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/*---------------------------------------------------------------------------*\
========= |
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
\\ / O peration |
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\\/ M anipulation |
-------------------------------------------------------------------------------
License
This file is part of OpenFOAM.
OpenFOAM is free software; you can redistribute it and/or modify it
under the terms of the GNU General Public License as published by the
Free Software Foundation; either version 2 of the License, or (at your
option) any later version.
OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
for more details.
You should have received a copy of the GNU General Public License
along with OpenFOAM; if not, write to the Free Software Foundation,
Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
InNamespace
Foam
Description
3D tensor transformation operations.
\*---------------------------------------------------------------------------*/
#ifndef transform_H
#define transform_H
#include "tensor.H"
#include "mathematicalConstants.H"
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
namespace Foam
{
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
inline tensor rotationTensor
(
const vector& n1,
const vector& n2
)
{
return
(n1 & n2)*I
+ (1 - (n1 & n2))*sqr(n1 ^ n2)/(magSqr(n1 ^ n2) + VSMALL)
+ (n2*n1 - n1*n2);
}
inline label transform(const tensor&, const label i)
{
return i;
}
inline scalar transform(const tensor&, const scalar s)
{
return s;
}
template<class Cmpt>
inline Vector<Cmpt> transform(const tensor& tt, const Vector<Cmpt>& v)
{
return tt & v;
}
template<class Cmpt>
inline Tensor<Cmpt> transform(const tensor& tt, const Tensor<Cmpt>& t)
{
//return tt & t & tt.T();
return Tensor<Cmpt>
(
(tt.xx()*t.xx() + tt.xy()*t.yx() + tt.xz()*t.zx())*tt.xx()
+ (tt.xx()*t.xy() + tt.xy()*t.yy() + tt.xz()*t.zy())*tt.xy()
+ (tt.xx()*t.xz() + tt.xy()*t.yz() + tt.xz()*t.zz())*tt.xz(),
(tt.xx()*t.xx() + tt.xy()*t.yx() + tt.xz()*t.zx())*tt.yx()
+ (tt.xx()*t.xy() + tt.xy()*t.yy() + tt.xz()*t.zy())*tt.yy()
+ (tt.xx()*t.xz() + tt.xy()*t.yz() + tt.xz()*t.zz())*tt.yz(),
(tt.xx()*t.xx() + tt.xy()*t.yx() + tt.xz()*t.zx())*tt.zx()
+ (tt.xx()*t.xy() + tt.xy()*t.yy() + tt.xz()*t.zy())*tt.zy()
+ (tt.xx()*t.xz() + tt.xy()*t.yz() + tt.xz()*t.zz())*tt.zz(),
(tt.yx()*t.xx() + tt.yy()*t.yx() + tt.yz()*t.zx())*tt.xx()
+ (tt.yx()*t.xy() + tt.yy()*t.yy() + tt.yz()*t.zy())*tt.xy()
+ (tt.yx()*t.xz() + tt.yy()*t.yz() + tt.yz()*t.zz())*tt.xz(),
(tt.yx()*t.xx() + tt.yy()*t.yx() + tt.yz()*t.zx())*tt.yx()
+ (tt.yx()*t.xy() + tt.yy()*t.yy() + tt.yz()*t.zy())*tt.yy()
+ (tt.yx()*t.xz() + tt.yy()*t.yz() + tt.yz()*t.zz())*tt.yz(),
(tt.yx()*t.xx() + tt.yy()*t.yx() + tt.yz()*t.zx())*tt.zx()
+ (tt.yx()*t.xy() + tt.yy()*t.yy() + tt.yz()*t.zy())*tt.zy()
+ (tt.yx()*t.xz() + tt.yy()*t.yz() + tt.yz()*t.zz())*tt.zz(),
(tt.zx()*t.xx() + tt.zy()*t.yx() + tt.zz()*t.zx())*tt.xx()
+ (tt.zx()*t.xy() + tt.zy()*t.yy() + tt.zz()*t.zy())*tt.xy()
