# Chapter 8 Spatial Operations and Vector Overlays

## 8.1 Selection by Attribute

Features in a GIS layer can be selected graphically or by querying attribute values. For example, if a GIS layer represents land parcels, one could use the Area field to select all parcels having an area greater than 2.0 acres.

Set algebra is used to define conditions that are to be satisfied while Boolean algebra is used to combine a set of conditions.

### 8.1.1 Set Algebra

Set algebra consists of four basic operators:

• less than (<),
• greater than (>),
• equal to (=)
• not equal to (<>).

In some programming environments (such as R and Python), the equality condition is presented as two equal signs, ==, and not one. In such an environment x = 3 is interpreted as “pass the value 3 to x” and x == 3 is interpreted as "is x equal to 3?.

If you have a GIS layer of major cities and you want to identify all census tracts having a population count greater than 50000, you would write the expression as "POP" > 50000 (of course, this assumes that the attribute field name for population count is POP).

The result of this operation is a selected subset of the Cities point layer. Note that in most GIS applications the selection process does not create a new layer.

### 8.1.2 Boolean Algebra

You can combine conditions from set algebra operations using the following Boolean algebra operators:

• or (two conditions can be met),
• and (two conditions must be met),
• not (condition must not be met).

Following up with the last example, let’s now select cities having a population greater than 50000 and that are in the US (and not Canada or Mexico). Assuming that the country field is labeled FIPS_CNTRY we could setup the expression as "POP" > 50000 AND "FIPS_CNTRY" = US. Note that a value need not be numeric. In this example we are asking that an attribute value equal a specific string value (i.e. that it equal the string 'US').

## 8.2 Selection by location

We can also select features from one GIS layer based on their spatial association with another GIS layer. This type of spatial association can be broken down into four categories: adjacency (whether features from one layer share a boundary with features of another), containment (whether features from one layer are inside features of another), intersection (whether features of one layer intersect features of another), and distance (whether one feature is within a certain distance from another).

Continuing with our working example, we might be interested in cities that are within 100 miles of recent earthquakes. The earthquake points are from another GIS layer called Earthquakes (Sep 2013).

You can, of course, combine multiple selection criteria (both by attribute and location), but be careful when selecting from an existing selection in ArcMap: in both the Selection by Location window and the Selection by Attribute window, you must explicitly set the option to select from an existing selection.

## 8.3 Vector Overlay

Map overlay refers to a group of procedures and techniques used in combining information from different data layers. This is an important capability of most GIS environments. Map overlays involve at least two input layers and result in at least one new output layer. A basic set of overlay tools include clipping, intersecting and unioning.

### 8.3.1 Clip

Clipping takes one GIS layer (the clip feature) and another GIS layer (the to-be-clipped input feature). The output is a clipped version of the original input layer. The output attributes table is a subset of the original attributes table where only records for the clipped polygons are preserved.

### 8.3.2 Intersect

Intersecting takes both layers as inputs then outputs the features from both layers that share the same spatial extent. Note that the output attribute table inherits attributes from both input layers (this differs from clipping where attributes from just one layer are carried through).

### 8.3.3 Union

Unioning overlays both input layers and outputs all features from the two layers. Features that overlap are intersected creating new polygons. This overlay usually produces more polygons than are present in both input layers combined. The output attributes table contains attribute values from both input features (note that only a subset of the output attributes table is shown in the following figure).