Cartesian Coordinates - GIS and Mapping - Lecture Slides, Slides of Geology

Download Cartesian Coordinates - GIS and Mapping - Lecture Slides and more Slides Geology in PDF only on Docsity! Cartesian Coordinates • Geodetic coordinates are a bit unwieldy for observations made from satellites, so a 3-dimenional Cartesian system is sometimes used. • Treating the centre of the spheroid as the origin, the Z-axis is aligned with the minor axis of the ellipsoid (i.e. through the north pole), and the X and Y axes lie on the equatorial plane. The X-axis intersects the equator at the prime meridian, and the Y axes is at right angles to it. • Any point in 3-D space can be expressed relative to the 3 axes. Docsity.com Greenwich meridian Docsity.com Measuring Distance • Measuring distance in a Cartesian system is a simple application of Pythagoras’s theorem: • However, the distance estimates will vary depending upon the projection used. • Measuring distance using geographic coordinates is more complex: • The calculations are even more complex for geodetic coordinates. ( ) ( )yyxxd 2121 22 −− += ( )[ ]2121211 coscoscossinsincos λλφφφφ −+= −Rd Docsity.com Datums • If you want data from different sources to ‘line up’, you may need to convert them from one projection to another. • To do this, you need to know not only what projection was used for each dataset, but also details about the reference system (i.e. size and shape of the spheroid, position of its centre, displacement of the false origin, etc.). • This information is referred to as the datum, and should form part of the metadata. • In the following example, a mapping agency is using the WGS84 spheroid, but it is displace to suit local conditions. Docsity.com ALOCAL Local datum a designed to fit here Docsity.com