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Commit d241c43a authored by graham's avatar graham
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Adding hard-coded tetraherdal solid inertia calculation. Can be used 

in a similar way to calculate the inertia of cells.
parent aa847562
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applications/test/momentOfInertia/momentOfInertiaTest.C
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......@@ -27,12 +27,14 @@ Application
Description
Calculates the inertia tensor and principal axes and moments of a
test face.
test face and tetrahedron.
\*---------------------------------------------------------------------------*/
#include "ListOps.H"
#include "face.H"
#include "tetPointRef.H"
#include "triFaceList.H"
#include "OFstream.H"
#include "meshTools.H"
......@@ -40,67 +42,310 @@ Description
using namespace Foam;
int main(int argc, char *argv[])
void massPropertiesSolid
(
const pointField& pts,
const triFaceList triFaces,
scalar density,
scalar& mass,
vector& cM,
tensor& J
)
{
label nPts = 6;
// Reimplemented from: Wm4PolyhedralMassProperties.cpp
// File Version: 4.10.0 (2009/11/18)
// Geometric Tools, LC
// Copyright (c) 1998-2010
// Distributed under the Boost Software License, Version 1.0.
// http://www.boost.org/LICENSE_1_0.txt
// http://www.geometrictools.com/License/Boost/LICENSE_1_0.txt
// Boost Software License - Version 1.0 - August 17th, 2003
// Permission is hereby granted, free of charge, to any person or
// organization obtaining a copy of the software and accompanying
// documentation covered by this license (the "Software") to use,
// reproduce, display, distribute, execute, and transmit the
// Software, and to prepare derivative works of the Software, and
// to permit third-parties to whom the Software is furnished to do
// so, all subject to the following:
// The copyright notices in the Software and this entire
// statement, including the above license grant, this restriction
// and the following disclaimer, must be included in all copies of
// the Software, in whole or in part, and all derivative works of
// the Software, unless such copies or derivative works are solely
// in the form of machine-executable object code generated by a
// source language processor.
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, TITLE AND
// NON-INFRINGEMENT. IN NO EVENT SHALL THE COPYRIGHT HOLDERS OR
// ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE FOR ANY DAMAGES OR
// OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE,
// ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE
// USE OR OTHER DEALINGS IN THE SOFTWARE.
const scalar r6 = 1.0/6.0;
const scalar r24 = 1.0/24.0;
const scalar r60 = 1.0/60.0;
const scalar r120 = 1.0/120.0;
// order: 1, x, y, z, x^2, y^2, z^2, xy, yz, zx
scalarField integrals(10, 0.0);
forAll(triFaces, i)
{
const triFace& tri(triFaces[i]);
// vertices of triangle i
vector v0 = pts[tri[0]];
vector v1 = pts[tri[1]];
vector v2 = pts[tri[2]];
// cross product of edges
vector eA = v1 - v0;
vector eB = v2 - v0;
