Which Method Reigns Supreme: Ray Tracing vs. Matplotlib for Point Inclusion in Polygons?

Checking Point Inclusion in a Polygon: A Performance Comparison

Identifying whether a point falls within a polygon is a commonly encountered problem in Python. Among the various approaches suggested, two primary methods stand out: ray tracing and matplotlib's path.contains_points function.

Ray Tracing Method

The ray tracing method relies on tracing rays from the point to infinity in various directions. If the number of intersections between the rays and the polygon's edges is odd, the point is considered inside the polygon.

Matplotlib's path.contains_points Function

This function utilizes a faster and more efficient algorithm based on the crossing number method. It determines the point's inclusion by considering its relationship to the polygon's boundaries.

Performance Comparison

Empirical testing revealed that the matplotlib function significantly outperforms the ray tracing method in terms of execution time, particularly for larger polygons. For instance, with a 100-sided polygon and 10,000 random points, the matplotlib function took approximately 0.0099 seconds, while ray tracing required 0.4413 seconds.

Shapely Library

For more complex geometric operations, the shapely library provides specialized functions. However, for the specific task of point inclusion testing, the matplotlib method remains the fastest and most efficient choice.

Pixel Tolerance Grid

If the required precision is within a "pixel" tolerance, using a NumPy boolean grid to represent the points within the polygon can offer even faster performance. This approach involves populating a grid with Boolean values, where points inside the polygon are marked as True. This grid can then be used to quickly determine if subsequent points fall within the polygon.

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