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