Point-in-Polygon: Ray Tracing vs. Matplotlib Path.contains_points: Which Method Reigns Supreme?

Determining Point Position Within a Polygon: Ray Tracing vs. Matplotlib Path

When checking if a point lies within a polygon, two widely known methods are the ray tracing method and matplotlib's path.contains_points function. While both approaches have their merits, objective testing reveals a significant performance difference between the two.

A comparative analysis was conducted on a large set of random points within a regular 100-sided polygon. The ray tracing method took approximately 0.44 seconds to complete the task, while matplotlib's path.contains_points required only 0.0099 seconds, indicating a substantial speed advantage.

Alternative Option: Shapely

For robust point-in-polygon checking, shapely, specifically its contains() method, is a highly regarded library. Its detailed documentation and comprehensive examples make it a valuable consideration.

Grid Optimization for Coarse-Grained Testing

If precision requirements are less stringent, creating a grid of boolean values to indicate point inclusion can significantly enhance speed. The numpy library's meshgrid function and matplotlib's path can be combined to generate a grid where each cell indicates whether a point within its boundary is inside the polygon.

This approach offers a level of tolerance and is ideal for situations where pixel-level accuracy is acceptable.

In summary, for high-precision point-in-polygon testing with large datasets, matplotlib's path.contains_points method stands out as the recommended choice due to its superior performance. Shapely is a solid alternative for specific geometric calculations, while grid optimization is a viable option for less demanding applications.

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