## Vector Based Spatial Data Analysis

Point-in-polygon overlay:

Output is point coverage with additional attributes.

No new point features are created.

### No polygon boundaries are copied.

Logical Operators: Overlay analysis manipulates spatial data organized in different layers to create combined spatial features according to logical conditions specified in Boolean algebra with the help of logical and conditional operators. The logical conditions are specified with operands (data elements) and operators (relationships among data elements).

Note: In vector overlay, arithmetic operations are performed with the help of logical operators. There is no direct way to it.

Common logical operators include AND, OR, XOR (Exclusive OR), and NOT. Each operation is characterized by specific logical checks of decision criteria to determine if a condition is true or false. Table 1 shows the true/ false conditions of the most common Boolean operations. In this table, A and B are two operands. One (1) implies a true condition and zero (0) implies false. Thus, if the A condition is true while the B condition is false, then the combined condition of A and B is false, whereas the combined condition of A OR B is true.

AND - Common Area/ Intersection / Clipping Operation

XOR - Minus

 A B A AND B A OR B A NOT B B NOT A A XOR B 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 1 1 0 1 1 1 1 1 0 0 0

The most common basic multi layer operations are union, intersection, and identify operations. All three operations merge spatial features on separate data layers to create new features from the original coverage. The main difference among these operations is in the way spatial features are selected for processing.

### Overlay operations

The Figure 10 shows different types of vector overlay operations and gives flexibility for geographic data manipulation and analysis. In polygon overlay, features from two map coverages are geometrically intersected to produce a

OPERATION

PRIMARY LAYER OPERATION LAYER

RESULT

CLIP

ERASE

SPLIT

IDENTITY

UNION

 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
 1 2 3 4
 INTERSECT 1 2 3 4
 3 4 J n 1 4 X \9 i "4V J rvi 9 kH iV

Figure 10 : Overlay operations new set of information. Attributes for these new features are derived from the attributes of both the original coverages, thereby contain new spatial and attribute data relationships.

One of the overlay operation is AND (or INTERSECT) in vector layer operations, in which two coverages are combined. Only those features in the area common to both are preserved. Feature attributes from both coverages are joined in the output coverage.

Input Coverage

Intersect Coverage

Output Coverage

Input Coverage

Intersect Coverage

Output Coverage

 INPUT COVERAGE # ATTRIBUTE 1 A 2 B 3 A 4 C 5 A 6 D 7 A
 INTERSECT COVERAGE # ATTRIBUTE 1 2 102 3 103
 OUTPUT COVERAGE INPUT COVERAGE INTERSECT COVERAGE # # ATTRIBUTE # ATTRIBUTE 1 1 A 2 102 2 2 B 2 102 3 3 A 2 102 4 3 A 3 103 5 5 A 3 103 6 4 C 3 103 7 4 C 2 102 8 6 D 3 103 9 7 A 2 102 10 6 D 2 102

### RASTER BASED SPATIAL DATA ANALYSIS

Present section discusses operational procedures and quantitative methods for the analysis of spatial data in raster format. In raster analysis, geographic units are regularly spaced, and the location of each unit is referenced by row and column positions. Because geographic units are of equal size and identical shape, area adjustment of geographic units is unnecessary and spatial properties of geographic entities are relatively easy to trace. All cells in a grid have a positive position reference, following the left-to-right and top-to-bottom data scan. Every cell in a grid is an individual unit and must be assigned a value. Depending on the nature of the grid, the value assigned to a cell can be an integer or a floating point. When data values are not available for particular cells, they are described as NODATA cells. NODATA cells differ from cells containing zero in the sense that zero value is considered to be data.

The regularity in the arrangement of geographic units allows for the underlying spatial relationships to be efficiently formulated. For instance, the distance between orthogonal neighbors (neighbors on the same row or column) is always a constant whereas the distance between two diagonal units can also be computed as a function of that constant. Therefore, the distance between any pair of units can be computed from differences in row and column positions. Furthermore, directional information is readily available for any pair of origin and destination cells as long as their positions in the grid are known.

Advantages of using the Raster Format in Spatial Analysis

Efficient processing: Because geographic units are regularly spaced with identical spatial properties, multiple layer operations can be processed very efficiently.

Numerous existing sources: Grids are the common format for numerous sources of spatial information including satellite imagery, scanned aerial photos, and digital elevation models, among others. These data sources have been adopted in many GIS projects and have become the most common sources of major geographic databases.

Different feature types organized in the same layer: For instance, the same grid may consist of point features, line features, and area features, as long as different features are assigned different values.

• Data redundancy: When data elements are organized in a regularly spaced system, there is a data point at the location of every grid cell, regardless of whether the data element is needed or not. Although, several compression techniques are available, the advantages of gridded data are lost whenever the gridded data format is altered through compression. In most cases, the compressed data cannot be directly processed for analysis. Instead, the compressed raster data must first be decompressed in order to take advantage of spatial regularity.

• Resolution confusion: Gridded data give an unnatural look and unrealistic presentation unless the resolution is sufficiently high. Conversely, spatial resolution dictates spatial properties. For instance, some spatial statistics derived from a distribution may be different, if spatial resolution varies, which is the result of the well-known scale problem.

• Cell value assignment difficulties: Different methods of cell value assignment may result in quite different spatial patterns.

### Grid Operations used in Map Algebra

Common operations in grid analysis consist of the following functions, which are used in Map Algebra to manipulate grid files. The Map Algebra language is a programming language developed to perform cartographic modeling. Map Algebra performs following four basic operations:

• Local functions: that work on every single cell,

• Focal functions: that process the data of each cell based on the information of a specified neighborhood,

• Zonal functions: that provide operations that work on each group of cells of identical values, and

• Global functions: that work on a cell based on the data of the entire grid.

The principal functionality of these operations is described here.

### Local Functions

Local functions process a grid on a cell-by-cell basis, that is, each cell is processed based solely on its own values, without reference to the values of other cells. In other words, the output value is a function of the value or values of the cell being processed, regardless of the values of surrounding cells. For single layer operations, a typical example is changing the value of each cell by adding or multiplying a constant. In the following example, the input grid contains values ranging from 0 to 4. Blank cells represent NODATA cells. A simple local function multiplies every cell by a constant of 3 (Fig. 11). The results are shown in the output grid at the right. When there is no data for a cell, the corresponding cell of the output grid remains a blank.

Input Grid

0 0