The effects of line simplification on planform geometry

Data on maps should retain accuracy regardless of scale. Yet, as cartographic lines are generalized, there can be impacts on properties such as topology, density, and planform geometry. Here, we investigate the use of the Scale Specific Sinuosity (S3) metric (Stanislawski et al., 2023) to evaluate the effects of line simplification on planform geometry, which is the bends of streams in map view. We employ an open-source Python S3 workflow to characterize the geometry of five diverse stream channels in the United States. The original data are extracted from the U.S. Geological Survey National Hydrography Dataset 1:24,000-scale vector data (U.S. Geological Survey, 2000) (Table 1), and the simplification is done using the Visvalingam and Whyatt method (2017) with a simplification tolerance of 0.5, 1.0, 1.5, and 2.0 km. The S3 analysis is calculated at each level of simplification and S3 derivatives are generated. Derivatives include measures of sinuosity, fractal dimension, and the dominant bend wavelength. The findings show that the change in planform geometry is scale-dependent, though simplification will have little effect on straighter lines. The change becomes more apparent in complex lines as the degree of simplification aligns with the scale of the dominant bend geometries. These logical conclusions are evidence that the S3 is a useful metric for automated characterization of bend geometry regardless of line complexity.