Python: Check whether a point (x,y) is in a triangle or not

Last update on April 17 2025 13:05:50 (UTC/GMT +8 hours)

Point in Triangle

Write a Python program to check if a point (x,y) is in a triangle or not. A triangle is formed by three points.

Input:
x1,y1,x2,y2,x3,y3,xp,yp separated by a single space.

Sample Solution:

Python Code:

# Prompt user to input coordinates of the triangle vertices (x1, y1), (x2, y2), (x3, y3),
# and the point (xp, yp) to check if it lies inside the triangle
print("Input x1, y1, x2, y2, x3, y3, xp, yp:")
x1, y1, x2, y2, x3, y3, xp, yp = map(float, input().split())

# Calculate the cross products (c1, c2, c3) for the point relative to each edge of the triangle
c1 = (x2 - x1) * (yp - y1) - (y2 - y1) * (xp - x1)
c2 = (x3 - x2) * (yp - y2) - (y3 - y2) * (xp - x2)
c3 = (x1 - x3) * (yp - y3) - (y1 - y3) * (xp - x3)

# Check if all cross products have the same sign (inside the triangle) or different signs (outside the triangle)
if (c1 < 0 and c2 < 0 and c3 < 0) or (c1 > 0 and c2 > 0 and c3 > 0):
    print("The point is in the triangle.")
else:
    print("The point is outside the triangle.")

Sample Output:

Input x1,y1,x2,y2,x3,y3,xp,yp:
 2 3 4 5 6 8 7 1
The point is outside the triangle.

Explanation:

The above Python code determines whether a given point (xp, yp) is inside or outside a triangle formed by three vertices (x1, y1), (x2, y2), and (x3, y3). Here is a breakdown of the above Python code:

Here's a brief explanation:

The code prompts the user to input the coordinates of the triangle vertices and the point to check.
The cross product (c1, c2, c3) is calculated for the point (xp, yp) relative to each edge of the triangle.
The code then checks whether all cross products have the same sign (either all negative or all positive), indicating that the point is inside the triangle. If the signs are different, the point is considered outside the triangle.
Finally, the code prints whether the point is inside or outside the triangle based on the cross product conditions.

Flowchart:

For more Practice: Solve these Related Problems:

Write a Python program to check if a given point lies inside a convex polygon.
Write a Python program to calculate the shortest distance from a point to the sides of a triangle.
Write a Python program to compute the barycentric coordinates of a point with respect to a triangle.
Write a Python program to verify whether a point lies exactly on the edge of a triangle.

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Python Code Editor:

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