diff --git a/applications/utilities/mesh/generation/foamyMesh/conformalVoronoiMesh/conformalVoronoiMesh/conformalVoronoiMeshZones.C b/applications/utilities/mesh/generation/foamyMesh/conformalVoronoiMesh/conformalVoronoiMesh/conformalVoronoiMeshZones.C
index 430cd32344..79abcb7e2e 100644
--- a/applications/utilities/mesh/generation/foamyMesh/conformalVoronoiMesh/conformalVoronoiMesh/conformalVoronoiMeshZones.C
+++ b/applications/utilities/mesh/generation/foamyMesh/conformalVoronoiMesh/conformalVoronoiMesh/conformalVoronoiMeshZones.C
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2013-2018 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2013-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -92,7 +92,7 @@ void Foam::conformalVoronoiMesh::selectSeparatedCoupledFaces
                 patches[patchi]
             );
 
-            if (cpp.separated() || !cpp.parallel())
+            if (cpp.transform().transformsPosition())
             {
                 forAll(cpp, i)
                 {
diff --git a/applications/utilities/mesh/manipulation/createPatch/createPatch.C b/applications/utilities/mesh/manipulation/createPatch/createPatch.C
index 5519810807..6725b427c6 100644
--- a/applications/utilities/mesh/manipulation/createPatch/createPatch.C
+++ b/applications/utilities/mesh/manipulation/createPatch/createPatch.C
@@ -357,15 +357,15 @@ void syncPoints
                 // Null any value which is not on neighbouring processor
                 nbrPatchInfo.setSize(procPatch.nPoints(), nullValue);
 
-                if (!procPatch.parallel())
+                if (procPatch.transform().rotates())
                 {
                     hasTransformation = true;
-                    transformList(procPatch.forwardT(), nbrPatchInfo);
+                    transformList(procPatch.transform().R(), nbrPatchInfo);
                 }
-                else if (procPatch.separated())
+                else if (procPatch.transform().translates())
                 {
                     hasTransformation = true;
-                    nbrPatchInfo -= procPatch.separation();
+                    nbrPatchInfo -= procPatch.transform().t();
                 }
 
                 const labelList& meshPts = procPatch.meshPoints();
@@ -407,15 +407,15 @@ void syncPoints
                 half0Values[i] = points[point0];
             }
 
-            if (!cycPatch.parallel())
+            if (cycPatch.transform().rotates())
             {
                 hasTransformation = true;
-                transformList(cycPatch.reverseT(), half0Values);
+                transformList(cycPatch.transform().R().T(), half0Values);
             }
-            else if (cycPatch.separated())
+            else if (cycPatch.transform().translates())
             {
                 hasTransformation = true;
-                half0Values += cycPatch.separation();
+                half0Values += cycPatch.transform().t();
             }
 
             forAll(coupledPoints, i)
@@ -765,11 +765,11 @@ int main(int argc, char *argv[])
                 const coupledPolyPatch& cpp =
                     refCast<const coupledPolyPatch>(pp);
 
-                if (cpp.separated())
+                if (cpp.transform().translates())
                 {
                     Info<< "On coupled patch " << pp.name()
                         << " separation was "
-                        << cpp.separation() << endl;
+                        << cpp.transform().t() << endl;
 
                     if (isA<cyclicPolyPatch>(pp) && pp.size())
                     {
@@ -784,20 +784,20 @@ int main(int argc, char *argv[])
                         {
                             const cyclicPolyPatch& nbr = cycpp.neighbPatch();
 
-                            const_cast<vector&>(cpp.separation()) =
+                            const_cast<vector&>(cpp.transform().t()) =
                                 nbr[0].centre(mesh.points())
                               - cycpp[0].centre(mesh.points());
                         }
                     }
                     Info<< "On coupled patch " << pp.name()
                         << " forcing uniform separation of "
-                        << cpp.separation() << endl;
+                        << cpp.transform().t() << endl;
                 }
-                else if (!cpp.parallel())
+                else if (cpp.transform().rotates())
                 {
                     Info<< "On coupled patch " << pp.name()
                         << " uniform rotation of "
-                        << cpp.forwardT() << endl;
+                        << cpp.transform().R() << endl;
                 }
             }
         }
diff --git a/src/OpenFOAM/fields/pointPatchFields/constraint/cyclic/cyclicPointPatchField.C b/src/OpenFOAM/fields/pointPatchFields/constraint/cyclic/cyclicPointPatchField.C
index 48e44111aa..354a8a0d80 100644
--- a/src/OpenFOAM/fields/pointPatchFields/constraint/cyclic/cyclicPointPatchField.C
+++ b/src/OpenFOAM/fields/pointPatchFields/constraint/cyclic/cyclicPointPatchField.C
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -138,7 +138,7 @@ void Foam::cyclicPointPatchField<Type>::swapAddSeparated
 
         const edgeList& pairs = cyclicPatch_.transformPairs();
 
-        if (doTransform())
+        if (transform().template transforms<Type>())
         {
             // Transform both sides.
             forAll(pairs, pairi)
@@ -147,8 +147,8 @@ void Foam::cyclicPointPatchField<Type>::swapAddSeparated
                 label nbrPointi = pairs[pairi][1];
 
                 Type tmp = pf[pointi];
-                pf[pointi] = transform(forwardT(), nbrPf[nbrPointi]);
-                nbrPf[nbrPointi] = transform(reverseT(), tmp);
+                pf[pointi] = transform().transform(nbrPf[nbrPointi]);
+                nbrPf[nbrPointi] = transform().invTransform(tmp);
             }
         }
         else
@@ -158,6 +158,7 @@ void Foam::cyclicPointPatchField<Type>::swapAddSeparated
                 Swap(pf[pairs[pairi][0]], nbrPf[pairs[pairi][1]]);
             }
         }
+
         this->addToInternalField(pField, pf);
         nbr.addToInternalField(pField, nbrPf);
     }
diff --git a/src/OpenFOAM/fields/pointPatchFields/constraint/cyclic/cyclicPointPatchField.H b/src/OpenFOAM/fields/pointPatchFields/constraint/cyclic/cyclicPointPatchField.H
index 4175beb71e..34edd903d3 100644
--- a/src/OpenFOAM/fields/pointPatchFields/constraint/cyclic/cyclicPointPatchField.H
+++ b/src/OpenFOAM/fields/pointPatchFields/constraint/cyclic/cyclicPointPatchField.H
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -141,19 +141,15 @@ public:
             //- Does the patch field perform the transformation
             virtual bool doTransform() const
             {
-                return !(cyclicPatch_.parallel() || pTraits<Type>::rank == 0);
+                return
+                    cyclicPatch_.transform().rotates()
+                 && pTraits<Type>::rank != 0;
             }
 
-            //- Return face transformation tensor
-            virtual const tensor& forwardT() const
+            //- Return transformation between the coupled patches
+            virtual const transformer& transform() const
             {
-                return cyclicPatch_.forwardT();
-            }
-
-            //- Return neighbour-cell transformation tensor
-            virtual const tensor& reverseT() const
-            {
-                return cyclicPatch_.reverseT();
+                return cyclicPatch_.transform();
             }
 
 
diff --git a/src/OpenFOAM/fields/pointPatchFields/constraint/processor/processorPointPatchField.H b/src/OpenFOAM/fields/pointPatchFields/constraint/processor/processorPointPatchField.H
index dbe32ddbcd..5d2ab59a0f 100644
--- a/src/OpenFOAM/fields/pointPatchFields/constraint/processor/processorPointPatchField.H
+++ b/src/OpenFOAM/fields/pointPatchFields/constraint/processor/processorPointPatchField.H
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -150,10 +150,8 @@ public:
             virtual bool doTransform() const
             {
                 return
-                   !(
-                        procPatch_.procPolyPatch().parallel()
-                     || pTraits<Type>::rank == 0
-                    );
+                    procPatch_.procPolyPatch().transform().rotates()
+                 && pTraits<Type>::rank != 0;
             }
 
 
diff --git a/src/OpenFOAM/fields/pointPatchFields/constraint/processorCyclic/processorCyclicPointPatchField.C b/src/OpenFOAM/fields/pointPatchFields/constraint/processorCyclic/processorCyclicPointPatchField.C
index d7a924d00b..6ed5ca2b02 100644
--- a/src/OpenFOAM/fields/pointPatchFields/constraint/processorCyclic/processorCyclicPointPatchField.C
+++ b/src/OpenFOAM/fields/pointPatchFields/constraint/processorCyclic/processorCyclicPointPatchField.C
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -24,7 +24,6 @@ License
 \*---------------------------------------------------------------------------*/
 
 #include "processorCyclicPointPatchField.H"
-#include "transformField.H"
 #include "processorPolyPatch.H"
 
 
@@ -165,10 +164,11 @@ void Foam::processorCyclicPointPatchField<Type>::swapAddSeparated
 
         if (doTransform())
         {
-            const processorCyclicPolyPatch& ppp =
-                procPatch_.procCyclicPolyPatch();
-
-            transform(receiveBuf_, ppp.forwardT(), receiveBuf_);
+            procPatch_.procCyclicPolyPatch().transform().transform
+            (
+                receiveBuf_,
+                receiveBuf_
+            );
         }
 
         // All points are separated
diff --git a/src/OpenFOAM/fields/pointPatchFields/constraint/processorCyclic/processorCyclicPointPatchField.H b/src/OpenFOAM/fields/pointPatchFields/constraint/processorCyclic/processorCyclicPointPatchField.H
index a3a4df7380..c7e1ddef54 100644
--- a/src/OpenFOAM/fields/pointPatchFields/constraint/processorCyclic/processorCyclicPointPatchField.H
+++ b/src/OpenFOAM/fields/pointPatchFields/constraint/processorCyclic/processorCyclicPointPatchField.H
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -154,10 +154,8 @@ public:
             virtual bool doTransform() const
             {
                 return
-                   !(
-                        pTraits<Type>::rank == 0
-                     || procPatch_.procPolyPatch().parallel()
-                    );
+                    procPatch_.procPolyPatch().transform().rotates()
+                 && pTraits<Type>::rank != 0;
             }
 
 
diff --git a/src/OpenFOAM/matrices/lduMatrix/lduAddressing/lduInterface/cyclicLduInterface.H b/src/OpenFOAM/matrices/lduMatrix/lduAddressing/lduInterface/cyclicLduInterface.H
index 46738f13d4..41ecf2af20 100644
--- a/src/OpenFOAM/matrices/lduMatrix/lduAddressing/lduInterface/cyclicLduInterface.H
+++ b/src/OpenFOAM/matrices/lduMatrix/lduAddressing/lduInterface/cyclicLduInterface.H
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -36,6 +36,7 @@ SourceFiles
 #define cyclicLduInterface_H
 
 #include "lduInterface.H"
+#include "transformer.H"
 #include "primitiveFieldsFwd.H"
 
 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
@@ -73,11 +74,8 @@ public:
             //- Return processor number
             virtual const cyclicLduInterface& neighbPatch() const = 0;
 
-            //- Return face transformation tensor
-            virtual const tensor& forwardT() const = 0;
-
-            //- Return face reverse transformation tensor
-            virtual const tensor& reverseT() const = 0;
+            //- Return transformation between the coupled patches
+            virtual const transformer& transform() const = 0;
 };
 
 
diff --git a/src/OpenFOAM/matrices/lduMatrix/lduAddressing/lduInterface/processorLduInterface.H b/src/OpenFOAM/matrices/lduMatrix/lduAddressing/lduInterface/processorLduInterface.H
index 37ee99bacd..c1ac67f464 100644
--- a/src/OpenFOAM/matrices/lduMatrix/lduAddressing/lduInterface/processorLduInterface.H
+++ b/src/OpenFOAM/matrices/lduMatrix/lduAddressing/lduInterface/processorLduInterface.H
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -37,6 +37,7 @@ SourceFiles
 #define processorLduInterface_H
 
