Polygonize function

[Newmanjack]

The polygonize function converts a collection of LineString features into a collection of Polygon features by detecting closed rings and properly organizing them into polygons with holes. Here's a detailed explanation of how it works:

Algorithm Overview

1. Graph Construction:

   • The algorithm begins by building a planar graph where each line segment becomes an edge, and line intersections become nodes.
   • Edges are stored with direction information and bearings for efficient traversal.
   • Duplicates are avoided through canonical edge keys based on coordinates.

2. Ring Detection:

   • Starting from any edge, the algorithm traverses the graph using the "right-hand rule" (always taking the rightmost turn).
   • This ensures consistent orientation as we walk along edges to form closed rings.
   • Each edge is used exactly once, and the process continues until all edges are processed.

3. Ring Classification:

   • Detected rings are then classified as either exterior boundaries or holes.
   • This is done by analyzing spatial relationships between rings.
   • Exterior rings are oriented counter-clockwise per RFC 7946 standard.
   • Interior rings (holes) are oriented clockwise.

4. Polygon Construction:

   • The classified rings are assembled into proper polygon structures.
   • Each polygon consists of one exterior ring and zero or more interior rings (holes).
   • Coordinates retain their altitude values if present.

Technical Innovations

• Bearing-based Traversal: Uses pre-computed edge bearings to make optimal right-hand rule decisions.
• Null-Safe Coordinate Handling: All coordinate access uses null-safety patterns to handle malformed inputs.
• Efficient Point Clustering: Detects separate polygons without requiring manual disconnection.
• RFC 7946 Compliant: Follows GeoJSON specification for ring orientation.

Performance Considerations

• Edge graph construction is O(n) where n is the number of line segments.
• Ring traversal is optimized to O(e) where e is the number of edges.
• Memory footprint is minimized by processing rings sequentially.

This implementation successfully handles all test cases including disjoint polygons, polygons with holes, and preserves altitude values where present.