+ (tt.zx()*t.xz() + tt.zy()*t.yz() + tt.zz()*t.zz())*tt.xz(),
(tt.zx()*t.xx() + tt.zy()*t.yx() + tt.zz()*t.zx())*tt.yx()
+ (tt.zx()*t.xy() + tt.zy()*t.yy() + tt.zz()*t.zy())*tt.yy()
+ (tt.zx()*t.xz() + tt.zy()*t.yz() + tt.zz()*t.zz())*tt.yz(),
(tt.zx()*t.xx() + tt.zy()*t.yx() + tt.zz()*t.zx())*tt.zx()
+ (tt.zx()*t.xy() + tt.zy()*t.yy() + tt.zz()*t.zy())*tt.zy()
+ (tt.zx()*t.xz() + tt.zy()*t.yz() + tt.zz()*t.zz())*tt.zz()
);
}
template<class Cmpt>
inline SphericalTensor<Cmpt> transform
(
const tensor& tt,
const SphericalTensor<Cmpt>& st
)
{
return st;
}
template<class Cmpt>
inline SymmTensor<Cmpt> transform(const tensor& tt, const SymmTensor<Cmpt>& st)
{
return SymmTensor<Cmpt>
(
(tt.xx()*st.xx() + tt.xy()*st.xy() + tt.xz()*st.xz())*tt.xx()
+ (tt.xx()*st.xy() + tt.xy()*st.yy() + tt.xz()*st.yz())*tt.xy()
+ (tt.xx()*st.xz() + tt.xy()*st.yz() + tt.xz()*st.zz())*tt.xz(),
(tt.xx()*st.xx() + tt.xy()*st.xy() + tt.xz()*st.xz())*tt.yx()
+ (tt.xx()*st.xy() + tt.xy()*st.yy() + tt.xz()*st.yz())*tt.yy()
+ (tt.xx()*st.xz() + tt.xy()*st.yz() + tt.xz()*st.zz())*tt.yz(),
(tt.xx()*st.xx() + tt.xy()*st.xy() + tt.xz()*st.xz())*tt.zx()
+ (tt.xx()*st.xy() + tt.xy()*st.yy() + tt.xz()*st.yz())*tt.zy()
+ (tt.xx()*st.xz() + tt.xy()*st.yz() + tt.xz()*st.zz())*tt.zz(),
(tt.yx()*st.xx() + tt.yy()*st.xy() + tt.yz()*st.xz())*tt.yx()
+ (tt.yx()*st.xy() + tt.yy()*st.yy() + tt.yz()*st.yz())*tt.yy()
+ (tt.yx()*st.xz() + tt.yy()*st.yz() + tt.yz()*st.zz())*tt.yz(),
(tt.yx()*st.xx() + tt.yy()*st.xy() + tt.yz()*st.xz())*tt.zx()
+ (tt.yx()*st.xy() + tt.yy()*st.yy() + tt.yz()*st.yz())*tt.zy()
+ (tt.yx()*st.xz() + tt.yy()*st.yz() + tt.yz()*st.zz())*tt.zz(),
(tt.zx()*st.xx() + tt.zy()*st.xy() + tt.zz()*st.xz())*tt.zx()
+ (tt.zx()*st.xy() + tt.zy()*st.yy() + tt.zz()*st.yz())*tt.zy()
+ (tt.zx()*st.xz() + tt.zy()*st.yz() + tt.zz()*st.zz())*tt.zz()
);
}
template<class Type1, class Type2>
inline Type1 transformMask(const Type2& t)
{
return t;
}
template<>
inline sphericalTensor transformMask<sphericalTensor>(const tensor& t)
{
return sph(t);
}
template<>
inline symmTensor transformMask<symmTensor>(const tensor& t)
{
return symm(t);
}
//- Estimate angle of vec in coordinate system (e0, e1, e0^e1).
// Is guaranteed to return increasing number but is not correct
// angle. Used for sorting angles. All input vectors need to be normalized.
//
// Calculates scalar which increases with angle going from e0 to vec in
// the coordinate system e0, e1, e0^e1
//
// Jumps from 2PI -> 0 at -SMALL so parallel vectors with small rounding errors
// should hopefully still get the same quadrant.
//
inline scalar pseudoAngle
(
const vector& e0,
const vector& e1,
const vector& vec
)
{
scalar cos = vec & e0;
scalar sin = vec & e1;
if (sin < -SMALL)
{
return (3.0 + cos)*mathematicalConstant::piByTwo;
}
else
{
return (1.0 - cos)*mathematicalConstant::piByTwo;
}
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
} // End namespace Foam
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
#endif
// ************************************************************************* //