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#define PJ_LIB__
#include <errno.h>
#include <math.h>
#include "proj.h"
#include "projects.h"
typedef struct { double r, Az; } VECT;
struct pj_opaque {
struct { /* control point data */
double phi, lam;
double cosphi, sinphi;
VECT v;
XY p;
double Az;
} c[3];
XY p;
double beta_0, beta_1, beta_2;
};
PROJ_HEAD(chamb, "Chamberlin Trimetric") "\n\tMisc Sph, no inv"
"\n\tlat_1= lon_1= lat_2= lon_2= lat_3= lon_3=";
#include <stdio.h>
#define THIRD 0.333333333333333333
#define TOL 1e-9
/* distance and azimuth from point 1 to point 2 */
static VECT vect(projCtx ctx, double dphi, double c1, double s1, double c2, double s2, double dlam) {
VECT v;
double cdl, dp, dl;
cdl = cos(dlam);
if (fabs(dphi) > 1. || fabs(dlam) > 1.)
v.r = aacos(ctx, s1 * s2 + c1 * c2 * cdl);
else { /* more accurate for smaller distances */
dp = sin(.5 * dphi);
dl = sin(.5 * dlam);
v.r = 2. * aasin(ctx,sqrt(dp * dp + c1 * c2 * dl * dl));
}
if (fabs(v.r) > TOL)
v.Az = atan2(c2 * sin(dlam), c1 * s2 - s1 * c2 * cdl);
else
v.r = v.Az = 0.;
return v;
}
/* law of cosines */
static double lc(projCtx ctx, double b,double c,double a) {
return aacos(ctx, .5 * (b * b + c * c - a * a) / (b * c));
}
static XY s_forward (LP lp, PJ *P) { /* Spheroidal, forward */
XY xy;
struct pj_opaque *Q = P->opaque;
double sinphi, cosphi, a;
VECT v[3];
int i, j;
sinphi = sin(lp.phi);
cosphi = cos(lp.phi);
for (i = 0; i < 3; ++i) { /* dist/azimiths from control */
v[i] = vect(P->ctx, lp.phi - Q->c[i].phi, Q->c[i].cosphi, Q->c[i].sinphi,
cosphi, sinphi, lp.lam - Q->c[i].lam);
if (v[i].r == 0.0)
break;
v[i].Az = adjlon(v[i].Az - Q->c[i].v.Az);
}
if (i < 3) /* current point at control point */
xy = Q->c[i].p;
else { /* point mean of intersepts */
xy = Q->p;
for (i = 0; i < 3; ++i) {
j = i == 2 ? 0 : i + 1;
a = lc(P->ctx,Q->c[i].v.r, v[i].r, v[j].r);
if (v[i].Az < 0.)
a = -a;
if (! i) { /* coord comp unique to each arc */
xy.x += v[i].r * cos(a);
xy.y -= v[i].r * sin(a);
} else if (i == 1) {
a = Q->beta_1 - a;
xy.x -= v[i].r * cos(a);
xy.y -= v[i].r * sin(a);
} else {
a = Q->beta_2 - a;
xy.x += v[i].r * cos(a);
xy.y += v[i].r * sin(a);
}
}
xy.x *= THIRD; /* mean of arc intercepts */
xy.y *= THIRD;
}
return xy;
}
PJ *PROJECTION(chamb) {
int i, j;
char line[10];
struct pj_opaque *Q = pj_calloc (1, sizeof (struct pj_opaque));
if (0==Q)
return pj_default_destructor (P, ENOMEM);
P->opaque = Q;
for (i = 0; i < 3; ++i) { /* get control point locations */
(void)sprintf(line, "rlat_%d", i+1);
Q->c[i].phi = pj_param(P->ctx, P->params, line).f;
(void)sprintf(line, "rlon_%d", i+1);
Q->c[i].lam = pj_param(P->ctx, P->params, line).f;
Q->c[i].lam = adjlon(Q->c[i].lam - P->lam0);
Q->c[i].cosphi = cos(Q->c[i].phi);
Q->c[i].sinphi = sin(Q->c[i].phi);
}
for (i = 0; i < 3; ++i) { /* inter ctl pt. distances and azimuths */
j = i == 2 ? 0 : i + 1;
Q->c[i].v = vect(P->ctx,Q->c[j].phi - Q->c[i].phi, Q->c[i].cosphi, Q->c[i].sinphi,
Q->c[j].cosphi, Q->c[j].sinphi, Q->c[j].lam - Q->c[i].lam);
if (Q->c[i].v.r == 0.0)
return pj_default_destructor (P, PJD_ERR_CONTROL_POINT_NO_DIST);
/* co-linearity problem ignored for now */
}
Q->beta_0 = lc(P->ctx,Q->c[0].v.r, Q->c[2].v.r, Q->c[1].v.r);
Q->beta_1 = lc(P->ctx,Q->c[0].v.r, Q->c[1].v.r, Q->c[2].v.r);
Q->beta_2 = M_PI - Q->beta_0;
Q->p.y = 2. * (Q->c[0].p.y = Q->c[1].p.y = Q->c[2].v.r * sin(Q->beta_0));
Q->c[2].p.y = 0.;
Q->c[0].p.x = - (Q->c[1].p.x = 0.5 * Q->c[0].v.r);
Q->p.x = Q->c[2].p.x = Q->c[0].p.x + Q->c[2].v.r * cos(Q->beta_0);
P->es = 0.;
P->fwd = s_forward;
return P;
}
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