# Legacy Distance geoprocessing functions

The Legacy Distance geoprocessing functions allow you to access the distance analysis geoprocessing functions available in previous releases of ArcGIS. These tools perform analysis that accounts for either straight-line (Euclidean) or weighted distance. Distance can be weighted by a simple cost (friction) surface, or in ways that account for vertical and horizontal restrictions to movement. The Legacy Distance tools utilize the original method of computing distance from earlier releases. To take advantage of the more accurate distance calculations now available, use the distance geoprocessing functions outside of the Legacy toolset.

The two main ways of performing distance analysis with the ArcGIS Spatial Analyst extension is with the Euclidean distance and the cost-weighted distance geoprocessing functions.

The Euclidean Distance geoprocessing function measures the 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 the closest source with Euclidean Allocation.

The Cost Distance (or cost-weighted distance) geoprocessing function 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 a shorter distance to climb over the mountain to the destination, but it is quicker to walk around it. The Cost Allocation geoprocessing function identifies the nearest (or least costly) source cell based on accumulated travel cost. The Cost Back Link geoprocessing function 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 geoprocessing functions.

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 and Cost Path as Polyline geoprocessing functions. The cost path travels from the destination to the source in what is guaranteed to be the least expensive 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 geoprocessing function to determine a collection of cells that do not exceed a specified cost.

The following table lists the available geoprocessing functions and provides a brief description of each.

Geoprocessing FunctionDescription

Cost Allocation

Calculates, for each cell, its least-cost 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 least-cost source.

Cost Connectivity

Produces the least-cost connectivity network between two or more input regions.

Cost Distance

Calculates the least accumulative cost distance for each cell from or to the least-cost source over a cost surface.

Cost Path

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

Cost Path as Polyline

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

Euclidean Allocation

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

Euclidean Back Direction

Calculates, for each cell, the direction, in degrees, to the neighboring cell along the shortest path back to the closest source while avoiding barriers.

Euclidean Direction

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

Euclidean Distance

Calculates, for each cell, the Euclidean distance to the closest source.

Path Distance

Calculates, for each cell, the least accumulative cost distance from or to the least-cost source, while accounting for surface distance along with horizontal and vertical cost factors.

Path Distance Allocation

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