Which Method is More Efficient for Point-in-Polygon Detection: Ray Tracing or Matplotlib\'s path.contains_points?

Efficient Point-in-Polygon Detection in Python

Determining whether a point lies within a polygon is a frequent task in computational geometry. Finding an efficient method for this task is advantageous when evaluating large numbers of points. Here, we explore and compare two commonly used methods: ray tracing and Matplotlib's path.contains_points function.

Ray Tracing Method

The ray tracing method intersects a horizontal ray from the point under examination with the polygon's sides. It counts the number of intersections and determines if the point is inside the polygon based on its parity.

Matplotlib's path.contains_points Function

Matplotlib's path.contains_points function employs a path object to represent the polygon. It checks if the given point lies within the defined path. This function is often faster than the ray tracing approach, as seen in the code snippet provided:

<br>from time import time<br>import matplotlib.path as mpltPath</p>
<h1 id="Polygon-and-random-points">Polygon and random points</h1>
<p>polygon = [[np.sin(x)   0.5, np.cos(x)   0.5] for x in np.linspace(0, 2*np.pi, 100)]<br>points = np.random.rand(10000, 2)</p>
<h1 id="Ray-tracing-elapsed-time">Ray tracing elapsed time</h1>
<p>start_time = time()<br>inside1 = [ray_tracing_method(point[0], point[1], polygon) for point in points]<br>print("Ray Tracing Elapsed time: "   str(time() - start_time))</p>
<h1 id="Matplotlib-contains-points-elapsed-time">Matplotlib contains_points elapsed time</h1>
<p>start_time = time()<br>path = mpltPath.Path(polygon)<br>inside2 = path.contains_points(points)<br>print("Matplotlib contains_points Elapsed time: "   str(time() - start_time))<br>

The code above reports significantly faster execution times for Matplotlib's approach compared to ray tracing.

Other Options

In addition to these methods, the Shapely package specifically designed for geometric operations provides efficient functions for point-in-polygon checks.

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