/*

 *                   Transverse Mercator implementations

 *

 * In this file two transverse mercator implementations are found. One of Gerald

 * Evenden/John Snyder origin and one of Knud Poder/Karsten Engsager origin. The

 * former is regarded as "approximate" in the following and the latter is

 * "exact". This word choice has been made to distinguish between the two

 * algorithms, where the Evenden/Snyder implementation is the faster, less

 * accurate implementation and the Poder/Engsager algorithm is a slightly

 * slower, but more accurate implementation.

 */

#include <errno.h>

#include <math.h>

#include "proj.h"

#include "proj_internal.h"

#include <math.h>

PROJ_HEAD(tmerc, "Transverse Mercator") "\n\tCyl, Sph&Ell\n\tapprox";

PROJ_HEAD(etmerc, "Extended Transverse Mercator") "\n\tCyl, Sph";

PROJ_HEAD(utm, "Universal Transverse Mercator (UTM)")

"\n\tCyl, Ell\n\tzone= south approx";

namespace { // anonymous namespace

// Approximate: Evenden/Snyder

struct EvendenSnyder {

    double esp;

    double ml0;

    double *en;

};

// More exact: Poder/Engsager

struct PoderEngsager {

    double Qn;     /* Merid. quad., scaled to the projection */

    double Zb;     /* Radius vector in polar coord. systems  */

    double cgb[6]; /* Constants for Gauss -> Geo lat */

    double cbg[6]; /* Constants for Geo lat -> Gauss */

    double utg[6]; /* Constants for transv. merc. -> geo */

    double gtu[6]; /* Constants for geo -> transv. merc. */

};

struct tmerc_data {

    EvendenSnyder approx;

    PoderEngsager exact;

};

} // anonymous namespace

/* Constants for "approximate" transverse mercator */

#define EPS10 1.e-10

#define FC1 1.

#define FC2 .5

#define FC3 .16666666666666666666

#define FC4 .08333333333333333333

#define FC5 .05

#define FC6 .03333333333333333333

#define FC7 .02380952380952380952

#define FC8 .01785714285714285714

/* Constant for "exact" transverse mercator */

#define PROJ_ETMERC_ORDER 6

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

//

//                  Approximate Transverse Mercator functions

//

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

static PJ_XY approx_e_fwd(PJ_LP lp, PJ *P) {

    PJ_XY xy = {0.0, 0.0};

    const auto *Q = &(static_cast<struct tmerc_data *>(P->opaque)->approx);

    double al, als, n, cosphi, sinphi, t;

    /*

     * Fail if our longitude is more than 90 degrees from the

     * central meridian since the results are essentially garbage.

     * Is error -20 really an appropriate return value?

     *

     *  http://trac.osgeo.org/proj/ticket/5

     */

    if (lp.lam < -M_HALFPI || lp.lam > M_HALFPI) {

        xy.x = HUGE_VAL;

        xy.y = HUGE_VAL;

        proj_context_errno_set(

            P->ctx, PROJ_ERR_COORD_TRANSFM_OUTSIDE_PROJECTION_DOMAIN);

        return xy;

    }

    sinphi = sin(lp.phi);

    cosphi = cos(lp.phi);

    t = fabs(cosphi) > 1e-10 ? sinphi / cosphi : 0.;

    t *= t;

    al = cosphi * lp.lam;

    als = al * al;

    al /= sqrt(1. - P->es * sinphi * sinphi);

    n = Q->esp * cosphi * cosphi;

    xy.x = P->k0 * al *

           (FC1 + FC3 * als *

                      (1. - t + n +

                       FC5 * als *

                           (5. + t * (t - 18.) + n * (14. - 58. * t) +

                            FC7 * als * (61. + t * (t * (179. - t) - 479.)))));

    xy.y =

        P->k0 *

        (pj_mlfn(lp.phi, sinphi, cosphi, Q->en) - Q->ml0 +

         sinphi * al * lp.lam * FC2 *

             (1. +

              FC4 * als *

                  (5. - t + n * (9. + 4. * n) +

                   FC6 * als *

                       (61. + t * (t - 58.) + n * (270. - 330 * t) +

                        FC8 * als * (1385. + t * (t * (543. - t) - 3111.))))));

    return (xy);

