646 lines
17 KiB
C
646 lines
17 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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command line specified triSurface. Inertia can either be of the
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solid body or of a thin shell.
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\*---------------------------------------------------------------------------*/
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#include "argList.H"
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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 "triSurface.H"
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#include "OFstream.H"
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#include "meshTools.H"
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#include "Random.H"
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#include "transform.H"
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#include "IOmanip.H"
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#include "Pair.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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void massPropertiesShell
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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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// Reset properties for accumulation
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mass = 0.0;
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cM = vector::zero;
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J = tensor::zero;
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// Find centre of mass
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forAll(triFaces, i)
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{
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const triFace& tri(triFaces[i]);
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triPointRef t
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(
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pts[tri[0]],
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pts[tri[1]],
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pts[tri[2]]
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);
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scalar triMag = t.mag();
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cM += triMag*t.centre();
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mass += triMag;
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}
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cM /= mass;
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mass *= density;
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// Find inertia around centre of mass
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forAll(triFaces, i)
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{
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const triFace& tri(triFaces[i]);
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J += triPointRef
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(
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pts[tri[0]],
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pts[tri[1]],
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pts[tri[2]]
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).inertia(cM, density);
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}
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}
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tensor applyParallelAxisTheorem
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(
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scalar m,
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const vector& cM,
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const tensor& J,
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const vector& refPt
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)
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{
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// The displacement vector (refPt = cM) is the displacement of the
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// new reference point from the centre of mass of the body that
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// the inertia tensor applies to.
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vector d = (refPt - cM);
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return J + m*((d & d)*I - d*d);
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}
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int main(int argc, char *argv[])
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{
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argList::addNote
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(
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"Calculates the inertia tensor and principal axes and moments "
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"of the specified surface.\n"
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"Inertia can either be of the solid body or of a thin shell."
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);
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argList::noParallel();
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argList::validArgs.append("surfaceFile");
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argList::addBoolOption
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(
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"shellProperties",
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"inertia of a thin shell"
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);
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argList::addOption
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(
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"density",
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"scalar",
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"Specify density, "
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"kg/m3 for solid properties, kg/m2 for shell properties"
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);
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argList::addOption
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(
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"referencePoint",
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"vector",
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"Inertia relative to this point, not the centre of mass"
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);
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argList args(argc, argv);
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const fileName surfFileName = args[1];
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const scalar density = args.optionLookupOrDefault("density", 1.0);
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vector refPt = vector::zero;
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bool calcAroundRefPt = args.optionReadIfPresent("referencePoint", refPt);
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triSurface surf(surfFileName);
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triFaceList faces(surf.size());
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forAll(surf, i)
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{
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faces[i] = triFace(surf[i]);
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}
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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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if (args.optionFound("shellProperties"))
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{
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massPropertiesShell
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(
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surf.points(),
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faces,
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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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}
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else
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{
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massPropertiesSolid
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(
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surf.points(),
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faces,
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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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}
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if (m < 0)
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{
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WarningIn(args.executable() + "::main")
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<< "Negative mass detected, the surface may be inside-out." << endl;
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}
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vector eVal = eigenValues(J);
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tensor eVec = eigenVectors(J);
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label pertI = 0;
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Random rand(57373);
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while ((magSqr(eVal) < VSMALL) && pertI < 10)
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{
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WarningIn(args.executable() + "::main")
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<< "No eigenValues found, shape may have symmetry, "
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<< "perturbing inertia tensor diagonal" << endl;
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J.xx() *= 1.0 + SMALL*rand.scalar01();
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J.yy() *= 1.0 + SMALL*rand.scalar01();
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J.zz() *= 1.0 + SMALL*rand.scalar01();
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eVal = eigenValues(J);
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eVec = eigenVectors(J);
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pertI++;
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}
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bool showTransform = true;
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if
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(
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(mag(eVec.x() ^ eVec.y()) > (1.0 - SMALL))
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&& (mag(eVec.y() ^ eVec.z()) > (1.0 - SMALL))
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&& (mag(eVec.z() ^ eVec.x()) > (1.0 - SMALL))
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)
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{
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// Make the eigenvectors a right handed orthogonal triplet
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eVec = tensor
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(
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eVec.x(),
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eVec.y(),
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eVec.z() * sign((eVec.x() ^ eVec.y()) & eVec.z())
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);
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// Finding the most natural transformation. Using Lists
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// rather than tensors to allow indexed permutation.
