area_ellipse.c

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#include <math.h>
#include <grass/gis.h>
#include "pi.h"


static double E;
static double M;


/*
 * a is semi-major axis, e2 is eccentricity squared, s is a scale factor
 * code will fail if e2==0 (sphere)
 */

int G_begin_zone_area_on_ellipsoid(double a, double e2, double s)
{
    E = sqrt(e2);
    M = s * a * a * M_PI * (1 - e2) / E;

    return 0;
}


double G_darea0_on_ellipsoid(double lat)
{
    double x;

    x = E * sin(Radians(lat));

    return (M * (x / (1.0 - x * x) + 0.5 * log((1.0 + x) / (1.0 - x))));
}


double G_area_for_zone_on_ellipsoid(double north, double south)
{
    return (G_darea0_on_ellipsoid(north) - G_darea0_on_ellipsoid(south));
}