}

static PJ_XY tmerc_spherical_fwd(PJ_LP lp, PJ *P) {

    PJ_XY xy = {0.0, 0.0};

    double b, cosphi;

    const auto *Q = &(static_cast<struct tmerc_data *>(P->opaque)->approx);

    cosphi = cos(lp.phi);

    b = cosphi * sin(lp.lam);

    if (fabs(fabs(b) - 1.) <= EPS10) {

        proj_errno_set(P, PROJ_ERR_COORD_TRANSFM_OUTSIDE_PROJECTION_DOMAIN);

        return xy;

    }

    xy.x = Q->ml0 * log((1. + b) / (1. - b));

    xy.y = cosphi * cos(lp.lam) / sqrt(1. - b * b);

    b = fabs(xy.y);

    if (cosphi == 1 && (lp.lam < -M_HALFPI || lp.lam > M_HALFPI)) {

        /* Helps to be able to roundtrip |longitudes| > 90 at lat=0 */

        /* We could also map to -M_PI ... */

        xy.y = M_PI;

    } else if (b >= 1.) {

        if ((b - 1.) > EPS10) {

            proj_errno_set(P, PROJ_ERR_COORD_TRANSFM_OUTSIDE_PROJECTION_DOMAIN);

            return xy;

        } else

            xy.y = 0.;

    } else

        xy.y = acos(xy.y);

    if (lp.phi < 0.)

        xy.y = -xy.y;

    xy.y = Q->esp * (xy.y - P->phi0);

    return xy;

}

static PJ_LP approx_e_inv(PJ_XY xy, PJ *P) {

    PJ_LP lp = {0.0, 0.0};

    const auto *Q = &(static_cast<struct tmerc_data *>(P->opaque)->approx);

    lp.phi = pj_inv_mlfn(Q->ml0 + xy.y / P->k0, Q->en);

    if (fabs(lp.phi) >= M_HALFPI) {

        lp.phi = xy.y < 0. ? -M_HALFPI : M_HALFPI;

        lp.lam = 0.;

    } else {

        double sinphi = sin(lp.phi), cosphi = cos(lp.phi);

        double t = fabs(cosphi) > 1e-10 ? sinphi / cosphi : 0.;

        const double n = Q->esp * cosphi * cosphi;

        double con = 1. - P->es * sinphi * sinphi;

        const double d = xy.x * sqrt(con) / P->k0;

        con *= t;

        t *= t;

        const double ds = d * d;

        lp.phi -=

            (con * ds / (1. - P->es)) * FC2 *

            (1. -

             ds * FC4 *

                 (5. + t * (3. - 9. * n) + n * (1. - 4 * n) -

                  ds * FC6 *

                      (61. + t * (90. - 252. * n + 45. * t) + 46. * n -

                       ds * FC8 *

                           (1385. + t * (3633. + t * (4095. + 1575. * t))))));

        lp.lam = d *

                 (FC1 -

                  ds * FC3 *

                      (1. + 2. * t + n -

                       ds * FC5 *

                           (5. + t * (28. + 24. * t + 8. * n) + 6. * n -

                            ds * FC7 *

                                (61. + t * (662. + t * (1320. + 720. * t)))))) /

                 cosphi;

    }

    return lp;

}

static PJ_LP tmerc_spherical_inv(PJ_XY xy, PJ *P) {

    PJ_LP lp = {0.0, 0.0};

    double h, g;

    const auto *Q = &(static_cast<struct tmerc_data *>(P->opaque)->approx);

    h = exp(xy.x / Q->esp);

    if (h == 0) {

        proj_errno_set(P, PROJ_ERR_COORD_TRANSFM_OUTSIDE_PROJECTION_DOMAIN);

        return proj_coord_error().lp;

    }

    g = .5 * (h - 1. / h);

