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