Automated Polygon Splitting Using Voronoi Diagrams and Clustering

Automated polygon splitting based on points is a common task in spatial analysis and geographic information systems (GIS). It is often used in various applications such as urban planning, resource allocation, and spatial clustering. The goal is to divide a larger geographic area (represented as a polygon) into smaller, more manageable areas based on specific criteria or points of interest.

In this tutorial, we will walk through the process of automating polygon splitting using Voronoi diagrams and clustering techniques in Python. Voronoi diagrams help to partition a space into regions based on proximity to a set of points, which aligns well with the task of splitting polygons based on points of interest.

Requirements

• Python (3.x preferred)
• Geopandas
• Shapely
• Numpy
• Scikit-learn (for KMeans clustering)

Understanding Polygon Splitting with K-Means Clustering and Voronoi Diagrams

Scenario:

• You have a large polygon representing a geographical area.
• You want to subdivide this area into smaller, more manageable regions based on the distribution of points of interest within it.

Approach:

1. Generate Random Points:
   • Define the number of points (num_points) you want to create within the polygon.
   • Use a loop to generate random points (Point objects) using np.random.uniform within the polygon’s bounding box (min_x, min_y, max_x, max_y). Check if each point falls inside the polygon using polygon.contains(point).
2. Clustering Points with K-Means:
   • Import KMeans from sklearn.cluster.
   • Create a KMeans object with the desired number of clusters (n_clusters).
   • Use kmeans.fit(points) to perform the clustering based on the point coordinates (points). This groups points with similar characteristics (e.g., proximity) together.
3. Separating Points into Clusters:
   • Obtain cluster labels (labels) using kmeans.labels_. These labels indicate which cluster each point belongs to.
   • Create a list of lists (cluster_points) to store points belonging to each cluster.
   • Iterate through point indices and labels:
     • For each point, use its label to determine the corresponding cluster index in cluster_points.
     • Append the point coordinates to the appropriate cluster list in cluster_points.
4. Constructing Convex Hulls:
   • Import MultiPoint from shapely.geometry.
   • For each cluster in cluster_points, convert its point coordinates to a MultiPoint object.
   • Use MultiPoint(x).convex_hull to compute the convex hull, which is the smallest possible polygon that encloses all points in the cluster.
5. Calculating Centroids:
   • Import centroid from shapely.geometry.
   • For each convex hull in the convex_hulls list, calculate its centroid using centroid method. The centroid represents the geometric center of the polygon.
6. Creating Voronoi Diagrams:
   • Import voronoi_diagram from shapely.ops.
   • Construct a MultiPoint object (centroid_points) containing all centroids from convex_hulls_centroids.
   • Generate the Voronoi diagram using voronoi_diagram(centroid_points). This creates a partition of the space into regions, where each region is closer to one specific centroid than any other.
7. Aligning Voronoi Polygons with Main Polygon:
   • Import buffer and intersection from shapely.geometry.
   • Create a list (aligned_polygon) to store the aligned polygons.
   • Iterate through individual Voronoi polygons in voronoi_polygons:
     • Create a buffer around each Voronoi polygon with a width of 0 (buffer(0)) to account for potential numerical precision issues.
     • Use intersection to clip the buffered Voronoi polygon with the main polygon, ensuring that the resulting polygon falls entirely within the original boundaries.
     • Append the intersected polygon to aligned_polygon

I hope this tutorial will create a good foundation for you. If you want tutorials on another GIS topic or you have any queries, please send an mail at contact@spatial-dev.guru.