    /* D, as in equation 8-8 of USGS "Map Projections - A Working Manual" */

    const double D = P->phi0 + xy.y / Q->esp;

    h = cos(D);

    lp.phi = asin(sqrt((1. - h * h) / (1. + g * g)));

    /* Make sure that phi is on the correct hemisphere when false northing is

     * used

     */

    lp.phi = copysign(lp.phi, D);

    lp.lam = (g != 0.0 || h != 0.0) ? atan2(g, h) : 0.;

    return lp;

}

static PJ *destructor(PJ *P, int errlev) {

    if (nullptr == P)

        return nullptr;

    if (nullptr == P->opaque)

        return pj_default_destructor(P, errlev);

    free(static_cast<struct tmerc_data *>(P->opaque)->approx.en);

    return pj_default_destructor(P, errlev);

}

static PJ *setup_approx(PJ *P) {

    auto *Q = &(static_cast<struct tmerc_data *>(P->opaque)->approx);

    if (P->es != 0.0) {

        if (!(Q->en = pj_enfn(P->n)))

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

        Q->ml0 = pj_mlfn(P->phi0, sin(P->phi0), cos(P->phi0), Q->en);

        Q->esp = P->es / (1. - P->es);

    } else {

        Q->esp = P->k0;

        Q->ml0 = .5 * Q->esp;

    }

    return P;

}

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

//

//                  Exact Transverse Mercator functions

//

//

// The code in this file is largly based upon procedures:

//

// Written by: Knud Poder and Karsten Engsager

//

// Based on math from: R.Koenig and K.H. Weise, "Mathematische

// Grundlagen der hoeheren Geodaesie und Kartographie,

// Springer-Verlag, Berlin/Goettingen" Heidelberg, 1951.

//

// Modified and used here by permission of Reference Networks

// Division, Kort og Matrikelstyrelsen (KMS), Copenhagen, Denmark

//

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

/* Complex Clenshaw summation */

inline static double clenS(const double *a, int size, double sin_arg_r,

                           double cos_arg_r, double sinh_arg_i,

                           double cosh_arg_i, double *R, double *I) {

    double r, i, hr, hr1, hr2, hi, hi1, hi2;

    /* arguments */

    const double *p = a + size;

    r = 2 * cos_arg_r * cosh_arg_i;

    i = -2 * sin_arg_r * sinh_arg_i;

    /* summation loop */

    hi1 = hr1 = hi = 0;

    hr = *--p;

    for (; a - p;) {

        hr2 = hr1;

        hi2 = hi1;

        hr1 = hr;

        hi1 = hi;

        hr = -hr2 + r * hr1 - i * hi1 + *--p;

        hi = -hi2 + i * hr1 + r * hi1;

    }

    r = sin_arg_r * cosh_arg_i;

    i = cos_arg_r * sinh_arg_i;

    *R = r * hr - i * hi;

    *I = r * hi + i * hr;

    return *R;

}

/* Ellipsoidal, forward */

static PJ_XY exact_e_fwd(PJ_LP lp, PJ *P) {

    PJ_XY xy = {0.0, 0.0};

    const auto *Q = &(static_cast<struct tmerc_data *>(P->opaque)->exact);

    /* ell. LAT, LNG -> Gaussian LAT, LNG */

    double Cn = pj_auxlat_convert(lp.phi, Q->cbg, PROJ_ETMERC_ORDER);

    /* Gaussian LAT, LNG -> compl. sph. LAT */

    const double sin_Cn = sin(Cn);

    const double cos_Cn = cos(Cn);

    const double sin_Ce = sin(lp.lam);

    const double cos_Ce = cos(lp.lam);

    const double cos_Cn_cos_Ce = cos_Cn * cos_Ce;

    Cn = atan2(sin_Cn, cos_Cn_cos_Ce);

    const double inv_denom_tan_Ce = 1. / hypot(sin_Cn, cos_Cn_cos_Ce);

    const double tan_Ce = sin_Ce * cos_Cn * inv_denom_tan_Ce;

