Map Projection - University of Nebraska...
Transcript of Map Projection - University of Nebraska...
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Map Projection
§Curved surface (3D) 2D Flat Surface§Approaches to transfer the spherical earth on
a two dimensional surface§Some distortions will always occur
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Projection cont.
n Visualize a light shining through the Earth onto a surface
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Distortionsn Fitting sphere to plane causes
stretching or shrinking of features
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Types of Distortion
nShape nAreanDistancenDirection
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Projection propertiesn Conformal
n maintains shapen Equal- area
n maintains arean Equidistant
n maintains distancen Azimuthal (Planar)
n maintains some directions
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Example
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Mercator Projection (Shape Preserved)
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Mollweide Projection (Area preserved)
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Developable Surfacesn Can be flattened without distortion
n Cylindersn Cones n Planesn Other
n A point or line of contact is created when surface is combined with a sphere
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Developable surfaces contacting spheres
n Tangentn projection surface touches sphere
n Secantn surface cuts through sphere
n No distortion at contact pointsn Increases away from contact points
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ExampleLambert’s Conformal Conic
From James R. Smith,page 194
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n Projecting a spherical surface onto a cylinder
• Longitudes equally spaced • Latitudes unequally spaced• Scale is true along equator• Shape and scale distortions increase near poles
•Best for equatorial or low latitudes
Cylindrical Projection
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Rotate cylinder to reduce distortion along a line- UTM is based on this- Cylinder right angles to the pole
Cylinder touches sphere alongtwo lines - both small circles
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Conic projections- result from projecting a spherical surface onto a cone.
Best for mid- latitudes with an East- West orientation
like Canada
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Azimuthal (Planar) projections- result from projecting a spherical surface onto a plane.
•Best for polar or circular regions•Direction always true from center
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Common Projections
n Mercatorn Universal Transverse Mercatorn Albers Equal Arean Lambert’s Conformal Conicn Azimuthal Equidistant
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-Projected on a cylinder -Any straight line is a line of constant direction (rhumb line)-Used for navigation-True Directions,-Conformal (angles and shapes true in small areas) but not equal area or equidistant-Cylindrical
Mercator Projection
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§Divides the earth from latitudes 84N to 80S in 60 vertical zones that are 6 deg wide.
§ Zones are numbered starting at 180th
meridian in eastward direction
§ Each zone is divided into sections of 8 deg latitude each§ Eastings (from Central meridian) and
Northings(from equator) can be designated for each zone§UTM preserves Area, Distance and Shape
well.
Universal Transverse Mercator
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Universal Transverse Mercator
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Albers Equal Area
• Conic (Secant case)• Well-suited for areas that
are mainly east-west in extent
• Areas - True• Directions - Reasonably
accurate in limited regions• Distances and Scale True
only along standard parallels
• Map - not conformal• Used for Thematic maps
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Lambert Conformal Conic
• Conic (Secant case)• Distances - True only along
standard parallels• Map - Conformal but not equal
area or equidistant• Area and Shape - Distortion
minimal at std. parallels• Directions - Reasonably
accurate• Shape - True for small areas• To map large ocean Areas and
regions in E-W extent
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Different map projections result in different spatial relationships between regions.
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• Extent - World; Eq/mid-lat/Polar
• Distances measured from centre are true; Distortion of other properties increases from centre point
• Useful for showing airline distances from centre point
• Useful for seismic & radio work
Azimuthal Equidistant
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Choosing a projection
n Often mandated by organizationn Or intended use:
n Thematic = equal- arean Presentation = conformal (also equal- area)n Navigation = Mercator, true direction or
equidistant
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Choosing, cont.
n Extentn Locationn Predominant extentn Projection supports spheroid/
datums?
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Combining data
n Data must be in common coordinate system
n Must know projection AND GCS (datum)
n Ex. Both in UTM, zone 10,n 1 is NAD27, 1 is NAD83 --n Y coordinates up to 200 meters off
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COMMON MAP PROJECTIONSEqual Area – Goode’s Homolosine
From Robinson, Sixth Edition, page 81
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COMMON MAP PROJECTIONSSpecial Purpose
Equidistant Cylindrical/Plane Chart
From Robinson, Sixth Edition, page 86
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COMMON MAP PROJECTIONSSpecial Purpose – Simple Conic
From Robinson, Sixth Edition, page 87
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COMMON MAP PROJECTIONSSpecial Purpose - Polyconic
From Robinson, Sixth Edition, page 88, 89
The distribution of scale factors on a polyconicprojection in the vacinity of 40° latitude. N-S SF values away from the central meridian are approximate. Note that the section of the projection which is used for a standard 7.5-minute quadrangle map would be 1/8 degree E-W and N-S along the central meridian.
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COMMON MAP PROJECTIONSSpecial Purpose
Robinson’s
Space
Oblique
Mercator
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