Location information—a map



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tarix30.04.2018
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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

  • 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








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