Cartography and Visualisation I: Projections

I am writing a post about the terminologies in relation to Cartography and Visualisation, and in specific, how cartographic projections (i.e., the maps we hold in our hands) come about.

This is Part I of the four-part instalment on:

1) projections,
2) geographical phenomenon and data representation,
3) map elements,
4) map design (colour, typography, planar organisation and hierarchical organisation) 

The aim of this post is to be as concise as possible, adding definitions and diagrams to aid in your understanding of how projections came about, and also partly to help in my revision for the examinations (heh heh). The definitions are adapted in my own words from the online resources that I have read and my Cartography and Visualisation lecture notes.

Just a teaser to start:

Adapted from GE2227 notes. Redrawn by Eunice Soh.

Geoid: a hypothetical surface representing the form the earth’s oceans would take if there was no land and the water were free to respond to the earth’s gravitational and centrifugal forces; can vary up to 75 metres above/ 100 metres below the ellipsoid (i.e., orthometric height)

Here's a geoid viewer: http://geomatica.como.polimi.it/elab/geoid/geoidViewer.html

A video on geodesy

How all the cartography terminology are linked. First, one starts off with an ellipsoid which is a mathematical representation of the geoid. The ellipsoid is defined by its geodetic datum, with the following parameters: origin, semi-major axis and semi-minor axis. 

Reference spheroid/sphere/ellipsoid: a mathematically-defined surface that approximates the geoid, the truer figure of the earth, or other planetary body (e.g., WGS1984)

Datum:  a set of values that act as a base to which a geoid is referenced at a single point; (as geodetic datum): a model that describes the location, direction and scale relationships with respect to an origin on the Earth’s surface (i.e., semi-major axis [a], semi-minor axis [b], flattening ratio [b/a], origin); Singapore’s datum is SVY21 which is based on the WGS84 datum except for the difference in origin

A geographic coordinate system is a coordinate system that enables every location on the Earth to be specified by a set of numbers or letters.

Prime meridian: a longtitude which is defined as 0^o; it is arbitrary, unlike the equator (vertical)

Equator: a latitude which is defined as 0^o_, at the axis of rotation of the earth (horizontal)

What is a rhumbline (loxodrome)

Projected Coordinate Systems and their various properties. The black box are the actual names of the projection.

A projected coordinate system is a coordinate system projected from a geographic coordinate system, where a map projection is the systematic transformation of the curved, three dimensional surface of the planet into flat, two dimensional plane, resulting in distortion.

For a great video on projections, look here: http://education.nationalgeographic.com/education/media/selecting-map-projection/ and a cute cartoon about map projections: http://xkcd.com/977/

Another video on projections

How did the Mercator projection (azimuthal) come about 

Distortion: any projection that distorts the earth in some way (e.g., conformal -> angles preserved, areas distorted; equal area -> area preserved, angles distorted)

Certain projections can be a "compromise" (figure above).

A good read would be http://en.wikipedia.org/wiki/Map_projection

Decisions of a projection would depend on

• Properties of the projection
• Characters (scale, interrupted, aspect)
• Deformation across mapped area
• Projection centre
• Familiarity

Properties of a projection

Major factors

• Equivalence: Equal area 
• Conformality: Equal angles 

Minor factors

• Distance: Equidistance 
• Direction: e.g., Azimuthal