From 4e6b366e07960b19ae4c10b84c527bc2a7028337 Mon Sep 17 00:00:00 2001
From: Kristian Evers <kristianevers@gmail.com>
Date: Mon, 25 Jun 2018 15:24:02 +0200
Subject: Add inverse lagrange projection

Courtesy of Michael Stumpf <mi12st34@gmail.com>
---
 src/PJ_lagrng.c | 45 ++++++++++++++++++++++++++++++++++++++-------
 1 file changed, 38 insertions(+), 7 deletions(-)

(limited to 'src')

diff --git a/src/PJ_lagrng.c b/src/PJ_lagrng.c
index d2b53b09..3856fcdc 100644
--- a/src/PJ_lagrng.c
+++ b/src/PJ_lagrng.c
@@ -1,19 +1,21 @@
 #define PJ_LIB__
-
 #include <errno.h>
 #include <math.h>
 
 #include "proj.h"
 #include "projects.h"
 
-PROJ_HEAD(lagrng, "Lagrange") "\n\tMisc Sph, no inv.\n\tW=";
+PROJ_HEAD(lagrng, "Lagrange") "\n\tMisc Sph\n\tW=";
 
 #define TOL 1e-10
 
 struct pj_opaque {
     double  a1;
+    double  a2;
     double  hrw;
+    double  hw;
     double  rw;
+    double  w;
 };
 
 
@@ -28,7 +30,9 @@ static XY s_forward (LP lp, PJ *P) {           /* Spheroidal, forward */
     } else {
         lp.phi = sin(lp.phi);
         v = Q->a1 * pow((1. + lp.phi)/(1. - lp.phi), Q->hrw);
-        if ((c = 0.5 * (v + 1./v) + cos(lp.lam *= Q->rw)) < TOL) {
+        lp.lam *= Q->rw;
+        c = 0.5 * (v + 1./v) + cos(lp.lam);
+        if (c < TOL) {
             proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
             return xy;
         }
@@ -39,6 +43,30 @@ static XY s_forward (LP lp, PJ *P) {           /* Spheroidal, forward */
 }
 
 
+static LP s_inverse (XY xy, PJ *P) {           /* Spheroidal, inverse */
+    LP lp = {0.0,0.0};
+    struct pj_opaque *Q = P->opaque;
+    double c, x2, y2p, y2m;
+
+    if (fabs(fabs(xy.y) - 2.) < TOL) {
+        lp.phi = xy.y < 0 ? -M_HALFPI : M_HALFPI;
+        lp.lam = 0;
+    } else {
+        x2 = xy.x * xy.x;
+        y2p = 2. + xy.y;
+        y2m = 2. - xy.y;
+        c = y2p * y2m - x2;
+        if (fabs(c) < TOL) {
+            proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
+            return lp;
+        }
+        lp.phi = 2. * atan(pow((y2p * y2p + x2) / (Q->a2 * (y2m * y2m + x2)), Q->hw)) - M_HALFPI;
+        lp.lam = Q->w * atan2(4. * xy.x, c);
+    }
+    return lp;
+}
+
+
 PJ *PROJECTION(lagrng) {
     double phi1;
     struct pj_opaque *Q = pj_calloc (1, sizeof (struct pj_opaque));
@@ -46,20 +74,23 @@ PJ *PROJECTION(lagrng) {
         return pj_default_destructor (P, ENOMEM);
     P->opaque = Q;
 
-    Q->rw = pj_param(P->ctx, P->params, "dW").f;
-    if (Q->rw <= 0)
+    Q->w = pj_param(P->ctx, P->params, "dW").f;
+    if (Q->w <= 0)
         return pj_default_destructor(P, PJD_ERR_W_OR_M_ZERO_OR_LESS);
-
-    Q->rw = 1. / Q->rw;
+    Q->hw = 0.5 * Q->w;
+    Q->rw = 1. / Q->w;
     Q->hrw = 0.5 * Q->rw;
     phi1 = sin(pj_param(P->ctx, P->params, "rlat_1").f);
     if (fabs(fabs(phi1) - 1.) < TOL)
         return pj_default_destructor(P, PJD_ERR_LAT_LARGER_THAN_90);
 
     Q->a1 = pow((1. - phi1)/(1. + phi1), Q->hrw);
+    Q->a2 = Q->a1 * Q->a1;
 
     P->es = 0.;
+    P->inv = s_inverse;
     P->fwd = s_forward;
 
     return P;
 }
+
-- 
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