#if 0

    // Variant of the above: found not to be measurably faster

    const double sin_Ce_cos_Cn = sin_Ce*cos_Cn;

    const double denom = sqrt(1 - sin_Ce_cos_Cn * sin_Ce_cos_Cn);

    const double tan_Ce = sin_Ce_cos_Cn / denom;

#endif

    /* compl. sph. N, E -> ell. norm. N, E */

    double Ce = asinh(tan_Ce); /* Replaces: Ce  = log(tan(FORTPI + Ce*0.5)); */

    /*

     *  Non-optimized version:

     *  const double sin_arg_r  = sin(2*Cn);

     *  const double cos_arg_r  = cos(2*Cn);

     *

     *  Given:

     *      sin(2 * Cn) = 2 sin(Cn) cos(Cn)

     *          sin(atan(y)) = y / sqrt(1 + y^2)

     *          cos(atan(y)) = 1 / sqrt(1 + y^2)

     *      ==> sin(2 * Cn) = 2 tan_Cn / (1 + tan_Cn^2)

     *

     *      cos(2 * Cn) = 2cos^2(Cn) - 1

     *                  = 2 / (1 + tan_Cn^2) - 1

     */

    const double two_inv_denom_tan_Ce = 2 * inv_denom_tan_Ce;

    const double two_inv_denom_tan_Ce_square =

        two_inv_denom_tan_Ce * inv_denom_tan_Ce;

    const double tmp_r = cos_Cn_cos_Ce * two_inv_denom_tan_Ce_square;

    const double sin_arg_r = sin_Cn * tmp_r;

    const double cos_arg_r = cos_Cn_cos_Ce * tmp_r - 1;

    /*

     *  Non-optimized version:

     *  const double sinh_arg_i = sinh(2*Ce);

     *  const double cosh_arg_i = cosh(2*Ce);

     *

     *  Given

     *      sinh(2 * Ce) = 2 sinh(Ce) cosh(Ce)

     *          sinh(asinh(y)) = y

     *          cosh(asinh(y)) = sqrt(1 + y^2)

     *      ==> sinh(2 * Ce) = 2 tan_Ce sqrt(1 + tan_Ce^2)

     *

     *      cosh(2 * Ce) = 2cosh^2(Ce) - 1

     *                   = 2 * (1 + tan_Ce^2) - 1

     *

     * and 1+tan_Ce^2 = 1 + sin_Ce^2 * cos_Cn^2 / (sin_Cn^2 + cos_Cn^2 *

     * cos_Ce^2) = (sin_Cn^2 + cos_Cn^2 * cos_Ce^2 + sin_Ce^2 * cos_Cn^2) /

     * (sin_Cn^2 + cos_Cn^2 * cos_Ce^2) = 1. / (sin_Cn^2 + cos_Cn^2 * cos_Ce^2)

     * = inv_denom_tan_Ce^2

     *

     */

    const double sinh_arg_i = tan_Ce * two_inv_denom_tan_Ce;

    const double cosh_arg_i = two_inv_denom_tan_Ce_square - 1;

    double dCn, dCe;

    Cn += clenS(Q->gtu, PROJ_ETMERC_ORDER, sin_arg_r, cos_arg_r, sinh_arg_i,

                cosh_arg_i, &dCn, &dCe);

    Ce += dCe;

    if (fabs(Ce) <= 2.623395162778) {

        xy.y = Q->Qn * Cn + Q->Zb; /* Northing */

        xy.x = Q->Qn * Ce;         /* Easting  */

    } else {

        proj_errno_set(P, PROJ_ERR_COORD_TRANSFM_OUTSIDE_PROJECTION_DOMAIN);

        xy.x = xy.y = HUGE_VAL;

    }

    return xy;

}

/* Ellipsoidal, inverse */

static PJ_LP exact_e_inv(PJ_XY xy, PJ *P) {

    PJ_LP lp = {0.0, 0.0};

    const auto *Q = &(static_cast<struct tmerc_data *>(P->opaque)->exact);

