From e809171540f804af238ddffce415b0de9ea922e9 Mon Sep 17 00:00:00 2001
From: Henry Weller <http://cfd.direct>
Date: Fri, 18 Mar 2016 21:52:27 +0000
Subject: [PATCH] SpatialVector: Added cross-product and dual cross-product
 operators SpatialTensor: Added SpatialVector cross-product and dual
 cross-product -> SpatialTensor operators

---
 .../SpatialTensor/SpatialTensorI.H            | 55 +++++++++++++-
 .../SpatialVector/SpatialVector.H             | 18 +++++
 .../SpatialVector/SpatialVectorI.H            | 75 +++++++++++++++++++
 3 files changed, 147 insertions(+), 1 deletion(-)

diff --git a/src/OpenFOAM/primitives/spatialVectorAlgebra/SpatialTensor/SpatialTensorI.H b/src/OpenFOAM/primitives/spatialVectorAlgebra/SpatialTensor/SpatialTensorI.H
index 4f76522bf..f3d431bce 100644
--- a/src/OpenFOAM/primitives/spatialVectorAlgebra/SpatialTensor/SpatialTensorI.H
+++ b/src/OpenFOAM/primitives/spatialVectorAlgebra/SpatialTensor/SpatialTensorI.H
@@ -23,6 +23,8 @@ License
 
 \*---------------------------------------------------------------------------*/
 
+#include "Identity.H"
+
 // * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
 
 template<class Cmpt>
@@ -131,7 +133,7 @@ inline Foam::SpatialTensor<Cmpt>::SpatialTensor(Istream& is)
 {}
 
 
-// * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
+// * * * * * * * * * * * * * * * Member Operators  * * * * * * * * * * * * * //
 
 template<class Cmpt>
 inline void Foam::SpatialTensor<Cmpt>::operator=(const Foam::zero z)
@@ -140,4 +142,55 @@ inline void Foam::SpatialTensor<Cmpt>::operator=(const Foam::zero z)
 }
 
 
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+namespace Foam
+{
+
+// * * * * * * * * * * * * * * * Global Operators  * * * * * * * * * * * * * //
+
+//- Return the cross-product tensor
+template<class Cmpt>
+inline Foam::SpatialTensor<Cmpt> operator^
+(
+    const SpatialVector<Cmpt>& v,
+    const Identity<Cmpt>&
+)
+{
+    return SpatialTensor<Cmpt>
+    (
+        0,       -v.wz(),   v.wy(),   0,        0,        0,
+        v.wz(),   0,       -v.wx(),   0,        0,        0,
+       -v.wy(),   v.wx(),   0,        0,        0,        0,
+        0,       -v.lz(),   v.ly(),   0,       -v.wz(),   v.wy(),
+        v.lz(),   0,       -v.lx(),   v.wz(),   0,       -v.wx(),
+       -v.ly(),   v.lx(),   0,       -v.wy(),   v.wx(),   0
+    );
+}
+
+
+//- Return the dual cross-product tensor
+template<class Cmpt>
+inline Foam::SpatialTensor<Cmpt> operator^
+(
+    const SpatialVector<Cmpt>& f,
+    const typename Identity<Cmpt>::dual&
+)
+{
+    return SpatialTensor<Cmpt>
+    (
+        0,       -f.wz(),   f.wy(),   0,       -f.lz(),   f.ly(),
+        f.wz(),   0,       -f.wx(),   f.lz(),   0,       -f.lx(),
+       -f.wy(),   f.wx(),   0,       -f.ly(),   f.lx(),   0,
+        0,        0,        0,        0,       -f.wz(),   f.wy(),
+        0,        0,        0,        f.wz(),   0,       -f.wx(),
+        0,        0,        0,       -f.wy(),   f.wx(),   0
+    );
+}
+
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+} // End namespace Foam
+
 // ************************************************************************* //
diff --git a/src/OpenFOAM/primitives/spatialVectorAlgebra/SpatialVector/SpatialVector.H b/src/OpenFOAM/primitives/spatialVectorAlgebra/SpatialVector/SpatialVector.H
index d60710d30..33741f314 100644
--- a/src/OpenFOAM/primitives/spatialVectorAlgebra/SpatialVector/SpatialVector.H
+++ b/src/OpenFOAM/primitives/spatialVectorAlgebra/SpatialVector/SpatialVector.H
@@ -71,6 +71,21 @@ public:
     enum components { WX, WY, WZ, LX, LY, LZ };
 
