Cleaning And Simplifying Polygon Geometries Prior To Centreline Extraction

Simplifying Complex Polygons

Polygon geometries derived from geospatial data often contain intricate details and complex boundaries. While this can accurately model real-world geographical formations, excessive vertex density increases data volume and slows analysis. Simplifying polygons by smoothing jagged edges and removing insignificant protuberances improves processing efficiency without sacrificing fidelity.

Generalization methods balance competing demands of conceptual accuracy, visual clarity, and computational performance. Careful simplification prior to essential geoprocessing workflows like centreline derivation preserves critical analytic objectives while enabling responsiveness and scalability.

Why Simplify Polygons?

Several motivations drive polygon generalization before conducting geospatial operations:

  • Faster processing – Eliminating unnecessary vertices speeds up computational geometry routines
  • Reduced storage – Compact representation decreases file sizes for archival and transfer
  • Clearer visualization – Smoothing rough edges removes unimportant map clutter
  • Improved analysis – Noise filtering exposes significant shape characteristics

The simplification process aims to lower polygon complexity while retaining fidelity. This balancing act judges each vertex by relevance to analytic objectives and overall structure.

Methods for Simplifying Polygon Geometry

Polygon simplification employs algorithmic methods to systematically remove vertices. Different techniques assess vertex relevance differently:

Simplifying Based on Area

The area method filters vertices that minimally impact the polygon’s total boundary area. A tolerance threshold catches vertices contributing area beneath some epsilon value. This heuristic executes quickly but may excessively smooth key shape features.

Simplifying Based on Number of Vertices

This technique reduces polygons to a target number of vertices by incrementally removing the “least important” point at each step. Importance ranks vertices by connecting adjacent midpoints to estimate deviation error after excluding that point. It balances shape preservation with generalization level.

Visvalingam-Whyatt Algorithm

The Visvalingam-Whyatt method judges vertex importance by the area of the triangle formed between it and its adjacent points. Vertices with the smallest triangular areas get removed first. Despite its intuitive geometric appeal and good performance, uneven point distribution can distort outcomes.

When to Simplify Polygons

Two primary use cases drive pre-processing polygon datasets:

Before Geoprocessing Operations

Most GIS packages offer tools to conduct geospatial analysis like centreline derivation, interpolation, and proximity buffers. These operations incur significant computational cost directly tied to dataset complexity. Simplifying first saves time and resources.

Before Display and Visualization

Rendering detailed polygons with large vertex counts stresses graphical capabilities causing slow redraws and ineffective visual communication. Simplification promotes responsiveness without sacrificing clarity. Interactive applications benefit greatly.

Example Python Code for Polygon Simplification

Modern scripting languages provide programmatic access to simplification algorithms on polygon geometry data structures:

Using Shapely Library

import shapely
from shapely import geometry

complex_polygon = geometry.Polygon([[0,0], [1,1], [2,0], [2,2], [1,2], [0,2]])  

simple_polygon = complex_polygon.simplify(0.5)


Using ArcPy Polygon Simplify Tool

import arcpy

input_features = 'blockgroups.shp' 
output_feature_class = 'simplified.shp'
arcpy.cartography.SimplifyPolygon(input_features, output_feature_class, 
                                   algorithm="POINT_REMOVE", tolerance=10, 
                                   minimum_area=0, error_option="RESOLVE_ERRORS")   

Special Considerations

Despite wide applicability, polygon simplification carries caveats:

Preserving Critical Shape Characteristics

Over-simplification erases essential structures like drainage networks and transportation corridors. Customizing algorithms by integrating geographic context and strategic tolerance tuning prevents misrepresentation.

Handling Self-Intersections

Excessive generalization risks invalidating geometry by introducing non-physical self-crossing substructures. Defensive code should test for defects and restore validity when detected.

Performance Impacts

Although simplification aims to accelerate analysis, for small or simple datasets the overhead of preprocessing may overwhelm subsequent savings. Profile expectations before deployment.

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