p Projection Theo and Usage
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Map Projection Theory and Usage
What is a map projection?
A transformation of spherical or ellipsoidal
Latitude,longitude (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
Latitude (φ) , Longitude (λ)
(x,y)
x
y
x = Radius × λ
y = Radius × ln (tan (45° + φ /2.0))
Mercator Projection
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 ProjectionScale 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
Actual Scale is the RF at a Point on the Projection in a Given Direction
1:50,000,000
Scale Factor
100,000,000___________
50,000,000
2.00 times as large
at the point=
Scale Distortion Patterns OnMajor Types of Projections
Cylindrical ProjectionsNormalAspect
TransverseAspect
ObliqueAspect
S.F.>1
S.F.>1S.F.=1
S.F.>1
S.F.>1
S.F.=1S
.F.>
1S
.F.>
1 S.F
.=1
Cylindrical Projection Cases
Normal Aspect, Tangent Case Example – Web Mercator
Transverse Aspect, Secant Case Example – UTM Zones
UniversalTransverseMercatorProjectionDetails
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--
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 andEqual Area at the same time
…Only aGlobe
can be!
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