#pointsXYcircle.py
#randomly generate (x,y) integer points inside a circle,
#Average distance each point to the center. ~.66 (unit circle)
#Average distance between points: 0.8948

import random
import math

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


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

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

'''
    alpha = random.random()*2*math.pi   #radians
    d = random.random()*radius
    X.append(math.cos(alpha) * d)   #too clumped near center???
    Y.append(math.sin(alpha) * d)   #avg. dist is ~.5
'''

for p in range(num_points):

    is_inside = False
    while not is_inside:
        x = random.random()*2*radius-radius
        y = random.random()*2*radius-radius
        if distance_pair_points(x,y, 0,0) <= radius:
            is_inside = True
            
    X.append(x)
    Y.append(y)
    #print("("+str(X[p])+","+str(Y[p])+")", end=" ")
print()

#print(X)
#print(Y)

distances = []    #distance each point to centroid
inners = 0
inner_inners =0
for p in range(num_points):
    distances.append(distance_pair_points(X[p],Y[p], 0,0))
    if distances[p] < .7071*radius:
        inners += 1
        if distances[p] < .5*radius:
            inner_inners += 1

print("Sum of distances to center:", sum(distances))
print("Average distance to center:", sum(distances)/num_points)
print("number within .7071 circle (~half):",inners)
print("number within .5 circle (~quarter):",inner_inners)

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()
canvas.drawLine(size/2,1, size/2,size)
canvas.drawLine(1,size/2, size,size/2)
scale = size/(radius*2)
canvas.setColor("red")
canvas.setFill()
canvas.drawOval(1,1,  size,size)
canvas.setColor("yellow")
canvas.setFill()
#half the points within .7071r of center
canvas.drawOval(.2929*size/2,.2929*size/2,  size*.7071,size*.7071)    # 1/root2=.707
canvas.drawOval(.25*size,.25*size,  size*.5,size*.5)    # 1/4 of points within .5 of center

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