# An overview of the Distance toolset

The Distance tools allow you to perform distance analysis in the following ways:

• Euclidean (straight-line) distance
• Cost-weighted distance
• Cost-weighted distance allowing for vertical and horizontal restrictions to movement
• Paths and corridors between sources with the least cost of travel

The two main ways of performing distance analysis in Spatial Analyst is with the Euclidean distance and the cost-weighted distance tools.

The Euclidean Distance tool measures straight-line distance from each cell to the closest source; the source identifies the objects of interest, such as wells, roads, or a school. The distance is measured from cell center to cell center. Not only can you determine the distance each cell is to the closest source, you can also calculate for each cell the direction with Euclidean Direction and determine which source is the closest with Euclidean Allocation.

The Cost Distance (or cost-weighted distance) tool modifies Euclidean distance by equating distance as a cost factor, which is the cost to travel through any given cell. For example, it may be shorter to climb over the mountain to the destination, but it is faster to walk around it. The Cost Allocation tool identifies the nearest (or least costly) source cell based on accumulated travel cost. The Cost Back Link tool provides a road map, identifying the route to take from any cell, along the least-cost path, back to the nearest source.

In addition to a single cost variable, vertical and horizontal restrictions to movement can be incorporated into your analysis with the Path Distance, Path Distance Allocation, and Path Distance Back Link tools.

Once you have performed the cost distance analysis, creating distance and direction rasters, you can compute the least-cost (or shortest) path from a chosen destination to your source location with the Cost Path tool. The cost path travels from the destination to the source in what is guaranteed to be the cheapest route relative to the cost units defined by the original cost raster. Using two cost rasters instead of a linear path, you can use the Corridor tool to determine a swath of cells that do not exceed a specified cost.

The following table lists the available Distance tools and provides a brief description of each.

Tool

Description

Calculates the sum of accumulative costs for two input accumulative cost rasters.

Calculates for each cell its nearest source based on the least accumulative cost over a cost surface.

Defines the neighbor that is the next cell on the least accumulative cost path to the nearest source.

Calculates the least accumulative cost distance for each cell to the nearest source over a cost surface.

Cost Path

Calculates the least-cost path from a source to a destination.

Calculates, for each cell, the nearest source based on Euclidean distance.

Calculates, for each cell, the direction, in degrees, to the nearest source.

Euclidean Distance

Calculates, for each cell, the direction, in degrees, to the nearest source.

Path Distance

Calculates, for each cell, the least accumulative cost distance to the nearest source, while accounting for surface distance and horizontal and vertical cost factors.

Path Distance Allocation

Calculates the nearest source for each cell based on the least accumulative cost over a cost surface, while accounting for surface distance and horizontal and vertical cost factors.

Defines the neighbor that is the next cell on the least accumulative cost path to the nearest source, while accounting for surface distance and horizontal and vertical cost factors.

Tools in the Distance toolset

6/29/2011