PJ_robin.c

#define PJ_LIB__
#include	<projects.h>
PROJ_HEAD(robin, "Robinson") "\n\tPCyl., Sph.";
#define V(C,z) (C.c0 + z * (C.c1 + z * (C.c2 + z * C.c3)))
#define DV(C,z) (C.c1 + z * (C.c2 + C.c2 + z * 3. * C.c3))

/* 
note: following terms based upon 5 deg. intervals in degrees.

Some background on these coefficients is available at:

http://article.gmane.org/gmane.comp.gis.proj-4.devel/6039
http://trac.osgeo.org/proj/ticket/113
*/

struct COEFS {
	float c0, c1, c2, c3;
};

static const struct COEFS X[] = {
    {1, 2.2199e-17, -7.15515e-05, 3.1103e-06},
    {0.9986, -0.000482243, -2.4897e-05, -1.3309e-06},
    {0.9954, -0.00083103, -4.48605e-05, -9.86701e-07},
    {0.99, -0.00135364, -5.9661e-05, 3.6777e-06},
    {0.9822, -0.00167442, -4.49547e-06, -5.72411e-06},
    {0.973, -0.00214868, -9.03571e-05, 1.8736e-08},
    {0.96, -0.00305085, -9.00761e-05, 1.64917e-06},
    {0.9427, -0.00382792, -6.53386e-05, -2.6154e-06},
    {0.9216, -0.00467746, -0.00010457, 4.81243e-06},
    {0.8962, -0.00536223, -3.23831e-05, -5.43432e-06},
    {0.8679, -0.00609363, -0.000113898, 3.32484e-06},
    {0.835, -0.00698325, -6.40253e-05, 9.34959e-07},
    {0.7986, -0.00755338, -5.00009e-05, 9.35324e-07},
    {0.7597, -0.00798324, -3.5971e-05, -2.27626e-06},
    {0.7186, -0.00851367, -7.01149e-05, -8.6303e-06},
    {0.6732, -0.00986209, -0.000199569, 1.91974e-05},
    {0.6213, -0.010418, 8.83923e-05, 6.24051e-06},
    {0.5722, -0.00906601, 0.000182, 6.24051e-06},
    {0.5322, -0.00677797, 0.000275608, 6.24051e-06}
};
static const struct COEFS Y[] = {
    {-5.20417e-18, 0.0124, 1.21431e-18, -8.45284e-11},
    {0.062, 0.0124, -1.26793e-09, 4.22642e-10},
    {0.124, 0.0124, 5.07171e-09, -1.60604e-09},
    {0.186, 0.0123999, -1.90189e-08, 6.00152e-09},
    {0.248, 0.0124002, 7.10039e-08, -2.24e-08},
    {0.31, 0.0123992, -2.64997e-07, 8.35986e-08},
    {0.372, 0.0124029, 9.88983e-07, -3.11994e-07},
    {0.434, 0.0123893, -3.69093e-06, -4.35621e-07},
    {0.4958, 0.0123198, -1.02252e-05, -3.45523e-07},
    {0.5571, 0.0121916, -1.54081e-05, -5.82288e-07},
    {0.6176, 0.0119938, -2.41424e-05, -5.25327e-07},
    {0.6769, 0.011713, -3.20223e-05, -5.16405e-07},
    {0.7346, 0.0113541, -3.97684e-05, -6.09052e-07},
    {0.7903, 0.0109107, -4.89042e-05, -1.04739e-06},
    {0.8435, 0.0103431, -6.4615e-05, -1.40374e-09},
    {0.8936, 0.00969686, -6.4636e-05, -8.547e-06},
    {0.9394, 0.00840947, -0.000192841, -4.2106e-06},
    {0.9761, 0.00616527, -0.000256, -4.2106e-06},
    {1, 0.00328947, -0.000319159, -4.2106e-06}
};
#define FXC	0.8487
#define FYC	1.3523
#define C1	11.45915590261646417544
#define RC1	0.08726646259971647884
#define NODES	18
#define ONEEPS	1.000001
#define EPS	1e-8
FORWARD(s_forward); /* spheroid */
	int i;
	double dphi;
	(void) P;

	i = floor((dphi = fabs(lp.phi)) * C1);
	if (i >= NODES) i = NODES - 1;
	dphi = RAD_TO_DEG * (dphi - RC1 * i);
	xy.x = V(X[i], dphi) * FXC * lp.lam;
	xy.y = V(Y[i], dphi) * FYC;
	if (lp.phi < 0.) xy.y = -xy.y;
	return (xy);
}
INVERSE(s_inverse); /* spheroid */
	int i;
	double t, t1;
	struct COEFS T;

	lp.lam = xy.x / FXC;
	lp.phi = fabs(xy.y / FYC);
	if (lp.phi >= 1.) { /* simple pathologic cases */
		if (lp.phi > ONEEPS) I_ERROR
		else {
			lp.phi = xy.y < 0. ? -HALFPI : HALFPI;
			lp.lam /= X[NODES].c0;
		}
	} else { /* general problem */
		/* in Y space, reduce to table interval */
		for (i = floor(lp.phi * NODES);;) {
			if (Y[i].c0 > lp.phi) --i;
			else if (Y[i+1].c0 <= lp.phi) ++i;
			else break;
		}
		T = Y[i];
		/* first guess, linear interp */
		t = 5. * (lp.phi - T.c0)/(Y[i+1].c0 - T.c0);
		/* make into root */
		T.c0 -= lp.phi;
		for (;;) { /* Newton-Raphson reduction */
			t -= t1 = V(T,t) / DV(T,t);
			if (fabs(t1) < EPS)
				break;
		}
		lp.phi = (5 * i + t) * DEG_TO_RAD;
		if (xy.y < 0.) lp.phi = -lp.phi;
		lp.lam /= V(X[i], t);
	}
	return (lp);
}
FREEUP; if (P) pj_dalloc(P); }
ENTRY0(robin) P->es = 0.; P->inv = s_inverse; P->fwd = s_forward; ENDENTRY(P)