1. Projections and Coordinates

2. Vital Resources John P. Snyder, 1987, Map Projections – A Working Manual, USGS Professional Paper 1395 To deal with the mathematics of map projections, you need to know trigonometry, logarithms, and radian angle measure Advanced projection methods involve calculus

3. Shape of the World The earth is flattened along its polar axis by 1/298 We approximate the shape of the earth as an ellipsoid Ellipsoid used for a given map is called a datum Ideal sea-level shape of world is called the geoid

4. Shape of the World Earth with topography Geoid: Ideal sea-level shape of the earth – Eliminate topography but keep the gravity – Gravity is what determines orbits and leveling of survey instruments – How do we know where the sea would be at some point inland? Datum: Ellipsoid that best fits the geoid Sphere: Globes and simple projections

5. The Datum

6. Datums In mapping, datums is the plural (bad Latin) Regional datums are used to fit the regional curve of the earth – May not be useful for whole earth Obsolete datums often needed to work with older maps or maintain continuity

7. Regional Datum

8. The Geoid

9. Distortion You cannot project a curved earth onto a flat surface without distortion You can project the earth so that certain properties are projected without distortion – Local shapes and angles – Distance along selected directions – Direction from a central point – Area A property projected without distortion is preserved

10. Preservation Local Shape or Angles: Conformal Direction from central point: Azimuthal Area: Equal Area The price you pay is distortion of other quantities Compromise projections don’t preserve any quantities exactly but they present several reasonably well

11. Projections Very few map “projections” are true projections that can be made by shining a light through a globe (Mercator is not) Projection = Mathematical transformation Many projections approximate earth with a surface that can be flattened – Plane – Cone – Cylinder Complex projections not based on simple surfaces

12. Choice of Projections For small areas almost all projections are pretty accurate Principal issues – Optimizing accuracy for legal uses – Fitting sheets for larger coverage Many projections are suitable only for global use

13. Projection Surfaces

14. Simple Projection Methods

15. Orthographic Projection

16. Gnomonic

17. Butterfly Projection

18. Dymaxion Projection

19. Azimuthal Equal Area

21. Azimuthal Equidistant

22. Stereographic

23. Equirectangular (Geographic)

24. Equirectangular Projection

25. Mercator

26. Transverse Mercator

27. Oblique Mercator

28. Lambert Equal Area Cylindrical

29. Peters Projection

30. Ptolemy’s Conic

31. Lambert Conformal Conic

32. Albers Equal Area Conic

33. Polyconic Projection

34. Bipolar Oblique Conic

35. Mollweide

36. Aitoff Projection

37. Sinusoidal

38. Robinson

39. Mollweide Interrupted

41. Homolosine Projection

42. Van der Grinten

43. Bonne

44. Specialized Projection

46. Transverse Mercator Projection

47. UTM Zones

48. UTM Pole to Pole

49. Halfway to the Pole

50. USA Congressional Surveys

51. Grid vs. No Grid

52. Wisconsin Grid Systems