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/****************************************************************************
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* VCGLib o o *
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* Visual and Computer Graphics Library o o *
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* _ O _ *
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* Copyright(C) 2005 \/)\/ *
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* Visual Computing Lab /\/| *
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* ISTI - Italian National Research Council | *
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* \ *
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* All rights reserved. *
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* *
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* This program is free software; you can redistribute it and/or modify *
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* it under the terms of the GNU General Public License as published by *
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* the Free Software Foundation; either version 2 of the License, or *
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* (at your option) any later version. *
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* *
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* This program is distributed in the hope that it will be useful, *
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* but WITHOUT ANY WARRANTY; without even the implied warranty of *
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
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* GNU General Public License (http://www.gnu.org/licenses/gpl.txt) *
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* for more details. *
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* *
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****************************************************************************/
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/****************************************************************************
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History
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$Log: not supported by cvs2svn $
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Revision 1.13 2005/11/17 00:42:03 cignoni
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****************************************************************************/
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/*
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The algorithm is based on a three step reduction of the volume integrals
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to successively simpler integrals. The algorithm is designed to minimize
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the numerical errors that can result from poorly conditioned alignment of
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polyhedral faces. It is also designed for efficiency. All required volume
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integrals of a polyhedron are computed together during a single walk over
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the boundary of the polyhedron; exploiting common subexpressions reduces
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floating point operations.
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For more information, check out:
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Brian Mirtich,
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``Fast and Accurate Computation of Polyhedral Mass Properties,''
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journal of graphics tools, volume 1, number 2, 1996
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*/
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#include <vcg/math/matrix33.h>
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template <class MESH>
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class Inertia
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{
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private :
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enum {X=0,Y=1,Z=2};
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inline MESH::scalar_type SQR(MESH::scalar_type &x) const { return x*x;}
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inline MESH::scalar_type CUBE(MESH::scalar_type &x) const { return x*x*x;}
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int A; /* alpha */
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int B; /* beta */
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int C; /* gamma */
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/* projection integrals */
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double P1, Pa, Pb, Paa, Pab, Pbb, Paaa, Paab, Pabb, Pbbb;
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/* face integrals */
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double Fa, Fb, Fc, Faa, Fbb, Fcc, Faaa, Fbbb, Fccc, Faab, Fbbc, Fcca;
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/* volume integrals */
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double T0, T1[3], T2[3], TP[3];
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public:
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/* compute various integrations over projection of face */
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void compProjectionIntegrals(MESH::face_type &f)
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{
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double a0, a1, da;
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double b0, b1, db;
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double a0_2, a0_3, a0_4, b0_2, b0_3, b0_4;
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double a1_2, a1_3, b1_2, b1_3;
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double C1, Ca, Caa, Caaa, Cb, Cbb, Cbbb;
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double Cab, Kab, Caab, Kaab, Cabb, Kabb;
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int i;
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P1 = Pa = Pb = Paa = Pab = Pbb = Paaa = Paab = Pabb = Pbbb = 0.0;
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for (i = 0; i < 3; i++) {
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a0 = f.V(i)->P()[A];
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b0 = f.V(i)->P()[B];
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a1 = f.V1(i)->P()[A];
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b1 = f.V1(i)->P()[B];
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da = a1 - a0;
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db = b1 - b0;
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a0_2 = a0 * a0; a0_3 = a0_2 * a0; a0_4 = a0_3 * a0;
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b0_2 = b0 * b0; b0_3 = b0_2 * b0; b0_4 = b0_3 * b0;
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a1_2 = a1 * a1; a1_3 = a1_2 * a1;
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b1_2 = b1 * b1; b1_3 = b1_2 * b1;
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C1 = a1 + a0;
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Ca = a1*C1 + a0_2; Caa = a1*Ca + a0_3; Caaa = a1*Caa + a0_4;
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Cb = b1*(b1 + b0) + b0_2; Cbb = b1*Cb + b0_3; Cbbb = b1*Cbb + b0_4;
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Cab = 3*a1_2 + 2*a1*a0 + a0_2; Kab = a1_2 + 2*a1*a0 + 3*a0_2;
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Caab = a0*Cab + 4*a1_3; Kaab = a1*Kab + 4*a0_3;
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Cabb = 4*b1_3 + 3*b1_2*b0 + 2*b1*b0_2 + b0_3;
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Kabb = b1_3 + 2*b1_2*b0 + 3*b1*b0_2 + 4*b0_3;
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P1 += db*C1;
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Pa += db*Ca;
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Paa += db*Caa;
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Paaa += db*Caaa;
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Pb += da*Cb;
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Pbb += da*Cbb;
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Pbbb += da*Cbbb;
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Pab += db*(b1*Cab + b0*Kab);
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Paab += db*(b1*Caab + b0*Kaab);
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Pabb += da*(a1*Cabb + a0*Kabb);
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}
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P1 /= 2.0;
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Pa /= 6.0;
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Paa /= 12.0;