 #include "lduInterface.H"
+#include "transformer.H"
 #include "primitiveFieldsFwd.H"
 
 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
@@ -93,12 +94,13 @@ public:
             //- Return neighbour processor number (rank in communicator)
             virtual int neighbProcNo() const = 0;
 
-            //- Return face transformation tensor
-            virtual const tensor& forwardT() const = 0;
+            //- Return transformation between the coupled patches
+            virtual const transformer& transform() const = 0;
 
             //- Return message tag used for sending
             virtual int tag() const = 0;
 
+
         // Transfer functions
 
             //- Raw send function
diff --git a/src/OpenFOAM/matrices/lduMatrix/lduAddressing/lduInterfaceFields/cyclicLduInterfaceField/cyclicLduInterfaceField.C b/src/OpenFOAM/matrices/lduMatrix/lduAddressing/lduInterfaceFields/cyclicLduInterfaceField/cyclicLduInterfaceField.C
index 7fe4188ced..c79e0cd3bf 100644
--- a/src/OpenFOAM/matrices/lduMatrix/lduAddressing/lduInterfaceFields/cyclicLduInterfaceField/cyclicLduInterfaceField.C
+++ b/src/OpenFOAM/matrices/lduMatrix/lduAddressing/lduInterfaceFields/cyclicLduInterfaceField/cyclicLduInterfaceField.C
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -30,7 +30,7 @@ License
 
 namespace Foam
 {
-defineTypeNameAndDebug(cyclicLduInterfaceField, 0);
+    defineTypeNameAndDebug(cyclicLduInterfaceField, 0);
 }
 
 
@@ -50,7 +50,7 @@ void Foam::cyclicLduInterfaceField::transformCoupleField
 {
     if (doTransform())
     {
-        f *= pow(diag(forwardT()).component(cmpt), rank());
+        f *= pow(diag(transform().R()).component(cmpt), rank());
     }
 }
 
diff --git a/src/OpenFOAM/matrices/lduMatrix/lduAddressing/lduInterfaceFields/cyclicLduInterfaceField/cyclicLduInterfaceField.H b/src/OpenFOAM/matrices/lduMatrix/lduAddressing/lduInterfaceFields/cyclicLduInterfaceField/cyclicLduInterfaceField.H
index 17fbc1d5b3..7bfa988d30 100644
--- a/src/OpenFOAM/matrices/lduMatrix/lduAddressing/lduInterfaceFields/cyclicLduInterfaceField/cyclicLduInterfaceField.H
+++ b/src/OpenFOAM/matrices/lduMatrix/lduAddressing/lduInterfaceFields/cyclicLduInterfaceField/cyclicLduInterfaceField.H
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -36,6 +36,7 @@ SourceFiles
 #define cyclicLduInterfaceField_H
 
 #include "primitiveFieldsFwd.H"
+#include "transformer.H"
 #include "typeInfo.H"
 
 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
@@ -74,11 +75,8 @@ public:
             //- Is the transform required
             virtual bool doTransform() const = 0;
 
-            //- Return face transformation tensor
-            virtual const tensor& forwardT() const = 0;
-
-            //- Return neighbour-cell transformation tensor
-            virtual const tensor& reverseT() const = 0;
+            //- Return the transformation
+            virtual const transformer& transform() const = 0;
 
             //- Return rank of component for transform
             virtual int rank() const = 0;
@@ -106,14 +104,14 @@ public:
 #include "tensorField.H"
 
 template<class Type>
-void Foam::cyclicLduInterfaceField::transformCoupleField
+inline void Foam::cyclicLduInterfaceField::transformCoupleField
 (
     Field<Type>& f
 ) const
 {
     if (doTransform())
     {
-        transform(f, forwardT(), f);
+        transform().transform(f, f);
     }
 }
 
diff --git a/src/OpenFOAM/matrices/lduMatrix/lduAddressing/lduInterfaceFields/processorLduInterfaceField/processorLduInterfaceField.C b/src/OpenFOAM/matrices/lduMatrix/lduAddressing/lduInterfaceFields/processorLduInterfaceField/processorLduInterfaceField.C
index b6177259c4..ea77a34bf8 100644
--- a/src/OpenFOAM/matrices/lduMatrix/lduAddressing/lduInterfaceFields/processorLduInterfaceField/processorLduInterfaceField.C
+++ b/src/OpenFOAM/matrices/lduMatrix/lduAddressing/lduInterfaceFields/processorLduInterfaceField/processorLduInterfaceField.C
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -50,7 +50,7 @@ void Foam::processorLduInterfaceField::transformCoupleField
 {
     if (doTransform())
     {
-        f *= pow(diag(forwardT()).component(cmpt), rank());
+        f *= pow(diag(transform().R()).component(cmpt), rank());
     }
 }
 
diff --git a/src/OpenFOAM/matrices/lduMatrix/lduAddressing/lduInterfaceFields/processorLduInterfaceField/processorLduInterfaceField.H b/src/OpenFOAM/matrices/lduMatrix/lduAddressing/lduInterfaceFields/processorLduInterfaceField/processorLduInterfaceField.H
index 66edd906eb..1e1ed83d20 100644
--- a/src/OpenFOAM/matrices/lduMatrix/lduAddressing/lduInterfaceFields/processorLduInterfaceField/processorLduInterfaceField.H
+++ b/src/OpenFOAM/matrices/lduMatrix/lduAddressing/lduInterfaceFields/processorLduInterfaceField/processorLduInterfaceField.H
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -36,6 +36,7 @@ SourceFiles
 #define processorLduInterfaceField_H
 
 #include "primitiveFieldsFwd.H"
+#include "transformer.H"
 #include "typeInfo.H"
 
 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
@@ -83,8 +84,8 @@ public:
             //- Is the transform required
             virtual bool doTransform() const = 0;
 
-            //- Return face transformation tensor
-            virtual const tensor& forwardT() const = 0;
+            //- Return transformation between the coupled patches
+            virtual const transformer& transform() const = 0;
 
             //- Return rank of component for transform
             virtual int rank() const = 0;
@@ -119,7 +120,7 @@ void Foam::processorLduInterfaceField::transformCoupleField
 {
     if (doTransform())
     {
-        transform(f, forwardT(), f);
+        transform().transform(f, f);
     }
 }
 
diff --git a/src/OpenFOAM/matrices/lduMatrix/solvers/GAMG/interfaceFields/cyclicGAMGInterfaceField/cyclicGAMGInterfaceField.H b/src/OpenFOAM/matrices/lduMatrix/solvers/GAMG/interfaceFields/cyclicGAMGInterfaceField/cyclicGAMGInterfaceField.H
index 078bdd4871..92167abb25 100644
--- a/src/OpenFOAM/matrices/lduMatrix/solvers/GAMG/interfaceFields/cyclicGAMGInterfaceField/cyclicGAMGInterfaceField.H
+++ b/src/OpenFOAM/matrices/lduMatrix/solvers/GAMG/interfaceFields/cyclicGAMGInterfaceField/cyclicGAMGInterfaceField.H
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -115,16 +115,10 @@ public:
                 return doTransform_;
             }
 
-            //- Return face transformation tensor
-            virtual const tensor& forwardT() const
+            //- Return the transformation
+            virtual const transformer& transform() const
             {
-                return cyclicInterface_.forwardT();
-            }
-
-            //- Return neighbour-cell transformation tensor
-            virtual const tensor& reverseT() const
-            {
-                return cyclicInterface_.reverseT();
+                return cyclicInterface_.transform();
             }
 
             //- Return rank of component for transform
diff --git a/src/OpenFOAM/matrices/lduMatrix/solvers/GAMG/interfaceFields/processorGAMGInterfaceField/processorGAMGInterfaceField.H b/src/OpenFOAM/matrices/lduMatrix/solvers/GAMG/interfaceFields/processorGAMGInterfaceField/processorGAMGInterfaceField.H
index 723956eaf4..a06eddd1a7 100644
--- a/src/OpenFOAM/matrices/lduMatrix/solvers/GAMG/interfaceFields/processorGAMGInterfaceField/processorGAMGInterfaceField.H
+++ b/src/OpenFOAM/matrices/lduMatrix/solvers/GAMG/interfaceFields/processorGAMGInterfaceField/processorGAMGInterfaceField.H
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -174,10 +174,10 @@ public:
                 return doTransform_;
             }
 
-            //- Return face transformation tensor
-            virtual const tensor& forwardT() const
+            //- Return transformation between the coupled patches
+            virtual const transformer& transform() const
             {
-                return procInterface_.forwardT();
+                return procInterface_.transform();
             }
 
             //- Return rank of component for transform
diff --git a/src/OpenFOAM/matrices/lduMatrix/solvers/GAMG/interfaces/cyclicGAMGInterface/cyclicGAMGInterface.C b/src/OpenFOAM/matrices/lduMatrix/solvers/GAMG/interfaces/cyclicGAMGInterface/cyclicGAMGInterface.C
index 0e1d1a62bb..27501a39d5 100644
--- a/src/OpenFOAM/matrices/lduMatrix/solvers/GAMG/interfaces/cyclicGAMGInterface/cyclicGAMGInterface.C
+++ b/src/OpenFOAM/matrices/lduMatrix/solvers/GAMG/interfaces/cyclicGAMGInterface/cyclicGAMGInterface.C
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2018 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -84,8 +84,7 @@ Foam::cyclicGAMGInterface::cyclicGAMGInterface
         refCast<const cyclicLduInterface>(fineInterface).neighbPatchID()
     ),
     owner_(refCast<const cyclicLduInterface>(fineInterface).owner()),
-    forwardT_(refCast<const cyclicLduInterface>(fineInterface).forwardT()),
-    reverseT_(refCast<const cyclicLduInterface>(fineInterface).reverseT())
+    transform_(refCast<const cyclicLduInterface>(fineInterface).transform())
 {
     // From coarse face to coarse cell
     DynamicList<label> dynFaceCells(localRestrictAddressing.size());
@@ -159,8 +158,7 @@ Foam::cyclicGAMGInterface::cyclicGAMGInterface
     GAMGInterface(index, coarseInterfaces, is),
     neighbPatchID_(readLabel(is)),
     owner_(readBool(is)),
-    forwardT_(is),
-    reverseT_(is)
+    transform_(is)
 {}
 
 
@@ -198,8 +196,7 @@ void Foam::cyclicGAMGInterface::write(Ostream& os) const
     GAMGInterface::write(os);
     os  << token::SPACE << neighbPatchID_
         << token::SPACE << owner_
-        << token::SPACE << forwardT_
-        << token::SPACE << reverseT_;
+        << token::SPACE << transform_;
 }
 
 
diff --git a/src/OpenFOAM/matrices/lduMatrix/solvers/GAMG/interfaces/cyclicGAMGInterface/cyclicGAMGInterface.H b/src/OpenFOAM/matrices/lduMatrix/solvers/GAMG/interfaces/cyclicGAMGInterface/cyclicGAMGInterface.H
index 27e1d5a4dc..34314062a3 100644
--- a/src/OpenFOAM/matrices/lduMatrix/solvers/GAMG/interfaces/cyclicGAMGInterface/cyclicGAMGInterface.H
+++ b/src/OpenFOAM/matrices/lduMatrix/solvers/GAMG/interfaces/cyclicGAMGInterface/cyclicGAMGInterface.H
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -60,11 +60,8 @@ class cyclicGAMGInterface
         //- Am I owner?
         bool owner_;
 
