MANUAL GEO Lib
MANUAL-GEO-lib
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GEO LIBRARY FOR MATLAB 1. Introduction This library contains a set of functions aimed to deal with different coordinate systems and includes several utilities to compute rhumbs and different kind of lines connecting points. Using it with the KML library is a useful tool in the context of the subject. Below is brief description of each function together with the parameters used. 2. Conversion between coordinate systems FUNCION NAME LLA2ECEF DESCRIPTION MATLAB SINTAXIS INPUT PARAMETERS OUTPUT PARAMETERS Converts lat/lon/height (LLA) coordinates to Earth-‐Centered Earth-‐Fixed (ECEF) coordinates, using WGS84 ellipsoid ecef = lla2ecef(llh); llh = 3x1 array containing lat, long, height location (rad, rad, user units) ecef = 3x1 array with x,y,z (user units) FUNCION NAME ECEF2LLA DESCRIPTION Converts cartesian (x,y,z) coordinates of a reference point (ECEF) to lat, lon, height (LLA) coordinates in the WGS 84 system MATLAB SINTAXIS INPUT PARAMETERS OUTPUT PARAMETERS llh = ecef2lla(ecef); ecef = 3x1 arrar x,y,z (user units) llh = 3x1 array lat, long, height location (rad, rad, user units) 3. Great circle and rhumb lines computation 3.1. Direct problem solution FUNCION NAME ORTO_RECKON DESCRIPTION MATLAB SINTAXIS INPUT PARAMETERS OUTPUT PARAMETERS Travels a given distance along a given azimuth starting at a given initial point, using the WGS-‐84 Earth ellipsoid. Returns the endpoint and final azimut. [lat2,lon2,a21] = orto_reckon(lat1,lon1,s,a12); lat1 = initial latitude (degrees) lon1 = initial longitude (degrees) s = distance (meters) a12 = initial azimuth (degrees) lat2, lon2 = endpoint (degrees) a21 = reverse azimuth (degrees), at final point facing back toward initial point FUNCION NAME LOXO_RECKON DESCRIPTION MATLAB SINTAXIS INPUT PARAMETERS OUTPUT PARAMETERS Travels a given distance following a rhumb line, i.e, with a constant azimuth. Returns the endpoint and final azimut. [lat2,lon2,a21] = loxo_reckon(lat1,lon1,s,a12) lat1 = inital latitude (degrees) lon1 = initial longitude (degrees) s = distance (meters) a12 = initial azimuth (degrees) lat2, lon2 = endpoint (degrees) a21 = reverse azimuth (degrees), at final point facing back toward initial point FUNCION NAME VINCENTY_RECKON DESCRIPTION MATLAB SINTAXIS INPUT PARAMETERS OUTPUT PARAMETERS Travels a given distance along a given azimuth starting at a given initial point, using the WGS-‐84 Earth ellipsoid. Returns the endpoint and final azimut within a few millimeters of accuracy using Vincenty's algorithm [lat2,lon2,a21] = vincenty_reckon(lat1,lon1,s,a12) lat1 = inital latitude (degrees) lon1 = initial longitude (degrees) s = distance (meters) a12 = initial azimuth (degrees) lat2, lon2 = endpoint (degrees) a21 = reverse azimuth (degrees), at final point facing back toward initial point 3.2. Inverse problem solution FUNCION NAME ORTO_DISTAZI DESCRIPTION MATLAB SINTAXIS INPUT PARAMETERS OUTPUT PARAMETERS Computes the distance between two points assuming a perfectly spherical earth and Haversine approximation. Computes also forward azimuth, and backward azimuth. s = orto_distazi(lat1,lon1,lat2,lon2); [s,a12] = orto_distazi(lat1,lon1,lat2,lon2); [s,a12,a21] = orto_distazi(lat1,lon1,lat2,lon2); lat1 = GEODETIC latitude of first point (degrees) lon1 = longitude of first point (degrees) lat2, lon2 = second point (degrees) (inputs may be scalars, vectors, or matrices) s = distance in meters a12 = azimuth in degrees from first point to second point (forward) a21 = azimuth in degrees from second point to first point (backward) (Azimuths are in degrees clockwise from north.) FUNCION NAME LOXO_DISTAZI DESCRIPTION MATLAB SINTAXIS INPUT PARAMETERS OUTPUT PARAMETERS Computes the distance between two points through a loxodromic (rhumb) line in a spher. Computes forward azimuth, and backward azimuth. The azimuth remains constant so forward and backward match. s = loxo_distazi(lat1,lon1,lat2,lon2); [s,a12] = loxo_distazi(lat1,lon1,lat2,lon2); [s,a12,a21] = loxo_distazi(lat1,lon1,lat2,lon2); lat1 = GEODETIC latitude of first point (degrees) lon1 = longitude of first point (degrees) lat2, lon2 = second point (degrees) (inputs may be scalars, vectors, or matrices) s = distance in meters a12 = azimuth in degrees from first point to second point (forward) a21 = azimuth in degrees from second point to first point (backward) (Azimuths are in degrees clockwise from north.) FUNCION NAME VINCENTY_DISTAZI DESCRIPTION MATLAB SINTAXIS INPUT PARAMETERS OUTPUT PARAMETERS Compute the distance between two points within a few millimeters of accuracy using the WGS-‐84 Earth ellipsoid. Compute forward azimuth, and compute backward azimuth, all using a vectorized version of Vincenty's algorithm s = vincenty_distazi(lat1,lon1,lat2,lon2); [s,a12] = vincenty_distazi(lat1,lon1,lat2,lon2); [s,a12,a21] = vincenty_distazi(lat1,lon1,lat2,lon2); lat1 = GEODETIC latitude of first point (degrees) lon1 = longitude of first point (degrees) lat2, lon2 = second point (degrees) (inputs may be scalars, vectors, or matrices) s = distance in meters a12 = azimuth in degrees from first point to second point (forward) a21 = azimuth in degrees from second point to first point (backward) (Azimuths are in degrees clockwise from north.) 4. Utilities FUNCION NAME SEX2DEC DESCRIPTION MATLAB SINTAXIS INPUT PARAMETERS OUTPUT PARAMETERS Converts from sex degrees to decimal degrees x = sex2dec(rfs); TWO FORMATS ADMITTED FORMAT 1 Format 'N039°29''22.00"' Format 'W028°30''54.00"' FORMAT 2 Format 402959N / ddmmss for latitude Format 0005020W / ddmmss for longitude x: result in decimal degrees FUNCION NAME DIST_POINT_TO_LINE DESCRIPTION MATLAB SINTAXIS INPUT PARAMETERS OUTPUT PARAMETERS Returns the distance in feets between a point and a line defined by two points dist = dist_point_to_line(Lonp1, Latp1, Lonr1, Latr1, Lonr2, Latr2); lonp1, Latp1: Longitude and latitude of the point Lonr1, Latr1, Lonr2, Latr2: Longitude and latitude of the points r1 and r2 that they define the line dist = in feets FUNCION NAME DIST_FLAT DESCRIPTION MATLAB SINTAXIS INPUT PARAMETERS OUTPUT PARAMETERS Returns the distance in kilometers between two points. It assumes 'flat earth' simplification. Aprox: 1 latitude degree = 110 km 1 longitud degrees= 111 km dist = dist_flat(lon1, lat1, lon2, lat2); lon1, lat1 = first point longitude and latitude lon2, lat2 = second point longitude and latitude dist = in km
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