/******************************************************************************

 * Project:  PROJ.4

 * Purpose:  Implementation of the aitoff (Aitoff) and wintri (Winkel Tripel)

 *           projections.

 * Author:   Gerald Evenden (1995)

 *           Drazen Tutic, Lovro Gradiser (2015) - add inverse

 *           Thomas Knudsen (2016) - revise/add regression tests

 *           Robert Kleffner (2026) - closed-form Aitoff inverse

 *

 ******************************************************************************

 * Copyright (c) 1995, Gerald 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 <errno.h>

#include <math.h>

#include "proj.h"

#include "proj_internal.h"

namespace pj_aitoff_ns {

enum Mode { AITOFF = 0, WINKEL_TRIPEL = 1 };

}

namespace { // anonymous namespace

struct pj_aitoff_data {

    double cosphi1;

    enum pj_aitoff_ns::Mode mode;

};

} // anonymous namespace

PROJ_HEAD(aitoff, "Aitoff") "\n\tMisc Sph";

PROJ_HEAD(wintri, "Winkel Tripel") "\n\tMisc Sph\n\tlat_1";

#if 0

FORWARD(aitoff_s_forward); /* spheroid */

#endif

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

    PJ_XY xy = {0.0, 0.0};

    struct pj_aitoff_data *Q = static_cast<struct pj_aitoff_data *>(P->opaque);

#if 0

    // Likely domain of validity for wintri in +over mode. Should be confirmed

    // Cf https://lists.osgeo.org/pipermail/gdal-dev/2023-April/057164.html

    if (Q->mode == WINKEL_TRIPEL && fabs(lp.lam) > 2 * M_PI) {

        proj_errno_set(P, PROJ_ERR_COORD_TRANSFM_OUTSIDE_PROJECTION_DOMAIN);

        return xy;

    }

#endif

    const double sin_half_lam = sin(0.5 * lp.lam);

    const double sin_phi = sin(lp.phi);

    const double cos_phi = cos(lp.phi);

    /* basic Aitoff; computing it with atan2 (instead of standard acos)

     * keeps relative accuracy near the origin. */

    const double sin_alpha = hypot(cos_phi * sin_half_lam, sin_phi);

    /* alpha / sin(alpha), with limit 1 at the origin */

    const double A =

        sin_alpha == 0

            ? 1.

            : atan2(sin_alpha, cos_phi * cos(0.5 * lp.lam)) / sin_alpha;

    xy.x = 2. * cos_phi * sin_half_lam * A;

    xy.y = sin_phi * A;

    if (Q->mode == pj_aitoff_ns::WINKEL_TRIPEL) {

        xy.x = (xy.x + lp.lam * Q->cosphi1) * 0.5;

        xy.y = (xy.y + lp.phi) * 0.5;

    }

    return (xy);

}

/******************************************************************************

 *

 * Closed-form inverse of the Aitoff projection. Short form equations are:

 *

 *     alpha  = hypot(x/2, y)      (angular distance to (phi, lambda/2))

 *     phi    = asin(y * sin(alpha) / alpha)

 *     lambda = 2 * atan2((x/2) * sin(alpha), alpha * cos(alpha))

 *

 * atan2 places lambda/2 in (-pi, pi]. The domain of the inverse is therefore

 * the whole ellipse x^2 + 4*y^2 <= (2*pi)^2, on which the sphere is double

 * covered; longitudes beyond +/-pi are returned only with +over. The poles

 * need no special case.

 *

 * Reference:

 *   J. P. Snyder (1987). Map Projections -- A Working Manual. USGS

 *   Professional Paper 1395, pp. 195-197.