-        //- Transformation tensor
-        tensor forwardT_;
-
-        //- Transformation tensor
-        tensor reverseT_;
+        //- Transformation
+        transformer transform_;
 
 
 public:
@@ -138,15 +135,9 @@ public:
             }
 
             //- Return face transformation tensor
-            virtual const tensor& forwardT() const
+            virtual const transformer& transform() const
             {
-                return forwardT_;
-            }
-
-            //- Return neighbour-cell transformation tensor
-            virtual const tensor& reverseT() const
-            {
-                return reverseT_;
+                return transform_;
             }
 
 
diff --git a/src/OpenFOAM/matrices/lduMatrix/solvers/GAMG/interfaces/processorGAMGInterface/processorGAMGInterface.C b/src/OpenFOAM/matrices/lduMatrix/solvers/GAMG/interfaces/processorGAMGInterface/processorGAMGInterface.C
index 3d85fe54ed..c0399d5791 100644
--- a/src/OpenFOAM/matrices/lduMatrix/solvers/GAMG/interfaces/processorGAMGInterface/processorGAMGInterface.C
+++ b/src/OpenFOAM/matrices/lduMatrix/solvers/GAMG/interfaces/processorGAMGInterface/processorGAMGInterface.C
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -72,7 +72,10 @@ Foam::processorGAMGInterface::processorGAMGInterface
     (
         refCast<const processorLduInterface>(fineInterface).neighbProcNo()
     ),
-    forwardT_(refCast<const processorLduInterface>(fineInterface).forwardT()),
+    transform_
+    (
+        refCast<const processorLduInterface>(fineInterface).transform()
+    ),
     tag_(refCast<const processorLduInterface>(fineInterface).tag())
 {
     // From coarse face to coarse cell
@@ -146,7 +149,7 @@ Foam::processorGAMGInterface::processorGAMGInterface
     const label coarseComm,
     const label myProcNo,
     const label neighbProcNo,
-    const tensor& forwardT,
+    const transformer& transform,
     const int tag
 )
 :
@@ -160,7 +163,7 @@ Foam::processorGAMGInterface::processorGAMGInterface
     comm_(coarseComm),
     myProcNo_(myProcNo),
     neighbProcNo_(neighbProcNo),
-    forwardT_(forwardT),
+    transform_(transform),
     tag_(tag)
 {}
 
@@ -176,7 +179,7 @@ Foam::processorGAMGInterface::processorGAMGInterface
     comm_(readLabel(is)),
     myProcNo_(readLabel(is)),
     neighbProcNo_(readLabel(is)),
-    forwardT_(is),
+    transform_(is),
     tag_(readLabel(is))
 {}
 
@@ -217,7 +220,7 @@ void Foam::processorGAMGInterface::write(Ostream& os) const
     os  << token::SPACE << comm_
         << token::SPACE << myProcNo_
         << token::SPACE << neighbProcNo_
-        << token::SPACE << forwardT_
+        << token::SPACE << transform_
         << token::SPACE << tag_;
 }
 
diff --git a/src/OpenFOAM/matrices/lduMatrix/solvers/GAMG/interfaces/processorGAMGInterface/processorGAMGInterface.H b/src/OpenFOAM/matrices/lduMatrix/solvers/GAMG/interfaces/processorGAMGInterface/processorGAMGInterface.H
index ce1cb0308f..c30429e793 100644
--- a/src/OpenFOAM/matrices/lduMatrix/solvers/GAMG/interfaces/processorGAMGInterface/processorGAMGInterface.H
+++ b/src/OpenFOAM/matrices/lduMatrix/solvers/GAMG/interfaces/processorGAMGInterface/processorGAMGInterface.H
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -63,8 +63,8 @@ class processorGAMGInterface
         //- Neighbouring processor rank in communicator
         label neighbProcNo_;
 
-        //- Transformation tensor
-        tensor forwardT_;
+        //- Transformation
+        transformer transform_;
 
         //- Message tag used for sending
         int tag_;
@@ -100,7 +100,7 @@ public:
             const label coarseComm,
             const label myProcNo,
             const label neighbProcNo,
-            const tensor& forwardT,
+            const transformer& transform,
             const int tag
         );
 
@@ -159,10 +159,10 @@ public:
                 return neighbProcNo_;
             }
 
-            //- Return face transformation tensor
-            virtual const tensor& forwardT() const
+            //- Return transformation between the coupled patches
+            virtual const transformer& transform() const
             {
-                return forwardT_;
+                return transform_;
             }
 
             //- Return message tag used for sending
diff --git a/src/OpenFOAM/meshes/lduMesh/lduPrimitiveMesh.C b/src/OpenFOAM/meshes/lduMesh/lduPrimitiveMesh.C
index dfcafd0a18..a6051cca5a 100644
--- a/src/OpenFOAM/meshes/lduMesh/lduPrimitiveMesh.C
+++ b/src/OpenFOAM/meshes/lduMesh/lduPrimitiveMesh.C
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2013-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2013-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -926,7 +926,7 @@ Foam::lduPrimitiveMesh::lduPrimitiveMesh
                 comm_,
                 myAgglom,
                 neighbProcNo,
-                Zero,                   // forwardT
+                transformer(),          // forwardT
                 Pstream::msgType()      // tag
             )
         );
diff --git a/src/OpenFOAM/meshes/pointMesh/pointPatches/constraint/cyclic/cyclicPointPatch.H b/src/OpenFOAM/meshes/pointMesh/pointPatches/constraint/cyclic/cyclicPointPatch.H
index 8dbb826516..a004be98aa 100644
--- a/src/OpenFOAM/meshes/pointMesh/pointPatches/constraint/cyclic/cyclicPointPatch.H
+++ b/src/OpenFOAM/meshes/pointMesh/pointPatches/constraint/cyclic/cyclicPointPatch.H
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -132,22 +132,10 @@ public:
                 return refCast<const cyclicPointPatch>(pp);
             }
 
-            //- Are the cyclic planes parallel
-            bool parallel() const
+            //- Return transformation between the coupled patches
+            virtual const transformer& transform() const
             {
-                return cyclicPolyPatch_.parallel();
-            }
-
-            //- Return face transformation tensor
-            const tensor& forwardT() const
-            {
-                return cyclicPolyPatch_.forwardT();
-            }
-
-            //- Return neighbour-cell transformation tensor
-            const tensor& reverseT() const
-            {
-                return cyclicPolyPatch_.reverseT();
+                return cyclicPolyPatch_.transform();
             }
 
 
diff --git a/src/OpenFOAM/meshes/polyMesh/mapPolyMesh/mapDistribute/mapDistribute.H b/src/OpenFOAM/meshes/polyMesh/mapPolyMesh/mapDistribute/mapDistribute.H
index 1282ccdc39..990fecec88 100644
--- a/src/OpenFOAM/meshes/polyMesh/mapPolyMesh/mapDistribute/mapDistribute.H
+++ b/src/OpenFOAM/meshes/polyMesh/mapPolyMesh/mapDistribute/mapDistribute.H
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -238,9 +238,9 @@ public:
             template<class Type>
             void operator()(const coupledPolyPatch& cpp, UList<Type>& fld) const
             {
-                if (!cpp.parallel())
+                if (cpp.transform().transforms())
                 {
-                    transformList(cpp.forwardT(), fld);
+                    transformList(cpp.transform().R(), fld);
                 }
             }
 
@@ -249,9 +249,9 @@ public:
             void operator()(const coupledPolyPatch& cpp, Container<Type>& map)
             const
             {
-                if (!cpp.parallel())
+                if (cpp.transform().transforms())
                 {
-                    transformList(cpp.forwardT(), map);
+                    transformList(cpp.transform().R(), map);
                 }
             }
         };
diff --git a/src/OpenFOAM/meshes/polyMesh/polyPatches/basic/coupled/coupledPolyPatch.H b/src/OpenFOAM/meshes/polyMesh/polyPatches/basic/coupled/coupledPolyPatch.H
index 37091325dd..46a19377b3 100644
--- a/src/OpenFOAM/meshes/polyMesh/polyPatches/basic/coupled/coupledPolyPatch.H
+++ b/src/OpenFOAM/meshes/polyMesh/polyPatches/basic/coupled/coupledPolyPatch.H
@@ -38,6 +38,7 @@ SourceFiles
 #define coupledPolyPatch_H
 
 #include "polyPatch.H"
+#include "transformer.H"
 #include "diagTensorField.H"
 
 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
@@ -107,6 +108,8 @@ protected:
         //- Neighbour-cell transformation tensor
         mutable tensor reverseT_;
 
+        //- Transformation between the coupled patches
+        mutable transformer transform_;
 
 
 protected:
@@ -270,34 +273,10 @@ public:
             //- Transform a patch-based position from other side to this side
             virtual void transformPosition(point&, const label facei) const = 0;
 
-            //- Are the cyclic planes parallel.
-            virtual bool parallel() const
+            //- Return transformation between the coupled patches
+            virtual const transformer& transform() const
             {
-                return parallel_;
-            }
-
-            //- Are the planes separated.
-            virtual bool separated() const
-            {
-                return separated_;
-            }
-
-            //- If the planes are separated the separation vector.
-            virtual const vector& separation() const
-            {
-                return separation_;
-            }
-
-            //- Return face transformation tensor.
-            virtual const tensor& forwardT() const
-            {
-                return forwardT_;
-            }
-
-            //- Return neighbour-cell transformation tensor.
-            virtual const tensor& reverseT() const
-            {
-                return reverseT_;
+                return transform_;
             }
 
             scalar matchTolerance() const
diff --git a/src/OpenFOAM/meshes/polyMesh/polyPatches/constraint/cyclic/cyclicPolyPatch.C b/src/OpenFOAM/meshes/polyMesh/polyPatches/constraint/cyclic/cyclicPolyPatch.C
index ff2ebc7e27..1f0b203982 100644
--- a/src/OpenFOAM/meshes/polyMesh/polyPatches/constraint/cyclic/cyclicPolyPatch.C
+++ b/src/OpenFOAM/meshes/polyMesh/polyPatches/constraint/cyclic/cyclicPolyPatch.C
@@ -85,6 +85,8 @@ void Foam::cyclicPolyPatch::calcTransformTensors
         // Dummy geometry. Assume non-separated, parallel.
         parallel_ = true;
         separated_ = false;
+
+        transform_ = transformer();
     }
     else
     {
@@ -129,6 +131,8 @@ void Foam::cyclicPolyPatch::calcTransformTensors
 
             forwardT_ = forwardT[0];
             reverseT_ = reverseT[0];
+
+            transform_ = transformer(forwardT[0]);
         }
         else
         {
@@ -188,6 +192,8 @@ void Foam::cyclicPolyPatch::calcTransformTensors
 
                     separated_ = false;
                     separation_ = Zero;
+
+                    transform_ = transformer();
                 }
                 else
                 {
@@ -200,6 +206,8 @@ void Foam::cyclicPolyPatch::calcTransformTensors
 
