Spherical tmerc forward: do not restrict to [-90,90] longitude range

The restriction was a copy&paste from the Evenden/Snyder approximate
ellipsoidal implementation, but the spherical one is exact, so this
restriction isn't needed.

Also tune a bit the handling of lat=0, |lon| > 90

2 files changed, 78 insertions, 19 deletions

diff --git a/src/projections/tmerc.cpp b/src/projections/tmerc.cpp
index 2d13b064..8f897061 100644
--- a/src/projections/tmerc.cpp
+++ b/src/projections/tmerc.cpp
@@ -115,25 +115,11 @@ static PJ_XY approx_e_fwd (PJ_LP lp, PJ *P)
     return (xy);
 }
 
-static PJ_XY approx_s_fwd (PJ_LP lp, PJ *P) {
+static PJ_XY tmerc_spherical_fwd (PJ_LP lp, PJ *P) {
     PJ_XY xy = {0.0,0.0};
     double b, cosphi;
     const auto *Q = &(static_cast<struct tmerc_data*>(P->opaque)->approx);
 
-    /*
-     * Fail if our longitude is more than 90 degrees from the
-     * central meridian since the results are essentially garbage.
-     * Is error -20 really an appropriate return value?
-     *
-     *  http://trac.osgeo.org/proj/ticket/5
-     */
-    if( lp.lam < -M_HALFPI || lp.lam > M_HALFPI ) {
-        xy.x = HUGE_VAL;
-        xy.y = HUGE_VAL;
-        proj_context_errno_set( P->ctx, PJD_ERR_LAT_OR_LON_EXCEED_LIMIT );
-        return xy;
-    }
-
     cosphi = cos(lp.phi);
     b = cosphi * sin (lp.lam);
     if (fabs (fabs (b) - 1.) <= EPS10) {
@@ -145,7 +131,12 @@ static PJ_XY approx_s_fwd (PJ_LP lp, PJ *P) {
     xy.y = cosphi * cos (lp.lam) / sqrt (1. - b * b);
 
     b = fabs ( xy.y );
-    if (b >= 1.) {
+    if (cosphi == 1 && (lp.lam < -M_HALFPI || lp.lam > M_HALFPI) ) {
+        /* Helps to be able to roundtrip |longitudes| > 90 at lat=0 */
+        /* We could also map to -M_PI ... */
+        xy.y = M_PI;
+    }
+    else if (b >= 1.) {
         if ((b - 1.) > EPS10) {
             proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
             return xy;
@@ -192,7 +183,7 @@ static PJ_LP approx_e_inv (PJ_XY xy, PJ *P) {
     return lp;
 }
 
-static PJ_LP approx_s_inv (PJ_XY xy, PJ *P) {
+static PJ_LP tmerc_spherical_inv (PJ_XY xy, PJ *P) {
     PJ_LP lp = {0.0, 0.0};
     double h, g;
     const auto *Q = &(static_cast<struct tmerc_data*>(P->opaque)->approx);
@@ -611,8 +602,8 @@ static PJ *setup(PJ *P, TMercAlgo eAlg) {
                 return nullptr;
             if( P->es == 0 )
             {
-                P->inv = approx_s_inv;
-                P->fwd = approx_s_fwd;
+                P->inv = tmerc_spherical_inv;
+                P->fwd = tmerc_spherical_fwd;
             }
             else
             {
diff --git a/test/gie/builtins.gie b/test/gie/builtins.gie
index 0f86bed2..e870f1d4 100644
--- a/test/gie/builtins.gie
+++ b/test/gie/builtins.gie
@@ -5771,6 +5771,74 @@ expect  -223413.466406322 111769.145040597
 accept  -2 -1
 expect  -223413.466406322 -111769.145040597
 
+accept    0      0
+expect    0      0
+roundtrip 1
+
+accept    0      90
+expect    0      10053096.491487337276
+roundtrip 1
+
+accept    0      -90
+expect    0      -10053096.491487337276
+roundtrip 1
+
+accept    170                       60
+expect    557076.820490954560       13361866.764138307422
+roundtrip 1
+
+accept    89                        0.01
+expect    30344312.098578717560     64001.116414904580
+roundtrip 1
+
+accept    91                        0.01
+expect    30344312.098578717560     20042191.866555366665
+roundtrip 1
+
+accept    179.999                   0.01
+expect    111.701070433669          20105075.972255337983
+roundtrip 1
+
+accept    -89                       0.01
+expect    -30344312.098578717560    64001.116414904580
+roundtrip 1
+
+accept    -91                       0.01
+expect    -30344312.098578717560    20042191.866555366665
+roundtrip 1
+
+accept    -179.999                  0.01
+expect    -111.701070433669         20105075.972255337983
+roundtrip 1
+
+accept    89                       -0.01
+expect    30344312.098578717560    -64001.116414904580
+roundtrip 1
+
+accept    91                       -0.01
+expect    30344312.098578717560    -20042191.866555366665
+roundtrip 1
+
+accept    179.999                  -0.01
+expect    111.701070433669         -20105075.972255337983
+roundtrip 1
+
+accept    -89                      -0.01
+expect    -30344312.098578717560   -64001.116414904580
+roundtrip 1
+
+accept    -91                       -0.01
+expect    -30344312.098578717560    -20042191.866555366665
+roundtrip 1
+
+accept    -179.999                  -0.01
+expect    -111.701070433669         -20105075.972255337983
+roundtrip 1
+
+accept    150                       0
+expect    3515559.323737951461      20106192.982974674553
+roundtrip 1
+
 direction inverse
 accept  200 100
 expect  0.001790493 0.000895247