Patrick’s Webpage BEng/Maps and Map Projections

Before trying to overlay the coordinates obtained from the GPS interface module, a method had to be devised whereby the user had the ability of first plotting the map, as well as zooming and panning by means of the keyboard. The maps of two local areas of Malta (Mosta and Luqa) were obtained from the Planning Authority. The street centre lines were obtained in vector form, i.e. each street centre line consists of a series of discrete points together with the street names and other miscellaneous data. The street data was obtained as a MIF/MID MapInfo file. MapInfo is a GIS application used mainly on desktop systems [Clarke, 1999]. The MapInfo Interchange Format (MIF) file is used to store the graphics, i.e. the street centre lines in our cases, and the .MID file contains the data. The textual data is delimited data, with one row per record and either Carriage Return, Carriage Return plus Line Feed, or Line Feed between lines. The MIF file has two areas – the file header area and the data section. The header contains information on how to create a MapInfo table, while the graphical object definitions are stored in the data section. The general structure of the MIF file header is given below, with the information in square brackets being optional. The data section of the .MIF file always follows the header and is introduced with the word DATA. The data section can have any number of graphical primitives, one for each graphic object. The graphical objects that can be specified are – POINT, LINE, POLYLINE, REGION, ARC, TEXT, RECTANGLE, ROUNDED RECTANGLE, and ELLIPSE. In this example, only ‘LINE’ and ‘POLYLINE’ are used. The MID file contains data, one record of data per row, delimited by the character specified in the delimiter statement. Each row in the MID file is associated with the corresponding object in the MIF file, first row with first object, second row with second object, etc. Below is a short sample of the corresponding .MID file. As one can note, this MID file contains 19 columns, as defined in the .MIF header section, each column being separated by a comma. Although for many mapping applications the earth can be assumed a perfect sphere, there is a small but significant difference between the distance around the earth pole to pole (39,939,593.9 meters) versus the distance around the equator (40,075,452.7 meters). This is because the earth resembles more closely the ellipsoid or oblate spheroid, the three-dimensional shape that is obtained by rotating an ellipse about its minor axis (Figure 5.3). Hundreds of geodetic datums are in use around the world. The Global Positioning system is based on the World Geodetic System 1984 (WGS-84). The two different datums, which were used to convert from the GPS coordinates to the map coordinates obtained from the Planning Authority, were the WGS84 datum and the European 1950 datum respectively. Table 5.2 is an extract from [DMA, 1990]. It lists the parameters, which are used by the Molodenskiy transformation (Appendix E) [Hager, 1989]. Datum conversions can be accomplished by various methods. Complete datum conversion is based on seven parameter transformations that include three translation parameters, three rotation parameters and a scale parameter. Simple three parameter conversion between latitude, longitude, and height in different datums can be accomplished by conversion through Earth-Centred, Earth Fixed (ECEF) XYZ Cartesian coordinates in one reference datum and three origin offsets that approximate differences in rotation, translation and scale. Map projections are attempts to portray the surface of the earth or a portion of the earth onto a flat surface. Some distortions of conformality, distance, direction, scale, and area always result from this process. Some projections minimize distortions in some of these properties at the expense of maximizing errors in others, while others attempt to only moderately distort all of these properties [Dana, 1999b]. The universal transverse Mercator (UTM) coordinate system has been in common use since the late 1950s. The transverse Mercator began with the equatorial Mercator projection. This projection distorts areas at the poles, but distortion along the equator is minimal. The Mercator projection was modified by J.H. Lambert in 1772 into its transverse form, in which the equator instead runs north-south. The effect is to minimise distortion in a narrow strip running from pole to pole. The projection was further improved by Gauss and Kruger, where the ellipsoidal formulas were adjusted for “polar flattening”. The UTM system has been used for mapping most of the United States, many other countries, and even the planet Mars. Source.

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