                     separated_ = true;
                     separation_ = separation[0];
+
+                    transform_ = transformer(separation[0]);
                 }
             }
             else
@@ -210,6 +218,8 @@ void Foam::cyclicPolyPatch::calcTransformTensors
 
                 separated_ = true;
                 separation_ = separation[0];
+
+                transform_ = transformer(separation[0]);
             }
         }
     }
@@ -463,6 +473,8 @@ void Foam::cyclicPolyPatch::calcTransforms
             separation_ = Zero;
             forwardT_ = revT.T();
             reverseT_ = revT;
+
+            transform_ = transformer(revT.T());
         }
         else if (transformType() == TRANSLATIONAL)
         {
@@ -507,6 +519,8 @@ void Foam::cyclicPolyPatch::calcTransforms
             separated_ = true;
             forwardT_ = Zero;
             reverseT_ = Zero;
+
+            transform_ = transformer();
         }
         else
         {
@@ -995,45 +1009,45 @@ Foam::label Foam::cyclicPolyPatch::neighbPatchID() const
 
 void Foam::cyclicPolyPatch::transformPosition(pointField& l) const
 {
-    if (!parallel())
+    if (transform().rotates())
     {
         if (transformType() == ROTATIONAL)
         {
             l =
-                Foam::transform(forwardT(), l-rotationCentre_)
+                Foam::transform(transform().R(), l-rotationCentre_)
               + rotationCentre_;
         }
         else
         {
-            l = Foam::transform(forwardT(), l);
+            l = Foam::transform(transform().R(), l);
         }
     }
-    else if (separated())
+    else if (transform().translates())
     {
         // transformPosition gets called on the receiving side,
         // separation gets calculated on the sending side so subtract.
-        l -= separation();
+        l -= transform().t();
     }
 }
 
 
 void Foam::cyclicPolyPatch::transformPosition(point& l, const label facei) const
 {
-    if (!parallel())
+    if (transform().rotates())
     {
         if (transformType() == ROTATIONAL)
         {
-            l = Foam::transform(forwardT(), l - rotationCentre_)
+            l = Foam::transform(transform().R(), l - rotationCentre_)
               + rotationCentre_;
         }
         else
         {
-            l = Foam::transform(forwardT(), l);
+            l = Foam::transform(transform().R(), l);
         }
     }
-    else if (separated())
+    else if (transform().translates())
     {
-        l -= separation();
+        l -= transform().t();
     }
 }
 
diff --git a/src/OpenFOAM/meshes/polyMesh/polyPatches/constraint/processorCyclic/processorCyclicPolyPatch.H b/src/OpenFOAM/meshes/polyMesh/polyPatches/constraint/processorCyclic/processorCyclicPolyPatch.H
index fc09eaf52c..bf030d538d 100644
--- a/src/OpenFOAM/meshes/polyMesh/polyPatches/constraint/processorCyclic/processorCyclicPolyPatch.H
+++ b/src/OpenFOAM/meshes/polyMesh/polyPatches/constraint/processorCyclic/processorCyclicPolyPatch.H
@@ -338,34 +338,10 @@ public:
             referPatch().transformPosition(l, facei);
         }
 
-        //- Are the planes separated.
-        virtual bool separated() const
+        //- Return transformation between the coupled patches
+        virtual const transformer& transform() const
         {
-            return referPatch().separated();
-        }
-
-        //- If the planes are separated the separation vector.
-        virtual const vector& separation() const
-        {
-            return referPatch().separation();
-        }
-
-        //- Are the cyclic planes parallel.
-        virtual bool parallel() const
-        {
-            return referPatch().parallel();
-        }
-
-        //- Return face transformation tensor.
-        virtual const tensor& forwardT() const
-        {
-            return referPatch().forwardT();
-        }
-
-        //- Return neighbour-cell transformation tensor.
-        virtual const tensor& reverseT() const
-        {
-            return referPatch().reverseT();
+            return referPatch().transform_;
         }
 
         //- Initialize ordering for primitivePatch. Does not
diff --git a/src/OpenFOAM/primitives/globalIndexAndTransform/globalIndexAndTransform.C b/src/OpenFOAM/primitives/globalIndexAndTransform/globalIndexAndTransform.C
index 9854ceeb53..eb3887d3e6 100644
--- a/src/OpenFOAM/primitives/globalIndexAndTransform/globalIndexAndTransform.C
+++ b/src/OpenFOAM/primitives/globalIndexAndTransform/globalIndexAndTransform.C
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -141,9 +141,9 @@ void Foam::globalIndexAndTransform::determineTransforms()
         {
             const coupledPolyPatch& cpp = refCast<const coupledPolyPatch>(pp);
 
-            if (cpp.separated())
+            if (cpp.transform().translates())
             {
-                const vector& sepVec = cpp.separation();
+                const vector& sepVec = cpp.transform().t();
 
                 if (mag(sepVec) > small)
                 {
@@ -166,9 +166,9 @@ void Foam::globalIndexAndTransform::determineTransforms()
                     }
                 }
             }
-            else if (!cpp.parallel())
+            else if (cpp.transform().rotates())
             {
-                const tensor& transT = cpp.reverseT();
+                const tensor& transT = cpp.transform().R().T();
 
                 if (mag(transT - I) > small)
                 {
@@ -299,9 +299,9 @@ void Foam::globalIndexAndTransform::determinePatchTransformSign()
         {
             const coupledPolyPatch& cpp = refCast<const coupledPolyPatch>(pp);
 
-            if (cpp.separated())
+            if (cpp.transform().translates())
             {
-                const vector& sepVec = cpp.separation();
+                const vector& sepVec = cpp.transform().t();
 
                 if (mag(sepVec) > small)
                 {
@@ -319,9 +319,9 @@ void Foam::globalIndexAndTransform::determinePatchTransformSign()
                     patchTransformSign_[patchi] = labelPair(matchTransI, sign);
                 }
             }
-            else if (!cpp.parallel())
+            else if (cpp.transform().rotates())
             {
-                const tensor& transT = cpp.reverseT();
+                const tensor& transT = cpp.transform().R().T();
 
                 if (mag(transT - I) > small)
                 {
diff --git a/src/OpenFOAM/primitives/transform/transformer/transformer.H b/src/OpenFOAM/primitives/transform/transformer/transformer.H
index 8089b60f37..f2e965bb67 100644
--- a/src/OpenFOAM/primitives/transform/transformer/transformer.H
+++ b/src/OpenFOAM/primitives/transform/transformer/transformer.H
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -133,9 +133,19 @@ public:
             //- Return true if the rotation tensor is non-I
             inline bool rotates() const;
 
-            //- Return true if the transformer either translates or rotates
+            //- Return true if the transformer transforms a type
+            //  (i.e. rotates)
             inline bool transforms() const;
 
+            //- Return true if the transformer transforms the given type
+            //  (i.e. rotates)
+            template<typename Type>
+            inline bool transforms() const;
+
+            //- Return true if the transformer transforms a point
+            // (i.e. translates or rotates)
+            inline bool transformsPosition() const;
+
 
         // Edit
 
@@ -170,6 +180,10 @@ public:
             template<class Type>
             Type transform(const Type&) const;
 
+            //- Transform the given field
+            template<class Type>
+            void transform(Field<Type>&, const Field<Type>&) const;
+
             //- Transform the given field
             template<class Type>
             tmp<Field<Type>> transform(const Field<Type>&) const;
diff --git a/src/OpenFOAM/primitives/transform/transformer/transformerI.H b/src/OpenFOAM/primitives/transform/transformer/transformerI.H
index 9bb526e648..3353ca9c49 100644
--- a/src/OpenFOAM/primitives/transform/transformer/transformerI.H
+++ b/src/OpenFOAM/primitives/transform/transformer/transformerI.H
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -103,6 +103,19 @@ inline bool Foam::transformer::rotates() const
 
 
 inline bool Foam::transformer::transforms() const
+{
+    return rotates_;
+}
+
+
+template<typename Type>
+inline bool Foam::transformer::transforms() const
+{
+    return pTraits<Type>::rank != 0 && (translates_ || rotates_);
+}
+
+
+inline bool Foam::transformer::transformsPosition() const
 {
     return translates_ || rotates_;
 }
diff --git a/src/OpenFOAM/primitives/transform/transformer/transformerTemplates.C b/src/OpenFOAM/primitives/transform/transformer/transformerTemplates.C
index d69b2aa43b..06f7decc84 100644
--- a/src/OpenFOAM/primitives/transform/transformer/transformerTemplates.C
+++ b/src/OpenFOAM/primitives/transform/transformer/transformerTemplates.C
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -39,6 +39,20 @@ Type Foam::transformer::transform(const Type& x) const
 }
 
 
+template<class Type>
+void Foam::transformer::transform
+(
+    Field<Type>& res,
+    const Field<Type>& fld
+) const
+{
+    if (rotates_)
+    {
+        return Foam::transform(res, R(), fld);
+    }
+}
+
+
 template<class Type>
 Foam::tmp<Foam::Field<Type>> Foam::transformer::transform
 (
diff --git a/src/dynamicMesh/motionSmoother/motionSmootherAlgo.C b/src/dynamicMesh/motionSmoother/motionSmootherAlgo.C
index 304e7af3b0..de22a56c73 100644
--- a/src/dynamicMesh/motionSmoother/motionSmootherAlgo.C
+++ b/src/dynamicMesh/motionSmoother/motionSmootherAlgo.C
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -861,9 +861,7 @@ bool Foam::motionSmootherAlgo::scaleMesh
                     refCast<const coupledPolyPatch>(patches[patchi]);
 
                 Pout<< '\t' << patchi << '\t' << pp.name()
-                    << " parallel:" << pp.parallel()
-                    << " separated:" << pp.separated()
-                    << " forwardT:" << pp.forwardT().size()
+                    << " transform:" << pp.transform()
                     << endl;
             }
         }
@@ -871,6 +869,7 @@ bool Foam::motionSmootherAlgo::scaleMesh
 
     const scalar errorReduction =
         paramDict.lookup<scalar>("errorReduction");
+
     const label nSmoothScale =
         paramDict.lookup<label>("nSmoothScale");
 
diff --git a/src/finiteVolume/fields/fvPatchFields/constraint/cyclic/cyclicFvPatchField.C b/src/finiteVolume/fields/fvPatchFields/constraint/cyclic/cyclicFvPatchField.C
index a5dd13d2c2..3229884d52 100644
--- a/src/finiteVolume/fields/fvPatchFields/constraint/cyclic/cyclicFvPatchField.C
+++ b/src/finiteVolume/fields/fvPatchFields/constraint/cyclic/cyclicFvPatchField.C
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -136,10 +136,7 @@ Foam::cyclicFvPatchField<Type>::patchNeighbourField() const
     {
         forAll(pnf, facei)
         {
-            pnf[facei] = transform
-            (
-                forwardT(), iField[nbrFaceCells[facei]]
-            );
+            pnf[facei] = transform().transform(iField[nbrFaceCells[facei]]);
         }
     }
     else
diff --git a/src/finiteVolume/fields/fvPatchFields/constraint/cyclic/cyclicFvPatchField.H b/src/finiteVolume/fields/fvPatchFields/constraint/cyclic/cyclicFvPatchField.H
index 8bed3bae51..6e72b4ac8c 100644
--- a/src/finiteVolume/fields/fvPatchFields/constraint/cyclic/cyclicFvPatchField.H
+++ b/src/finiteVolume/fields/fvPatchFields/constraint/cyclic/cyclicFvPatchField.H
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -186,19 +186,15 @@ public:
             //- Does the patch field perform the transformation
             virtual bool doTransform() const
             {
-                return !(cyclicPatch_.parallel() || pTraits<Type>::rank == 0);
+                return
+                    cyclicPatch_.transform().rotates()
+                 && pTraits<Type>::rank != 0;
             }
 
