist = random.normalvariate(0,1) 
    x = dist*math.cos(alpha)
    y = dist*math.sin(alpha)
    X.append(x)
    Y.append(y)
    #print("("+str(X[p])+","+str(Y[p])+")", end=" ")
print()

#print(X)
#print(Y) 

distances = []    #distance each point to origin
less1 = more1_less2 = more2_less3 = more3 = 0
for p in range(num_points):
    distances.append(distance_pair_points(X[p],Y[p], 0,0))
    if distances[p] <= 3:
        if distances[p] <= 2:
            if distances[p] <= 1:
                less1 += 1
            else:
                more1_less2 += 1
        else:
            more2_less3 += 1
    else:
        more3 += 1
        
print("Sum of distances to origin:", sum(distances))
print("Average distance to origin:", sum(distances)/num_points)
print("number within 1 sigma:",less1," %",less1/num_points)
print("number between 1 and 2 sigma:",more1_less2," %",more1_less2/num_points)
print("number between 2 and 3 sigma:",more2_less3," %",more2_less3/num_points)
print("number more than 3 sigma:",more3," %",more3/num_points)

dist_pt_pt = [[0 for j in range(num_points)] for i in range(num_points) ]
for i in range(num_points):
    for j in range(num_points):   #could be more eff., do only half...
        dist_pt_pt[i][j] = distance_pair_points(X[i],Y[i], X[j],Y[j])
    #i_avg_dist = sum(dist_pt_pt[i])/(num_points-1)
    #print("i",i,"avg. dist:",i_avg_dist) #not itself
total_distances = 0
for i in range(num_points):
    total_distances += sum(dist_pt_pt[i])
print("Average distance between points:",total_distances/(num_points*(num_points-1)))


from ezgraphics import GraphicsWindow

size = int(input("Enter square size of graphics window: "))
win = GraphicsWindow(size,size)
canvas = win.canvas()
#margin = 10
canvas.drawLine(size/2,1, size/2,size)
canvas.drawLine(1,size/2, size,size/2)
scale = size/(1*3*2)
canvas.setColor("red")
canvas.setFill()
canvas.drawOval(1,1,  size,size)
canvas.setColor("yellow")
canvas.setFill()

canvas.drawOval(1,1,  size,size)
canvas.drawOval(.1666*size,.1666*size,  size*.6666,size*.6666)
canvas.drawOval(.3333*size,.3333*size,  size*.3333,size*.3333)

canvas.setColor("blue")
for p in range(num_points):
    canvas.drawOval(X[p]*scale+size/2,size-(Y[p]*scale+size/2),  2,2)