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// Cartesian basis vectors - right handed orthogonal triplet
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List<vector> cartesian(3);
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cartesian[0] = vector(1, 0, 0);
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cartesian[1] = vector(0, 1, 0);
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cartesian[2] = vector(0, 0, 1);
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// Principal axis basis vectors - right handed orthogonal
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// triplet
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List<vector> principal(3);
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principal[0] = eVec.x();
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principal[1] = eVec.y();
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principal[2] = eVec.z();
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scalar maxMagDotProduct = -GREAT;
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// Matching axis indices, first: cartesian, second:principal
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Pair<label> match(-1, -1);
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forAll(cartesian, cI)
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{
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forAll(principal, pI)
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{
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scalar magDotProduct = mag(cartesian[cI] & principal[pI]);
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if (magDotProduct > maxMagDotProduct)
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{
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maxMagDotProduct = magDotProduct;
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match.first() = cI;
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match.second() = pI;
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}
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}
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}
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scalar sense = sign
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(
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cartesian[match.first()] & principal[match.second()]
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);
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if (sense < 0)
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{
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// Invert the best match direction and swap the order of
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// the other two vectors
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List<vector> tPrincipal = principal;
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tPrincipal[match.second()] *= -1;
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tPrincipal[(match.second() + 1) % 3] =
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principal[(match.second() + 2) % 3];
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tPrincipal[(match.second() + 2) % 3] =
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principal[(match.second() + 1) % 3];
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principal = tPrincipal;
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vector tEVal = eVal;
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tEVal[(match.second() + 1) % 3] = eVal[(match.second() + 2) % 3];
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tEVal[(match.second() + 2) % 3] = eVal[(match.second() + 1) % 3];
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eVal = tEVal;
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}
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label permutationDelta = match.second() - match.first();
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if (permutationDelta != 0)
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{
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// Add 3 to the permutationDelta to avoid negative indices
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permutationDelta += 3;
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List<vector> tPrincipal = principal;
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vector tEVal = eVal;
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for (label i = 0; i < 3; i++)
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{
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tPrincipal[i] = principal[(i + permutationDelta) % 3];
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tEVal[i] = eVal[(i + permutationDelta) % 3];
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}
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principal = tPrincipal;
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eVal = tEVal;
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}
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label matchedAlready = match.first();
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match =Pair<label>(-1, -1);
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maxMagDotProduct = -GREAT;
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forAll(cartesian, cI)
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{
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if (cI == matchedAlready)
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{
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continue;
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}
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forAll(principal, pI)
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{
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if (pI == matchedAlready)
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{
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continue;
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}
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scalar magDotProduct = mag(cartesian[cI] & principal[pI]);
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if (magDotProduct > maxMagDotProduct)
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{
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maxMagDotProduct = magDotProduct;
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match.first() = cI;
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match.second() = pI;
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}
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}
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}
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sense = sign
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(
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cartesian[match.first()] & principal[match.second()]
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);
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if (sense < 0 || (match.second() - match.first()) != 0)
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{
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principal[match.second()] *= -1;
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List<vector> tPrincipal = principal;
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tPrincipal[(matchedAlready + 1) % 3] =
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principal[(matchedAlready + 2) % 3]*-sense;
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tPrincipal[(matchedAlready + 2) % 3] =
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principal[(matchedAlready + 1) % 3]*-sense;
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principal = tPrincipal;
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vector tEVal = eVal;
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tEVal[(matchedAlready + 1) % 3] = eVal[(matchedAlready + 2) % 3];
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tEVal[(matchedAlready + 2) % 3] = eVal[(matchedAlready + 1) % 3];
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|
|
|
eVal = tEVal;
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|
}
|
|
|
|
eVec = tensor(principal[0], principal[1], principal[2]);
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|
|
|
// {
|
|
// tensor R = rotationTensor(vector(1, 0, 0), eVec.x());
|
|
|
|
// R = rotationTensor(R & vector(0, 1, 0), eVec.y()) & R;
|
|
|
|
// Info<< "R = " << nl << R << endl;
|
|
|
|
// Info<< "R - eVec.T() " << R - eVec.T() << endl;
|
|
// }
|
|
}
|
|
else
|
|
{
|
|
WarningIn(args.executable() + "::main")
|
|
<< "Non-unique eigenvectors, cannot compute transformation "
|
|
<< "from Cartesian axes" << endl;
|
|
|
|
showTransform = false;
|
|
}
|
|
|
|
Info<< nl << setprecision(10)
|
|
<< "Density: " << density << nl
|
|
<< "Mass: " << m << nl
|
|
<< "Centre of mass: " << cM << nl
|
|
<< "Inertia tensor around centre of mass: " << nl << J << nl
|
|
<< "eigenValues (principal moments): " << eVal << nl
|
|
<< "eigenVectors (principal axes): " << nl
|
|
<< eVec.x() << nl << eVec.y() << nl << eVec.z() << endl;
|
|
|
|
if (showTransform)
|
|
{
|
|
Info<< "Transform tensor from reference state (orientation):" << nl
|
|
<< eVec.T() << nl
|
|
<< "Rotation tensor required to transform "
|
|
"from the body reference frame to the global "
|
|
"reference frame, i.e.:" << nl
|
|
<< "globalVector = orientation & bodyLocalVector"
|
|
<< endl;
|
|
|
|
Info<< nl
|
|
<< "Entries for sixDoFRigidBodyDisplacement boundary condition:"
|
|
<< nl
|
|
<< " mass " << m << token::END_STATEMENT << nl
|
|
<< " centreOfMass " << cM << token::END_STATEMENT << nl
|
|
<< " momentOfInertia " << eVal << token::END_STATEMENT << nl
|
|
<< " orientation " << eVec.T() << token::END_STATEMENT
|
|
<< endl;
|
|
}
|
|
|
|
if (calcAroundRefPt)
|
|
{
|
|
Info<< nl << "Inertia tensor relative to " << refPt << ": " << nl
|
|
<< applyParallelAxisTheorem(m, cM, J, refPt)
|
|
<< endl;
|
|
}
|
|
|
|
OFstream str("axes.obj");
|
|
|
|
Info<< nl << "Writing scaled principal axes at centre of mass of "
|
|
<< surfFileName << " to " << str.name() << endl;
|
|
|
|
scalar scale = mag(cM - surf.points()[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 = 1; i < 4; i++)
|
|
{
|
|
str << "l " << 1 << ' ' << i + 1 << endl;
|
|
}
|
|
|
|
Info<< nl << "End" << nl << endl;
|
|
|
|
return 0;
|
|
}
|
|
|
|
|
|
// ************************************************************************* //
|