-            //- Return face transformation tensor
-            virtual const tensor& forwardT() const
+            //- Return transformation between the coupled patches
+            virtual const transformer& transform() const
             {
-                return cyclicPatch_.forwardT();
-            }
-
-            //- Return neighbour-cell transformation tensor
-            virtual const tensor& reverseT() const
-            {
-                return cyclicPatch_.reverseT();
+                return cyclicPatch_.transform();
             }
 
             //- Return rank of component for transform
diff --git a/src/finiteVolume/fields/fvPatchFields/constraint/cyclicAMI/cyclicAMIFvPatchField.C b/src/finiteVolume/fields/fvPatchFields/constraint/cyclicAMI/cyclicAMIFvPatchField.C
index dab70f35ee..2acbe9a65b 100644
--- a/src/finiteVolume/fields/fvPatchFields/constraint/cyclicAMI/cyclicAMIFvPatchField.C
+++ b/src/finiteVolume/fields/fvPatchFields/constraint/cyclicAMI/cyclicAMIFvPatchField.C
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -158,7 +158,7 @@ Foam::cyclicAMIFvPatchField<Type>::patchNeighbourField() const
 
     if (doTransform())
     {
-        tpnf.ref() = transform(forwardT(), tpnf());
+        transform().transform(tpnf.ref(), tpnf());
     }
 
     return tpnf;
diff --git a/src/finiteVolume/fields/fvPatchFields/constraint/cyclicAMI/cyclicAMIFvPatchField.H b/src/finiteVolume/fields/fvPatchFields/constraint/cyclicAMI/cyclicAMIFvPatchField.H
index 3e59faa445..5645e9c597 100644
--- a/src/finiteVolume/fields/fvPatchFields/constraint/cyclicAMI/cyclicAMIFvPatchField.H
+++ b/src/finiteVolume/fields/fvPatchFields/constraint/cyclicAMI/cyclicAMIFvPatchField.H
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -192,19 +192,14 @@ public:
             virtual bool doTransform() const
             {
                 return
-                    !(cyclicAMIPatch_.parallel() || pTraits<Type>::rank == 0);
+                    cyclicAMIPatch_.transform().rotates()
+                 && pTraits<Type>::rank != 0;
             }
 
-            //- Return face transformation tensor
-            virtual const tensor& forwardT() const
+            //- Return transformation between the coupled patches
+            virtual const transformer& transform() const
             {
-                return cyclicAMIPatch_.forwardT();
-            }
-
-            //- Return neighbour-cell transformation tensor
-            virtual const tensor& reverseT() const
-            {
-                return cyclicAMIPatch_.reverseT();
+                return cyclicAMIPatch_.transform();
             }
 
             //- Return rank of component for transform
diff --git a/src/finiteVolume/fields/fvPatchFields/constraint/jumpCyclic/jumpCyclicFvPatchField.C b/src/finiteVolume/fields/fvPatchFields/constraint/jumpCyclic/jumpCyclicFvPatchField.C
index 0d7c5310bb..09b33663c7 100644
--- a/src/finiteVolume/fields/fvPatchFields/constraint/jumpCyclic/jumpCyclicFvPatchField.C
+++ b/src/finiteVolume/fields/fvPatchFields/constraint/jumpCyclic/jumpCyclicFvPatchField.C
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -110,10 +110,9 @@ Foam::jumpCyclicFvPatchField<Type>::patchNeighbourField() const
     {
         forAll(*this, facei)
         {
-            pnf[facei] = transform
-            (
-                this->forwardT(), iField[nbrFaceCells[facei]]
-            ) - jf[facei];
+            pnf[facei] =
+                this->transform().transform(iField[nbrFaceCells[facei]])
+              - jf[facei];
         }
     }
     else
diff --git a/src/finiteVolume/fields/fvPatchFields/constraint/jumpCyclicAMI/jumpCyclicAMIFvPatchField.C b/src/finiteVolume/fields/fvPatchFields/constraint/jumpCyclicAMI/jumpCyclicAMIFvPatchField.C
index 6029eb898b..28e837a057 100644
--- a/src/finiteVolume/fields/fvPatchFields/constraint/jumpCyclicAMI/jumpCyclicAMIFvPatchField.C
+++ b/src/finiteVolume/fields/fvPatchFields/constraint/jumpCyclicAMI/jumpCyclicAMIFvPatchField.C
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2012-2018 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2012-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -117,7 +117,7 @@ Foam::jumpCyclicAMIFvPatchField<Type>::patchNeighbourField() const
 
     if (this->doTransform())
     {
-        tpnf = transform(this->forwardT(), tpnf);
+        this->transform().transform(tpnf.ref(), tpnf());
     }
 
     tmp<Field<Type>> tjf = jump();
diff --git a/src/finiteVolume/fields/fvPatchFields/constraint/processor/processorFvPatchField.C b/src/finiteVolume/fields/fvPatchFields/constraint/processor/processorFvPatchField.C
index 3338bc11a7..f86946f21e 100644
--- a/src/finiteVolume/fields/fvPatchFields/constraint/processor/processorFvPatchField.C
+++ b/src/finiteVolume/fields/fvPatchFields/constraint/processor/processorFvPatchField.C
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -297,7 +297,7 @@ void Foam::processorFvPatchField<Type>::evaluate
 
         if (doTransform())
         {
-            transform(*this, procPatch_.forwardT(), *this);
+            procPatch_.transform().transform<Type>(*this, *this);
         }
     }
 }
diff --git a/src/finiteVolume/fields/fvPatchFields/constraint/processor/processorFvPatchField.H b/src/finiteVolume/fields/fvPatchFields/constraint/processor/processorFvPatchField.H
index 556cb9924f..705d189bb9 100644
--- a/src/finiteVolume/fields/fvPatchFields/constraint/processor/processorFvPatchField.H
+++ b/src/finiteVolume/fields/fvPatchFields/constraint/processor/processorFvPatchField.H
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -264,13 +264,15 @@ public:
             //- Does the patch field perform the transformation
             virtual bool doTransform() const
             {
-                return !(procPatch_.parallel() || pTraits<Type>::rank == 0);
+                return
+                    procPatch_.transform().rotates()
+                 && pTraits<Type>::rank != 0;
             }
 
-            //- Return face transformation tensor
-            virtual const tensor& forwardT() const
+            //- Return transformation between the coupled patches
+            virtual const transformer& transform() const
             {
-                return procPatch_.forwardT();
+                return procPatch_.transform();
             }
 
             //- Return rank of component for transform
@@ -278,7 +280,6 @@ public:
             {
                 return pTraits<Type>::rank;
             }
-
 };
 
 
diff --git a/src/finiteVolume/fields/fvPatchFields/constraint/processorCyclic/processorCyclicFvPatchField.H b/src/finiteVolume/fields/fvPatchFields/constraint/processorCyclic/processorCyclicFvPatchField.H
index e60735cbfc..8cff755919 100644
--- a/src/finiteVolume/fields/fvPatchFields/constraint/processorCyclic/processorCyclicFvPatchField.H
+++ b/src/finiteVolume/fields/fvPatchFields/constraint/processorCyclic/processorCyclicFvPatchField.H
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -157,13 +157,15 @@ public:
             //- Does the patch field perform the transformation
             virtual bool doTransform() const
             {
-                return !(procPatch_.parallel() || pTraits<Type>::rank == 0);
+                return
+                    procPatch_.transform().rotates()
+                 && pTraits<Type>::rank != 0;
             }
 
-            //- Return face transformation tensor
-            virtual const tensor& forwardT() const
+            //- Return transformation between the coupled patches
+            virtual const transformer& transform() const
             {
-                return procPatch_.forwardT();
+                return procPatch_.transform();
             }
 };
 
diff --git a/src/finiteVolume/fvMesh/extendedStencil/cellToCell/extendedCellToCellStencil.C b/src/finiteVolume/fvMesh/extendedStencil/cellToCell/extendedCellToCellStencil.C
index bb33c65ff0..788adce48b 100644
--- a/src/finiteVolume/fvMesh/extendedStencil/cellToCell/extendedCellToCellStencil.C
+++ b/src/finiteVolume/fvMesh/extendedStencil/cellToCell/extendedCellToCellStencil.C
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2013-2018 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2013-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -41,7 +41,7 @@ Foam::extendedCellToCellStencil::extendedCellToCellStencil(const polyMesh& mesh)
             const coupledPolyPatch& cpp =
                 refCast<const coupledPolyPatch>(patches[patchi]);
 
-            if (!cpp.parallel() || cpp.separated())
+            if (cpp.transform().transformsPosition())
             {
                 FatalErrorInFunction
                     << "Coupled patches with transformations not supported."
diff --git a/src/finiteVolume/fvMesh/extendedStencil/cellToFace/extendedCellToFaceStencil.C b/src/finiteVolume/fvMesh/extendedStencil/cellToFace/extendedCellToFaceStencil.C
index 54bd6ad0d0..854e8a562b 100644
--- a/src/finiteVolume/fvMesh/extendedStencil/cellToFace/extendedCellToFaceStencil.C
+++ b/src/finiteVolume/fvMesh/extendedStencil/cellToFace/extendedCellToFaceStencil.C
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2018 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -111,7 +111,7 @@ Foam::extendedCellToFaceStencil::extendedCellToFaceStencil(const polyMesh& mesh)
             const coupledPolyPatch& cpp =
                 refCast<const coupledPolyPatch>(patches[patchi]);
 
-            if (!cpp.parallel() || cpp.separated())
+            if (cpp.transform().transformsPosition())
             {
                 FatalErrorInFunction
                     << "Coupled patches with transformations not supported."
diff --git a/src/finiteVolume/fvMesh/extendedStencil/faceToCell/extendedFaceToCellStencil.C b/src/finiteVolume/fvMesh/extendedStencil/faceToCell/extendedFaceToCellStencil.C
index d0ba904812..2905fdd9ce 100644
--- a/src/finiteVolume/fvMesh/extendedStencil/faceToCell/extendedFaceToCellStencil.C
+++ b/src/finiteVolume/fvMesh/extendedStencil/faceToCell/extendedFaceToCellStencil.C
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2018 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -43,7 +43,7 @@ Foam::extendedFaceToCellStencil::extendedFaceToCellStencil(const polyMesh& mesh)
             const coupledPolyPatch& cpp =
                 refCast<const coupledPolyPatch>(patches[patchi]);
 
-            if (!cpp.parallel() || cpp.separated())
+            if (cpp.transform().transformsPosition())
             {
                 FatalErrorInFunction
                     << "Coupled patches with transformations not supported."
diff --git a/src/finiteVolume/fvMesh/fvPatches/basic/coupled/coupledFvPatch.H b/src/finiteVolume/fvMesh/fvPatches/basic/coupled/coupledFvPatch.H
index c04cd4a201..1c93d40b0e 100644
--- a/src/finiteVolume/fvMesh/fvPatches/basic/coupled/coupledFvPatch.H
+++ b/src/finiteVolume/fvMesh/fvPatches/basic/coupled/coupledFvPatch.H
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -100,14 +100,8 @@ public:
                 return coupledPolyPatch_.coupled();
             }
 
