diff --git a/autotest/osr/osr_ct.py b/autotest/osr/osr_ct.py
index e8b2f62d3711..ec4ab4b2dd48 100755
--- a/autotest/osr/osr_ct.py
+++ b/autotest/osr/osr_ct.py
@@ -90,6 +90,21 @@ def test_osr_ct_2():
         and result[2] == pytest.approx(0.0, abs=0.01)
     ), "Wrong LL to UTM result"
 
+    result = ct.TransformPoint([32.0, -117.5, 10.0])
+    assert (
+        result[0] == pytest.approx(452772.06, abs=0.01)
+        and result[1] == pytest.approx(3540544.89, abs=0.01)
+        and result[2] == 10
+    ), "Wrong LL to UTM result"
+
+    result = ct.TransformPoint([32.0, -117.5, 10.0, 2000.0])
+    assert (
+        result[0] == pytest.approx(452772.06, abs=0.01)
+        and result[1] == pytest.approx(3540544.89, abs=0.01)
+        and result[2] == 10
+        and result[3] == 2000
+    ), "Wrong LL to UTM result"
+
 
 ###############################################################################
 # Transform an OGR geometry ... this is mostly aimed at ensuring that
diff --git a/swig/include/ogr.i b/swig/include/ogr.i
index ba48e705df6d..3f582d744b4e 100644
--- a/swig/include/ogr.i
+++ b/swig/include/ogr.i
@@ -619,7 +619,6 @@ typedef int OGRErr;
 %{
 #include "gdal.h"
 %}
-typedef int CPLErr;
 #define FROM_PYTHON_OGR_I
 %include MajorObject.i
 #undef FROM_PYTHON_OGR_I
diff --git a/swig/include/osr.i b/swig/include/osr.i
index 714db177c4d2..8ae1900839b9 100644
--- a/swig/include/osr.i
+++ b/swig/include/osr.i
@@ -1237,7 +1237,11 @@ public:
 %apply (double argout[ANY]) {(double inout[3])};
 %apply (double argin[ANY]) {(double inout[3])};
 #endif
+#if SWIGPYTHON
+  void _TransformPoint3Double( double inout[3] ) {
+#else
   void TransformPoint( double inout[3] ) {
+#endif
     if (self == NULL)
         return;
     OCTTransform( self, 1, &inout[0], &inout[1], &inout[2] );
@@ -1250,7 +1254,11 @@ public:
 %apply (double argout[ANY]) {(double inout[4])};
 %apply (double argin[ANY]) {(double inout[4])};
 #endif
+#if SWIGPYTHON
+  void _TransformPoint4Double( double inout[4] ) {
+#else
   void TransformPoint( double inout[4] ) {
+#endif
     if (self == NULL)
         return;
     OCTTransform4D( self, 1, &inout[0], &inout[1], &inout[2], &inout[3], NULL );
diff --git a/swig/include/python/osr_python.i b/swig/include/python/osr_python.i
index 34fac68483f9..c73b99da8087 100644
--- a/swig/include/python/osr_python.i
+++ b/swig/include/python/osr_python.i
@@ -67,3 +67,28 @@ def _WarnIfUserHasNotSpecifiedIfUsingExceptions():
 
   %}
 }
+
+%extend OSRCoordinateTransformationShadow {
+
+%feature("shadow") TransformPoint %{
+
+def TransformPoint(self, *args):
+    """
+    TransformPoint(CoordinateTransformation self, double [3] inout)
+    TransformPoint(CoordinateTransformation self, double [4] inout)
+    TransformPoint(CoordinateTransformation self, double x, double y, double z=0.0)
+    TransformPoint(CoordinateTransformation self, double x, double y, double z, double t)
+    """
+
+    import collections.abc
+    if len(args) == 1 and isinstance(args[0], collections.abc.Sequence):
+        len_args = len(args[0])
+        if len_args == 3:
+            return self._TransformPoint3Double(args[0])
+        elif len_args == 4:
+            return self._TransformPoint4Double(args[0])
+
+    return $action(self, *args)
+%}
+
+}