How can I efficiently detect and outline holes within a scattered set of 2D points using a bitmap and vector approach in Python?

This Python code provides an implementation of a bitmap vector approach similar to the one described in the previous answer. It finds holes in a set of 2D points by computing data density in a bitmap, identifying unused areas, segmenting the output, and polygonizing the results.

import numpy as np
import cv2
import matplotlib.pyplot as plt

def find_holes(points, resolution=100):
    """Find holes in a set of 2D points.

    Args:
        points: A list of (x, y) tuples representing the points.
        resolution: The resolution of the bitmap to use. Higher resolution
            results in more accurate results, but is slower.

    Returns:
        A list of (x, y) tuples representing the vertices of the holes.
    """
    # Create a bitmap of the points.
    bitmap = np.zeros((resolution, resolution), dtype=np.uint8)
    for point in points:
        x, y = point
        bitmap[int(y * resolution), int(x * resolution)] = 255

    # Compute data density in the bitmap.
    density = cv2.dilate(bitmap, np.ones((3, 3))) - cv2.erode(bitmap, np.ones((3, 3)))

    # Identify unused areas in the bitmap.
    unused_areas = np.where(density == 0)

    # Segment the unused areas.
    segmented_areas = cv2.watershed(density, np.zeros((resolution, resolution), dtype=np.int32), markers=unused_areas[0], mask=bitmap)

    # Polygonize the segmented areas.
    holes = []
    for i in range(1, np.max(segmented_areas) + 1):
        mask = np.zeros((resolution, resolution), dtype=np.uint8)
        mask[segmented_areas == i] = 255
        _, contours, _ = cv2.findContours(mask, cv2.RETR_EXTERNAL, cv2.CHAIN_APPROX_SIMPLE)
        for contour in contours:
            hole = []
            for point in contour:
                x, y = point[0]
                hole.append((x / resolution, y / resolution))
            holes.append(hole)

    return holes


# Example usage

# Generate a set of random points.
points = [(np.random.rand(), np.random.rand()) for _ in range(1000)]

# Find the holes in the set of points.
holes = find_holes(points, resolution=50)

# Plot the points and the holes.
plt.scatter([x for (x, y) in points], [y for (x, y) in points], s=1, c='black')
for hole in holes:
    plt.plot([x for (x, y) in hole], [y for (x, y) in hole], c='red')
plt.show()

This code uses OpenCV for bitmap operations, NumPy for array manipulation, and matplotlib for plotting. It can be easily modified to work with different data types and coordinate systems.

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