In many cases we need to know the distance
for each location in a geographic area to certain features  roads, shopping
malls, police stations, etc. Generally this is a task performed in a raster
environment because the raster model is better suited for representing continuous
data. In order to use raster analysis in
ArcGIS however one needs to have Spatial Analyst which is an excellent but
costly option. If somebody needs to perform heavy spatial analysis on continuous
data this additional cost will be justified, but if someone needs occasionally
to derive a dataset that describes continuous phenomenon the price of
Spatial Analyst is an overkill.
In this article we will discuss how to derive
distance datasets using plain ArcGIS (any license) with the help of the ET
GeoWizards functions.
Point
dataset representing the sources
The point grid created
For the example with extent of about 150 x 90 kilometers we
used a cell size of 1 kilometer. The point grid created has about
4000 points.

Source dataset has the
features to which we want to calculate the distances. The features can
represent many different entities:
 points  towns, police stations, schools, cell towers,
etc.
 lines  streets, rivers, etc.
STEP1: In order to split spatially the area of interest we will create a grid
of regularly spaced point using the Point
Grid function of ET GeoWizards.
 The extent of the point grid should be a bit larger of the
source points.
 The cell size (the distance between the points of the point
grid) should be carefully selected:
 It should be small enough to be able to represent the
distances adequately
 It should not be too small, because this will create a very
large dataset and the processing will be difficult.
The functions of ET GeoWizards are tested on point grids with
up to 500,000 points, but we do not recommend using grids with
more than 200,000 points.

Result of Point Distance symbolized using the distance field.

STEP 2: The Point
Distance function will calculate the distance from each point of
the grid to the closest point of the source dataset. The search
tolerance should be large enough to find the distance to the furthermost
points of the point grid.

The TIN derived symbolized
with the minimum elevation.
The TIN derived symbolized with the azimuth calculated  shows the
direction for each point to the closest source

STEP 3: The next step will be
to create a continuous surface from the point grid with assigned distance to the source
points.
 Build
TIN function using the ET_Distance field as elevation source
will create a continuous PolygonZ dataset. The z values will
represent the distance to the closest source point.
 Analyze
TIN function will calculate several characteristics for each
3D polygon
We can use:
 the Minimum elevation field to symbolize the distance to the
closest point
 the Aspect field to represent the Euclidian direction from each
location to the closest source.

Distance Contours.

STEP 4: The Interpolate
Contours function will generate isolines connecting the points
with equal distance from the source points. Each polyline will
have Height attribute which in this case will reflect the distance
from the source points.

Thiessen Polygons

Creating Thiessen polygons from the dataset derived in STEP 2 above
can give us another continuous dataset representing the distances to
the source points. 
Distances to a polyline
dataset

The same approach can be
applied to calculate the distances to a polyline source
features. 
See ET GeoWizards
User Guide for
more information 