vector n = eA ^ eB;
// compute integral terms
scalar tmp0, tmp1, tmp2;
scalar f1x, f2x, f3x, g0x, g1x, g2x;
tmp0 = v0.x() + v1.x();
f1x = tmp0 + v2.x();
tmp1 = v0.x()*v0.x();
tmp2 = tmp1 + v1.x()*tmp0;
f2x = tmp2 + v2.x()*f1x;
f3x = v0.x()*tmp1 + v1.x()*tmp2 + v2.x()*f2x;
g0x = f2x + v0.x()*(f1x + v0.x());
g1x = f2x + v1.x()*(f1x + v1.x());
g2x = f2x + v2.x()*(f1x + v2.x());
scalar f1y, f2y, f3y, g0y, g1y, g2y;
tmp0 = v0.y() + v1.y();
f1y = tmp0 + v2.y();
tmp1 = v0.y()*v0.y();
tmp2 = tmp1 + v1.y()*tmp0;
f2y = tmp2 + v2.y()*f1y;
f3y = v0.y()*tmp1 + v1.y()*tmp2 + v2.y()*f2y;
g0y = f2y + v0.y()*(f1y + v0.y());
g1y = f2y + v1.y()*(f1y + v1.y());
g2y = f2y + v2.y()*(f1y + v2.y());
scalar f1z, f2z, f3z, g0z, g1z, g2z;
tmp0 = v0.z() + v1.z();
f1z = tmp0 + v2.z();
tmp1 = v0.z()*v0.z();
tmp2 = tmp1 + v1.z()*tmp0;
f2z = tmp2 + v2.z()*f1z;
f3z = v0.z()*tmp1 + v1.z()*tmp2 + v2.z()*f2z;
g0z = f2z + v0.z()*(f1z + v0.z());
g1z = f2z + v1.z()*(f1z + v1.z());
g2z = f2z + v2.z()*(f1z + v2.z());
// update integrals
integrals[0] += n.x()*f1x;
integrals[1] += n.x()*f2x;
integrals[2] += n.y()*f2y;
integrals[3] += n.z()*f2z;
integrals[4] += n.x()*f3x;
integrals[5] += n.y()*f3y;
integrals[6] += n.z()*f3z;
integrals[7] += n.x()*(v0.y()*g0x + v1.y()*g1x + v2.y()*g2x);
integrals[8] += n.y()*(v0.z()*g0y + v1.z()*g1y + v2.z()*g2y);
integrals[9] += n.z()*(v0.x()*g0z + v1.x()*g1z + v2.x()*g2z);
}
pointField pts(nPts);
integrals[0] *= r6;
integrals[1] *= r24;
integrals[2] *= r24;
integrals[3] *= r24;
integrals[4] *= r60;
integrals[5] *= r60;
integrals[6] *= r60;
integrals[7] *= r120;
integrals[8] *= r120;
integrals[9] *= r120;
// mass
mass = integrals[0];
// center of mass
cM = vector(integrals[1], integrals[2], integrals[3])/mass;
// inertia relative to origin
J.xx() = integrals[5] + integrals[6];
J.xy() = -integrals[7];
J.xz() = -integrals[9];
J.yx() = J.xy();
J.yy() = integrals[4] + integrals[6];
J.yz() = -integrals[8];
J.zx() = J.xz();
J.zy() = J.yz();
J.zz() = integrals[4] + integrals[5];
// inertia relative to center of mass
J -= mass*((cM & cM)*I - cM*cM);
// Apply density
mass *= density;
J *= density;
}
pts[0] = point(4.495, 3.717, -4.112);
pts[1] = point(4.421, 3.932, -4.112);
pts[2] = point(4.379, 4.053, -4.112);
pts[3] = point(4.301, 4.026, -4.300);
pts[4] = point(4.294, 4.024, -4.317);
pts[5] = point(4.409, 3.687, -4.317);
int main(int argc, char *argv[])
{
scalar density = 1.0;
face f(identity(nPts));
{
label nPts = 6;
point Cf = f.centre(pts);
pointField pts(nPts);
tensor J = tensor::zero;
pts[0] = point(4.495, 3.717, -4.112);
pts[1] = point(4.421, 3.932, -4.112);
pts[2] = point(4.379, 4.053, -4.112);
pts[3] = point(4.301, 4.026, -4.300);
pts[4] = point(4.294, 4.024, -4.317);
pts[5] = point(4.409, 3.687, -4.317);
J = f.inertia(pts, Cf, density);
face f(identity(nPts));
vector eVal = eigenValues(J);
point Cf = f.centre(pts);
tensor eVec = eigenVectors(J);
tensor J = tensor::zero;
Info<< nl << "Inertia tensor of test face " << J << nl
<< "eigenValues (principal moments) " << eVal << nl
<< "eigenVectors (principal axes) " << eVec
<< endl;