    /* normalize N, E */

    double Cn = (xy.y - Q->Zb) / Q->Qn;

    double Ce = xy.x / Q->Qn;

    if (fabs(Ce) <= 2.623395162778) { /* 150 degrees */

        /* norm. N, E -> compl. sph. LAT, LNG */

        const double sin_arg_r = sin(2 * Cn);

        const double cos_arg_r = cos(2 * Cn);

        // const double sinh_arg_i = sinh(2*Ce);

        // const double cosh_arg_i = cosh(2*Ce);

        const double exp_2_Ce = exp(2 * Ce);

        const double half_inv_exp_2_Ce = 0.5 / exp_2_Ce;

        const double sinh_arg_i = 0.5 * exp_2_Ce - half_inv_exp_2_Ce;

        const double cosh_arg_i = 0.5 * exp_2_Ce + half_inv_exp_2_Ce;

        double dCn_ignored, dCe;

        Cn += clenS(Q->utg, PROJ_ETMERC_ORDER, sin_arg_r, cos_arg_r, sinh_arg_i,

                    cosh_arg_i, &dCn_ignored, &dCe);

        Ce += dCe;

        /* compl. sph. LAT -> Gaussian LAT, LNG */

        const double sin_Cn = sin(Cn);

        const double cos_Cn = cos(Cn);

#if 0

        // Non-optimized version:

        double sin_Ce, cos_Ce;

        Ce = atan (sinh (Ce));  // Replaces: Ce = 2*(atan(exp(Ce)) - FORTPI);

        sin_Ce = sin (Ce);

        cos_Ce = cos (Ce);

        Ce     = atan2 (sin_Ce, cos_Ce*cos_Cn);

        Cn     = atan2 (sin_Cn*cos_Ce,  hypot (sin_Ce, cos_Ce*cos_Cn));

#else

        /*

         *      One can divide both member of Ce = atan2(...) by cos_Ce, which

         * gives: Ce     = atan2 (tan_Ce, cos_Cn) = atan2(sinh(Ce), cos_Cn)

         *

         *      and the same for Cn = atan2(...)

         *      Cn     = atan2 (sin_Cn, hypot (sin_Ce, cos_Ce*cos_Cn)/cos_Ce)

         *             = atan2 (sin_Cn, hypot (sin_Ce/cos_Ce, cos_Cn))

         *             = atan2 (sin_Cn, hypot (tan_Ce, cos_Cn))

         *             = atan2 (sin_Cn, hypot (sinhCe, cos_Cn))

         */

        const double sinhCe = sinh(Ce);

        Ce = atan2(sinhCe, cos_Cn);

        const double modulus_Ce = hypot(sinhCe, cos_Cn),

          rr = hypot(sin_Cn, modulus_Ce);

        Cn = atan2(sin_Cn, modulus_Ce);

#endif

        /* Gaussian LAT, LNG -> ell. LAT, LNG */

        lp.phi = pj_auxlat_convert(Cn, sin_Cn/rr, modulus_Ce/rr,

                                   Q->cgb, PROJ_ETMERC_ORDER);

        lp.lam = Ce;

    } else {

        proj_errno_set(P, PROJ_ERR_COORD_TRANSFM_OUTSIDE_PROJECTION_DOMAIN);

        lp.phi = lp.lam = HUGE_VAL;

    }

    return lp;

}

static PJ *setup_exact(PJ *P) {

    auto *Q = &(static_cast<struct tmerc_data *>(P->opaque)->exact);

    assert(P->es > 0);

    static_assert( PROJ_ETMERC_ORDER == int(AuxLat::ORDER),

                   "Inconsistent orders etmerc vs auxorder" );

    /* third flattening */

    const double n = P->n;

    // N.B., Engsager and Poder terminology (simplifying a little here...)

