map projections

MAP PROJECTIONS

Cartographic Design for GIS (Geog. 340)Prof. Hugh HowardAmerican River College

MAP PROJECTION DEFINED

MAP PROJECTION• Method by which Earth’s geographic

coordinates are converted to projected (Cartesian) coordinates

• The “flattening” of Earth onto a plane

Geographic Coordinates (lon,lat) Projected (Cartesian) Coordinates (x,y)

MAP PROJECTION• A great challenge faced by ancient

(and modern) cartographers– Ancient Babylonians introduced the idea

of scale, and 360 degrees in a circle– Ancient Greeks introduced the idea of

meridians and parallels (diaphragma)– Claudius Ptolemy introduced the idea of

map projections in the 2nd century AD

Claudius Ptolemy, 2nd Century AD

MAP PROJECTION• How are projections created?

– Today, most projections are created mathematically using computers

– A Reference Globe is created as a scale model of Earth

– A “rule” is derived that can be applied to every point on the globe

MAP PROJECTION• Projective Geometry has been used to

create projections, and still serves as a conceptual explanation

– A semi-transparent reference globe is fitted with a Point of Projection

– Surface of reference globe is projected onto a Developable Surface

– Surface is traced on developable surface

PROJECTION CLASSES (According to Projective Geometry)

THREE CLASSESPlanar

CylindricalConic

PROJECTION CLASSESClassification According to Projective Geometry

Good for:Polar regions

Developable Surface

THREE CLASSESPlanar

CylindricalConic

Good for:Equatorial regions

Developable Surface


THREE CLASSESPlanar

CylindricalConic

Good for:Midlatitude regions

Developable Surface


Originally developed by Claudius Ptolemy, 2nd Century AD

THREE CLASSESPlanar

CylindricalConic

Mathematical ProjectionsSome projections are developed mathematically, not according to projective geometry; developable

surfaces are not involved.Pseudocylindrical, Sinusoidal, etc.


PROJECTIONCASE and ASPECT

PROJECTION CASE• Case

– Describes how the developable surface is positioned, relative to the reference globe

– Tangent– Secant

PROJECTION CASE• Case (cont.)

– Lines of contact are Standard Lines

Standard Lines have same scale as reference globe

Distortion increases away from Standard Lines

• Aspect – The orientation of the developable

surface, relative to the reference globe

PROJECTION ASPECT

Equatorial Aspect Polar/Transverse Aspect

Oblique Aspect(Mercator) (Transverse Mercator)

(Oblique Mercator)

PROJECTION CLASSES (According to Properties Preserved)

• Distortion always results from the projection process– The larger the area of Earth projected, the

greater the distortion – Smaller areas are subject to less distortion

PROJECTION CLASSESClassification According to Properties Preserved

Smaller Area (closer to flat)Large Area

(strongly curved)

• Types of distortion:– Angle (shape)

– Area

– Distance

– Direction


• Projections can be classified according to the type of distortion they do not produce…

• Projections can be classified by the Properties They Preserve– Angle (shape)

– Area

– Distance

– Direction


• Conformal projections:– Preserve Angles (shapes of small areas)

• Equivalent (Equal Area) projections:– Preserve relative sizes of Areas

• Equidistant projections:– Preserve Distances…

• Azimuthal projections:– Preserve Directions…


Conformal: Lambert Conformal Conic

FOUR CLASSESConformalEquivalentEquidistantAzimuthal

Good for:Topographic maps

Weather mapsNavigational maps


Conformal: Mercator


Good for:Topographic maps

Weather mapsNavigational maps


Equivalent: Eckert IV


Good for:Thematic mapsPolitical maps


Equivalent: Sinusoidal


Good for:Thematic mapsPolitical maps



Conformal and Equal Area projections are mutually exclusive

No projection can be both conformal and Equal Area

!



Conformal and Equivalent projections are mutually exclusive

No projection can be both conformal and Equivalent


Equidistant: Azimuthal Equidistant


Good for:Airline distance maps

Seismic maps


Distances are correct from the center of the projection, to all other locations(and along standard lines)

Azimuthal: Loximuthal


Good for:Navigational maps


Directions are correct from the center of the projection, to all other locations(and along standard lines)

Robinson


Compromise ProjectionsDistort shape, size, distance, and direction,

but distribute distortion in a way that looks natural

Good for:Non-critical applications



Compromise ProjectionsDistort shape, size, distance, and direction,

but distribute distortion in a way that looks natural

Good for:General, non-critical

applications


Van der Grinten

Winkel Tripel

SELECTING an APPROPRIATE PROJECTION

SELECTING A PROJECTION• Selection of an appropriate projection

requires consideration of– Data– Symbolization method– Intended audience– Region of Earth– Map scale– Level of generalization, etc.

SELECTING A PROJECTION• John Snyder’s Guidelines provide a

hierarchical mechanism for choosing projections, based on

– Region to be mapped (world, hemisphere, continent or smaller)

– Desired projection property (conformal, equivalent, azimuthal, equidistant)

– Desired projection characteristic (class, case, aspect)

SELECTING A PROJECTION• World Map of Literacy Rates (choropleth)

Preserves relative areas of enumeration units

SELECTING A PROJECTION

SELECTING A PROJECTION• Map of Russian Population (proportional

symbol and dot)

Preserves relative areas of enumeration units


Standard Parallels located ~1/6 from top, and ~1/6 from bottom

Central Meridian located midway of E-W extent

SELECTING A PROJECTION• Map of Kansas Tornado Paths (flow)

Angular relationships of paths are important

No need to preserve relative areas of

enumeration units


Lambert Conformal Conic


Albers Equal Area Conic

Virtually no difference!

The smaller the area, the less important the projection!


Lambert Conformal Conic

Lambert Conformal Conic would be the correct

choice…

MAP PROJECTIONS

Cartographic Design for GIS (Geog. 340)Prof. Hugh HowardAmerican River College

map projections

Documents

projective geometrygood

projective geometryoriginally

reference globedistortion

computersa reference

idea of map projections

properties preserveddistortion

idea of scale

developable surfacesurface