Location information—a map

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

• Point 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

• 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.
• Called a “guard zone”

Raster Model

• Raster Model

• area is covered by grid with (usually) equal-size, 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): 0-dimensions

• point (node): 0-dimensions

• single x,y coordinate pair
• zero area
• tree, oil well, location for label

• line (arc): 1-dimension

• two connected x,y coordinates
• road, stream
• A network is simply 2 or more connected lines

• polygon : 2-dimensions

• 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 non-overlapping triangles formed from irregularly spaced points

• a set of non-overlapping 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

• not accurate

• 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:

• Node-ARC relationship:

• specifies which points (nodes) are connected to form arcs (lines)

• Arc-Arc relationship

• specifies which arcs are connected to form networks

• Polygon-Arc relationship

• defines polygons (areas) by specifying which arcs form their boundary

• From-To 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.

A 3 4

• A 3 4

• A 4 4

• A 4 2

• A 3 2

• A 3 4

• B 4 4

• B 5 4

• B 5 2

• B 4 2

• B 4 4

• C 3 2

• C 4 2

• C 4 0

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

1 3 4

• 1 3 4

• 2 4 4

• 3 4 2

• 4 3 2

• 5 5 4

• 6 5 2

• 7 5 0

• 8 4 0

• 9 3 0

• 10 1 0

• 11 1 5

• 12 5 5