Simplification is a type of generalization operation (ESRI, 1996) that removes extraneous bends and small intrusions and extrusions from a line without destroying its essential shape. The POINT_REMOVE and BEND_SIMPLIFY are the simplification algorithms.

### Choosing which operator to use

POINT_REMOVE applies a published algorithm (Douglas and Peucker, 1973) with enhancements. It is a fast, simple line simplification algorithm. It keeps the so-called critical points that depict the essential shape of a line and removes all other points. The algorithm connects 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 (see the diagram below).

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 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 is 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.

### Choosing a suitable tolerance

The tolerance value determines the degree of simplification. To produce cartographic outputs, set the tolerance equal to or greater than the threshold of separation (the minimum allowable spacing between graphic elements). Since the tolerance is used for the entire input, trial and error may be required to find a suitable tolerance for all features. Using the same tolerance, POINT_REMOVE produces rougher and more simplified result than BEND_SIMPLIFY.

### Analyzing and improving the results

When the RESOLVE_ERRORS option is used in the command line or in script, or when the Resolve topological errors checkbox is checked on the dialog box, 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 re-simplify 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. The two fields, MaxSimpTol and MinSimpTol, will be added even if no errors were found in the process.

If the output feature class contains MaxSimpTol and MinSimpTol fields, you can have an estimate on how the specified tolerance worked for the data. If the values of the MaxSimpTol and MinSimpTol fields for the majority of output lines are smaller than the specified tolerance, it means there were many conflicts found during the process and you might want to lower the tolerance.

For lines with values of MaxSimpTol and MinSimpTol smaller than the tolerance, they may represent a narrow area, such as a narrow, double-line river or two very close boundary lines. In that case, simplification of the lines may not be the right solution. The narrow features may need to be represented differently, for example, by single lines.

The tool simplifies lines one by one; 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.

### References

Technical paper, ESRI Inc., "Automation of Map Generalization: The Cutting-Edge Technology", 1996. It can be found in the White Papers section of ArcOnline at this Internet address:

http://downloads.esri.com/support/whitepapers/ao_/mapgen.pdf
David H. Douglas and Thomas K. Peucker, "Algorithms for the Reduction of the Number of Points Required to Represent a Digitized Line or Its Caricature", Canadian Cartographer, 10, No. 2 (December 1973).

Zeshen Wang, "Manual versus Automated Line Generalization", GIS/LIS '96 Proceedings, p.94-106(1996).