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# Spatial Concepts

Spatial Concepts. Mathematical Types of Space Euclidean Network Metric Topologic. 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. Spatial Concepts. Euclidean space

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## Spatial Concepts

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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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