Map Projections

What is a map projection

mathematical transformation of points from the sphere or ellipsoid onto a plane

Developable surfaces

term used for surfaces in geometric form used in projection process

-plane

-cylinder

-cone

Tangent Case

A projection whose surface touches the globe's without piercing it. A tangent planar projection touches the globe at one point, while tangent conic and cylindrical projections touch the globe along a line. At the point or line of tangency, the projection is free from distortion.

Secant Case

A projection whose surface intersects the surface of a globe. A secant conic or cylindrical projection, for example, is recessed into a globe, intersecting it at two circles. At the lines of intersection, the projection is free from distortion.

Standard Line

point or line where the projection surface touches the reference globe; usually a standard parallel or central meridian.

Polar Aspect

A projection whose central point/line is located at either the north or south pole.

Equatorial Aspect

A projection whose central point/line is located at the equator.

Oblique Aspect

A planar or cylindrical projection whose point of tangency is neither on the equator nor at a pole or a conic projection whose axis does not line up with the polar axis of the globe.

Normal Aspect

The developable surface's axis of symmetry coincides with the Earth's axis. It is the position of the developable surface that produces the simplest graticule (i.e., the simplest geometry). The normal aspect will either be equatorial or polar, depending on the developable surface.

Transverse Aspect

The developable surface�s axis of symmetry is at right angles to the Earth�s axis. If normal is equatorial, transverse is polar and vice versa.

Rotated 90 degrees from normal aspect

Azimuthal (planar) Projection

A map projection that transforms points from a spheroid or sphere onto a tangent or secant plane. The azimuthal projection is also known as a planar projection.

normal aspect is polar, concentric circles, radiate out from center

Gnomonic

A planar projection, tangent to the earth at one point, projected from the center of the globe. All great circles appear as straight lines on this projection, so that the shortest distance between two points is a straight line. The gnomonic projection is useful in navigation.

Sterographic

Projected from teh opposite pole

Orthographic

infinite light source, sun

Cylindrical Projection

A projection that transforms points from a spheroid or sphere onto a tangent or secant cylinder.

every cylindrical projection is a rectangular map

the normal aspect is the equator

no curves in cylindrical projection, all right angles

Conic Projections

Normal = polar

only represent on hemisphere

farther from standard parallel, the more distortion increases

used for mid-latitudes

Secant Conic Projections

A projection whose surface intersects the surface of a globe. A secant conic or cylindrical projection, for example, is recessed into a globe, intersecting it at two circles. At the lines of intersection, the projection is free from distortion.

two standard parallels

less overall distortion than tangent projections

Polyconic projections

As a specific projection, the polyconic is conceptualized as "rolling" a cone tangent to the Earth at all parallels of latitude, instead of a single cone as in a normal conic projection. Each parallel is a circular arc of true scale. The scale is also true on the central meridian of the projection.

Pseudocylindrical projection

A projection which resembles a cylindrical projections but is actually compromise projection. Parallels are horizontal lines with meridians equally spaced. Meridians curve toward the poles.

Space Oblique Mercator projection

A projection developed to accommodate scanning of satellite devices. Essentially it is a conformal projection, but is different from the Transverse Mercator in that the central line of the projection is the satellite groundtrack, along which distortion is minimized.

4 types of distortion

-shape

-area (sizee)

-Distance

-direction

Equivalent (equal -area) projections

A projection in which the whole of the map as well as each part has the same proportional area as the corresponding part of the earth. An equal-area projection may distort shape, angle, scale, or any combination thereof. No flat map can be both equal-area and conformal.

Conformal Projections (maintains shape)

A projection that preserves the correct shapes of small areas. In a conformal projection, graticule lines intersect at 90-degree angles, and at any point on the map the scale is the same in all directions. A conformal projection maintains all angles at each point, including those between the intersections of arcs; therefore, the size of areas enclosed by many arcs may be greatly distorted. No map projection can preserve the shapes of larger regions.

Distort area, meridians never converge

Equidistant projections

Distance in preserved selectively

-refers to preservation of great circle distances

-no map projection preserves distance

-not used very often

Azimuthal Projections

-maintain true direction with respect to the map center

-shortest route between two points

Compromise projections

A projection that does not have equal area, conformal, or equidistant characteristics. The compromise projection is an attempt at balance between these characteristics, and is often used in thematic mapping.

Interrupted maps

A world projection that reduces distortion by cutting or slicing the projection, thus dividing the projected area into gores, each with its own central meridian.

Lambert Azimuthal Equal Area

best choices for mapping a hemisphere

Bonne Projection

Used for asia, america, australia and other large areas

North-south countries

use transverse mercator