Checking Point Containment in a Polygon: Ray Tracing vs. Matplotlib

To determine if a point lies within a polygon, two primary methods are commonly used: ray tracing and Matplotlib's path.contains_points. However, a third option, Shapely, offers a dedicated solution for geometric computations.

Matplotlib's path.contains_points

This method has been demonstrated to be significantly faster in benchmarks, as shown in the code snippet provided. Its speed advantage makes it a suitable choice for scenarios involving frequent point containment checks.

Ray Tracing Method

Although ray tracing was initially considered the recommended approach, its performance has been surpassed by Matplotlib's path.contains_points. The code demonstrates the implementation of this method, which involves iterating through the polygon edges and calculating intersections. While it is slower than path.contains_points, it remains a reliable alternative.

Shapely

Shapely provides a specialized library for geometric operations, including point containment in polygons. Its contains method offers an easy-to-use interface for determining point membership. However, it is worth noting that its precision may not be suitable for all applications, as it assumes a continuous polygon without vertices at the query point.

Pixel-Based Grid Optimization

In scenarios where a high degree of precision is not required, creating a pixel-based grid of Boolean values can offer an efficient and rapid alternative. By assigning True to grid elements that fall within the polygon and False to those outside, subsequent point containment checks can be computed using the grid indices.