Sect_11.1.10

11.1.10 Transforming GPS Surveying Results: Coordinate Systems & Datums

PROJECTION COORDINATES

Often ellipsoidal coordinates , are converted to plane projection coordinates x, y. There are many map projections which strive to somehow accommodate the complex curvature of the ellipsoid on a flat map sheet without too much distortion (MATHER, 1978). In general, conformal projections are used in surveying and mapping. Conformality means that an angle on the ellipsoid caused by a pair of geodesic lines is preserved. However, the geodesics themselves are curved lines after projection. Common classes of conformal projections are (HOFMANN-WELLENHOF et al, 1998):

Conical projection: formed by considering a cone tangential to the ellipsoid at some standard parallel of latitude. After the cone is flattened out, the meridians of longitude are straight lines converging to an apex, which is also the centre of circles representing the projected parallels. The Lambert projection is one example of this type of projection.
Azimuthal projection: is a special case of the conical projection where the apex is the pole and the cone degenerates to a plane tangential at the pole. The pole is therefore the centre of circles representing the parallels and of the straight lines representing the meridians. One example of this projection is the stereographic projection.
Cylindrical projection: is a special case of the conical projection where the apex is moved to infinity so that the cone becomes a cylinder which is tangential to the equator. After the cylinder is unrolled, the equator is mapped without distortion. The Universal Transverse Mercator (UTM) projection is one of the most widely used of all projection systems. In the transverse position the cylinder is tangential to a standard meridian.

In the conventional Transverse Mercator (TM) projection the standard meridian (or "central meridian") is mapped without distortion as it is the line of tangency of the spherical approximation of the ellipsoid with the cylinder. The central meridian is the y-axis (north direction) of the projection, while the x-axis is the mapping of the equator. The ellipsoid is partitioned into 120 zones of 3° longitude, each with the central meridian in the centre of the zone. As a point moves away from the central meridian the distortions grow larger as the scale factor increases. A modification of the TM is the UTM. Firstly, the ellipsoid is partitioned into 60 zones, each 6° longitude in width. Secondly, the scale factor at the central meridian is 0.9996 to reduce the large distortions in the fringes of the zone.

Detailed formulae defining the conformal mappings for the various projection systems can be found in standard texts on maps and projections (for example, MATHER, 1978).

Back to Chapter 11 Contents / Next Topic / Previous Topic