-            //- Are the cyclic planes parallel
-            virtual bool parallel() const = 0;
-
-            //- Return face transformation tensor
-            virtual const tensor& forwardT() const = 0;
-
-            //- Return neighbour-cell transformation tensor
-            virtual const tensor& reverseT() const = 0;
+            //- Return transformation between the coupled patches
+            virtual const transformer& transform() const = 0;
 
             //- Return faceCell addressing
             virtual const labelUList& faceCells() const
diff --git a/src/finiteVolume/fvMesh/fvPatches/constraint/cyclic/cyclicFvPatch.C b/src/finiteVolume/fvMesh/fvPatches/constraint/cyclic/cyclicFvPatch.C
index 93f00ba92b..5a47f72688 100644
--- a/src/finiteVolume/fvMesh/fvPatches/constraint/cyclic/cyclicFvPatch.C
+++ b/src/finiteVolume/fvMesh/fvPatches/constraint/cyclic/cyclicFvPatch.C
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -80,14 +80,14 @@ Foam::tmp<Foam::vectorField> Foam::cyclicFvPatch::delta() const
     vectorField& pdv = tpdv.ref();
 
     // To the transformation if necessary
-    if (parallel())
+    if (transform().rotates())
     {
         forAll(patchD, facei)
         {
             vector ddi = patchD[facei];
             vector dni = nbrPatchD[facei];
 
-            pdv[facei] = ddi - dni;
+            pdv[facei] = ddi - transform().transform(dni);
         }
     }
     else
@@ -97,7 +97,7 @@ Foam::tmp<Foam::vectorField> Foam::cyclicFvPatch::delta() const
             vector ddi = patchD[facei];
             vector dni = nbrPatchD[facei];
 
-            pdv[facei] = ddi - transform(forwardT(), dni);
+            pdv[facei] = ddi - dni;
         }
     }
 
diff --git a/src/finiteVolume/fvMesh/fvPatches/constraint/cyclic/cyclicFvPatch.H b/src/finiteVolume/fvMesh/fvPatches/constraint/cyclic/cyclicFvPatch.H
index 3494baa99c..42dfa85126 100644
--- a/src/finiteVolume/fvMesh/fvPatches/constraint/cyclic/cyclicFvPatch.H
+++ b/src/finiteVolume/fvMesh/fvPatches/constraint/cyclic/cyclicFvPatch.H
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -113,22 +113,10 @@ public:
                 );
             }
 
-            //- Are the cyclic planes parallel
-            virtual bool parallel() const
+            //- Return transformation between the coupled patches
+            virtual const transformer& transform() const
             {
-                return cyclicPolyPatch_.parallel();
-            }
-
-            //- Return face transformation tensor
-            virtual const tensor& forwardT() const
-            {
-                return cyclicPolyPatch_.forwardT();
-            }
-
-            //- Return neighbour-cell transformation tensor
-            virtual const tensor& reverseT() const
-            {
-                return cyclicPolyPatch_.reverseT();
+                return cyclicPolyPatch_.transform();
             }
 
             const cyclicFvPatch& neighbFvPatch() const
diff --git a/src/finiteVolume/fvMesh/fvPatches/constraint/cyclicAMI/cyclicAMIFvPatch.C b/src/finiteVolume/fvMesh/fvPatches/constraint/cyclicAMI/cyclicAMIFvPatch.C
index 874343f39d..111a70c37e 100644
--- a/src/finiteVolume/fvMesh/fvPatches/constraint/cyclicAMI/cyclicAMIFvPatch.C
+++ b/src/finiteVolume/fvMesh/fvPatches/constraint/cyclicAMI/cyclicAMIFvPatch.C
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -139,14 +139,14 @@ Foam::tmp<Foam::vectorField> Foam::cyclicAMIFvPatch::delta() const
         vectorField& pdv = tpdv.ref();
 
         // do the transformation if necessary
-        if (parallel())
+        if (transform().rotates())
         {
             forAll(patchD, facei)
             {
                 const vector& ddi = patchD[facei];
                 const vector& dni = nbrPatchD[facei];
 
-                pdv[facei] = ddi - dni;
+                pdv[facei] = ddi - transform().transform(dni);
             }
         }
         else
@@ -156,7 +156,7 @@ Foam::tmp<Foam::vectorField> Foam::cyclicAMIFvPatch::delta() const
                 const vector& ddi = patchD[facei];
                 const vector& dni = nbrPatchD[facei];
 
-                pdv[facei] = ddi - transform(forwardT(), dni);
+                pdv[facei] = ddi - dni;
             }
         }
 
diff --git a/src/finiteVolume/fvMesh/fvPatches/constraint/cyclicAMI/cyclicAMIFvPatch.H b/src/finiteVolume/fvMesh/fvPatches/constraint/cyclicAMI/cyclicAMIFvPatch.H
index f390493fbb..24c9110c46 100644
--- a/src/finiteVolume/fvMesh/fvPatches/constraint/cyclicAMI/cyclicAMIFvPatch.H
+++ b/src/finiteVolume/fvMesh/fvPatches/constraint/cyclicAMI/cyclicAMIFvPatch.H
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -139,22 +139,10 @@ public:
                 return cyclicAMIPolyPatch_.applyLowWeightCorrection();
             }
 
-            //- Are the cyclic planes parallel
-            virtual bool parallel() const
+            //- Return transformation between the coupled patches
+            virtual const transformer& transform() const
             {
-                return cyclicAMIPolyPatch_.parallel();
-            }
-
-            //- Return face transformation tensor
-            virtual const tensor& forwardT() const
-            {
-                return cyclicAMIPolyPatch_.forwardT();
-            }
-
-            //- Return neighbour-cell transformation tensor
-            virtual const tensor& reverseT() const
-            {
-                return cyclicAMIPolyPatch_.reverseT();
+                return cyclicAMIPolyPatch_.transform();
             }
 
             const cyclicAMIFvPatch& neighbFvPatch() const
diff --git a/src/finiteVolume/fvMesh/fvPatches/constraint/processor/processorFvPatch.C b/src/finiteVolume/fvMesh/fvPatches/constraint/processor/processorFvPatch.C
index f86304b399..4c4794f775 100644
--- a/src/finiteVolume/fvMesh/fvPatches/constraint/processor/processorFvPatch.C
+++ b/src/finiteVolume/fvMesh/fvPatches/constraint/processor/processorFvPatch.C
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -93,11 +93,12 @@ Foam::tmp<Foam::vectorField> Foam::processorFvPatch::delta() const
     if (Pstream::parRun())
     {
         // To the transformation if necessary
-        if (parallel())
+        if (transform().rotates())
         {
             return
                 coupledFvPatch::delta()
-              - (
+               -transform().transform
+                (
                     procPolyPatch_.neighbFaceCentres()
                   - procPolyPatch_.neighbFaceCellCentres()
                 );
@@ -106,13 +107,9 @@ Foam::tmp<Foam::vectorField> Foam::processorFvPatch::delta() const
         {
             return
                 coupledFvPatch::delta()
-              - transform
-                (
-                    forwardT(),
-                    (
-                        procPolyPatch_.neighbFaceCentres()
-                      - procPolyPatch_.neighbFaceCellCentres()
-                    )
+              - (
+                    procPolyPatch_.neighbFaceCentres()
+                  - procPolyPatch_.neighbFaceCellCentres()
                 );
         }
     }
diff --git a/src/finiteVolume/fvMesh/fvPatches/constraint/processor/processorFvPatch.H b/src/finiteVolume/fvMesh/fvPatches/constraint/processor/processorFvPatch.H
index 33155229e5..16e62b18c1 100644
--- a/src/finiteVolume/fvMesh/fvPatches/constraint/processor/processorFvPatch.H
+++ b/src/finiteVolume/fvMesh/fvPatches/constraint/processor/processorFvPatch.H
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -126,22 +126,10 @@ public:
             return procPolyPatch_;
         }
 
-        //- Are the cyclic planes parallel
-        virtual bool parallel() const
+        //- Return transformation between the coupled patches
+        virtual const transformer& transform() const
         {
-            return procPolyPatch_.parallel();
-        }
-
-        //- Return face transformation tensor
-        virtual const tensor& forwardT() const
-        {
-            return procPolyPatch_.forwardT();
-        }
-
-        //- Return neighbour-cell transformation tensor.
-        virtual const tensor& reverseT() const
-        {
-            return procPolyPatch_.reverseT();
+            return procPolyPatch_.transform();
         }
 
         //- Return delta (P to N) vectors across coupled patch
diff --git a/src/finiteVolume/fvMesh/fvPatches/constraint/processorCyclic/processorCyclicFvPatch.H b/src/finiteVolume/fvMesh/fvPatches/constraint/processorCyclic/processorCyclicFvPatch.H
index ce05321432..da036f2507 100644
--- a/src/finiteVolume/fvMesh/fvPatches/constraint/processorCyclic/processorCyclicFvPatch.H
+++ b/src/finiteVolume/fvMesh/fvPatches/constraint/processorCyclic/processorCyclicFvPatch.H
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -85,22 +85,10 @@ public:
             return procPolyPatch_;
         }
 
-        //- Are the cyclic planes parallel
-        virtual bool parallel() const
+        //- Return transformation between the coupled patches
+        virtual const transformer& transform() const
         {
-            return procPolyPatch_.parallel();
-        }
-
-        //- Return face transformation tensor
-        virtual const tensor& forwardT() const
-        {
-            return procPolyPatch_.forwardT();
-        }
-
-        //- Return neighbour-cell transformation tensor
-        virtual const tensor& reverseT() const
-        {
-            return procPolyPatch_.reverseT();
+            return procPolyPatch_.transform();
         }
 };
 
diff --git a/src/lagrangian/basic/particle/particle.C b/src/lagrangian/basic/particle/particle.C
index 601fdf7c60..187e0f3f59 100644
--- a/src/lagrangian/basic/particle/particle.C
+++ b/src/lagrangian/basic/particle/particle.C
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -1067,13 +1067,13 @@ void Foam::particle::correctAfterParallelTransfer
     const coupledPolyPatch& ppp =
         refCast<const coupledPolyPatch>(mesh_.boundaryMesh()[patchi]);
 
-    if (!ppp.parallel())
+    if (ppp.transform().rotates())
     {
-        transformProperties(ppp.forwardT());
+        transformProperties(ppp.transform().R());
     }
-    else if (ppp.separated())
+    else if (ppp.transform().translates())
     {
-        transformProperties(-ppp.separation());
+        transformProperties(-ppp.transform().t());
     }
 
     // Set the topology
diff --git a/src/lagrangian/basic/particle/particleTemplates.C b/src/lagrangian/basic/particle/particleTemplates.C
index 4cadcc4ce8..6bfb5b8b02 100644
--- a/src/lagrangian/basic/particle/particleTemplates.C
+++ b/src/lagrangian/basic/particle/particleTemplates.C
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -277,13 +277,13 @@ void Foam::particle::hitCyclicPatch(TrackCloudType&, trackingData&)
     reflect();
 
     // Transform the properties
-    if (!receiveCpp.parallel())
+    if (receiveCpp.transform().rotates())
     {
-        transformProperties(receiveCpp.forwardT());
+        transformProperties(receiveCpp.transform().R());
     }
-    else if (receiveCpp.separated())
+    else if (receiveCpp.transform().translates())
     {
-        transformProperties(-receiveCpp.separation());
+        transformProperties(-receiveCpp.transform().t());
     }
 }
 