    //   geodetic coordinates = geographic latitude

    //   Soldner sphere + complex gaussian coordinates = conformal latitude

    //   transverse Mercator coordinates = rectifying latitude

    /* COEF. OF TRIG SERIES GEO <-> GAUSS */

    /* cgb := Gaussian -> Geodetic, KW p190 - 191 (61) - (62) */

    /* cbg := Geodetic -> Gaussian, KW p186 - 187 (51) - (52) */

    /* PROJ_ETMERC_ORDER = 6th degree : Engsager and Poder: ICC2007 */

    pj_auxlat_coeffs(n, AuxLat::CONFORMAL, AuxLat::GEOGRAPHIC, Q->cgb);

    pj_auxlat_coeffs(n, AuxLat::GEOGRAPHIC, AuxLat::CONFORMAL, Q->cbg);

    /* Constants of the projections */

    /* Transverse Mercator (UTM, ITM, etc) */

    /* Norm. mer. quad, K&W p.50 (96), p.19 (38b), p.5 (2) */

    Q->Qn = P->k0 * pj_rectifying_radius(n);

    /* coef of trig series */

    /* utg := ell. N, E -> sph. N, E,  KW p194 (65) */

    /* gtu := sph. N, E -> ell. N, E,  KW p196 (69) */

    pj_auxlat_coeffs(n, AuxLat::RECTIFYING, AuxLat::CONFORMAL, Q->utg);

    pj_auxlat_coeffs(n, AuxLat::CONFORMAL, AuxLat::RECTIFYING, Q->gtu);

    /* Gaussian latitude value of the origin latitude */

    const double Z = pj_auxlat_convert(P->phi0, Q->cbg, PROJ_ETMERC_ORDER);

    /* Origin northing minus true northing at the origin latitude */

    /* i.e. true northing = N - P->Zb                         */

    Q->Zb = -Q->Qn * pj_auxlat_convert(Z, Q->gtu, PROJ_ETMERC_ORDER);

    return P;

}

static PJ_XY auto_e_fwd(PJ_LP lp, PJ *P) {

    if (fabs(lp.lam) > 3 * DEG_TO_RAD)

        return exact_e_fwd(lp, P);

    else

        return approx_e_fwd(lp, P);

}

static PJ_LP auto_e_inv(PJ_XY xy, PJ *P) {

    // For k = 1 and long = 3 (from central meridian),

    // At lat = 0, we get x ~= 0.052, y = 0

    // At lat = 90, we get x = 0, y ~= 1.57

    // And the shape of this x=f(y) frontier curve is very very roughly a

    // parabola. Hence:

    if (fabs(xy.x) > 0.053 - 0.022 * xy.y * xy.y)

        return exact_e_inv(xy, P);

    else

        return approx_e_inv(xy, P);

}

static PJ *setup(PJ *P, TMercAlgo eAlg) {

    struct tmerc_data *Q =

        static_cast<struct tmerc_data *>(calloc(1, sizeof(struct tmerc_data)));

    if (nullptr == Q)

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

    P->opaque = Q;

    if (P->es == 0)

        eAlg = TMercAlgo::EVENDEN_SNYDER;

    switch (eAlg) {

    case TMercAlgo::EVENDEN_SNYDER: {

        P->destructor = destructor;

        if (!setup_approx(P))

            return nullptr;

        if (P->es == 0) {

            P->inv = tmerc_spherical_inv;

            P->fwd = tmerc_spherical_fwd;

        } else {

            P->inv = approx_e_inv;

            P->fwd = approx_e_fwd;

        }

        break;

    }

    case TMercAlgo::PODER_ENGSAGER: {

        setup_exact(P);

        P->inv = exact_e_inv;

        P->fwd = exact_e_fwd;

        break;

    }

    case TMercAlgo::AUTO: {

        P->destructor = destructor;

        if (!setup_approx(P))

            return nullptr;

        setup_exact(P);

        P->inv = auto_e_inv;

        P->fwd = auto_e_fwd;

        break;

    }

    }

    return P;

}

static bool getAlgoFromParams(PJ *P, TMercAlgo &algo) {

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

        algo = TMercAlgo::EVENDEN_SNYDER;

        return true;

    }

    const char *algStr = pj_param(P->ctx, P->params, "salgo").s;

    if (algStr) {

        if (strcmp(algStr, "evenden_snyder") == 0) {

            algo = TMercAlgo::EVENDEN_SNYDER;

            return true;