J = f.inertia(pts, Cf, density);
OFstream str("momentOfInertiaTest.obj");
vector eVal = eigenValues(J);
Info<< nl << "Writing test face and scaled principal axes to "
<< str.name() << endl;
tensor eVec = eigenVectors(J);
forAll(pts, ptI)
{
meshTools::writeOBJ(str, pts[ptI]);
}
Info<< nl << "Inertia tensor of test face " << J << nl
<< "eigenValues (principal moments) " << eVal << nl
<< "eigenVectors (principal axes) " << eVec
<< endl;
str << "l";
OFstream str("momentOfInertiaTestFace.obj");
forAll(f, fI)
{
str << ' ' << fI + 1;
}
Info<< nl << "Writing test face and scaled principal axes to "
<< str.name() << endl;
forAll(pts, ptI)
{
meshTools::writeOBJ(str, pts[ptI]);
}
str << "l";
str << " 1" << endl;
forAll(f, fI)
{
str << ' ' << fI + 1;
}
scalar scale = mag(Cf - pts[f[0]])/eVal.component(findMin(eVal));
str << " 1" << endl;
meshTools::writeOBJ(str, Cf);
meshTools::writeOBJ(str, Cf + scale*eVal.x()*eVec.x());
meshTools::writeOBJ(str, Cf + scale*eVal.y()*eVec.y());
meshTools::writeOBJ(str, Cf + scale*eVal.z()*eVec.z());
scalar scale = mag(Cf - pts[f[0]])/eVal.component(findMin(eVal));
meshTools::writeOBJ(str, Cf);
meshTools::writeOBJ(str, Cf + scale*eVal.x()*eVec.x());
meshTools::writeOBJ(str, Cf + scale*eVal.y()*eVec.y());
meshTools::writeOBJ(str, Cf + scale*eVal.z()*eVec.z());
for (label i = nPts + 1; i < nPts + 4; i++)
{
str << "l " << nPts + 1 << ' ' << i + 1 << endl;
}
}
for (label i = nPts + 1; i < nPts + 4; i++)
{
str << "l " << nPts + 1 << ' ' << i + 1 << endl;
label nPts = 4;
pointField pts(nPts);
pts[0] = point(0, 0, 0);
pts[1] = point(1, 0, 0);
pts[2] = point(0.5, 1, 0);
pts[3] = point(0.5, 0.5, 1);
tetPointRef tet(pts[0], pts[1], pts[2], pts[3]);
triFaceList tetFaces(4);
tetFaces[0] = triFace(0, 2, 1);
tetFaces[1] = triFace(1, 2, 3);
tetFaces[2] = triFace(0, 3, 2);
tetFaces[3] = triFace(0, 1, 3);
scalar m = 0.0;
vector cM = vector::zero;
tensor J = tensor::zero;
massPropertiesSolid
(
pts,
tetFaces,
density,
m,
cM,
J
);
vector eVal = eigenValues(J);
tensor eVec = eigenVectors(J);
Info<< nl
<< "Mass of tetrahedron " << m << nl
<< "Centre of mass of tetrahedron " << cM << nl
<< "Inertia tensor of tetrahedron " << J << nl
<< "eigenValues (principal moments) " << eVal << nl
<< "eigenVectors (principal axes) " << eVec
<< endl;
OFstream str("momentOfInertiaTestTet.obj");
Info<< nl << "Writing test tetrahedron and scaled principal axes to "
<< str.name() << endl;
forAll(pts, ptI)
{
meshTools::writeOBJ(str, pts[ptI]);
}
forAll(tetFaces, tFI)
{
const triFace& f = tetFaces[tFI];
str << "l";
forAll(f, fI)
{
str << ' ' << f[fI] + 1;
}
str << ' ' << f[0] + 1 << endl;
}
scalar scale = mag(cM - pts[0])/eVal.component(findMin(eVal));
meshTools::writeOBJ(str, cM);
meshTools::writeOBJ(str, cM + scale*eVal.x()*eVec.x());
meshTools::writeOBJ(str, cM + scale*eVal.y()*eVec.y());
meshTools::writeOBJ(str, cM + scale*eVal.z()*eVec.z());
for (label i = nPts + 1; i < nPts + 4; i++)
{
str << "l " << nPts + 1 << ' ' << i + 1 << endl;
}
}
Info<< nl << "End" << nl << endl;
......
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