@@ -373,14 +373,14 @@ void Foam::particle::hitCyclicAMIPatch
         transformProperties(AMITransform.t());
     }
 
-    if (!receiveCpp.parallel())
+    if (receiveCpp.transform().rotates())
     {
-        transformProperties(receiveCpp.forwardT());
-        displacementT = transform(receiveCpp.forwardT(), displacementT);
+        transformProperties(receiveCpp.transform().R());
+        displacementT = transform(receiveCpp.transform().R(), displacementT);
     }
-    else if (receiveCpp.separated())
+    else if (receiveCpp.transform().translates())
     {
-        transformProperties(-receiveCpp.separation());
+        transformProperties(-receiveCpp.transform().t());
     }
 
     // If on a boundary and the displacement points into the receiving face
diff --git a/src/mesh/snappyHexMesh/meshRefinement/meshRefinement.C b/src/mesh/snappyHexMesh/meshRefinement/meshRefinement.C
index a8623f1f03..1fc9fc8d36 100644
--- a/src/mesh/snappyHexMesh/meshRefinement/meshRefinement.C
+++ b/src/mesh/snappyHexMesh/meshRefinement/meshRefinement.C
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -2078,7 +2078,7 @@ void Foam::meshRefinement::selectSeparatedCoupledFaces(boolList& selected) const
                 patches[patchi]
             );
 
-            if (cpp.separated() || !cpp.parallel())
+            if (cpp.transform().transformsPosition())
             {
                 forAll(cpp, i)
                 {
diff --git a/src/meshTools/AMIInterpolation/GAMG/interfaceFields/cyclicAMIGAMGInterfaceField/cyclicAMIGAMGInterfaceField.H b/src/meshTools/AMIInterpolation/GAMG/interfaceFields/cyclicAMIGAMGInterfaceField/cyclicAMIGAMGInterfaceField.H
index c99d49ddff..8a474c5945 100644
--- a/src/meshTools/AMIInterpolation/GAMG/interfaceFields/cyclicAMIGAMGInterfaceField/cyclicAMIGAMGInterfaceField.H
+++ b/src/meshTools/AMIInterpolation/GAMG/interfaceFields/cyclicAMIGAMGInterfaceField/cyclicAMIGAMGInterfaceField.H
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -131,16 +131,10 @@ public:
                 return doTransform_;
             }
 
-            //- Return face transformation tensor
-            virtual const tensor& forwardT() const
+            //- Return transformation between the coupled patches
+            virtual const transformer& transform() const
             {
-                return cyclicAMIInterface_.forwardT();
-            }
-
-            //- Return neighbour-cell transformation tensor
-            virtual const tensor& reverseT() const
-            {
-                return cyclicAMIInterface_.reverseT();
+                return cyclicAMIInterface_.transform();
             }
 
             //- Return rank of component for transform
diff --git a/src/meshTools/AMIInterpolation/GAMG/interfaces/cyclicAMIGAMGInterface/cyclicAMIGAMGInterface.H b/src/meshTools/AMIInterpolation/GAMG/interfaces/cyclicAMIGAMGInterface/cyclicAMIGAMGInterface.H
index f1f7e9977a..cf13aefa39 100644
--- a/src/meshTools/AMIInterpolation/GAMG/interfaces/cyclicAMIGAMGInterface/cyclicAMIGAMGInterface.H
+++ b/src/meshTools/AMIInterpolation/GAMG/interfaces/cyclicAMIGAMGInterface/cyclicAMIGAMGInterface.H
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -141,16 +141,10 @@ public:
                 return AMITransforms_;
             }
 
-            //- Return face transformation tensor
-            virtual const tensor& forwardT() const
+            //- Return transformation between the coupled patches
+            virtual const transformer& transform() const
             {
-                return fineCyclicAMIInterface_.forwardT();
-            }
-
-            //- Return neighbour-cell transformation tensor
-            virtual const tensor& reverseT() const
-            {
-                return fineCyclicAMIInterface_.reverseT();
+                return fineCyclicAMIInterface_.transform();
             }
 
 
diff --git a/src/meshTools/AMIInterpolation/patches/cyclicAMI/cyclicAMILduInterfaceField/cyclicAMILduInterface.H b/src/meshTools/AMIInterpolation/patches/cyclicAMI/cyclicAMILduInterfaceField/cyclicAMILduInterface.H
index 18f1a95f1c..f9941574ec 100644
--- a/src/meshTools/AMIInterpolation/patches/cyclicAMI/cyclicAMILduInterfaceField/cyclicAMILduInterface.H
+++ b/src/meshTools/AMIInterpolation/patches/cyclicAMI/cyclicAMILduInterfaceField/cyclicAMILduInterface.H
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -87,11 +87,8 @@ public:
             virtual const List<transformer>&
                 AMITransforms() const = 0;
 
-            //- Return face transformation tensor
-            virtual const tensor& forwardT() const = 0;
-
-            //- Return face reverse transformation tensor
-            virtual const tensor& reverseT() const = 0;
+            //- Return transformation between the coupled patches
+            virtual const transformer& transform() const = 0;
 };
 
 
diff --git a/src/meshTools/AMIInterpolation/patches/cyclicAMI/cyclicAMILduInterfaceField/cyclicAMILduInterfaceField.C b/src/meshTools/AMIInterpolation/patches/cyclicAMI/cyclicAMILduInterfaceField/cyclicAMILduInterfaceField.C
index 3f088dc83a..add5f898ab 100644
--- a/src/meshTools/AMIInterpolation/patches/cyclicAMI/cyclicAMILduInterfaceField/cyclicAMILduInterfaceField.C
+++ b/src/meshTools/AMIInterpolation/patches/cyclicAMI/cyclicAMILduInterfaceField/cyclicAMILduInterfaceField.C
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -30,7 +30,7 @@ License
 
 namespace Foam
 {
-defineTypeNameAndDebug(cyclicAMILduInterfaceField, 0);
+    defineTypeNameAndDebug(cyclicAMILduInterfaceField, 0);
 }
 
 
@@ -50,7 +50,7 @@ void Foam::cyclicAMILduInterfaceField::transformCoupleField
 {
     if (doTransform())
     {
-        f *= pow(diag(forwardT()).component(cmpt), rank());
+        f *= pow(diag(transform().R()).component(cmpt), rank());
     }
 }
 
diff --git a/src/meshTools/AMIInterpolation/patches/cyclicAMI/cyclicAMILduInterfaceField/cyclicAMILduInterfaceField.H b/src/meshTools/AMIInterpolation/patches/cyclicAMI/cyclicAMILduInterfaceField/cyclicAMILduInterfaceField.H
index 5f892b39e8..cfe6f78d1e 100644
--- a/src/meshTools/AMIInterpolation/patches/cyclicAMI/cyclicAMILduInterfaceField/cyclicAMILduInterfaceField.H
+++ b/src/meshTools/AMIInterpolation/patches/cyclicAMI/cyclicAMILduInterfaceField/cyclicAMILduInterfaceField.H
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -36,6 +36,7 @@ SourceFiles
 #define cyclicAMILduInterfaceField_H
 
 #include "primitiveFieldsFwd.H"
+#include "transformer.H"
 
 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
@@ -73,11 +74,8 @@ public:
             //- Is the transform required
             virtual bool doTransform() const = 0;
 
-            //- Return face transformation tensor
-            virtual const tensor& forwardT() const = 0;
-
-            //- Return neighbour-cell transformation tensor
-            virtual const tensor& reverseT() const = 0;
+            //- Return transformation between the coupled patches
+            virtual const transformer& transform() const = 0;
 
             //- Return rank of component for transform
             virtual int rank() const = 0;
@@ -112,7 +110,7 @@ void Foam::cyclicAMILduInterfaceField::transformCoupleField
 {
     if (doTransform())
     {
-        transform(f, forwardT(), f);
+        transform().transform(f, f);
     }
 }
 
diff --git a/src/meshTools/AMIInterpolation/patches/cyclicAMI/cyclicAMIPointPatch/cyclicAMIPointPatch.H b/src/meshTools/AMIInterpolation/patches/cyclicAMI/cyclicAMIPointPatch/cyclicAMIPointPatch.H
index 23237bcf19..71d86096ec 100644
--- a/src/meshTools/AMIInterpolation/patches/cyclicAMI/cyclicAMIPointPatch/cyclicAMIPointPatch.H
+++ b/src/meshTools/AMIInterpolation/patches/cyclicAMI/cyclicAMIPointPatch/cyclicAMIPointPatch.H
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -129,22 +129,10 @@ public:
             return refCast<const cyclicAMIPointPatch>(pp);
         }
 
-        //- Are the cyclic planes parallel
-        bool parallel() const
+        //- Return transformation between the coupled patches
+        virtual const transformer& transform() const
         {
-            return cyclicAMIPolyPatch_.parallel();
-        }
-
-        //- Return face transformation tensor
-        const tensor& forwardT() const
-        {
-            return cyclicAMIPolyPatch_.forwardT();
-        }
-
-        //- Return neighbour-cell transformation tensor
-        const tensor& reverseT() const
-        {
-            return cyclicAMIPolyPatch_.reverseT();
+            return cyclicAMIPolyPatch_.transform();
         }
 
 
diff --git a/src/meshTools/AMIInterpolation/patches/cyclicAMI/cyclicAMIPointPatchField/cyclicAMIPointPatchField.C b/src/meshTools/AMIInterpolation/patches/cyclicAMI/cyclicAMIPointPatchField/cyclicAMIPointPatchField.C
index af05eaf937..0e7a544173 100644
--- a/src/meshTools/AMIInterpolation/patches/cyclicAMI/cyclicAMIPointPatchField/cyclicAMIPointPatchField.C
+++ b/src/meshTools/AMIInterpolation/patches/cyclicAMI/cyclicAMIPointPatchField/cyclicAMIPointPatchField.C
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -154,8 +154,8 @@ void Foam::cyclicAMIPointPatchField<Type>::swapAddSeparated
 
         if (doTransform())
         {
-            transform(ptFld, this->reverseT(), ptFld);
-            transform(nbrPtFld, this->forwardT(), nbrPtFld);
+            ptFld = transform().invTransform(ptFld);
+            nbrPtFld = transform().transform(nbrPtFld);
         }
 
         // convert point field to face field, AMI interpolate, then
diff --git a/src/meshTools/AMIInterpolation/patches/cyclicAMI/cyclicAMIPointPatchField/cyclicAMIPointPatchField.H b/src/meshTools/AMIInterpolation/patches/cyclicAMI/cyclicAMIPointPatchField/cyclicAMIPointPatchField.H
index 114b9f8ede..0f2f3f52f6 100644
--- a/src/meshTools/AMIInterpolation/patches/cyclicAMI/cyclicAMIPointPatchField/cyclicAMIPointPatchField.H
+++ b/src/meshTools/AMIInterpolation/patches/cyclicAMI/cyclicAMIPointPatchField/cyclicAMIPointPatchField.H
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -187,22 +187,14 @@ public:
             virtual bool doTransform() const
             {
                 return
-                   !(
-                        cyclicAMIPatch_.parallel()
-                     || pTraits<Type>::rank == 0
-                    );
+                    cyclicAMIPatch_.transform().rotates()
+                 && pTraits<Type>::rank != 0;
             }
 
