Detecting Regions Divided by a Diagonal Line | Maths Explanation for Python Kids
In this tutorial, you'll learn how to detect when an object crosses a straight line in Python. We'll explore how to check which side of a line a point lies on, and how to apply this logic to a Python canvas animation.
When working with graphics or simulations in Python, you might need to check which side of a line a ball or object is on. This technique is common in Python canvas collision detection and helps define regions divided by a line.
Consider a moving body (circle). When it moves across a diagonal straight line, we can perform an action - such as changing the ball's colour - after it crosses from one region to another.
Understanding the Straight Line Equation in Python
We use the slope-intercept formula (y = mx + c) to define boundaries for region detection in Python.
To implement straight line region detection, we'll compare the ball's x-position with the
position of the line at the same y-coordinate, using the line equation in Python.
If the ball's midpoint is (xb, yb)
and the line at that height is (xl, yl),
then:
xl = myd + c
The ball crosses the line when:
xd >= xl.
This logic uses the line equation in Python to check when an object moves from one region to another.
This can also help with collision detection and
boundary demarcation in Python graphics or HTML canvas.
Python Code: Detecting Line Crossing in Canvas
To determine which side of a diagonal boundary a point belongs to, we use a simple line equation. This Python example demonstrates line region detection using the slope-intercept method.
Create 2 new Python files; File, New File.
Call them Facet.py and StraightLineRegion.py.
Type out the adjoining Pythonbody travel code for detecting the
instance a travelling body crosses the path of a straight line.
This Python line crossing detection example changes the ball's colour once it moves across the line.
Important: When trying to click on the button to get things started, you might need to click away from the button text.
Summary: Detecting Line Boundaries with Python
You've learned how to use the line equation in Python to **detect regions divided by a straight line and trigger actions when objects cross the line**. This simple logic forms the foundation of Python graphics and animation algorithms.
By now, you can use Python to detect when an object crosses a straight line and determine which region it belongs to. This simple mathematical approach is useful for animations, physics simulations, and canvas line region detection.
Applying the Line Region Detection Logic in Python
This tutorial teaches you to:
- Detect when a ball crosses a straight or diagonal line.
- Identify which side of a line a point lies on.
- Create interactive Python canvas projects with region-based logic.
You can extend this principle to handle collision detection, line-segment intersection, or more complex 2D graphics region detection.
So! Python Fun Practice Exercise - Detect Straight Line Boundary
As a fun practice exercise, try modifying the Python code to explore different coordinates and intercepts. This will be a great way to connect mathematics and programming, and help you understand more about Python animations and linear boundaries.
Python Straight Line Boundary Code for Turtle Template - Facet Class
class Template:
def __init__(self):
screen = turtle.getscreen()
screen.title("usingMaths.com")
screen.setup(width=0.9, height=0.9, startx=None, starty=None)
screen.colormode(255)
self.bgcolour = "#cccccc"
screen.bgcolor(self.bgcolour)
screen.delay(0)
self.screen = screen
self.wnd_width = self.screen.window_width()
self.wnd_height = self.screen.window_height()
def controlButtons(self):
self.button = turtle.clone()
turtle.speed(0)
turtle.penup()
turtle.setposition(-self.wnd_width/2, self.wnd_height/2)
turtle.color("black", "pink")
turtle.pendown()
# draw button region
turtle.begin_fill()
turtle.forward(self.wnd_width)
turtle.right(90)
turtle.forward(50)
turtle.right(90)
turtle.forward(self.wnd_width)
turtle.right(90)
turtle.forward(50)
turtle.end_fill()
self.button.speed(0)
self.button.penup()
# draw button
self.button.setposition(0, self.wnd_height/2 - 25)
self.button.shape("square")
self.button.resizemode("user")
self.button.shapesize(2, 8)
self.button.color("black", (255, 0, 255))
return turtle.getturtle()
Python Animation Code for Straight Line Region file
from Facet import Template
def prep():
global x_line, x_ball, y_ball
# bind fun function
scene.button.onrelease(play)
screen.delay(20)
turtle.penup()
# button text
turtle.setposition(scene.button.xcor(), scene.button.ycor()-10)
turtle.pendown()
turtle.write("Move", align="center", font=("Arial",16,"bold"))
# diagonal parameters
x1 = 0; y1 = scene.wnd_height/3
x2 = 200; y2 = -scene.wnd_height/3
m = (y2 - y1) / (x2 - x1)
c = (x2*y1 - x1*y2) / (x2 - x1)
# ball parameters
diameter = 5
ball_colour = "#ffff00"
x_ball = 100 - scene.wnd_width/2; y_ball = 0
# x-coordinate where ball will cross line
x_line = (y_ball - c) / m
# draw diagonal
turtle.penup()
turtle.setposition(x1, y1)
turtle.pendown()
turtle.setposition(x2, y2)
# transform turtle into a ball
turtle.penup()
turtle.setposition(x_ball, y_ball)
turtle.setheading(0)
turtle.shape("turtle")
turtle.shapesize(diameter, diameter)
turtle.color(ball_colour, ball_colour)
# fun function when button is clicked
# just moves turtle until it hits the right boundary
def play(x, y):
global x_ball, y_ball, x_line
if x_ball < scene.wnd_width/2 - 10*turtle.shapesize()[1]:
# yellow to the left of the line
ball_colour = "#ffff00"
if x_ball >= x_line:
# green to the right of the line
ball_colour = "#00ff00"
turtle.color(ball_colour, ball_colour)
# change ball's coordinates
turtle.setposition(x_ball, y_ball)
x_ball += 10
screen.ontimer(play(0,0), 500)
else:
x_ball = 100 - scene.wnd_width/2; y_ball = 0
screen.mainloop()
# Let fly
scene = Template();
turtle = scene.controlButtons()
screen = scene.screen
prep()