#250: Inverse solution for Winkel Tripel from Drazan Tutic

git-svn-id: http://svn.osgeo.org/metacrs/proj/trunk@2609 4e78687f-474d-0410-85f9-8d5e500ac6b2

2 files changed, 88 insertions, 3 deletions

diff --git a/ChangeLog b/ChangeLog
index f3abb646..a30e5ccc 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,4 +1,8 @@
 2015-02-17 Howard Butler <howard@hobu.co>
+	* src/PJ_aitoff.c: #250 Inverse solution for Winkel Tripel 
+	from Drazan Tutic 
+
+2015-02-17 Howard Butler <howard@hobu.co>
 	* CMakeLists.txt cmake/policies.cmake src/lib_proj.cmake: #256 
 	CMake tweaks to shut off some noisy policies, fix installation 
 	of proj_config header, and shut off Framework building by 
diff --git a/src/PJ_aitoff.c b/src/PJ_aitoff.c
index c8d2b56b..f13327cc 100644
--- a/src/PJ_aitoff.c
+++ b/src/PJ_aitoff.c
@@ -36,8 +36,8 @@
 
 PJ_CVSID("$Id$");
 
-PROJ_HEAD(aitoff, "Aitoff") "\n\tMisc Sph, no inv.";
-PROJ_HEAD(wintri, "Winkel Tripel") "\n\tMisc Sph, no inv.\n\tlat_1";
+PROJ_HEAD(aitoff, "Aitoff") "\n\tMisc Sph";
+PROJ_HEAD(wintri, "Winkel Tripel") "\n\tMisc Sph\n\tlat_1";
 
 FORWARD(s_forward); /* spheroid */
 	double c, d;
@@ -53,10 +53,91 @@ FORWARD(s_forward); /* spheroid */
 	}
 	return (xy);
 }
+
+/***********************************************************************************
+*
+* Inverse functions added by Drazen Tutic and Lovro Gradiser based on paper:
+*           
+* I.Özbug Biklirici and Cengizhan Ipbüker. A General Algorithm for the Inverse 
+* Transformation of Map Projections Using Jacobian Matrices. In Proceedings of the
+* Third International Symposium Mathematical & Computational Applications,
+* pages 175{182, Turkey, September 2002.
+*
+* Expected accuracy is defined by EPSILON = 1e-12. Should be appropriate for 
+* most applications of Aitoff and Winkel Tripel projections.
+*
+* Longitudes of 180W and 180E can be mixed in solution obtained.
+*
+* Inverse for Aitoff projection in poles is undefined, longitude value of 0 is assumed.
+*
+* Contact : dtutic@geof.hr
+* Date: 2015-02-16
+*
+************************************************************************************/
+
+INVERSE(s_inverse); /* sphere */  
+        int iter, MAXITER = 10, round = 0, MAXROUND = 20;
+	double EPSILON = 1e-12, D, C, f1, f2, f1p, f1l, f2p, f2l, dp, dl, sl, sp, cp, cl, x, y;
+
+	if ((fabs(xy.x) < EPSILON) && (fabs(xy.y) < EPSILON )) { lp.phi = 0.; lp.lam = 0.; return (lp); }
+
+	/* intial values for Newton-Raphson method */
+	lp.phi = xy.y; lp.lam = xy.x; 
+	do {
+		iter = 0; 
+		do { 
+			sl = sin(lp.lam * 0.5); cl = cos(lp.lam * 0.5); 
+			sp = sin(lp.phi); cp = cos(lp.phi); 
+			D = cp * cl;
+ 		      	C = 1. - D * D;
+			D = acos(D) / pow(C, 1.5);
+	       		f1 = 2. * D * C * cp * sl;
+		       	f2 = D * C * sp;
+		       	f1p = 2.* (sl * cl * sp * cp / C - D * sp * sl);
+		       	f1l = cp * cp * sl * sl / C + D * cp * cl * sp * sp;
+		    	f2p = sp * sp * cl / C + D * sl * sl * cp;
+		      	f2l = 0.5 * (sp * cp * sl / C - D * sp * cp * cp * sl * cl);
+		      	if (P->mode) { /* Winkel Tripel */
+				f1 = 0.5 * (f1 + lp.lam * P->cosphi1);
+				f2 = 0.5 * (f2 + lp.phi);
+				f1p *= 0.5;
+				f1l = 0.5 * (f1l + P->cosphi1);
+				f2p = 0.5 * (f2p + 1.);
+				f2l *= 0.5;
+			}
+			f1 -= xy.x; f2 -= xy.y;
+			dl = (f2 * f1p - f1 * f2p) / (dp = f1p * f2l - f2p * f1l);
+			dp = (f1 * f2l - f2 * f1l) / dp;
+			while (dl > M_PI) dl -= M_PI; /* set to interval [-M_PI, M_PI]  */
+			while (dl < -M_PI) dl += M_PI; /* set to interval [-M_PI, M_PI]  */
+			lp.phi -= dp;	lp.lam -= dl;
+		} while ((fabs(dp) > EPSILON || fabs(dl) > EPSILON) && (iter++ < MAXITER));
+		if (lp.phi > M_PI_2) lp.phi -= 2.*(lp.phi-M_PI_2); /* correct if symmetrical solution for Aitoff */ 
+		if (lp.phi < -M_PI_2) lp.phi -= 2.*(lp.phi+M_PI_2); /* correct if symmetrical solution for Aitoff */ 
+		if ((fabs(fabs(lp.phi) - M_PI_2) < EPSILON) && (!P->mode)) lp.lam = 0.; /* if pole in Aitoff, return longitude of 0 */ 
+
+		/* calculate x,y coordinates with solution obtained */
+		if((D = acos(cos(lp.phi) * cos(C = 0.5 * lp.lam)))) {/* Aitoff */
+			x = 2. * D * cos(lp.phi) * sin(C) * (y = 1. / sin(D));
+			y *= D * sin(lp.phi);
+		} else
+			x = y = 0.;
+		if (P->mode) { /* Winkel Tripel */
+			x = (x + lp.lam * P->cosphi1) * 0.5;
+			y = (y + lp.phi) * 0.5;
+		}
+	/* if too far from given values of x,y, repeat with better approximation of phi,lam */
+	} while (((fabs(xy.x-x) > EPSILON) || (fabs(xy.y-y) > EPSILON)) && (round++ < MAXROUND));
+
+	if (iter == MAXITER && round == MAXROUND) fprintf(stderr, "Warning: Accuracy of 1e-12 not reached. Last increments: dlat=%e and dlon=%e\n", dp, dl);
+
+	return (lp);
+}
+
 FREEUP; if (P) pj_dalloc(P); }
 	static PJ *
 setup(PJ *P) {
-	P->inv = 0;
+	P->inv = s_inverse;
 	P->fwd = s_forward;
 	P->es = 0.;
 	return P;