How to print a standard circle in the console window?

I am trying to print an arbitrary math function through a callback function, the execute() function will iterate over all integer coordinates (x,y), if the callback returns true then canvas[x][y] = ‘*’.

But my implementation only works when printing straight lines, always fails to print hollow circles

width = 80
height = 30
canvas = [[' '] * width for i in range(height)]

def PrintCanvas():
    for i in range(len(canvas)):
        for j in range(len(canvas[0])):
            print(canvas[i][j], end='')
        print()

def execute(callback):
    for i in range(len(canvas)):
        for j in range(len(canvas[0])):
            if callback(i, j):
                canvas[i][j] = '*'

# The ratio of the height and width of the grid in the console
# If you don't set x=x*rate, the resulting graph will be flat
zoom = 819/386
# Since x and y are both integers, when x is multiplied by a floating-point number, y!=f(x)
# So we use y-f(x)<=deviation here
deviation = 0.5

# print x size 20
def fun_x(x, y):
    r = 20
    x *= zoom
    return x < r and abs(y-x) <= deviation or abs(y-(-x+r-1)) <= deviation

# How to print a standard circle in the console window?
# print circle size 13
def fun_circle(x, y):
    r = 13
    x *= zoom
    a = (pow(x-r, 2)+pow(y-r, 2)) - r*r
    r = r - 2
    b = (pow(x-r, 2)+pow(y-r, 2)) - r*r
    return a <= 0 and b >= 0

# execute(fun_x)
execute(fun_circle)
PrintCanvas()

The following two pictures are the printed x shape and the wrong ring shape.

Answer

You are also shifting the center here

r = r - 2
b = (pow(x-r, 2)+pow(y-r, 2)) - r*r

Consider not changing the center as following

r2 = r - 2
b = (pow(x-r, 2)+pow(y-r, 2)) - r2*r2

On a side note, now you know how to draw a crescent too.

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Answer