 *

 *****************************************************************************/

/* Returns false, leaving *lp untouched, when (x, y) is outside the ellipse

 * x^2 + 4*y^2 = (2*pi)^2 and so has no preimage. */

static bool aitoff_s_inverse_closed(PJ_XY xy, PJ_LP *lp) {

    const double half_x = 0.5 * xy.x;

    const double alpha = hypot(half_x, xy.y);

    const double sin_alpha = sin(alpha);

    const double cos_alpha = cos(alpha);

    /* Testing sin_alpha is needed because with long doubles sin(M_PI) < 0. */

    if (alpha > M_PI || sin_alpha < 0)

        return false;

    /* The asin argument is guaranteed to lie in [-1, 1]: hypot(a, b) >= |b|

     * and 0 <= sin_alpha <= 1. */

    lp->phi = alpha == 0.0 ? xy.y : asin((xy.y / alpha) * sin_alpha);

    lp->lam = 2. * atan2(half_x * sin_alpha, alpha * cos_alpha);

    return true;

}

/******************************************************************************

 *

 * Inverse of the Aitoff and Winkel Tripel projections.

 *

 * Aitoff uses the closed form above. Winkel Tripel, the mean of the Aitoff and

 * equirectangular projections, has no known closed-form inverse; it is inverted

 * with the Newton-Raphson method of Bildirici and Ipbuker (2002), added by

 * Drazen Tutic and Lovro Gradiser (2015). Expected accuracy is defined by

 * EPSILON = 1e-12, appropriate for most applications of the projection.

 *

 * Reference:

 *   I. O. Bildirici and C. Ipbuker (2002). A General Algorithm for the Inverse

 *   Transformation of Map Projections Using Jacobian Matrices. Proceedings of

 *   the Third International Symposium on Mathematical and Computational

 *   Applications, pp. 175-182, Turkey.

 *

 * Contact: dtutic at geof.hr, 2015-02-16

 *

 *****************************************************************************/

static PJ_LP aitoff_s_inverse(PJ_XY xy, PJ *P) { /* Spheroidal, inverse */

    PJ_LP lp = {0.0, 0.0};

    struct pj_aitoff_data *Q = static_cast<struct pj_aitoff_data *>(P->opaque);

    if (Q->mode == pj_aitoff_ns::AITOFF) {

        if (!aitoff_s_inverse_closed(xy, &lp)) {

            proj_errno_set(P, PROJ_ERR_COORD_TRANSFM_OUTSIDE_PROJECTION_DOMAIN);

            lp.lam = lp.phi = HUGE_VAL;

        }

        return lp;

    }

    int iter, MAXITER = 10, round = 0, MAXROUND = 20;

    double EPSILON = 1e-12, D, C, f1, f2, f1p, f1l, f2p, f2l, dp, dl, sl, sp,

           cp, cl, x, y;

    if ((fabs(xy.x) < EPSILON) && (fabs(xy.y) < EPSILON)) {

        lp.phi = 0.;

        lp.lam = 0.;

        return lp;

    }

    /* initial values for Newton-Raphson method */

    lp.phi = xy.y;

    lp.lam = xy.x;

    do {

        iter = 0;

        do {

            sl = sin(lp.lam * 0.5);

            cl = cos(lp.lam * 0.5);

            sp = sin(lp.phi);

            cp = cos(lp.phi);

            D = cp * cl;

            C = 1. - D * D;

            const double denom = pow(C, 1.5);

            if (denom == 0) {

                proj_errno_set(

                    P, PROJ_ERR_COORD_TRANSFM_OUTSIDE_PROJECTION_DOMAIN);

                return lp;

            }

            D = acos(D) / denom;

            f1 = 2. * D * C * cp * sl;

            f2 = D * C * sp;

            f1p = 2. * (sl * cl * sp * cp / C - D * sp * sl);

            f1l = cp * cp * sl * sl / C + D * cp * cl * sp * sp;

            f2p = sp * sp * cl / C + D * sl * sl * cp;

            f2l = 0.5 * (sp * cp * sl / C - D * sp * cp * cp * sl * cl);

            if (Q->mode == pj_aitoff_ns::WINKEL_TRIPEL) {

                f1 = 0.5 * (f1 + lp.lam * Q->cosphi1);

                f2 = 0.5 * (f2 + lp.phi);

                f1p *= 0.5;

                f1l = 0.5 * (f1l + Q->cosphi1);

                f2p = 0.5 * (f2p + 1.);

                f2l *= 0.5;

