Essentially, a roving (usually 3x3 cell) window is used to obtain a new value for each cell, resulting in a new layer.  The cell values within the window are used to provide:

1.  Statistical summary of the neighbourhood

• mean, variance, standard deviation
• maximum or minimum
• percentile
• ranking
• etc...


2.  Slope and aspect

3.  Filtering

• smooth out sharp breaks
• edge enhancement

Extended neighbourhood operations

Extended neighbourhood operations examine the values of neighbouring cells beyond the local neighbourhood and potentially to the edge of the mapped area.  The extended neighbourhood may be constrained by distance or by additional features and used to calculate new values on a new resulting layer.

Extended neighbourhood operations may involve:

• Calculation of drainage paths
• find the quickest path downhill
• Interpolation
• interpolate unknown values from a number of given known sample values
• various methods exist involving triangulation, distance weighting, kriging, etc.
• Buffering
• involves "spreading" out from one or more given cells to produce a buffer

Buffering

Various types of buffering can occur, based on the known amount of information prior to buffering:

For grid GIS, the buffering process involves creating a region from given cell or region features. For example, buffers could be placed around cells representing post office locations, or around regions representing lakes or roads.

The buffering process may involve variable buffers whose sizes vary depending on the attributes of the particular features being buffered (eg. 100m buffers for main roads and 50m buffers for minor roads).

 

Restricted buffering

During the buffering process, the growth of buffers can be restricted by:

• Barriers
• prevent any movement through the barrier
• two types exist:
• absolute barrier - prevents movement entirely

(eg. cliff, lake, fence, forest, etc.)
• relative barrier - restricts movement at particular locations or times

(eg. narrow bridge, dried-up salt lake in summer, shallow streams, etc.)
 
• Friction surfaces
• movement is restricted across a surface representing "cost of movement"
• a cost is incurred for movement, in effect slowing or restricting movement while not preventing it entirely

(eg. up-hill or down-hill slopes, swamps, sandy soils, etc. may all contribute to reducing or increasing the buffer size)
• a layer of impedance values (providing cost of movement) can be used to represent the friction surface

  Spatial overlay

  The spatial overlay function involves combining information (cells) from two or more layers to form a new layer.  Of course the layers (and cells)  must be geographically aligned (georeferenced) with each other in order for the overlay to take place. Two types of overlay operations exist:

  • Boolean overlays - combining cells using boolean (also referred to as binary or logical) operators (ie. mathematical set operators):

  • AND - logical intersection
  • OR - logical union, and
  • NOT - logical negation
   
  • Weighted overlays - combining cells using algebraic operators such as:

  • arithmetic:  addition "+", subtraction "-", multiplication "*", division "/", exponentiation "^" (or "**")
  • statistical: mean, maximum, minimum, variance, standard deviation
  • merge: 
  • cover - one layer "covers" another, except where zeros occur
  • cross - assign a new value to each combination of values from the two layers

  Intersection overlay (AND)

  
  
  Various types of overlay operations exist.  One of these is the intersection overlay operation in which two layers are overlayed resulting in a third layer which is the intersection (AND operation) of the two layers.

  For example:

  Which areas are both grasslands (2) AND sandy soils (25)?

  
  

   

   

   

   

  Union overlay (OR)

  
  
  The union overlay operation causes two layers to be overlayed resulting in a third layer which is the union (OR logical operation) of the two layers.

  For example:

  Which areas are either grasslands (2) OR sandy soils (25)?

   

   

   

   

   

   

  Weighted overlay

  
  
  The weighted overlay operation allows values other than binary to be included as cell values.  The cell values are then combined using arithmetic, statistical or merge operators (as already indicated).

  For example, consider the problem:

  
  Can we predict our crop yield based on fertiliser rates and last year's crop yields?

   

   

The fundamental primitive is the line (or point as some people prefer) from which three basic spatial primitives are constructed: 

The endpoints of a line are sometimes referred to as nodes, whereas the intermediate points (making up the line segments within a line) are distinguished as vertices. 

Note that even though the above example shows a line being made up of line segments, it is possible to use mathematical parametric equations (splines) to store the line more accurately.

Topological
 

relationships between objects are stored reduces redundancy and improves integrity of database can record, for example, from/to nodes and left/right polygons for each line; this relates the nodes and polygons to the lines the area outside the mapped area is also treated as a polygon and is referred to as the world or envelope polygon (denoted with a zero (0) value

Topology and geometry are the two components of spatial data. The geometry can change without affecting topology, and likewise the topology can change without affecting the geometry. Some operations require geometry only, others require topology only, and still others require both geometry and topology.

Vector functionality

Because vector data consist of three different data primitives (points, lines, polygons) instead of one as for grid (the grid cell) and because all the components (location, topology, attributes) need to be maintained, vector operations are more complex than raster operations in general. Both the spatial data and the attribute data must be handled. Further the link between spatial and attribute data must be maintained. 

Vector operations include: 
 

Display and query of spatial and attribute data, both individually and in combination Data generalisation and abstraction building desired points, lines, areas and relationships from input data Data manipulation manipulate data coordinates to provide georeferencing, remove distortion, etc.

Measurement measure distance, shape, volume, etc. Topological overlay overlay points, lines and polygons Buffering buffer points, lines or polygons to produce new polygons

Data generalisation and abstraction

Generalisation and abstraction may involve: matching data across map sheet edges thinning out coordinates (vertices) to simplify lines and polygon boundaries calculation of centroids and label points in polygons automatic contouring proximal mapping - finding areas of proximity vector/raster conversion
		Data generalisation and abstraction also may involve: reclassification of points, lines and areas dissolving polygons and dropping lines between them - note that the attributes of such polygons must be merged

The spatial overlay of two coverages results in a new coverage which is subjected to planar enforcement.  In an overlay operation, both the spatial and the attribute data must be updated to reflect the new geometry/topology/attributes.

A number of different types of spatial overlay exist:

• point-in-polygon
• line-on-polygon
• polygon overlay (polygon-on-polygon