1 files changed, 132 insertions, 0 deletions
diff --git a/src/projections/labrd.cpp b/src/projections/labrd.cpp
new file mode 100644
index 00000000..d3930243
--- /dev/null
+++ b/src/projections/labrd.cpp
@@ -0,0 +1,132 @@
+#define PJ_LIB__
+
+#include <errno.h>
+#include <math.h>
+
+#include "projects.h"
+
+PROJ_HEAD(labrd, "Laborde") "\n\tCyl, Sph\n\tSpecial for Madagascar";
+#define EPS 1.e-10
+
+namespace { // anonymous namespace
+struct pj_opaque {
+    double  kRg, p0s, A, C, Ca, Cb, Cc, Cd;
+};
+} // anonymous namespace
+
+
+static XY e_forward (LP lp, PJ *P) {          /* Ellipsoidal, forward */
+    XY xy = {0.0,0.0};
+    struct pj_opaque *Q = static_cast<struct pj_opaque*>(P->opaque);
+    double V1, V2, ps, sinps, cosps, sinps2, cosps2;
+    double I1, I2, I3, I4, I5, I6, x2, y2, t;
+
+    V1 = Q->A * log( tan(M_FORTPI + .5 * lp.phi) );
+    t = P->e * sin(lp.phi);
+    V2 = .5 * P->e * Q->A * log ((1. + t)/(1. - t));
+    ps = 2. * (atan(exp(V1 - V2 + Q->C)) - M_FORTPI);
+    I1 = ps - Q->p0s;
+    cosps = cos(ps);    cosps2 = cosps * cosps;
+    sinps = sin(ps);    sinps2 = sinps * sinps;
+    I4 = Q->A * cosps;
+    I2 = .5 * Q->A * I4 * sinps;
+    I3 = I2 * Q->A * Q->A * (5. * cosps2 - sinps2) / 12.;
+    I6 = I4 * Q->A * Q->A;
+    I5 = I6 * (cosps2 - sinps2) / 6.;
+    I6 *= Q->A * Q->A *
+        (5. * cosps2 * cosps2 + sinps2 * (sinps2 - 18. * cosps2)) / 120.;
+    t = lp.lam * lp.lam;
+    xy.x = Q->kRg * lp.lam * (I4 + t * (I5 + t * I6));
+    xy.y = Q->kRg * (I1 + t * (I2 + t * I3));
+    x2 = xy.x * xy.x;
+    y2 = xy.y * xy.y;
+    V1 = 3. * xy.x * y2 - xy.x * x2;
+    V2 = xy.y * y2 - 3. * x2 * xy.y;
+    xy.x += Q->Ca * V1 + Q->Cb * V2;
+    xy.y += Q->Ca * V2 - Q->Cb * V1;
+    return xy;
+}
+
+
+static LP e_inverse (XY xy, PJ *P) {          /* Ellipsoidal, inverse */
+    LP lp = {0.0,0.0};
+    struct pj_opaque *Q = static_cast<struct pj_opaque*>(P->opaque);
+    /* t = 0.0 optimization is to avoid a false positive cppcheck warning */
+    /* (cppcheck git beaf29c15867984aa3c2a15cf15bd7576ccde2b3). Might no */
+    /* longer be necessary with later versions. */
+    double x2, y2, V1, V2, V3, V4, t = 0.0, t2, ps, pe, tpe, s;
+    double I7, I8, I9, I10, I11, d, Re;
+    int i;
+
+    x2 = xy.x * xy.x;
+    y2 = xy.y * xy.y;
+    V1 = 3. * xy.x * y2 - xy.x * x2;
+    V2 = xy.y * y2 - 3. * x2 * xy.y;
+    V3 = xy.x * (5. * y2 * y2 + x2 * (-10. * y2 + x2 ));
+    V4 = xy.y * (5. * x2 * x2 + y2 * (-10. * x2 + y2 ));
+    xy.x += - Q->Ca * V1 - Q->Cb * V2 + Q->Cc * V3 + Q->Cd * V4;
+    xy.y +=   Q->Cb * V1 - Q->Ca * V2 - Q->Cd * V3 + Q->Cc * V4;
+    ps = Q->p0s + xy.y / Q->kRg;
+    pe = ps + P->phi0 - Q->p0s;
+
+    for ( i = 20; i; --i) {
+        V1 = Q->A * log(tan(M_FORTPI + .5 * pe));
+        tpe = P->e * sin(pe);
+        V2 = .5 * P->e * Q->A * log((1. + tpe)/(1. - tpe));
+        t = ps - 2. * (atan(exp(V1 - V2 + Q->C)) - M_FORTPI);
+        pe += t;
+        if (fabs(t) < EPS)
+            break;
+    }
+
+    t = P->e * sin(pe);
+    t = 1. - t * t;
+    Re = P->one_es / ( t * sqrt(t) );
+    t = tan(ps);
+    t2 = t * t;
+    s = Q->kRg * Q->kRg;
+    d = Re * P->k0 * Q->kRg;
+    I7 = t / (2. * d);
+    I8 = t * (5. + 3. * t2) / (24. * d * s);
+    d = cos(ps) * Q->kRg * Q->A;
+    I9 = 1. / d;
+    d *= s;
+    I10 = (1. + 2. * t2) / (6. * d);
+    I11 = (5. + t2 * (28. + 24. * t2)) / (120. * d * s);
+    x2 = xy.x * xy.x;
+    lp.phi = pe + x2 * (-I7 + I8 * x2);
+    lp.lam = xy.x * (I9 + x2 * (-I10 + x2 * I11));
+    return lp;
+}
+
+
+PJ *PROJECTION(labrd) {
+    double Az, sinp, R, N, t;
+    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;
+
+    Az = pj_param(P->ctx, P->params, "razi").f;
+    sinp = sin(P->phi0);
+    t = 1. - P->es * sinp * sinp;
+    N = 1. / sqrt(t);
+    R = P->one_es * N / t;
+    Q->kRg = P->k0 * sqrt( N * R );
+    Q->p0s = atan( sqrt(R / N) * tan(P->phi0) );
+    Q->A = sinp / sin(Q->p0s);
+    t = P->e * sinp;
+    Q->C = .5 * P->e * Q->A * log((1. + t)/(1. - t)) +
+          - Q->A * log( tan(M_FORTPI + .5 * P->phi0))
+          + log( tan(M_FORTPI + .5 * Q->p0s));
+    t = Az + Az;
+    Q->Ca = (1. - cos(t)) * ( Q->Cb = 1. / (12. * Q->kRg * Q->kRg) );
+    Q->Cb *= sin(t);
+    Q->Cc = 3. * (Q->Ca * Q->Ca - Q->Cb * Q->Cb);
+    Q->Cd = 6. * Q->Ca * Q->Cb;
+
+    P->inv = e_inverse;
+    P->fwd = e_forward;
+
+    return P;
+}