The Round Earth to Flat Map: Map Projections for Designers

SP 240 CartographyAlex Chaucer

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The Size and Shape of the Earth

Geodesy – the science of earth measurementGeoid – term used to describe the shape of the

earth, means earth-shapedEllipsoid – geometrical solid with major and minor

axis to represent the shape of the earth

Clarke Ellipsoid of 1866 – was the reference ellipsoid for establishing a datum

Geodetic Reference System (GRS80) – reference ellipsoid used for NAD 83 datum

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Coordinate Geometry for the Cartographer

Cartesian coordinate geometry – the system of intersecting perpendicular lines on a plane that contains two principal axes.

Digitizing – specifying the locations of geographical points on a map in plane Cartesian space, usually by electronic means.

Geoferencing – when cartographers specify Cartesian coordinates into their geographic reference points, or when other source documents (air photos, remotely sensed images) are referenced to a common coordinate system

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Earth Coordinate Geometry

Latitude – location on the earth between the equator and the north and south poles, identifying the parallel passing through the position.

Longitude – position east or west of the prime meridian; designation is by identifying the meridian passing through the position.

Meridian – half of a circle intersecting the earth from pole to pole is a meridian.

Prime Meridian – has the angular designation of 0 degrees.

Global Positioning System – a “constellation” of 21 high altitude satellites (called NAVSTARS) that beam radio signals to earth-based receivers. The receivers can then take the signals and give latitude, longitude, elevation, and precise time.

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An Introduction to Map Projections for the Designer

Map projection – the systematic arrangement of the the earth’s spherical or geographic coordinate system onto a plane; a transformation process.

Map Scale = map distance earth distance

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Surface Transformation and Map Distortion

It is impossible to render the spherical surface of a globe to the flat map without some degree of tearing, shearing, or compression.

http://www-personal.umich.edu/~sarhaus/darcy.jpg

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Surface Transformation and Map Distortion

• You can’t spread out a basketball onto a flat surface – it’ll tear!

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Surface Transformation and Map Distortion

Distortion is not significant when mapping small areas.

But it is a significant design problem when portraying the whole earth or continents.

At these scales, area, shape, distance or direction must be compromised.

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Map Projection Properties

Equal Area Mapping - all mapped areas have the same proportional relationship to the areas on the Earth that they represent

http://www.colorado.edu/geography/gcraft/notes/mapproj/mapproj_f.html

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Map Projection PropertiesConformal Mapping (or orthomorphic) – the scale of a map at any point

on the map is the same in any direction, the projection is conformal. Meridians (lines of longitude) and parallels (lines of latitude) intersect at right angles. Shape is preserved locally on conformal maps.

http://www.colorado.edu/geography/gcraft/notes/mapproj/mapproj_f.html

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Map Projection Properties

http://www.colorado.edu/geography/gcraft/notes/mapproj/mapproj_f.html

Equidistance Mapping - A map is equidistant when it portrays distances from the center of the projection to any other place on the map.

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Map Projection Properties

http://www.colorado.edu/geography/gcraft/notes/mapproj/mapproj_f.html

Azimuthal Mapping - Direction

A map preserves direction when azimuths (angles from a point on a line to another point) are portrayed correctly in all directions.

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Determining Deformation and Its Distribution over the Projection

Scale Factor – a ratio representing the transformation of a projection based on that of a reference globe

< 1 – Compression has taken place> 1 – Stretching has taken place

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Patterns of Deformation

• There are 3 basic developable projections(based on 3 surfaces)

Plane Cylindar Cone

Azimuthal Cylindrical Conic

And even ones that are generated mathematically are classified into one of these families. Some are different enough and they are classed as…

Pseudoazimuthal, pseudocylindrical, and pseudoconic!!

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Tangent? Secant?

•

http://www.clas.ucsb.edu/staff/lee/Secant%20and%20Tangent%20lines.gif

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Plane/Azimuthal – tangent and secant

http://www.colorado.edu/geography/gcraft/notes/mapproj/mapproj_f.html

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Cylindrical – tangent and secant

http://www.colorado.edu/geography/gcraft/notes/mapproj/mapproj_f.html

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Conic – tangent and secant

http://www.colorado.edu/geography/gcraft/notes/mapproj/mapproj_f.html

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Others??

Pseudocylindrical projections resemble cylindrical projections, with straight and parallel latitude lines and equally spaced meridians, but the other meridians are curves.

http://www.colorado.edu/geography/gcraft/notes/mapproj/mapproj_f.html

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Credits

Many of these great maps came from:http://www.colorado.edu/geography/gcraft/contents.html

http://www.colorado.edu/geography/gcraft/notes/mapproj/mapproj_f.html