#define PJ_LIB__
#include	<projects.h>
PROJ_HEAD(mbtfpq, "McBryde-Thomas Flat-Polar Quartic") "\n\tCyl., Sph.";
#define NITER	20
#define EPS	1e-7
#define ONETOL 1.000001
#define C	1.70710678118654752440
#define RC	0.58578643762690495119
#define FYC	1.87475828462269495505
#define RYC	0.53340209679417701685
#define FXC	0.31245971410378249250
#define RXC	3.20041258076506210122
FORWARD(s_forward); /* spheroid */
	double th1, c;
	int i;
	(void) P;

	c = C * sin(lp.phi);
	for (i = NITER; i; --i) {
		lp.phi -= th1 = (sin(.5*lp.phi) + sin(lp.phi) - c) /
			(.5*cos(.5*lp.phi)  + cos(lp.phi));
		if (fabs(th1) < EPS) break;
	}
	xy.x = FXC * lp.lam * (1.0 + 2. * cos(lp.phi)/cos(0.5 * lp.phi));
	xy.y = FYC * sin(0.5 * lp.phi);
	return (xy);
}
INVERSE(s_inverse); /* spheroid */
	double t;

	lp.phi = RYC * xy.y;
	if (fabs(lp.phi) > 1.) {
		if (fabs(lp.phi) > ONETOL)	I_ERROR
		else if (lp.phi < 0.) { t = -1.; lp.phi = -PI; }
		else { t = 1.; lp.phi = PI; }
	} else
		lp.phi = 2. * asin(t = lp.phi);
	lp.lam = RXC * xy.x / (1. + 2. * cos(lp.phi)/cos(0.5 * lp.phi));
	lp.phi = RC * (t + sin(lp.phi));
	if (fabs(lp.phi) > 1.)
		if (fabs(lp.phi) > ONETOL)	I_ERROR
		else			lp.phi = lp.phi < 0. ? -HALFPI : HALFPI;
	else
		lp.phi = asin(lp.phi);
	return (lp);
}
FREEUP; if (P) pj_dalloc(P); }
ENTRY0(mbtfpq) P->es = 0.; P->inv = s_inverse; P->fwd = s_forward; ENDENTRY(P)
