What's the fastest way of checking if a point is inside a polygon in Python?

Checking if a point is inside a polygon is a common computational geometry problem. Python offers several approaches, with matplotlib's Path class being one of the fastest and most reliable methods for this task.

Using matplotlib.path for Point-in-Polygon Testing

The matplotlib library provides an efficient implementation through the mplPath.Path class, which uses optimized algorithms for point-in-polygon testing.

Steps

• Create a list of points to define the polygon vertices.

• Create a path object using mplPath.Path() with the polygon coordinates.

• Use the contains_point() method to check if a point lies inside the polygon.

Example

import matplotlib.path as mplPath
import numpy as np

# Define polygon vertices (triangle-like shape)
polygon_vertices = np.array([[190, 50],
                            [50, 500],
                            [500, 310],
                            [310, 190]])

poly_path = mplPath.Path(polygon_vertices)

# Test points
point1 = (200, 100)
point2 = (1200, 1000)

print(point1, "is in polygon:", poly_path.contains_point(point1))
print(point2, "is in polygon:", poly_path.contains_point(point2))

(200, 100) is in polygon: True
(1200, 1000) is in polygon: False

Testing Multiple Points Efficiently

For checking multiple points at once, use contains_points() method which is more efficient than individual calls ?

import matplotlib.path as mplPath
import numpy as np

# Define polygon
polygon_vertices = np.array([[0, 0], [10, 0], [10, 10], [0, 10]])
poly_path = mplPath.Path(polygon_vertices)

# Multiple test points
test_points = np.array([[5, 5], [15, 15], [2, 8], [12, 3]])

results = poly_path.contains_points(test_points)
for i, point in enumerate(test_points):
    print(f"Point {point} is in polygon: {results[i]}")

Point [5 5] is in polygon: True
Point [15 15] is in polygon: False
Point [2 8] is in polygon: True
Point [12  3] is in polygon: False

Alternative Approaches

Conclusion

The matplotlib.path.Path method is the fastest built-in approach for point-in-polygon testing in Python. Use contains_point() for single points and contains_points() for batch processing multiple points efficiently.