2 files changed, 36 insertions, 3 deletions

diff --git a/src/coordinateoperation.cpp b/src/coordinateoperation.cpp
index a1f305bf..ac170bbf 100644
--- a/src/coordinateoperation.cpp
+++ b/src/coordinateoperation.cpp
@@ -1503,10 +1503,35 @@ bool SingleOperation::_isEquivalentTo(const util::IComparable *other,
     const int methodEPSGCode = d->method_->getEPSGCode();
     const int otherMethodEPSGCode = otherSO->d->method_->getEPSGCode();
 
-    const bool equivalentMethods =
+    bool equivalentMethods =
         (criterion == util::IComparable::Criterion::EQUIVALENT &&
          methodEPSGCode != 0 && methodEPSGCode == otherMethodEPSGCode) ||
         d->method_->_isEquivalentTo(otherSO->d->method_.get(), criterion);
+    if (!equivalentMethods &&
+        criterion == util::IComparable::Criterion::EQUIVALENT) {
+        if ((methodEPSGCode == EPSG_CODE_METHOD_LAMBERT_AZIMUTHAL_EQUAL_AREA &&
+             otherMethodEPSGCode ==
+                 EPSG_CODE_METHOD_LAMBERT_AZIMUTHAL_EQUAL_AREA_SPHERICAL) ||
+            (otherMethodEPSGCode ==
+                 EPSG_CODE_METHOD_LAMBERT_AZIMUTHAL_EQUAL_AREA &&
+             methodEPSGCode ==
+                 EPSG_CODE_METHOD_LAMBERT_AZIMUTHAL_EQUAL_AREA_SPHERICAL) ||
+            (methodEPSGCode == EPSG_CODE_METHOD_EQUIDISTANT_CYLINDRICAL &&
+             otherMethodEPSGCode ==
+                 EPSG_CODE_METHOD_EQUIDISTANT_CYLINDRICAL_SPHERICAL) ||
+            (otherMethodEPSGCode == EPSG_CODE_METHOD_EQUIDISTANT_CYLINDRICAL &&
+             methodEPSGCode ==
+                 EPSG_CODE_METHOD_EQUIDISTANT_CYLINDRICAL_SPHERICAL)) {
+            auto geodCRS =
+                dynamic_cast<const crs::GeodeticCRS *>(sourceCRS().get());
+            auto otherGeodCRS = dynamic_cast<const crs::GeodeticCRS *>(
+                otherSO->sourceCRS().get());
+            if (geodCRS && otherGeodCRS && geodCRS->ellipsoid()->isSphere() &&
+                otherGeodCRS->ellipsoid()->isSphere()) {
+                equivalentMethods = true;
+            }
+        }
+    }
 
     if (!equivalentMethods) {
         if (criterion == util::IComparable::Criterion::EQUIVALENT) {
diff --git a/src/io.cpp b/src/io.cpp
index 71d029ea..caf9b53d 100644
--- a/src/io.cpp
+++ b/src/io.cpp
@@ -6500,8 +6500,7 @@ CRSNNPtr PROJStringParser::Private::buildProjectedCRS(
         }
     } else if (step.name == "aeqd" && hasParamValue(step, "guam")) {
         mapping = getMapping(EPSG_CODE_METHOD_GUAM_PROJECTION);
-    } else if (step.name == "cea" &&
-               !geogCRS->datum()->ellipsoid()->isSphere()) {
+    } else if (step.name == "cea" && !geogCRS->ellipsoid()->isSphere()) {
         mapping = getMapping(EPSG_CODE_METHOD_LAMBERT_CYLINDRICAL_EQUAL_AREA);
     } else if (step.name == "geos" && getParamValue(step, "sweep") == "x") {
         mapping =
@@ -6598,6 +6597,15 @@ CRSNNPtr PROJStringParser::Private::buildProjectedCRS(
                 axisType = AxisType::SOUTH_POLE;
             }
         }
+        if (geogCRS->ellipsoid()->isSphere()) {
+            mapping = getMapping(
+                EPSG_CODE_METHOD_LAMBERT_AZIMUTHAL_EQUAL_AREA_SPHERICAL);
+        }
+    } else if (step.name == "eqc") {
+        if (geogCRS->ellipsoid()->isSphere()) {
+            mapping =
+                getMapping(EPSG_CODE_METHOD_EQUIDISTANT_CYLINDRICAL_SPHERICAL);
+        }
     }
 
     UnitOfMeasure unit = buildUnit(step, "units", "to_meter");