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 100,000,000 = at the point 50,000,000
___________ =
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. Which one is spinning correctly?
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!