Location information—a map Location information—a map An attribute dataset: e.g population, rainfall Links between the locations and the attributes Spatial proximity information  Knowledge about relative spatial location
 Topological information
Continuous (surface) data Continuous (surface) data Polygon (lattice) data Network data
Spatially continuous data Spatially continuous data  attributes exist everywhere
 There are an infinite number locations
 But, attributes are usually only measured at a few locations
 There is a sample of point measurements
 e.g. precipitation, elevation
 A surface is used to represent continuous data
polygons completely covering the area* polygons completely covering the area*  Attributes exist and are measured at each location
 Area can be:
 irregular (e.g. US state or China province boundaries)
 regular (e.g. remote sensing images in raster format)

Point pattern Point pattern  The locations are the focus
 In many cases, there is no attribute involved
Attributes may measure Attributes may measure  the network itself (the roads)
 Objects on the network (cars)
We often treat network objects as point data, which can cause serious errors  Crimes occur at addresses on networks, but we often treat them as points
Point data Point data (point pattern analysis: clustering and dispersion) Polygon data* (polygon analysis: spatial autocorrelation and spatial regression) Continuous data* (Surface analysis: interpolation, trend surface analysis and kriging)
Finding attribute values at locations where there is no data, using locations with known data values Finding attribute values at locations where there is no data, using locations with known data values Usually based on  Value at known location
 Distance from known location
Methods used  Inverse distance weighting
 Kriging
Polygons created from a point layer Polygons created from a point layer Each point has a polygon (and each polygon has one point) any location within the polygon is closer to the enclosed point than to any other point space is divided as ‘evenly’ as possible between the polygons
Centroid—the balancing point for a polygon used to apply point pattern analysis to polygon data More about this later
the smallest convex polygon able to contain a set of points the smallest convex polygon able to contain a set of points  no concave angles pointing inward
A rubber band wrapped around a set of points “reverse” of the centroid Convex hull often used to create the boundary of a study area  a “buffer” zone often added
 Used in point pattern analysis to solve the boundary problem.
Raster Model Raster Model area is covered by grid with (usually) equalsize, square cells attributes are recorded by giving each cell a single value based on the majority feature (attribute) in the cell, such as land use type or soil type Image data is a special case of raster data in which the “attribute” is a reflectance value from the geomagnetic spectrum  cells in image data often called pixels (picture elements)
Vector Model The fundamental concept of vector GIS is that all geographic features in the real work can be represented either as: points or dots (nodes): trees, poles, fire plugs, airports, cities lines (arcs): streams, streets, sewers, areas (polygons): land parcels, cities, counties, forest, rock type Because representation depends on shape, ArcGIS refers to files containing vector data as shapefiles
point (node): 0dimensions point (node): 0dimensions line (arc): 1dimension  two connected x,y coordinates
 road, stream
 A network is simply 2 or more connected lines
polygon : 2dimensions  four or more ordered and connected x,y coordinates
 first and last x,y pairs are the same
 encloses an area
 county, lake
Contour lines Contour lines  Lines of equal surface value
 Good for maps but not computers!
Digital elevation model (raster)  raster cells record surface value
TIN (vector)  Triangulated Irregular Network (TIN)
 triangle vertices (corners) record surface value
Advantages Advantages Easy to understand (for most people!)  Circle = hill top (or basin)
 Downhill > = ridge
 Uphill < = valley
 Closer lines = steeper slope
Disadvantages Not good for computer representation Lines difficult to store in computer
Each cell in the raster records the height (elevation) of the surface Each cell in the raster records the height (elevation) of the surface
a set of nonoverlapping triangles formed from irregularly spaced points a set of nonoverlapping triangles formed from irregularly spaced points preferably, points are located at “significant” locations,  bottom of valleys, tops of ridges
Each corner of the triangle (vertex) has:  x, y horizontal coordinates
 z vertical coordinate measuring elevation.
Raster model not good Raster model not good Also a big challenge for the vector model  but much more accurate
 the solution to this challenge resulted in the modern GIS system
The relationships between all spatial elements (points, lines, and polygons) defined by four concepts: The relationships between all spatial elements (points, lines, and polygons) defined by four concepts: NodeARC relationship:  specifies which points (nodes) are connected to form arcs (lines)
 specifies which arcs are connected to form networks
PolygonArc relationship  defines polygons (areas) by specifying which arcs form their boundary
FromTo relationship on all arcs  Every arc has a direction from a node to a node
 This allows
 This establishes left side and right side of an arc (e.g. street)
 Also polygon on the left and polygon on the right for
 every side of the polygon
2. Whole polygon structure 2. Whole polygon structure 3. Points and Polygons structure Used in earlier GIS systems before node/arc/polygon system invented Still used today for some, more simple, spatial data (e.g. shapefiles) Discuss these if we have time!
Whole Polygon (boundary structure): list coordinates of points in order as you ‘walk around’ the outside boundary of the polygon. Whole Polygon (boundary structure): list coordinates of points in order as you ‘walk around’ the outside boundary of the polygon.  all data stored in one file
 coordinates/borders for adjacent polygons stored twice;
 may not be same, resulting in slivers (gaps), or overlap
 all lines are ‘double’ (except for those on the outside periphery)
 no topological information about polygons
 which are adjacent and have a common boundary?
 used by the first computer mapping program, SYMAP, in late 1960s
 used by SAS/GRAPH and many later business mapping programs
 Still used by shapefiles.
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Points and Polygons: list ID numbers of points in order as you ‘walk around’ the outside boundary Points and Polygons: list ID numbers of points in order as you ‘walk around’ the outside boundary a second file lists all points and their coordinates.  solves the duplicate coordinate/double border problem
 still no topological information
 Do not know which polygons have a common border
 first used by CALFORM, the second generation mapping package, from the Laboratory for Computer Graphics and Spatial Analysis at Harvard in early ‘70s
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