Implement ellipsoidal formulation of +proj=ortho (fixes #397)

- Map ESRI 'Local' to +proj=ortho when Scale_Factor = 1 and Azimuth = 0
- Map ESRI 'Orthographic' to a PROJ WKT2 'Orthographic (Spherical)'
  which maps to +proj=ortho +f=0 to froce spherical evaluation

2 files changed, 36 insertions, 3 deletions

diff --git a/src/iso19111/coordinateoperation.cpp b/src/iso19111/coordinateoperation.cpp
index 65ef2b77..ef262cc8 100644
--- a/src/iso19111/coordinateoperation.cpp
+++ b/src/iso19111/coordinateoperation.cpp
@@ -4251,7 +4251,7 @@ ConversionNNPtr Conversion::createObliqueStereographic(
  * This method is defined as [EPSG:9840]
  * (https://www.epsg-registry.org/export.htm?gml=urn:ogc:def:method:EPSG::9840)
  *
- * \note At the time of writing, PROJ only implements the spherical formulation
+ * \note Before PROJ 7.2, only the spherical formulation was implemented.
  *
  * @param properties See \ref general_properties of the conversion. If the name
  * is not provided, it is automatically set.
diff --git a/src/iso19111/io.cpp b/src/iso19111/io.cpp
index 6680ab00..16ab22f7 100644
--- a/src/iso19111/io.cpp
+++ b/src/iso19111/io.cpp
@@ -3290,7 +3290,7 @@ ConversionNNPtr WKTParser::Private::buildProjectionFromESRI(
     }
 
     // Compare parameters present with the ones expected in the mapping
-    const ESRIMethodMapping *esriMapping = esriMappings[0];
+    const ESRIMethodMapping *esriMapping = nullptr;
     int bestMatchCount = -1;
     for (const auto &mapping : esriMappings) {
         int matchCount = 0;
@@ -3298,12 +3298,20 @@ ConversionNNPtr WKTParser::Private::buildProjectionFromESRI(
             auto iter = mapParamNameToValue.find(param->esri_name);
             if (iter != mapParamNameToValue.end()) {
                 if (param->wkt2_name == nullptr) {
+                    bool ok = true;
                     try {
                         if (io::asDouble(param->fixed_value) ==
                             io::asDouble(iter->second)) {
                             matchCount++;
+                        } else {
+                            ok = false;
                         }
                     } catch (const std::exception &) {
+                        ok = false;
+                    }
+                    if (!ok) {
+                        matchCount = -1;
+                        break;
                     }
                 } else {
                     matchCount++;
@@ -3317,6 +3325,10 @@ ConversionNNPtr WKTParser::Private::buildProjectionFromESRI(
             bestMatchCount = matchCount;
         }
     }
+    if (esriMapping == nullptr) {
+        return buildProjectionStandard(baseGeodCRS, projCRSNode, projectionNode,
+                                       defaultLinearUnit, defaultAngularUnit);
+    }
 
     std::map<std::string, const char *> mapWKT2NameToESRIName;
     for (const auto *param = esriMapping->params; param->esri_name; ++param) {
@@ -8898,8 +8910,29 @@ static bool is_in_stringlist(const std::string &str, const char *stringlist) {
 CRSNNPtr PROJStringParser::Private::buildProjectedCRS(
     int iStep, GeographicCRSNNPtr geogCRS, int iUnitConvert, int iAxisSwap) {
     auto &step = steps_[iStep];
-    auto mappings = getMappingsFromPROJName(step.name);
+    const auto mappings = getMappingsFromPROJName(step.name);
     const MethodMapping *mapping = mappings.empty() ? nullptr : mappings[0];
+
+    if (mappings.size() >= 2) {
+        // To distinguish for example +ortho from +ortho +f=0
+        for (const auto *mappingIter : mappings) {
+            if (mappingIter->proj_name_aux != nullptr &&
+                strchr(mappingIter->proj_name_aux, '=') == nullptr &&
+                hasParamValue(step, mappingIter->proj_name_aux)) {
+                mapping = mappingIter;
+                break;
+            } else if (mappingIter->proj_name_aux != nullptr &&
+                       strchr(mappingIter->proj_name_aux, '=') != nullptr) {
+                const auto tokens = split(mappingIter->proj_name_aux, '=');
+                if (tokens.size() == 2 &&
+                    getParamValue(step, tokens[0]) == tokens[1]) {
+                    mapping = mappingIter;
+                    break;
+                }
+            }
+        }
+    }
+
     if (mapping) {
         mapping = selectSphericalOrEllipsoidal(mapping, geogCRS);
     }