Weighted Thiessen Polygons

Purpose

Input features:
Output features:

The tool allows building Thiessen polygons from point features with taking into account their weights.

Most use-cases of Thiessen polygons are the influence analysis of the point data such as shopping centers, factories or other economy objects. When some weight parameter of points is taken into account, the output polygons show input features influence on the environment closer to reality.

Description

Weighted Thiessen Polygons tool is different from classic tool Thiessen Polygons by forming non-linear structures, because the point weights are taken into account. Point with greater weight has greater influence than point with smaller weight and this results in creating a polygon of larger area. This is why the borders of output polygons may be arcs.

Using this tool, you can also densify arcs in the output polygons.

Usage

Select the "Weighted Thiessen Polygons" tool from the XTools Pro Analysis Tools menu.
Select the input layer containing points to build weighted Thiessen polygons for.
Specify the name and location of the output feature class.
Select to use extent if required and specify the extent (from input feature class, full extent, current extent, other layer or dataset extent, from all and selected graphic extent or specifying extent manually).
Select the input field for weighting input features (it must be numeric).
Select maximum segment parameter for densifying arcs if you wish.
Specify ID field to store input features IDs.
Press Run to build weighted Thiessen polygons.

Densify arcs

Weighted Thiessen polygons with arcs are mathematically correct polygons. If you need correct weighted Thiessen polygons as a result, you may keep arcs in the output dataset (this is a default output). However, if you wish to work with the output polygon feature class using other tools, it may be recommended to densify arcs for in the output polygons.

You need to specify maximum segment parameter to get linear segments in the output polygon borders. If this parameter is empty (as default), the output polygons will keep arcs.

Using this parameter, the tool follows the next algorithm:

All output linear segments will be equal to one arc element and its length can’t be greater than maximum segment specified by the user.
Number of linear segments can’t be less than 2 for one arc element and can’t be less than 1 for each 10 degrees of long arc.
Straight linear borders of output polygons will keep their length anyway.
Densified polygons will have valid topology.

Note:

With any of the options above the extent of the output Weighted Thiessen polygon feature class is the selected extent plus additional 10% (this can be switched off in the XTools Pro Options dialog).
Only positive values of weights are taken into consideration when building weighted Thiessen polygons.
You may specify only positive maximum segment to densify arcs of output polygons.
Input point feature class can’t contain duplicate features.