#include "proj.h"

#include "proj_internal.h"

#include <errno.h>

#include <math.h>

PROJ_HEAD(tpeqd, "Two Point Equidistant")

"\n\tMisc Sph\n\tlat_1= lon_1= lat_2= lon_2=";

namespace { // anonymous namespace

struct pj_tpeqd {

    double cp1, sp1, cp2, sp2, ccs, cs, sc, r2z0, z02, dlam2;

    double hz0, thz0, rhshz0, ca, sa, lp, lamc;

};

} // anonymous namespace

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

    PJ_XY xy = {0.0, 0.0};

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

    double t, z1, z2, dl1, dl2, sp, cp;

    sp = sin(lp.phi);

    cp = cos(lp.phi);

    z1 =

        aacos(P->ctx, Q->sp1 * sp + Q->cp1 * cp * cos(dl1 = lp.lam + Q->dlam2));

    z2 =

        aacos(P->ctx, Q->sp2 * sp + Q->cp2 * cp * cos(dl2 = lp.lam - Q->dlam2));

    z1 *= z1;

    z2 *= z2;

    t = z1 - z2;

    xy.x = Q->r2z0 * t;

    t = Q->z02 - t;

    xy.y = Q->r2z0 * asqrt(4. * Q->z02 * z2 - t * t);

    if ((Q->ccs * sp - cp * (Q->cs * sin(dl1) - Q->sc * sin(dl2))) < 0.)

        xy.y = -xy.y;

    return xy;

}

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

    PJ_LP lp = {0.0, 0.0};

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

    double cz1, cz2, s, d, cp, sp;

    cz1 = cos(hypot(xy.y, xy.x + Q->hz0));

    cz2 = cos(hypot(xy.y, xy.x - Q->hz0));

    s = cz1 + cz2;

    d = cz1 - cz2;

    lp.lam = -atan2(d, (s * Q->thz0));

    lp.phi = aacos(P->ctx, hypot(Q->thz0 * s, d) * Q->rhshz0);

    if (xy.y < 0.)

        lp.phi = -lp.phi;

    /* lam--phi now in system relative to P1--P2 base equator */

    sp = sin(lp.phi);

    cp = cos(lp.phi);

    lp.lam -= Q->lp;

    s = cos(lp.lam);

    lp.phi = aasin(P->ctx, Q->sa * sp + Q->ca * cp * s);

    lp.lam = atan2(cp * sin(lp.lam), Q->sa * cp * s - Q->ca * sp) + Q->lamc;

    return lp;

}

PJ *PJ_PROJECTION(tpeqd) {

    double lam_1, lam_2, phi_1, phi_2, A12;

    struct pj_tpeqd *Q =

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

    if (nullptr == Q)

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

    P->opaque = Q;

    /* get control point locations */

    phi_1 = pj_param(P->ctx, P->params, "rlat_1").f;

    lam_1 = pj_param(P->ctx, P->params, "rlon_1").f;

    phi_2 = pj_param(P->ctx, P->params, "rlat_2").f;

    lam_2 = pj_param(P->ctx, P->params, "rlon_2").f;

    if (phi_1 == phi_2 && lam_1 == lam_2) {

        proj_log_error(P, _("Invalid value for lat_1/lon_1/lat_2/lon_2: the 2 "

                            "points should be distinct."));

        return pj_default_destructor(P, PROJ_ERR_INVALID_OP_ILLEGAL_ARG_VALUE);

    }

    P->lam0 = adjlon(0.5 * (lam_1 + lam_2));

    Q->dlam2 = adjlon(lam_2 - lam_1);

    Q->cp1 = cos(phi_1);

    Q->cp2 = cos(phi_2);

    Q->sp1 = sin(phi_1);

    Q->sp2 = sin(phi_2);

    Q->cs = Q->cp1 * Q->sp2;

    Q->sc = Q->sp1 * Q->cp2;

    Q->ccs = Q->cp1 * Q->cp2 * sin(Q->dlam2);

    const auto SQ = [](double x) { return x * x; };

    // Numerically stable formula for computing the central angle from

    // (phi_1, lam_1) to (phi_2, lam_2).

    // Special case of Vincenty formula on the sphere.

    // https://en.wikipedia.org/wiki/Great-circle_distance#Computational_formulae

    const double cs_minus_sc_cos_dlam = Q->cs - Q->sc * cos(Q->dlam2);

    Q->z02 = atan2(sqrt(SQ(Q->cp2 * sin(Q->dlam2)) + SQ(cs_minus_sc_cos_dlam)),

                   Q->sp1 * Q->sp2 + Q->cp1 * Q->cp2 * cos(Q->dlam2));

    if (Q->z02 == 0.0) {

        // Actually happens when both lat_1 = lat_2 and |lat_1| = 90

        proj_log_error(P, _("Invalid value for lat_1 and lat_2: their absolute "

                            "value should be < 90°."));

        return pj_default_destructor(P, PROJ_ERR_INVALID_OP_ILLEGAL_ARG_VALUE);

    }

    Q->hz0 = .5 * Q->z02;

    A12 = atan2(Q->cp2 * sin(Q->dlam2), cs_minus_sc_cos_dlam);

    const double pp = aasin(P->ctx, Q->cp1 * sin(A12));

    Q->ca = cos(pp);

    Q->sa = sin(pp);

    Q->lp = adjlon(atan2(Q->cp1 * cos(A12), Q->sp1) - Q->hz0);

    Q->dlam2 *= .5;

    Q->lamc = M_HALFPI - atan2(sin(A12) * Q->sp1, cos(A12)) - Q->dlam2;

    Q->thz0 = tan(Q->hz0);

    Q->rhshz0 = .5 / sin(Q->hz0);

    Q->r2z0 = 0.5 / Q->z02;

    Q->z02 *= Q->z02;

    P->inv = tpeqd_s_inverse;

    P->fwd = tpeqd_s_forward;

    P->es = 0.;

    return P;

}