#include <math.h>

#include "proj.h"

#include "proj_internal.h"

PROJ_HEAD(boggs, "Boggs Eumorphic") "\n\tPCyl, no inv, Sph";

#define NITER 20

#define EPS 1e-7

#define FXC 2.00276

#define FXC2 1.11072

#define FYC 0.49931

static PJ_XY boggs_s_forward(PJ_LP lp, PJ *P) { /* Spheroidal, forward */

    PJ_XY xy = {0.0, 0.0};

    double theta, th1, c;

    int i;

    (void)P;

    theta = lp.phi;

    if (fabs(fabs(lp.phi) - M_HALFPI) < EPS)

        xy.x = 0.;

    else {

        c = sin(theta) * M_PI;

        for (i = NITER; i; --i) {

            th1 = (theta + sin(theta) - c) / (1. + cos(theta));

            theta -= th1;

            if (fabs(th1) < EPS)

                break;

        }

        theta *= 0.5;

        xy.x = FXC * lp.lam / (1. / cos(lp.phi) + FXC2 / cos(theta));

    }

    xy.y = FYC * (lp.phi + M_SQRT2 * sin(theta));

    return (xy);

}

PJ *PJ_PROJECTION(boggs) {

    P->es = 0.;

    P->fwd = boggs_s_forward;

    return P;

}

#undef NITER

#undef EPS

#undef FXC

#undef FXC2

#undef FYC