# Location information—a map

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 tarix 30.04.2018 ölçüsü 487 b.
:

• ## Spatial proximity information

• Knowledge about relative spatial location
• Topological information

• ## 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*

• 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

• The locations are the focus
• In many cases, there is no attribute involved

• ## 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

• ## Methods used

• Inverse distance weighting
• Kriging

• ## the smallest convex polygon able to contain a set of points

• no concave angles pointing inward

• ## 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”

• ## 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)

• ## line (arc): 1-dimension

• two connected x,y coordinates
• 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

• 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

• ## Easy to understand (for most people!)

• Circle = hill top (or basin)
• Downhill > = ridge
• Uphill < = valley
• Closer lines = steeper slope

• ## 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.

• ## Also a big challenge for the vector model

• but much more accurate
• the solution to this challenge resulted in the modern GIS system

• ## Node-ARC relationship:

• specifies which points (nodes) are connected to form arcs (lines)
• ## Arc-Arcrelationship

• 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

• ## 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 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

• ## 12 5 5

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