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#define PJ_LIB__
#include <errno.h>
#include <math.h>
#include "projects.h"
PROJ_HEAD(moll, "Mollweide") "\n\tPCyl, Sph";
PROJ_HEAD(wag4, "Wagner IV") "\n\tPCyl, Sph";
PROJ_HEAD(wag5, "Wagner V") "\n\tPCyl, Sph";
#define MAX_ITER 10
#define LOOP_TOL 1e-7
struct pj_opaque {
double C_x, C_y, C_p;
};
static XY s_forward (LP lp, PJ *P) { /* Spheroidal, forward */
XY xy = {0.0,0.0};
struct pj_opaque *Q = P->opaque;
double k, V;
int i;
k = Q->C_p * sin(lp.phi);
for (i = MAX_ITER; i ; --i) {
lp.phi -= V = (lp.phi + sin(lp.phi) - k) /
(1. + cos(lp.phi));
if (fabs(V) < LOOP_TOL)
break;
}
if (!i)
lp.phi = (lp.phi < 0.) ? -M_HALFPI : M_HALFPI;
else
lp.phi *= 0.5;
xy.x = Q->C_x * lp.lam * cos(lp.phi);
xy.y = Q->C_y * sin(lp.phi);
return xy;
}
static LP s_inverse (XY xy, PJ *P) { /* Spheroidal, inverse */
LP lp = {0.0,0.0};
struct pj_opaque *Q = P->opaque;
lp.phi = aasin(P->ctx, xy.y / Q->C_y);
lp.lam = xy.x / (Q->C_x * cos(lp.phi));
if (fabs(lp.lam) < M_PI) {
lp.phi += lp.phi;
lp.phi = aasin(P->ctx, (lp.phi + sin(lp.phi)) / Q->C_p);
} else {
lp.lam = lp.phi = HUGE_VAL;
}
return lp;
}
static PJ * setup(PJ *P, double p) {
struct pj_opaque *Q = P->opaque;
double r, sp, p2 = p + p;
P->es = 0;
sp = sin(p);
r = sqrt(M_TWOPI * sp / (p2 + sin(p2)));
Q->C_x = 2. * r / M_PI;
Q->C_y = r / sp;
Q->C_p = p2 + sin(p2);
P->inv = s_inverse;
P->fwd = s_forward;
return P;
}
PJ *PROJECTION(moll) {
struct pj_opaque *Q = pj_calloc (1, sizeof (struct pj_opaque));
if (0==Q)
return pj_default_destructor (P, ENOMEM);
P->opaque = Q;
return setup(P, M_HALFPI);
}
PJ *PROJECTION(wag4) {
struct pj_opaque *Q = pj_calloc (1, sizeof (struct pj_opaque));
if (0==Q)
return pj_default_destructor (P, ENOMEM);
P->opaque = Q;
return setup(P, M_PI/3.);
}
PJ *PROJECTION(wag5) {
struct pj_opaque *Q = pj_calloc (1, sizeof (struct pj_opaque));
if (0==Q)
return pj_default_destructor (P, ENOMEM);
P->opaque = Q;
P->es = 0;
Q->C_x = 0.90977;
Q->C_y = 1.65014;
Q->C_p = 3.00896;
P->inv = s_inverse;
P->fwd = s_forward;
return P;
}
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