About simplifying and smoothing a feature

The Advanced Editing toolbar provides tools to enable you to smooth and simplify features. This includes line and polygon features.

The Generalize command simplifies the shape of the selected features using the published algorithm (Douglas and Peucker, 1973). The degree to which the geometry is simplified depends on the maximum allowable offset, which limits how far the output geometry can be from the input geometry. For features composed of linear segments, the output vertices are a subset of the original feature vertices.

Simplifying a feature

The Smooth command is used to smooth the straight edges and angular corners of a feature. The feature geometry is replaced by a series of smoothed line segments.

Smoothing a feature

The Smooth tool combines the following steps:

• Simplification with the specified maximum allowable offset (see the description of the Generalize tool, above) to produce a subset (indicated by the blue dashed line in the illustration below) of the original feature vertices (indicated by the black line in the illustration below).
• Bézier interpolation without any parameters, which fits Bézier curves through the subset vertices from the above simplification. The Bessel tangent is used to connect the curves smoothly at vertices (Farin, 1997). The resulting geometry (the red line in the illustration below) can be farther away from the input geometry than the specified maximum allowable offset.

Detailed area of the smoothed feature in the illustration above

References

Douglas, D.H., and T.K. Peucker. "Algorithms for the reduction of the number of points required to represent a digitized line or its caricature." The Canadian Cartographer 10(2), pp. 112–122, 1973.

Farin, G.,Curves and Surfaces for CAGD: A Practical Guide. 4th Edition. Academic Press, 1997.