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Map Projections: Theory and Usage

Learn about map projections, transforming spherical to planar coordinates, Mercator Projection, geometric distortion, scale factors, distortion patterns, different projection types, conformality, and equal area projections. Explore the world of maps!

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Map Projections: Theory and Usage

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  1. Map Projection Theory and Usage

  2. What is a map projection? A transformation of spherical or ellipsoidal Latitude,longitude (f,l) coordinates to planar (x,y) coordinates on a flat surface.

  3. The Map Projection process in more depth

  4. How can we make a Map projection? … By using coordinate transformation equations (x,y) Latitude (φ) , Longitude (λ) y x Mercator Projection x = Radius × λ y = Radius × ln (tan (45° + φ/2.0))

  5. Geometric Distortion is Unavoidable when Transforming from a Spherical to a Flat Surface

  6. Different Projections have Different Types of Geometric Distortion

  7. Understanding Scale Distortion by Studying Scale Factors across the Projection Scale Factor = Denominator of Principal Scale RF _________________________ Denominator of Actual Scale RF RF stands for Representative Fraction

  8. Principal Scale is the RF of the Generating Globe 1:100,000,000 1:50,000,000 Actual Scale is the RF at a Point on the Projection in a Given Direction

  9. Scale Factor 2.00 times as large at the point 100,000,000 ___________ = 50,000,000

  10. Scale Distortion Patterns On Major Types of Projections

  11. Cylindrical Projections Normal Aspect Transverse Aspect Oblique Aspect S.F.=1 S.F.>1 S.F.>1 S.F.>1 S.F.>1 S.F.=1 S.F.=1 S.F.>1 S.F.>1

  12. Cylindrical Projection Cases

  13. Normal Aspect, Tangent Case Example – Web Mercator

  14. Transverse Aspect, Secant Case Example – UTM Zones

  15. Universal Transverse Mercator Projection Details

  16. Conical Projections

  17. Normal Aspect, Secant Case Example --Sectional Aeronautical Charts --

  18. Azimuthal Projections

  19. Tangent and Secant Case Azimuthal Map Projection

  20. Polar Aspect, Secant Case Example --Universal Polar Stereographic Grid Zones --

  21. Oblique Aspect, Tangent Case Example --Great Circle Sailing Chart on Gnomonic Projection--

  22. Oblique Aspect, Tangent Case Example -- Earth Day and Night on Orthographic Projection--

  23. Oblique and Equatorial Aspect, Tangent Case Examples -- Rotating Globes on Orthographic Projection-- Which one is spinning correctly?

  24. Shape Distortion and Conformality

  25. A Conformal Map Projection is one where Shapes and Directions are preserved locally

  26. A Conformal Map Projection is one where Shapes and Directions are preserved locally

  27. A Conformal Map Projection is one where Shapes and Directions are preserved locally

  28. Normal Aspect, Secant Case Conformal Projection --Sectional Aeronautical Charts --

  29. Area Distortion and Equivalency

  30. Mollweide Elliptical Equal Area Projection

  31. Mollweide Elliptical Equal Area Projection

  32. Albers Conic Equal Area Projection for U.S.

  33. No Flat Map can be Conformal and Equal Area at the same time …Only a Globe can be!

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