        }

        if (strcmp(algStr, "poder_engsager") == 0) {

            algo = TMercAlgo::PODER_ENGSAGER;

            return true;

        }

        if (strcmp(algStr, "auto") == 0) {

            algo = TMercAlgo::AUTO;

            // Don't return so that we can run a later validity check

        } else {

            proj_log_error(P, "unknown value for +algo");

            return false;

        }

    } else {

        pj_load_ini(P->ctx); // if not already done

        proj_context_errno_set(

            P->ctx,

            0); // reset error in case proj.ini couldn't be found

        algo = P->ctx->defaultTmercAlgo;

    }

    // We haven't worked on the criterion on inverse transformation

    // when phi0 != 0 or if k0 is not close to 1 or for very oblate

    // ellipsoid (es > 0.1 is ~ rf < 200)

    if (algo == TMercAlgo::AUTO &&

        (P->es > 0.1 || P->phi0 != 0 || fabs(P->k0 - 1) > 0.01)) {

        algo = TMercAlgo::PODER_ENGSAGER;

    }

    return true;

}

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

//

//                                Operation Setups

//

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

PJ *PJ_PROJECTION(tmerc) {

    /* exact transverse mercator only exists in ellipsoidal form, */

    /* use approximate version if +a sphere is requested          */

    TMercAlgo algo;

    if (!getAlgoFromParams(P, algo)) {

        proj_log_error(P, _("Invalid value for algo"));

        return pj_default_destructor(P, PROJ_ERR_INVALID_OP_ILLEGAL_ARG_VALUE);

    }

    return setup(P, algo);

}

PJ *PJ_PROJECTION(etmerc) {

    if (P->es == 0.0) {

        proj_log_error(

            P, _("Invalid value for eccentricity: it should not be zero"));

        return pj_default_destructor(P, PROJ_ERR_INVALID_OP_ILLEGAL_ARG_VALUE);

    }

    return setup(P, TMercAlgo::PODER_ENGSAGER);

}

/* UTM uses the Poder/Engsager implementation for the underlying projection */

/* UNLESS +approx is set in which case the Evenden/Snyder implementation is

 * used. */

PJ *PJ_PROJECTION(utm) {

    long zone;

    if (P->es == 0.0) {

        proj_log_error(

            P, _("Invalid value for eccentricity: it should not be zero"));

        return pj_default_destructor(P, PROJ_ERR_INVALID_OP_ILLEGAL_ARG_VALUE);

    }

    if (P->lam0 < -1000.0 || P->lam0 > 1000.0) {

        proj_log_error(P, _("Invalid value for lon_0"));

        return pj_default_destructor(P, PROJ_ERR_INVALID_OP_ILLEGAL_ARG_VALUE);

    }

    P->y0 = pj_param(P->ctx, P->params, "bsouth").i ? 10000000. : 0.;

    P->x0 = 500000.;

    if (pj_param(P->ctx, P->params, "tzone").i) /* zone input ? */

    {

        zone = pj_param(P->ctx, P->params, "izone").i;

        if (zone > 0 && zone <= 60)

            --zone;

        else {

            proj_log_error(P, _("Invalid value for zone"));

            return pj_default_destructor(P,

                                         PROJ_ERR_INVALID_OP_ILLEGAL_ARG_VALUE);

        }

    } else /* nearest central meridian input */

    {

        zone = lround((floor((adjlon(P->lam0) + M_PI) * 30. / M_PI)));

        if (zone < 0)

            zone = 0;

        else if (zone >= 60)

            zone = 59;

    }

    P->lam0 = (zone + .5) * M_PI / 30. - M_PI;

    P->k0 = 0.9996;

    P->phi0 = 0.;

    TMercAlgo algo;

    if (!getAlgoFromParams(P, algo)) {

        proj_log_error(P, _("Invalid value for algo"));

        return pj_default_destructor(P, PROJ_ERR_INVALID_OP_ILLEGAL_ARG_VALUE);

    }

    return setup(P, algo);

}