/******************************************************************************
 * Project:  PROJ.4
 * Purpose:  Implementation of the nzmg (New Zealand Map Grid) projection.
 *           Very loosely based upon DMA code by Bradford W. Drew
 * Author:   Gerald Evenden
 *
 ******************************************************************************
 * 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.
 *****************************************************************************/
#define PJ_LIB__

#include <math.h>

#include "proj.h"
#include "proj_internal.h"

PROJ_HEAD(nzmg, "New Zealand Map Grid") "\n\tfixed Earth";

#define EPSLN 1e-10
#define SEC5_TO_RAD 0.4848136811095359935899141023
#define RAD_TO_SEC5 2.062648062470963551564733573

static const COMPLEX bf[] = {
    { .7557853228, 0.0},
    { .249204646,  0.003371507},
    {-.001541739,  0.041058560},
    {-.10162907,   0.01727609},
    {-.26623489,  -0.36249218},
    {-.6870983,   -1.1651967} };

static const double tphi[] = { 1.5627014243, .5185406398, -.03333098,
                               -.1052906,   -.0368594,     .007317,
                                .01220,      .00394,      -.0013 };

static const double tpsi[] = { .6399175073, -.1358797613, .063294409, -.02526853, .0117879,
                              -.0055161,     .0026906,   -.001333,     .00067,   -.00034 };

#define Nbf 5
#define Ntpsi 9
#define Ntphi 8


static PJ_XY nzmg_e_forward (PJ_LP lp, PJ *P) {          /* Ellipsoidal, forward */
    PJ_XY xy = {0.0,0.0};
    COMPLEX p;
    const double *C;
    int i;

    lp.phi = (lp.phi - P->phi0) * RAD_TO_SEC5;
    for (p.r = *(C = tpsi + (i = Ntpsi)); i ; --i)
        p.r = *--C + lp.phi * p.r;
    p.r *= lp.phi;
    p.i = lp.lam;
    p = pj_zpoly1(p, bf, Nbf);
    xy.x = p.i;
    xy.y = p.r;

    return xy;
}


static PJ_LP nzmg_e_inverse (PJ_XY xy, PJ *P) {          /* Ellipsoidal, inverse */
    PJ_LP lp = {0.0,0.0};
    int nn, i;
    COMPLEX p, f, fp, dp;
    double den;
    const double *C;

    p.r = xy.y;
    p.i = xy.x;
    for (nn = 20; nn ;--nn) {
        f = pj_zpolyd1(p, bf, Nbf, &fp);
        f.r -= xy.y;
        f.i -= xy.x;
        den = fp.r * fp.r + fp.i * fp.i;
        p.r += dp.r = -(f.r * fp.r + f.i * fp.i) / den;
        p.i += dp.i = -(f.i * fp.r - f.r * fp.i) / den;
        if ((fabs(dp.r) + fabs(dp.i)) <= EPSLN)
            break;
    }
    if (nn) {
        lp.lam = p.i;
        for (lp.phi = *(C = tphi + (i = Ntphi)); i ; --i)
            lp.phi = *--C + p.r * lp.phi;
        lp.phi = P->phi0 + p.r * lp.phi * SEC5_TO_RAD;
    } else
        lp.lam = lp.phi = HUGE_VAL;

    return lp;
}


PJ *PROJECTION(nzmg) {
    /* force to International major axis */
    P->ra = 1. / (P->a = 6378388.0);
    P->lam0 = DEG_TO_RAD * 173.;
    P->phi0 = DEG_TO_RAD * -41.;
    P->x0 = 2510000.;
    P->y0 = 6023150.;

    P->inv = nzmg_e_inverse;
    P->fwd = nzmg_e_forward;


    return P;
}
