# How Simplify Line works

Simplification removes extraneous bends and small intrusions and extrusions from a line without destroying its essential shape. The Simplify Line tool uses one of two simplification algorithms, called point remove and bend simplify.

## Choosing which operator to use

### Point remove

The point remove option applies a published algorithm (Douglas and Peucker, 1973) with enhancements. It is a fast, simple line simplification algorithm. It keeps critical points that depict the essential shape of a line and removes all other points. The algorithm begins by connecting the endpoints of a line with a trend line. The distance of each vertex to the trend line is measured perpendicularly. Vertices closer to the line than the tolerance are eliminated. The line is then divided by the vertex farthest from the trend line, which makes two new trend lines. The remaining vertices are measured against these lines, and the process continues until all vertices within the tolerance are eliminated.

Point remove is efficient for data compression and for eliminating redundant details; however, the line that results may contain unpleasant sharp angles and spikes that reduce the cartographic quality of the line. Use point remove for relatively small amounts of data reduction or compression and when you don't need high cartographic quality.

### Bend simplify

Bend simplify applies shape recognition techniques that detect bends, analyze their characteristics, and eliminate insignificant ones. A linear feature can be seen as composed by a series of bends (Wang, 1996), each defined as having the same sign (positive or negative) for the inflection angles at its consecutive vertices. Several geometrical properties of each bend are compared with those of a reference half circle, the diameter of which equals the specified simplification tolerance. These measures determine whether a bend is kept or eliminated, meaning replacing the bend by its baseline (the line connecting the endpoints of the bend). The simplification takes place iteratively such that the smaller bends may "disappear" in the early rounds and, therefore, form bigger bends. The resulting line follows the main shape of the original line more faithfully and shows better cartographic quality than from point remove.

## Analyzing and improving the results

The tool simplifies lines one at a time; the longer a line runs, the more pleasing the result will be. Keep this in mind when you collect or construct the source data. Wherever possible, position endpoints of lines on long, smooth sections of lines, rather than severely bent sections.

When the resolve topological errors option is used, the process will check for topological errors, line-crossing, coincident lines, or collapsed zero-length lines. If any of these errors are detected after the first round of simplification, the involved line segments (not the entire lines) will be located and a reduced tolerance, 50 percent of that previously used, will be applied to resimplify these segments. This iteration will repeat as many times as needed until no more topological errors are found. The output feature class will contain two new attributes, MaxSimpTol and MinSimpTol, which show the range of tolerances actually used in simplifying each line. These fields will be added even if no errors were found in the process. Using these fields, you can estimate how the specified tolerance worked for the data. If the MaxSimpTol and MinSimpTol values are smaller than the specified tolerance for the majority of output lines, it means many conflicts were found during processing. Consider using a smaller tolerance in this event. MaxSimpTol and MinSimpTol values smaller than the tolerance may represent a fine detail, such as a narrow, double-line river or two very close boundary lines. In this case, simplification may not provide the ideal cartographic solution. The narrow features may need to be represented differently, for example, by a single representative line.