/*

** libproj -- library of cartographic projections

**

** Copyright (c) 2003   Gerald I. Evenden

*/

/*

** Permission is hereby granted, free of charge, to any person obtaining

** a copy of this software and associated documentation files (the

** "Software"), to deal in the Software without restriction, including

** without limitation the rights to use, copy, modify, merge, publish,

** distribute, sublicense, and/or sell copies of the Software, and to

** permit persons to whom the Software is furnished to do so, subject to

** the following conditions:

**

** The above copyright notice and this permission notice shall be

** included in all copies or substantial portions of the Software.

**

** THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,

** EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF

** MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.

** IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY

** CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,

** TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE

** SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

*/

#include <math.h>

#include <stdlib.h>

#include "proj.h"

#include "proj_internal.h"

#define MAX_ITER 20

namespace { // anonymous namespace

struct GAUSS {

    double C;

    double K;

    double e;

    double ratexp;

};

} // anonymous namespace

#define DEL_TOL 1e-14

static double srat(double esinp, double ratexp) {

    return (pow((1. - esinp) / (1. + esinp), ratexp));

}

void *pj_gauss_ini(double e, double phi0, double *chi, double *rc) {

    double sphi, cphi, es;

    struct GAUSS *en;

    if ((en = (struct GAUSS *)malloc(sizeof(struct GAUSS))) == nullptr)

        return (nullptr);

    es = e * e;

    en->e = e;

    sphi = sin(phi0);

    cphi = cos(phi0);

    cphi *= cphi;

    *rc = sqrt(1. - es) / (1. - es * sphi * sphi);

    en->C = sqrt(1. + es * cphi * cphi / (1. - es));

    if (en->C == 0.0) {

        free(en);

        return nullptr;

    }

    *chi = asin(sphi / en->C);

    en->ratexp = 0.5 * en->C * e;

    double srat_val = srat(en->e * sphi, en->ratexp);

    if (srat_val == 0.0) {

        free(en);

        return nullptr;

    }

    if (.5 * phi0 + M_FORTPI < 1e-10) {

        en->K = 1.0 / srat_val;

    } else {

        en->K = tan(.5 * *chi + M_FORTPI) /

                (pow(tan(.5 * phi0 + M_FORTPI), en->C) * srat_val);

    }

    return ((void *)en);

}

PJ_LP pj_gauss(PJ_CONTEXT *ctx, PJ_LP elp, const void *data) {

    const struct GAUSS *en = (const struct GAUSS *)data;

    PJ_LP slp;

    (void)ctx;

    slp.phi = 2. * atan(en->K * pow(tan(.5 * elp.phi + M_FORTPI), en->C) *

                        srat(en->e * sin(elp.phi), en->ratexp)) -

              M_HALFPI;

    slp.lam = en->C * (elp.lam);

    return (slp);

}

PJ_LP pj_inv_gauss(PJ_CONTEXT *ctx, PJ_LP slp, const void *data) {

    const struct GAUSS *en = (const struct GAUSS *)data;

    PJ_LP elp;

    double num;

    int i;

    elp.lam = slp.lam / en->C;

    num = pow(tan(.5 * slp.phi + M_FORTPI) / en->K, 1. / en->C);

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

        elp.phi =

            2. * atan(num * srat(en->e * sin(slp.phi), -.5 * en->e)) - M_HALFPI;

        if (fabs(elp.phi - slp.phi) < DEL_TOL)

            break;

        slp.phi = elp.phi;

    }

    /* convergence failed */

    if (!i)

        proj_context_errno_set(

            ctx, PROJ_ERR_COORD_TRANSFM_OUTSIDE_PROJECTION_DOMAIN);

    return (elp);

}