src/projections/aitoff.cpp

/******************************************************************************
 * 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
 *
 ******************************************************************************
 * 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 <errno.h>
#include <math.h>

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


namespace { // anonymous namespace
enum Mode {
    AITOFF = 0,
    WINKEL_TRIPEL = 1
};
} // anonymous namespace

namespace { // anonymous namespace
struct pj_opaque {
    double  cosphi1;
    enum 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_opaque *Q = static_cast<struct pj_opaque*>(P->opaque);
    double c, d;

    c = 0.5 * lp.lam;
    d = acos(cos(lp.phi) * cos(c));
    if(d != 0.0) {/* basic Aitoff */
        xy.x = 2. * d * cos(lp.phi) * sin(c) * (xy.y = 1. / sin(d));
        xy.y *= d * sin(lp.phi);
    } else
        xy.x = xy.y = 0.;
    if (Q->mode == WINKEL_TRIPEL) {
        xy.x = (xy.x + lp.lam * Q->cosphi1) * 0.5;
        xy.y = (xy.y + lp.phi) * 0.5;
    }
    return (xy);
}

/***********************************************************************************
*
* Inverse functions added by Drazen Tutic and Lovro Gradiser based on paper:
*
* I.Özbug Biklirici and Cengizhan Ipbüker. A General Algorithm for the Inverse
* Transformation of Map Projections Using Jacobian Matrices. In Proceedings of the
* Third International Symposium Mathematical & Computational Applications,
* pages 175{182, Turkey, September 2002.
*
* Expected accuracy is defined by EPSILON = 1e-12. Should be appropriate for
* most applications of Aitoff and Winkel Tripel projections.
*
* Longitudes of 180W and 180E can be mixed in solution obtained.
*
* Inverse for Aitoff projection in poles is undefined, longitude value of 0 is assumed.
*
* Contact : dtutic@geof.hr
* Date: 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_opaque *Q = static_cast<struct pj_opaque*>(P->opaque);
    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, PJD_ERR_NON_CONVERGENT);
                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 == 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 */
        if ((fabs(fabs(lp.phi) - M_PI_2) < EPSILON) && (Q->mode == AITOFF)) lp.lam = 0.; /* if pole in Aitoff, return longitude of 0 */

        /* 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 == 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)
    {
        pj_ctx_set_errno( P->ctx, PJD_ERR_NON_CONVERGENT );
        /* fprintf(stderr, "Warning: Accuracy of 1e-12 not reached. Last increments: dlat=%e and dlon=%e\n", dp, dl); */
    }

    return lp;
}


static PJ *setup(PJ *P) {
    P->inv = aitoff_s_inverse;
    P->fwd = aitoff_s_forward;
    P->es = 0.;
    return P;
}


PJ *PROJECTION(aitoff) {
    struct pj_opaque *Q = static_cast<struct pj_opaque*>(pj_calloc (1, sizeof (struct pj_opaque)));
    if (nullptr==Q)
        return pj_default_destructor(P, ENOMEM);
    P->opaque = Q;

    Q->mode = AITOFF;
    return setup(P);
}


PJ *PROJECTION(wintri) {
    struct pj_opaque *Q = static_cast<struct pj_opaque*>(pj_calloc (1, sizeof (struct pj_opaque)));
    if (nullptr==Q)
        return pj_default_destructor(P, ENOMEM);
    P->opaque = Q;

    Q->mode = 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.)
            return pj_default_destructor (P, PJD_ERR_LAT_LARGER_THAN_90);
    }
    else /* 50d28' or acos(2/pi) */
        Q->cosphi1 = 0.636619772367581343;
    return setup(P);
}