 
+    //- Class to represent the dual spatial vector
+    class dual
+    {
+        const SpatialVector& v_;
+
+    public:
+
+        //- Construct the dual of the given SpatialVector
+        inline dual(const SpatialVector& v);
+
+        //- Return the parent SpatialVector
+        inline const SpatialVector& v() const;
+    };
+
+
     // Constructors
 
         //- Construct null
@@ -137,6 +152,9 @@ public:
     // Member Operators
 
         inline void operator=(const Foam::zero);
+
+        //- Return the dual spatial vector
+        inline dual operator*() const;
 };
 
 
diff --git a/src/OpenFOAM/primitives/spatialVectorAlgebra/SpatialVector/SpatialVectorI.H b/src/OpenFOAM/primitives/spatialVectorAlgebra/SpatialVector/SpatialVectorI.H
index 6dd73d36f..9c8c862c5 100644
--- a/src/OpenFOAM/primitives/spatialVectorAlgebra/SpatialVector/SpatialVectorI.H
+++ b/src/OpenFOAM/primitives/spatialVectorAlgebra/SpatialVector/SpatialVectorI.H
@@ -90,6 +90,13 @@ inline Foam::SpatialVector<Cmpt>::SpatialVector(Istream& is)
 {}
 
 
+template<class Cmpt>
+inline Foam::SpatialVector<Cmpt>::dual::dual(const SpatialVector& v)
+:
+    v_(v)
+{}
+
+
 // * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
 
 template<class Cmpt>
@@ -189,6 +196,13 @@ inline Foam::Vector<Cmpt> Foam::SpatialVector<Cmpt>::l() const
 }
 
 
+template<class Cmpt>
+const Foam::SpatialVector<Cmpt>& Foam::SpatialVector<Cmpt>::dual::v() const
+{
+    return v_;
+}
+
+
 // * * * * * * * * * * * * * * * Member Operators  * * * * * * * * * * * * * //
 
 template<class Cmpt>
@@ -198,4 +212,65 @@ inline void Foam::SpatialVector<Cmpt>::operator=(const Foam::zero z)
 }
 
 
+template<class Cmpt>
+inline typename Foam::SpatialVector<Cmpt>::dual
+Foam::SpatialVector<Cmpt>::operator*() const
+{
+    return dual(*this);
+}
+
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+namespace Foam
+{
+
+// * * * * * * * * * * * * * * * Global Operators  * * * * * * * * * * * * * //
+
+//- Return the cross-product between two spatial vectors
+template<class Cmpt>
+inline SpatialVector<Cmpt> operator^
+(
+    const SpatialVector<Cmpt>& u,
+    const SpatialVector<Cmpt>& v
+)
+{
+    return SpatialVector<Cmpt>
+    (
+       -u.wz()*v.wy() + u.wy()*v.wz(),
+        u.wz()*v.wx() - u.wx()*v.wz(),
+       -u.wy()*v.wx() + u.wx()*v.wy(),
+       -u.lz()*v.wy() + u.ly()*v.wz() - u.wz()*v.ly() + u.wy()*v.lz(),
+        u.lz()*v.wx() - u.lx()*v.wz() + u.wz()*v.lx() - u.wx()*v.lz(),
+       -u.ly()*v.wx() + u.lx()*v.wy() - u.wy()*v.lx() + u.wx()*v.ly()
+    );
+}
+
+
+//- Return the dual cross-product between two spatial vectors
+template<class Cmpt>
+inline SpatialVector<Cmpt> operator^
+(
+    const SpatialVector<Cmpt>& v,
+    const typename SpatialVector<Cmpt>::dual& df
+)
+{
+    const SpatialVector<Cmpt>& f = df.v();
+
+    return SpatialVector<Cmpt>
+    (
+       -v.wz()*f.wy() + v.wy()*f.wz() - v.lz()*f.ly() + v.ly()*f.lz(),
+        v.wz()*f.wx() - v.wx()*f.wz() + v.lz()*f.lx() - v.lx()*f.lz(),
+       -v.wy()*f.wx() + v.wx()*f.wy() - v.ly()*f.lx() + v.lx()*f.ly(),
+       -v.wz()*f.ly() + v.wy()*f.lz(),
+        v.wz()*f.lx() - v.wx()*f.lz(),
+       -v.wy()*f.lx() + v.wx()*f.ly()
+    );
+}
+
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+} // End namespace Foam
+
 // ************************************************************************* //