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/*
Created by Jacques Bertin in 1953, this projection was the go-to choice
of the French cartographic school when they wished to represent phenomena
on a global scale.
Formula designed by Philippe Rivière, 2017.
https://visionscarto.net/bertin-projection-1953
Port to PROJ by Philippe Rivière, 21 September 2018
*/
#define PJ_LIB__
#include <errno.h>
#include <math.h>
#include "proj_internal.h"
#include "proj.h"
#include "projects.h"
PROJ_HEAD(bertin1953, "Bertin 1953")
"\n\tMisc Sph no inv.";
struct pj_opaque {
double cos_delta_phi, sin_delta_phi, cos_delta_gamma, sin_delta_gamma, deltaLambda;
};
static XY s_forward (LP lp, PJ *P) {
XY xy = {0.0,0.0};
struct pj_opaque *Q = static_cast<struct pj_opaque*>(P->opaque);
double fu = 1.4, k = 12., w = 1.68, d;
/* Rotate */
double cosphi, x, y, z, z0;
lp.lam += PJ_TORAD(-16.5);
cosphi = cos(lp.phi);
x = cos(lp.lam) * cosphi;
y = sin(lp.lam) * cosphi;
z = sin(lp.phi);
z0 = z * Q->cos_delta_phi + x * Q->sin_delta_phi;
lp.lam = atan2(y * Q->cos_delta_gamma - z0 * Q->sin_delta_gamma,
x * Q->cos_delta_phi - z * Q->sin_delta_phi);
z0 = z0 * Q->cos_delta_gamma + y * Q->sin_delta_gamma;
lp.phi = asin(z0);
lp.lam = adjlon(lp.lam);
/* Adjust pre-projection */
if (lp.lam + lp.phi < -fu) {
d = (lp.lam - lp.phi + 1.6) * (lp.lam + lp.phi + fu) / 8.;
lp.lam += d;
lp.phi -= 0.8 * d * sin(lp.phi + M_PI / 2.);
}
/* Project with Hammer (1.68,2) */
cosphi = cos(lp.phi);
d = sqrt(2./(1. + cosphi * cos(lp.lam / 2.)));
xy.x = w * d * cosphi * sin(lp.lam / 2.);
xy.y = d * sin(lp.phi);
/* Adjust post-projection */
d = (1. - cos(lp.lam * lp.phi)) / k;
if (xy.y < 0.) {
xy.x *= 1. + d;
}
if (xy.y > 0.) {
xy.x *= 1. + d / 1.5 * xy.x * xy.x;
}
return xy;
}
PJ *PROJECTION(bertin1953) {
struct pj_opaque *Q = static_cast<struct pj_opaque*>(pj_calloc (1, sizeof (struct pj_opaque)));
if (0==Q)
return pj_default_destructor (P, ENOMEM);
P->opaque = Q;
P->lam0 = 0;
P->phi0 = PJ_TORAD(-42.);
Q->cos_delta_phi = cos(P->phi0);
Q->sin_delta_phi = sin(P->phi0);
Q->cos_delta_gamma = 1.;
Q->sin_delta_gamma = 0.;
P->es = 0.;
P->fwd = s_forward;
return P;
}
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