rhumbline.c

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/*!
 * \file lib/gis/rhumbline.c
 *
 * \brief GIS Library - Rhumbline calculation routines.
 *
 * From "Map Projections" by Peter Richardus and Ron K. Alder, 1972<br>
 * (526.8 R39m in Map & Geography Library)<br>
 * Page 20,21, formulas 2.21, 2.22
 *
 * Formula is the equation of a rhumbline from (lat1,lon1) to
 * (lat2,lon2). Input is lon, output is lat (all in degrees).
 *
 * <b>Note:</b> Formula only works if 0 < abs(lon2-lon1) < 180.
 * If lon1 == lon2 then rhumbline is the merdian lon1 (and the formula
 * will fail).
 * <br>
 * <b>WARNING:</b> This code is preliminary. It may not even be correct.
 *
 * (C) 2001-2014 by the GRASS Development Team
 *
 * This program is free software under the GNU General Public License
 * (>=v2). Read the file COPYING that comes with GRASS for details.
 *
 * \author GRASS Development Team
 *
 * \date 1999-2014
 */
 
#include <math.h>
#include <grass/gis.h>
#include "pi.h"
 
static void adjust_lat(double *);
 
#if 0
static void adjust_lon(double *);
#endif /* unused */
 
static struct state {
    double TAN_A, TAN1, TAN2, L;
    int parallel;
} state;
 
static struct state *st = &state;
 
/**
 * \brief Start rhumbline calculations.
 *
 * <b>Note:</b> This function must be called before other rhumbline
 * functions to initialize parameters.
 *
 * \param[in] lon1,lat1 longitude, latitude of first point
 * \param[in] lon2,lat2 longitude, latitude of second point
 * \return 1 on success
 * \return 0 on error
 */
int G_begin_rhumbline_equation(double lon1, double lat1, double lon2,
                               double lat2)
{
    adjust_lat(&lat1);
    adjust_lat(&lat2);
 
    if (lon1 == lon2) {
        st->parallel = 1; /* a lie */
        st->L = lat1;
        return 0;
    }
    if (lat1 == lat2) {
        st->parallel = 1;
        st->L = lat1;
        return 1;
    }
    st->parallel = 0;
    lon1 = Radians(lon1);
    lon2 = Radians(lon2);
    lat1 = Radians(lat1);
    lat2 = Radians(lat2);
 
    st->TAN1 = tan(M_PI_4 + lat1 / 2.0);
    st->TAN2 = tan(M_PI_4 + lat2 / 2.0);
    st->TAN_A = (lon2 - lon1) / (log(st->TAN2) - log(st->TAN1));
    st->L = lon1;
 
    return 1;
}
 
/**
 * \brief Calculates rhumbline latitude.
 *
 * <b>Note:</b> Function only works if lon1 < lon < lon2.
 *
 * \param[in] lon longitude
 * \return double latitude in degrees
 */
double G_rhumbline_lat_from_lon(double lon)
{
    if (st->parallel)
        return st->L;
 
    lon = Radians(lon);
 
    return Degrees(2 * atan(exp((lon - st->L) / st->TAN_A) * st->TAN1) -
                   M_PI_2);
}
 
#if 0
static void adjust_lon(double *lon)
{
    while (*lon > 180.0)
        *lon -= 360.0;
    while (*lon < -180.0)
        *lon += 360.0;
}
#endif /* unused */
 
static void adjust_lat(double *lat)
{
    if (*lat > 90.0)
        *lat = 90.0;
    if (*lat < -90.0)
        *lat = -90.0;
}