Map Projection - University of Nebraska...
Transcript of Map Projection - University of Nebraska...
Map Projection
§Curved surface (3D) 2D Flat Surface§Approaches to transfer the spherical earth on
a two dimensional surface§Some distortions will always occur
Projection cont.
n Visualize a light shining through the Earth onto a surface
Distortionsn Fitting sphere to plane causes
stretching or shrinking of features
Types of Distortion
nShape nAreanDistancenDirection
Projection propertiesn Conformal
n maintains shapen Equal- area
n maintains arean Equidistant
n maintains distancen Azimuthal (Planar)
n maintains some directions
Example
Mercator Projection (Shape Preserved)
Mollweide Projection (Area preserved)
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
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
ExampleLambert’s Conformal Conic
From James R. Smith,page 194
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
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
Conic projections- result from projecting a spherical surface onto a cone.
Best for mid- latitudes with an East- West orientation
like Canada
Azimuthal (Planar) projections- result from projecting a spherical surface onto a plane.
•Best for polar or circular regions•Direction always true from center
Common Projections
n Mercatorn Universal Transverse Mercatorn Albers Equal Arean Lambert’s Conformal Conicn Azimuthal Equidistant
-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
§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
Universal Transverse Mercator
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
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
Different map projections result in different spatial relationships between regions.
• 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
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
Choosing, cont.
n Extentn Locationn Predominant extentn Projection supports spheroid/
datums?
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
COMMON MAP PROJECTIONSEqual Area – Goode’s Homolosine
From Robinson, Sixth Edition, page 81
COMMON MAP PROJECTIONSSpecial Purpose
Equidistant Cylindrical/Plane Chart
From Robinson, Sixth Edition, page 86
COMMON MAP PROJECTIONSSpecial Purpose – Simple Conic
From Robinson, Sixth Edition, page 87
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.
COMMON MAP PROJECTIONSSpecial Purpose
Robinson’s
Space
Oblique
Mercator