# Map Projection Tutorial

## Why are map projections an issue in GIS?

In many respects, GIS has freed us from the constraints of modelling the spatial relationships using a drawing on paper. For example:
• Easy customizing of what features are displayed and how they look.

• attachment of database attributes to features.

• easier filing.

• quick creation of buffers.

• overlays and area calculations.

However, the spatial representation of data in GIS remains tied to a mapping plane. Map projections are the means of representing an ellipsoidal Earth on a mapping plane. Area calculations are done on the mapping plane, not on the ellipsoid

By definition, topological relationships are not affected by projection transformations. However, areas, shapes, angles and distances are affected.

## Map projection characteristics

Different map projections retain or distort the following quantities. It is not possible for any one projection to retain more than one of them over a large area of the earth.

• area: equal-area means that a spatial unit on one part of the map covers exactly an equal area of the actual Earth as a spatial unit of the same size in any other part of the map

• shape: conformal projections preserve the relative local angles about every point on the map, so that meridians intersect parallels at 90 degrees; no map can be both equal-area and conformal

• scale: no map projection shows scale correctly throughout the entire map; equidistant projections show true scale between one or two points and every other point on the map, or along every meridian

• direction: azimuthal projections show correctly the directions from all points on the map to the centre

## Common projections

Some of the common projections in use are:

• Universal Transverse Mercator (UTM): conformal, best for north south extents; scale is true along the two meridians halfway between the Central Meridian and the edge of the zone (too small between these lines and too large outside of these lines); standard projection for basemapping and thematic mapping in BC; BCE regions extend across more than one UTM zone preventing the construction of a seamless GIS database

• Polyconic: preserves area, shape, distance and azimuth for small area s; best for north-south extents; scale increases away from the central meridian; used for the 1:2 Million map of BC (CM of 129:00:00 W used for source paper map so that province would sit straight up and down on sheet); generally considered that the scale distortion is acceptable only up to 9 degrees away from the Central Meridian; BC spans 115:00:00 W to 140:00:00 W which is 12 1/2 degrees on either side of the Central Meridian; former projection for US topographic maps of 1 degree extent, but not recommended for larger areas because of distortion

• Lambert Conformal Conic: conformal, best for east-west extents away from the equator; used in National Atlas of Canada and for Agriculture Canada 1:1 Million soil maps; US state basemaps; scale is too small between standard parallels and too large beyond them

• Albers Equal-Area Conic: equal-area, best for east-west extents away from the equator; scale is too small between standard parallels and too large beyond them; one of most commonly used projections for maps of conterminous USA