-            //- Return face transformation tensor
-            virtual const tensor& forwardT() const
+            //- Return transformation between the coupled patches
+            virtual const transformer& transform() const
             {
-                return cyclicAMIPatch_.forwardT();
-            }
-
-            //- Return neighbour-cell transformation tensor
-            virtual const tensor& reverseT() const
-            {
-                return cyclicAMIPatch_.reverseT();
+                return cyclicAMIPatch_.transform();
             }
 
 
diff --git a/src/meshTools/AMIInterpolation/patches/cyclicAMI/cyclicAMIPolyPatch/cyclicAMIPolyPatch.C b/src/meshTools/AMIInterpolation/patches/cyclicAMI/cyclicAMIPolyPatch/cyclicAMIPolyPatch.C
index 76308db480..a91b21b85f 100644
--- a/src/meshTools/AMIInterpolation/patches/cyclicAMI/cyclicAMIPolyPatch/cyclicAMIPolyPatch.C
+++ b/src/meshTools/AMIInterpolation/patches/cyclicAMI/cyclicAMIPolyPatch/cyclicAMIPolyPatch.C
@@ -233,6 +233,8 @@ void Foam::cyclicAMIPolyPatch::calcTransforms
             forwardT_ = revT.T();
             reverseT_ = revT;
 
+            transform_ = transformer(revT.T());
+
             break;
         }
         case TRANSLATIONAL:
@@ -249,6 +251,8 @@ void Foam::cyclicAMIPolyPatch::calcTransforms
             forwardT_ = Zero;
             reverseT_ = Zero;
 
+            transform_ = transformer(separation_);
+
             break;
         }
         default:
@@ -265,6 +269,8 @@ void Foam::cyclicAMIPolyPatch::calcTransforms
             forwardT_ = Zero;
             reverseT_ = Zero;
 
+            transform_ = transformer();
+
             break;
         }
     }
@@ -272,9 +278,7 @@ void Foam::cyclicAMIPolyPatch::calcTransforms
     if (debug)
     {
         Pout<< "patch: " << name() << nl
-            << "    forwardT = " << forwardT() << nl
-            << "    reverseT = " << reverseT() << nl
-            << "    separation = " << separation() << nl << endl;
+            << "    transform = " << transform() << nl << endl;
     }
 }
 
@@ -382,9 +386,7 @@ void Foam::cyclicAMIPolyPatch::calcTransforms()
     if (debug)
     {
         Pout<< "calcTransforms() : patch: " << name() << nl
-            << "    forwardT = " << forwardT() << nl
-            << "    reverseT = " << reverseT() << nl
-            << "    separation = " << separation() << nl << endl;
+            << "    transform = " << transform() << nl << endl;
     }
 }
 
@@ -872,23 +874,23 @@ const Foam::scalarField& Foam::cyclicAMIPolyPatch::neighbWeightsSum() const
 
 void Foam::cyclicAMIPolyPatch::transformPosition(pointField& l) const
 {
-    if (!parallel())
+    if (transform().rotates())
     {
         if (transformType() == ROTATIONAL)
         {
-            l = Foam::transform(forwardT(), l - rotationCentre_)
+            l = Foam::transform(transform().R(), l - rotationCentre_)
               + rotationCentre_;
         }
         else
         {
-            l = Foam::transform(forwardT(), l);
+            l = Foam::transform(transform().R(), l);
         }
     }
-    else if (separated())
+    else if (transform().translates())
     {
         // transformPosition gets called on the receiving side,
         // separation gets calculated on the sending side so subtract
-        l -= separation();
+        l -= transform().t();
     }
 }
 
@@ -899,21 +901,21 @@ void Foam::cyclicAMIPolyPatch::transformPosition
     const label facei
 ) const
 {
-    if (!parallel())
+    if (transform().rotates())
     {
         if (transformType() == ROTATIONAL)
         {
-            l = Foam::transform(forwardT(), l - rotationCentre_)
+            l = Foam::transform(transform().R(), l - rotationCentre_)
               + rotationCentre_;
         }
         else
         {
-            l = Foam::transform(forwardT(), l);
+            l = Foam::transform(transform().R(), l);
         }
     }
-    else if (separated())
+    else if (transform().translates())
     {
-        l -= separation();
+        l -= transform().t();
     }
 }
 
@@ -924,9 +926,9 @@ void Foam::cyclicAMIPolyPatch::transformDirection
     const label facei
 ) const
 {
-    if (!parallel())
+    if (transform().rotates())
     {
-        d = Foam::transform(forwardT(), d);
+        d = Foam::transform(transform().R(), d);
     }
 }
 
@@ -937,21 +939,21 @@ void Foam::cyclicAMIPolyPatch::reverseTransformPosition
     const label facei
 ) const
 {
-    if (!parallel())
+    if (transform().rotates())
     {
         if (transformType() == ROTATIONAL)
         {
-            l = Foam::transform(reverseT(), l - rotationCentre_)
+            l = Foam::transform(transform().R().T(), l - rotationCentre_)
               + rotationCentre_;
         }
         else
         {
-            l = Foam::transform(reverseT(), l);
+            l = Foam::transform(transform().R().T(), l);
         }
     }
-    else if (separated())
+    else if (transform().translates())
     {
-        l += separation();
+        l += transform().t();
     }
 }
 
@@ -962,9 +964,9 @@ void Foam::cyclicAMIPolyPatch::reverseTransformDirection
     const label facei
 ) const
 {
-    if (!parallel())
+    if (transform().rotates())
     {
-        d = Foam::transform(reverseT(), d);
+        d = Foam::transform(transform().R().T(), d);
     }
 }
 
diff --git a/src/meshTools/AMIInterpolation/patches/cyclicRepeatAMI/cyclicRepeatAMILduInterfaceField/cyclicRepeatAMILduInterfaceField.C b/src/meshTools/AMIInterpolation/patches/cyclicRepeatAMI/cyclicRepeatAMILduInterfaceField/cyclicRepeatAMILduInterfaceField.C
index 5b59428090..2df59860e4 100644
--- a/src/meshTools/AMIInterpolation/patches/cyclicRepeatAMI/cyclicRepeatAMILduInterfaceField/cyclicRepeatAMILduInterfaceField.C
+++ b/src/meshTools/AMIInterpolation/patches/cyclicRepeatAMI/cyclicRepeatAMILduInterfaceField/cyclicRepeatAMILduInterfaceField.C
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2018 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2018-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -30,7 +30,7 @@ License
 
 namespace Foam
 {
-defineTypeNameAndDebug(cyclicRepeatAMILduInterfaceField, 0);
+    defineTypeNameAndDebug(cyclicRepeatAMILduInterfaceField, 0);
 }
 
 
diff --git a/src/meshTools/AMIInterpolation/patches/cyclicRepeatAMI/cyclicRepeatAMIPolyPatch/cyclicRepeatAMIPolyPatch.C b/src/meshTools/AMIInterpolation/patches/cyclicRepeatAMI/cyclicRepeatAMIPolyPatch/cyclicRepeatAMIPolyPatch.C
index b204046100..c5bfe73939 100644
--- a/src/meshTools/AMIInterpolation/patches/cyclicRepeatAMI/cyclicRepeatAMIPolyPatch/cyclicRepeatAMIPolyPatch.C
+++ b/src/meshTools/AMIInterpolation/patches/cyclicRepeatAMI/cyclicRepeatAMIPolyPatch/cyclicRepeatAMIPolyPatch.C
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2018-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2018-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -103,17 +103,7 @@ void Foam::cyclicRepeatAMIPolyPatch::resetAMI() const
         Tuple2<bool, transformer> bt
         (
             transformPatch.size(),
-            transformer
-            (
-                transformPatch.separated()
-              ? transformPatch.separation()
-              : vector::zero,
-                transformPatch.separated(),
-               !transformPatch.parallel()
-              ? transformPatch.forwardT()
-              : tensor::zero,
-               !transformPatch.parallel()
-            )
+            transformPatch.transform()
         );
 
         reduce(bt, keepIfTrueOp<transformer>());
diff --git a/src/meshTools/algorithms/MeshWave/FaceCellWave.C b/src/meshTools/algorithms/MeshWave/FaceCellWave.C
index 5ebf681366..5e8484c320 100644
--- a/src/meshTools/algorithms/MeshWave/FaceCellWave.C
+++ b/src/meshTools/algorithms/MeshWave/FaceCellWave.C
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -597,11 +597,11 @@ void Foam::FaceCellWave<Type, TrackingData>::handleProcPatches()
         }
 
         // Apply transform to received data for non-parallel planes
-        if (!procPatch.parallel())
+        if (procPatch.transform().rotates())
         {
             transform
             (
-                procPatch.forwardT(),
+                procPatch.transform().R(),
                 receiveFaces.size(),
                 receiveFacesInfo
             );
@@ -669,12 +669,12 @@ void Foam::FaceCellWave<Type, TrackingData>::handleCyclicPatches()
             const cyclicPolyPatch& cycPatch =
                 refCast<const cyclicPolyPatch>(patch);
 
-            if (!cycPatch.parallel())
+            if (cycPatch.transform().rotates())
             {
                 // received data from other half
                 transform
                 (
-                    cycPatch.forwardT(),
+                    cycPatch.transform().R(),
                     nReceiveFaces,
                     receiveFacesInfo
                 );
@@ -743,7 +743,7 @@ void Foam::FaceCellWave<Type, TrackingData>::handleAMICyclicPatches()
                     )
                 );
 
-                if (!nbrPatch.parallel() || nbrPatch.separated())
+                if (nbrPatch.transform().transformsPosition())
                 {
                     // Adapt sendInfo for leaving domain
                     const vectorField::subField fc = nbrPatch.faceCentres();
@@ -805,17 +805,17 @@ void Foam::FaceCellWave<Type, TrackingData>::handleAMICyclicPatches()
             }
 
             // Apply transform to received data for non-parallel planes
-            if (!cycPatch.parallel())
+            if (cycPatch.transform().rotates())
             {
                 transform
                 (
-                    cycPatch.forwardT(),
+                    cycPatch.transform().R(),
                     receiveInfo.size(),
                     receiveInfo
                 );
             }
 
-            if (!cycPatch.parallel() || cycPatch.separated())
+            if (cycPatch.transform().transformsPosition())
             {
                 // Adapt receiveInfo for entering domain
                 const vectorField::subField fc = cycPatch.faceCentres();
diff --git a/src/meshTools/algorithms/PointEdgeWave/PointEdgeWave.C b/src/meshTools/algorithms/PointEdgeWave/PointEdgeWave.C
index 00af3c13f0..d5483fc78d 100644
--- a/src/meshTools/algorithms/PointEdgeWave/PointEdgeWave.C
+++ b/src/meshTools/algorithms/PointEdgeWave/PointEdgeWave.C
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -368,9 +368,9 @@ void Foam::PointEdgeWave<Type, TrackingData>::handleProcPatches()
         //}
 
         // Apply transform to received data for non-parallel planes
-        if (!procPatch.parallel())
+        if (procPatch.transform().rotates())
         {
-            transform(procPatch, procPatch.forwardT(), patchInfo);
+            transform(procPatch, procPatch.transform().R(), patchInfo);
         }
 
         // Adapt for entering domain
@@ -453,10 +453,10 @@ void Foam::PointEdgeWave<Type, TrackingData>::handleCyclicPatches()
 
             // Apply rotation for non-parallel planes
 
-            if (!cycPatch.parallel())
+            if (cycPatch.transform().rotates())
             {
                 // received data from half1
-                transform(cycPatch, cycPatch.forwardT(), nbrInfo);
+                transform(cycPatch, cycPatch.transform().R(), nbrInfo);
             }
 
             // if (debug)