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Understanding Spatial Concepts and Measurement Levels

Explore the various spatial concepts such as Euclidean space, network space, metric space, and topologic space, along with different measurement levels and patterns in spatial arrangement. Discover map projections and coordinate systems used in depicting Earth on a two-dimensional medium.

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Understanding Spatial Concepts and Measurement Levels

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  1. Spatial Concepts • Mathematical Types of Space • Euclidean • Network • Metric • Topologic

  2. Spatial Concepts • Euclidean space • Regular coordinate space that allows for the measurement of distance and bearing 5 4 3 2 1 0 2 0 1 2 3 4 5

  3. Spatial Concepts • Euclidean space • geometric primitives: • points • lines • polygons 5 4 3 2 1 0 0 1 2 3 4 5

  4. Spatial Concepts • Network space • connectors between points • can be directed network 5 4 3 2 1 0 0 1 2 3 4 5

  5. Spatial Concepts • Metric space • distance between 2 points is the same no matter the direction of measurement 5 4 3 2 1 0 3 3 0 1 2 3 4 5

  6. Spatial Concepts • Measuring distance is different in Euclidean space than in network space Euclidean Network 5 4 3 2 1 0 5 4 3 2 1 0 0 1 2 3 4 5 0 1 2 3 4 5

  7. Spatial Concepts • Measuring distance is different in Euclidean space than in network space Euclidean Network Distance(1,1 to 4,4) = sq. root of [(4-1) sq. + (4-1) sq.] = 4.24 Distance(1,1 to 4,4) = 2 + 2 + +1 + 2 + 1 = 8 5 4 3 2 1 0 5 4 3 2 1 0 1 2 3 1 2 2 3 0 1 2 3 4 5 0 1 2 3 4 5

  8. Spatial Concepts • Is this example of Network space a metric space? Distance(1,1 to 4,4) = 2 + 2 + +1 + 2 + 1 = 8 Distance(4,4 to 1,1) = ? 5 4 3 2 1 0 5 4 3 2 1 0 1 2 1 2 2 0 1 2 3 4 5 0 1 2 3 4 5

  9. Spatial Concepts • Topologic space • generally, spatial relationships between geometric elements A B adjacency A B containment a’ a neighborhood

  10. Spatial Concepts • Topologic space

  11. Spatial Concepts Spatial Measurement Levels

  12. Spatial Concepts Spatial Measurement Levels

  13. Spatial Concepts • Spatial pattern concepts: • proximity - the quality of being near something 1 mile

  14. Spatial Concepts • Spatial pattern concepts: • spatial arrangement regular clustered random

  15. Spatial Concepts • Spatial pattern concepts: • spatial orientation

  16. Spatial Concepts Spatial pattern concepts: diffusion of things (objects, people, styles) moving over time

  17. Spatial Concepts • Spatial pattern concepts: spatial association Percent Minority Urban density

  18. Projections and Coordinate Systems • Map Projections • a means to depict the spherical earth on a two dimensional medium • cannot simultaneously preserve all of these properties of the earth in two dimensions: • shape (of a region) • distance (between two points) • direction (bearing from one point to another) • area (of a region)

  19. Projections and Coordinate Systems • Three families of map projections planar cylindrical conical

  20. Projections and Coordinate Systems • Conformal projection • preserves direction • e.g. Mercator • Equal area projection • preserves area • e.g. Alber’s equal area

  21. Mercator projection Equal area projection

  22. Projections and Coordinate Systems • Coordinate (grid) systems • provide a spatial referencing system to locate points on the earth surface • spherical coordinate system • coordinates that describe locations on a sphere • planar coordinate system • coordinates that describe locations within a two dimensional Cartesian space

  23. Projections and Coordinate Systems • Spherical coordinate system: latitude and longitude • parallel: lines parallel to equator • meridian: lines going from pole to pole

  24. Projections and Coordinate Systems Planar Coordinate System • rectangular grid • X and Y axes • X: easting • Y: northing • point is defined by X,Y coordinate

  25. Projections and Coordinate Systems • Planar coordinate system: Universal Transverse Mercator (UTM) • units in meters • transverse cylindrical projection • 60 vertical zones cover globe • northing in meters from equator • easting in meters from false origin 500,000 meters west of zone central meridian

  26. Projections and Coordinate Systems Universal Transverse Mercator (UTM)

  27. Projections and Coordinate Systems • Planar coordinate system: United States State Plane Coordinate System • units in feet • projection in transverse Mercator or Lambert’s conformal conic • tied to U.S. datum • two or more zones for each state with a false origin southwest of the zone

  28. Projections and Coordinate Systems United States State Plane Coordinate System

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