1. Location Reference Systems
GTECH 201 Lecture 06

2. Flattening the Earth

3. Historical Projections
Marinus
Ptolemy
Mercator

4. Distortions
Shape
Area
Distance
Direction

5. Preserving Properties
If two properties are to be preserved then one is always direction
These properties are incompatible:

6. Shape Property
Conformal
Non-conformal

7. Area Property

8. Distance Property

9. Direction Property

10. Direction Property Mercator with rhumb line or loxodrome
Azimuthal map with shortest distance

11. Tissot Indicatrices

12. Distortions
Mercator
Sinusoidal
Equal-area cylindrical
Robinson

13. Cylindrical Projections

14. Conic Projections

15. Planar Projections

16. Refining Map Projections
Transverse Mercator
Lambert conformal conic
Albers equal area conic
Lambert azimuthal equal area

17. Equatorial (normal) Aspect

18. Transverse Aspect

19. Oblique Aspect

20. Aspects for Planar Projections
Polar
Gnomic
Stereographic Orthographic

21. Aspects for Planar Projections
Equatorial Aspect
Gnomic
Stereographic Orthographic

22. Aspects for Planar Projections
Oblique Aspect
Gnomic
Stereographic Orthographic

23. Aspects for Conic Projections
Normal aspect

24. Polyconic Projection
Hassler, 1820s US Coastal Survey

25. Perspective
Position of the light source

26. Perspectives

27. Other Perspective Projections
Lambert cylindrical equal area

28. Classifying Projections
Cylindrical and pseudo-cylindrical

29. Classifying Projections
Conic and pseudo-conic

30. Classifying Projections
Planar and modified planar

31. Classifying Projections

32. Classifying Projections
Cylindrical
straight parallels; straight meridians
Pseudo-cylindrical
straight parallels, curved meridians
Conic
partial concentric circles for parallels; straight meridians
Pseudo-conic
partial concentric circles for parallels; curved meridians
Planar
Concentric circles for parallels; straight meridians
Modified planar
No common appearance of parallels and meridians

33. Projections Parameters
Angular parameters
Central meridian
Latitude of origin
Standard parallel
Latitude of center
Central parallel
Linear parameters
False easting
False northing
Scale factor

34. Origin of X, Y Coordinates

35. Central Parallel

36. False Easting/northing

37. Scale
Mercator
UTM

38. Choosing a Map Projection
Conformal (shape-preserving) maps
Topographic and cadastral
Navigation
Civil engineering
Weather

39. Choosing a Map Projection
Area-preserving maps
Population density
Land use
Quantitative attributes

40. Choosing a Map Projection
Scale-preserving maps no map preserves true distance for all measurements
Airline distances
Distance from epicenter of an earthquake
Cost calculations

41. Rules of Thumb

42. Rules of Thumb

43. Rules of Thumb

44. Coordinate Systems
Two ways to identify a position on a plane

45. Coordinate Systems
.. and on a sphere

46. Geographic Coordinate Systems
Latitude and longitude defined on a sphere

47. Geographic Coordinate Systems
Latitude defined on a spheroid (longitude is as on a sphere)

48. Components of a GCS An angular unit of measure A prime meridian
A datum, which includes a spheroid

49. Planar Coordinate Systems

50. Cartesian Coordinates
Calculate distance A-B

51. Universal Transverse Mercator
UTM zones

52. UTM Zones
.. as seen from the North Pole

53. UTM Projections
Each zone uses a custom Transverse Mercator projection with its own central meridian

54. Universal Polar Stereographic
Fills the holes of UTM in polar regions

55. State Plane Coordinate System

56. SPC N-S zones use Transverse Mercator
E-W zones use Lambert Conformal Conic
Maximal scale error is 1:10,000
NAD27 or NAD83 datum

57. Public Land Survey System
PLS are shown in purple

58. PLS It is used to locate areas, not points
It is not rigorous enough for spatial analysis like the calculation of distance or direction
It is not a grid imposed on a map projection (a system invented in a room), but lines measured on the ground by surveyors

59. PLS Meridians and Baselines

60. PLS Area Unit Hierarchy

61. PLS Township Sections
A township is divided into 36 sections, each a square mile (640 acres)
A section is divided into 160-acre quarters, which can be further divided into halves, quarters, and so on