tmerc: add a +alg=auto/evenden_snyder/poder_engsager parameter

The default remains +alg=poder_engsager.
This default value can be changed in proj.ini

+alg=auto will use Evenden Synder implementation if the error in
doing so remains below 0.1 mm on Earth-sized ellipsoid

data/proj.ini

@@ -14,3 +14,11 @@ cache_enabled = on
 cache_size_MB = 300
 
 cache_ttl_sec = 86400
+
+; Transverse Mercator default algorithm: auto, evenden_snyder or poder_engsager
+; * evenden_snyder is the fastest, but less accurate far from central meridian
+; * poder_engsager is slower, but more accurate far from central meridian
+; * default will auto-select between the two above depending on the coordinate
+;   to transform and will use evenden_snyder if the error in doing so is below
+;   0.1 mm (for an ellipsoid of the size of Earth)
+tmerc_default_alg = poder_engsager

docs/source/operations/projections/tmerc.rst

@@ -83,6 +83,21 @@ Parameters
     It is faster than the default algorithm, but also diverges faster
     as the distance from the central meridian increases.
 
+.. option:: +alg=auto/evenden_snyder/poder_engsager
+
+    .. versionadded:: 7.1
+
+    Selects the algorithm to use. The hardcoded value and the one defined in
+    :ref:`proj-ini` default to ``poder_engsager``, that is the most precise
+    one.
+
+    When using auto, a heuristics based on the input coordinate to transform
+    is used to determine if the faster Evenden-Snyder method can be used, for
+    faster computation, without causing an error greater than 0.1 mm (for an
+    ellipsoid of the size of Earth)
+
+    Note that :option:`+approx` and :option:`+alg` are mutually exclusive.
+
 .. include:: ../options/lon_0.rst
 
 .. include:: ../options/lat_0.rst

docs/source/resource_files.rst

@@ -107,6 +107,14 @@ Its default content is:
 
     cache_ttl_sec = 86400
 
+    ; Transverse Mercator default algorithm: auto, evenden_snyder or poder_engsager
+    ; * evenden_snyder is the fastest, but less accurate far from central meridian
+    ; * poder_engsager is slower, but more accurate far from central meridian
+    ; * default will auto-select between the two above depending on the coordinate
+    ;   to transform and will use evenden_snyder if the error in doing so is below
+    ;   0.1 mm (for an ellipsoid of the size of Earth)
+    tmerc_default_alg = poder_engsager
+
 
 Transformation grids
 -------------------------------------------------------------------------------

src/filemanager.cpp

@@ -1848,6 +1848,18 @@ void pj_load_ini(projCtx ctx) {
                     val > 0 ? static_cast<long long>(val) * 1024 * 1024 : -1;
             } else if (key == "cache_ttl_sec") {
                 ctx->gridChunkCache.ttl = atoi(value.c_str());
+            } else if (key == "tmerc_default_alg") {
+                if (value == "auto") {
+                    ctx->defaultTmercAlg = TMercAlg::AUTO;
+                } else if (value == "evenden_snyder") {
+                    ctx->defaultTmercAlg = TMercAlg::EVENDEN_SNYDER;
+                } else if (value == "poder_engsager") {
+                    ctx->defaultTmercAlg = TMercAlg::PODER_ENGSAGER;
+                } else {
+                    pj_log(
+                        ctx, PJ_LOG_ERROR,
+                        "pj_load_ini(): Invalid value for tmerc_default_alg");
+                }
             }
         }
 

src/proj_internal.h

@@ -339,6 +339,13 @@ struct CoordOperation
     }
 };
 
+enum class TMercAlg
+{
+    AUTO, // Poder/Engsager if far from central meridian, otherwise Evenden/Snyder
+    EVENDEN_SNYDER,
+    PODER_ENGSAGER,
+};
+
 /* base projection data structure */
 struct PJconsts {
 
@@ -741,6 +748,8 @@ struct projCtx_t {
 
     int projStringParserCreateFromPROJStringRecursionCounter = 0; // to avoid potential infinite recursion in PROJStringParser::createFromPROJString()
 
+    TMercAlg defaultTmercAlg = TMercAlg::PODER_ENGSAGER; // can be overriden by content of proj.ini
+
     projCtx_t() = default;
     projCtx_t(const projCtx_t&);
     ~projCtx_t();