Circular Region in Python

Checking the Boundaries of a Circle in Python

From the equation (x - a)² + (y - b)² = r² ;
It can be deduced that y = b ± √(r² - (x - a)²) ;
And conversely x = a ± √(r² - (y - b)²).

Hence, the boundaries of any circle lie in the range
b - √(r² - (x_external - a)²) ≤ y ≤ b + √(r² - (x_external - a)²)
and
a - √(r² - (y_external - b)²) ≤ x ≤ a + √(r² - (y_external - b)²)

Code to Detect Entrance into Circular Region in Python

To check for when a second graphic enters the circle, we will continually use the x position of this second graphic in the circle equation to detect when its y position lies between the up and down limits at the x position in question:
y_{2nd_img}(top) > b - √(r² - (x_{2nd_img} - a)²)
and y_{2nd_img}(bottom) < b + √(r² - (x_{2nd_img} - a)²) ;
At the same time, we will use the y position of the second graphic in the circle equation to detect when its x position lies between the left and right limits at the y position in question:
x_{2nd_img}(left) > a - √(r² - (y_{2nd_img} - b)²)
and x_{2nd_img}(right) < a + √(r² - (y_{2nd_img} - b)²)

Create a new file; File, New File.
Call it CircularRegion.py.
Type out the adjoining Python / Turtle code for detecting the instance a travelling body crosses the boundary of a circle.

Python code for CircularRegion file

#!usr/bin/env python3

import math
from Facet import Template

def prep():
    global sq_colour, x_square, y_square, a, b, r, turtle_radius

    # bind fun function
    scene.button.onrelease(play)

    # square parameters
    diameter = 5
    sq_colour = "#ffff00"
    x_square = 100 - scene.wnd_width/2; y_square = 0

    # centre point
    a = 0
    b = 0
    r = round(scene.wnd_height / 3)
    # draw circle
    turtle.penup()
    turtle.setposition(a+r, b)
    turtle.pendown()
    turtle.circle(r)

    turtle.penup()
    # button text
    turtle.setposition(scene.button.xcor(), scene.button.ycor()-10)
    turtle.pendown()
    turtle.write("Move", align="center", font=("Arial",16,"bold"))

    screen.delay(20)

    # transform turtle into a square
    turtle.penup()
    turtle.setposition(x_square, y_square)
    turtle.setheading(0)
    turtle.shape("turtle")
    turtle.shapesize(diameter, diameter)
    turtle.color(sq_colour, sq_colour)

    turtle_radius = 10*turtle.shapesize()[1]

# fun function when button is clicked
# just moves turtle until it hits the right boundary
def play(x, y):
    global sq_colour, x_square, y_square, a, b, r, turtle_radius

    if x_square < scene.wnd_width/2 - turtle_radius:

        square_left = x_square - turtle_radius
        square_right = x_square + turtle_radius
        square_top = y_square + turtle_radius
        square_bottom = y_square - turtle_radius

        # determinants for each side of the square
        x_left_det = math.sqrt(abs(math.pow(r, 2) - math.pow((square_left - a), 2)))
        x_right_det = math.sqrt(abs(math.pow(r, 2) - math.pow((square_right - a), 2)))
        y_up_det = math.sqrt(abs(math.pow(r, 2) - math.pow((square_top - b), 2)))
        y_down_det = math.sqrt(abs(math.pow(r, 2) - math.pow((square_bottom - b), 2)))

        # yellow outside the circle
        sq_colour = "#ffff00"
        if square_top > b - x_left_det and square_bottom < b + x_left_det and\
           square_top > b - x_right_det and square_bottom < b + x_right_det and\
           square_left > a - y_up_det and square_right < a + y_up_det and\
           square_left > a - y_down_det and square_right < a + y_down_det:
            # green inside the circle
            sq_colour = "#00ff00"
        turtle.color(sq_colour, sq_colour)

        # change ball's coordinates
        turtle.setposition(x_square, y_square)

        x_square += 10
        screen.ontimer(play(0,0), 500)
    else:
        x_square = 100 - scene.wnd_width/2; y_square = 0
        screen.mainloop()

# Let fly
scene = Template();
turtle = scene.controlButtons()
screen = scene.screen

prep()

Important: When trying to click on the button to get things started, you might need to click away from the button text.

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