Map Projection Theory and Usage
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.
The Map Projection process in more depth
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))
Geometric Distortion is Unavoidable when Transforming from a Spherical to a Flat Surface
Different Projections have Different Types of Geometric Distortion
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
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
Scale Factor 2.00 times as large 100,000,000 = at the point 50,000,000 ___________ = 50,000,000
Scale Distortion Patterns On Major Types of Projections
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
Cylindrical Projection Cases
Normal Aspect, Tangent Case Example – Web Mercator
Transverse Aspect, Secant Case Example – UTM Zones
Universal Transverse Mercator Projection Details
Conical Projections
Normal Aspect, Secant Case Example --Sectional Aeronautical Charts --
Azimuthal Projections
Tangent and Secant Case Azimuthal Map Projection
Polar Aspect, Secant Case Example --Universal Polar Stereographic Grid Zones --
Oblique Aspect, Tangent Case Example --Great Circle Sailing Chart on Gnomonic Projection--
Oblique Aspect, Tangent Case Example -- Earth Day and Night on Orthographic Projection--
Which one is spinning correctly? Oblique and Equatorial Aspect, Tangent Case Examples -- Rotating Globes on Orthographic Projection-- Which one is spinning correctly?
Shape Distortion and Conformality
A Conformal Map Projection is one where Shapes and Directions are preserved locally
A Conformal Map Projection is one where Shapes and Directions are preserved locally
A Conformal Map Projection is one where Shapes and Directions are preserved locally
Normal Aspect, Secant Case Conformal Projection --Sectional Aeronautical Charts --
Area Distortion and Equivalency
Mollweide Elliptical Equal Area Projection
Mollweide Elliptical Equal Area Projection
Albers Conic Equal Area Projection for U.S.
No Flat Map can be Conformal and Equal Area at the same time …Only a Globe can be!