            }

            f1 -= xy.x;

            f2 -= xy.y;

            dp = f1p * f2l - f2p * f1l;

            dl = (f2 * f1p - f1 * f2p) / dp;

            dp = (f1 * f2l - f2 * f1l) / dp;

            dl = fmod(dl, M_PI); /* set to interval [-M_PI, M_PI] */

            lp.phi -= dp;

            lp.lam -= dl;

        } while ((fabs(dp) > EPSILON || fabs(dl) > EPSILON) &&

                 (iter++ < MAXITER));

        if (lp.phi > M_PI_2)

            lp.phi -=

                2. * (lp.phi -

                      M_PI_2); /* correct if symmetrical solution for Aitoff */

        if (lp.phi < -M_PI_2)

            lp.phi -=

                2. * (lp.phi +

                      M_PI_2); /* correct if symmetrical solution for Aitoff */

        /* calculate x,y coordinates with solution obtained */

        if ((D = acos(cos(lp.phi) * cos(C = 0.5 * lp.lam))) !=

            0.0) { /* Aitoff */

            y = 1. / sin(D);

            x = 2. * D * cos(lp.phi) * sin(C) * y;

            y *= D * sin(lp.phi);

        } else

            x = y = 0.;

        if (Q->mode == pj_aitoff_ns::WINKEL_TRIPEL) {

            x = (x + lp.lam * Q->cosphi1) * 0.5;

            y = (y + lp.phi) * 0.5;

        }

        /* if too far from given values of x,y, repeat with better approximation

         * of phi,lam */

    } while (((fabs(xy.x - x) > EPSILON) || (fabs(xy.y - y) > EPSILON)) &&

             (round++ < MAXROUND));

    if (iter == MAXITER && round == MAXROUND) {

        proj_context_errno_set(

            P->ctx, PROJ_ERR_COORD_TRANSFM_OUTSIDE_PROJECTION_DOMAIN);

        /* fprintf(stderr, "Warning: Accuracy of 1e-12 not reached. Last

         * increments: dlat=%e and dlon=%e\n", dp, dl); */

    }

    return lp;

}

static PJ *pj_aitoff_setup(PJ *P) {

    P->inv = aitoff_s_inverse;

    P->fwd = aitoff_s_forward;

    P->es = 0.;

    return P;

}

PJ *PJ_PROJECTION(aitoff) {

    struct pj_aitoff_data *Q = static_cast<struct pj_aitoff_data *>(

        calloc(1, sizeof(struct pj_aitoff_data)));

    if (nullptr == Q)

        return pj_default_destructor(P, PROJ_ERR_OTHER /*ENOMEM*/);

    P->opaque = Q;

    Q->mode = pj_aitoff_ns::AITOFF;

    return pj_aitoff_setup(P);

}

PJ *PJ_PROJECTION(wintri) {

    struct pj_aitoff_data *Q = static_cast<struct pj_aitoff_data *>(

        calloc(1, sizeof(struct pj_aitoff_data)));

    if (nullptr == Q)

        return pj_default_destructor(P, PROJ_ERR_OTHER /*ENOMEM*/);

    P->opaque = Q;

    Q->mode = pj_aitoff_ns::WINKEL_TRIPEL;

    if (pj_param(P->ctx, P->params, "tlat_1").i) {

        if ((Q->cosphi1 = cos(pj_param(P->ctx, P->params, "rlat_1").f)) == 0.) {

            proj_log_error(

                P, _("Invalid value for lat_1: |lat_1| should be < 90°"));

            return pj_default_destructor(P,

                                         PROJ_ERR_INVALID_OP_ILLEGAL_ARG_VALUE);

        }

    } else /* 50d28' or acos(2/pi) */

        Q->cosphi1 = 0.636619772367581343;

    return pj_aitoff_setup(P);

}