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#define PJ_LIB__
# include <projects.h>
PROJ_HEAD(vandg, "van der Grinten (I)") "\n\tMisc Sph";
# define TOL 1.e-10
# define THIRD .33333333333333333333
# define TWO_THRD .66666666666666666666
# define C2_27 .07407407407407407407
# define PI4_3 4.18879020478639098458
# define PISQ 9.86960440108935861869
# define TPISQ 19.73920880217871723738
# define HPISQ 4.93480220054467930934
FORWARD(s_forward); /* spheroid */
double al, al2, g, g2, p2;
p2 = fabs(lp.phi / HALFPI);
if ((p2 - TOL) > 1.) F_ERROR;
if (p2 > 1.)
p2 = 1.;
if (fabs(lp.phi) <= TOL) {
xy.x = lp.lam;
xy.y = 0.;
} else if (fabs(lp.lam) <= TOL || fabs(p2 - 1.) < TOL) {
xy.x = 0.;
xy.y = PI * tan(.5 * asin(p2));
if (lp.phi < 0.) xy.y = -xy.y;
} else {
al = .5 * fabs(PI / lp.lam - lp.lam / PI);
al2 = al * al;
g = sqrt(1. - p2 * p2);
g = g / (p2 + g - 1.);
g2 = g * g;
p2 = g * (2. / p2 - 1.);
p2 = p2 * p2;
xy.x = g - p2; g = p2 + al2;
xy.x = PI * (al * xy.x + sqrt(al2 * xy.x * xy.x - g * (g2 - p2))) / g;
if (lp.lam < 0.) xy.x = -xy.x;
xy.y = fabs(xy.x / PI);
xy.y = 1. - xy.y * (xy.y + 2. * al);
if (xy.y < -TOL) F_ERROR;
if (xy.y < 0.) xy.y = 0.;
else xy.y = sqrt(xy.y) * (lp.phi < 0. ? -PI : PI);
}
return (xy);
}
INVERSE(s_inverse); /* spheroid */
double t, c0, c1, c2, c3, al, r2, r, m, d, ay, x2, y2;
x2 = xy.x * xy.x;
if ((ay = fabs(xy.y)) < TOL) {
lp.phi = 0.;
t = x2 * x2 + TPISQ * (x2 + HPISQ);
lp.lam = fabs(xy.x) <= TOL ? 0. :
.5 * (x2 - PISQ + sqrt(t)) / xy.x;
return (lp);
}
y2 = xy.y * xy.y;
r = x2 + y2; r2 = r * r;
c1 = - PI * ay * (r + PISQ);
c3 = r2 + TWOPI * (ay * r + PI * (y2 + PI * (ay + HALFPI)));
c2 = c1 + PISQ * (r - 3. * y2);
c0 = PI * ay;
c2 /= c3;
al = c1 / c3 - THIRD * c2 * c2;
m = 2. * sqrt(-THIRD * al);
d = C2_27 * c2 * c2 * c2 + (c0 * c0 - THIRD * c2 * c1) / c3;
if (((t = fabs(d = 3. * d / (al * m))) - TOL) <= 1.) {
d = t > 1. ? (d > 0. ? 0. : PI) : acos(d);
lp.phi = PI * (m * cos(d * THIRD + PI4_3) - THIRD * c2);
if (xy.y < 0.) lp.phi = -lp.phi;
t = r2 + TPISQ * (x2 - y2 + HPISQ);
lp.lam = fabs(xy.x) <= TOL ? 0. :
.5 * (r - PISQ + (t <= 0. ? 0. : sqrt(t))) / xy.x;
} else
I_ERROR;
return (lp);
}
FREEUP; if (P) pj_dalloc(P); }
ENTRY0(vandg) P->es = 0.; P->inv = s_inverse; P->fwd = s_forward; ENDENTRY(P)
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