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Paaa /= 20.0;
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Pb /= -6.0;
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Pbb /= -12.0;
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Pbbb /= -20.0;
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Pab /= 24.0;
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Paab /= 60.0;
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Pabb /= -60.0;
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}
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void CompFaceIntegrals(MESH::face_type &f)
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{
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MESH::vectorial_type n;
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MESH::scalar_type w;
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double k1, k2, k3, k4;
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compProjectionIntegrals(f);
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n = f.N();
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w = -f.V(0)->P()*n;
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k1 = 1 / n[C]; k2 = k1 * k1; k3 = k2 * k1; k4 = k3 * k1;
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Fa = k1 * Pa;
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Fb = k1 * Pb;
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Fc = -k2 * (n[A]*Pa + n[B]*Pb + w*P1);
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Faa = k1 * Paa;
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Fbb = k1 * Pbb;
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Fcc = k3 * (SQR(n[A])*Paa + 2*n[A]*n[B]*Pab + SQR(n[B])*Pbb
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+ w*(2*(n[A]*Pa + n[B]*Pb) + w*P1));
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Faaa = k1 * Paaa;
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Fbbb = k1 * Pbbb;
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Fccc = -k4 * (CUBE(n[A])*Paaa + 3*SQR(n[A])*n[B]*Paab
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+ 3*n[A]*SQR(n[B])*Pabb + CUBE(n[B])*Pbbb
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+ 3*w*(SQR(n[A])*Paa + 2*n[A]*n[B]*Pab + SQR(n[B])*Pbb)
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+ w*w*(3*(n[A]*Pa + n[B]*Pb) + w*P1));
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Faab = k1 * Paab;
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Fbbc = -k2 * (n[A]*Pabb + n[B]*Pbbb + w*Pbb);
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Fcca = k3 * (SQR(n[A])*Paaa + 2*n[A]*n[B]*Paab + SQR(n[B])*Pabb
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+ w*(2*(n[A]*Paa + n[B]*Pab) + w*Pa));
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}
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void Compute(MESH &m)
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{
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//
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double nx, ny, nz;
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T0 = T1[X] = T1[Y] = T1[Z]
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= T2[X] = T2[Y] = T2[Z]
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= TP[X] = TP[Y] = TP[Z] = 0;
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MESH::face_iterator fi;
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for (fi=m.face.begin(); fi!=m.face.end();++fi) if(!(*fi).IsD()) {
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MESH::face_type &f=(*fi);
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nx = fabs(f.N()[0]);
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ny = fabs(f.N()[1]);
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nz = fabs(f.N()[2]);
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if (nx > ny && nx > nz) C = X;
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else C = (ny > nz) ? Y : Z;
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A = (C + 1) % 3;
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B = (A + 1) % 3;
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CompFaceIntegrals(f);
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T0 += f.N()[X] * ((A == X) ? Fa : ((B == X) ? Fb : Fc));
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T1[A] += f.N()[A] * Faa;
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T1[B] += f.N()[B] * Fbb;
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T1[C] += f.N()[C] * Fcc;
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T2[A] += f.N()[A] * Faaa;
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T2[B] += f.N()[B] * Fbbb;
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T2[C] += f.N()[C] * Fccc;
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TP[A] += f.N()[A] * Faab;
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TP[B] += f.N()[B] * Fbbc;
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TP[C] += f.N()[C] * Fcca;
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}
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T1[X] /= 2; T1[Y] /= 2; T1[Z] /= 2;
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T2[X] /= 3; T2[Y] /= 3; T2[Z] /= 3;
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TP[X] /= 2; TP[Y] /= 2; TP[Z] /= 2;
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}
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MESH::scalar_type Mass()
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{
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return T0;
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}
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MESH::vectorial_type CenterOfMass()
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{
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MESH::vectorial_type r;
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r[X] = T1[X] / T0;
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r[Y] = T1[Y] / T0;
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r[Z] = T1[Z] / T0;
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return r;
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}
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void InertiaTensor(Matrix33<MESH::scalar_type> &J ){
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MESH::vectorial_type r;
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r[X] = T1[X] / T0;
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r[Y] = T1[Y] / T0;
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r[Z] = T1[Z] / T0;
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/* compute inertia tensor */
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J[X][X] = (T2[Y] + T2[Z]);
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J[Y][Y] = (T2[Z] + T2[X]);
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J[Z][Z] = (T2[X] + T2[Y]);
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J[X][Y] = J[Y][X] = - TP[X];
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J[Y][Z] = J[Z][Y] = - TP[Y];
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J[Z][X] = J[X][Z] = - TP[Z];
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J[X][X] -= T0 * (r[Y]*r[Y] + r[Z]*r[Z]);
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J[Y][Y] -= T0 * (r[Z]*r[Z] + r[X]*r[X]);
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J[Z][Z] -= T0 * (r[X]*r[X] + r[Y]*r[Y]);
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J[X][Y] = J[Y][X] += T0 * r[X] * r[Y];
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J[Y][Z] = J[Z][Y] += T0 * r[Y] * r[Z];
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J[Z][X] = J[X][Z] += T0 * r[Z] * r[X];
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}
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void InertiaTensor(Matrix44<MESH::scalar_type> &J )
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{
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J.SetIdentity();
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MESH::vectorial_type r;
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r[X] = T1[X] / T0;
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r[Y] = T1[Y] / T0;
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r[Z] = T1[Z] / T0;
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/* compute inertia tensor */
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J[X][X] = (T2[Y] + T2[Z]);
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J[Y][Y] = (T2[Z] + T2[X]);
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J[Z][Z] = (T2[X] + T2[Y]);
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J[X][Y] = J[Y][X] = - TP[X];
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J[Y][Z] = J[Z][Y] = - TP[Y];
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J[Z][X] = J[X][Z] = - TP[Z];
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J[X][X] -= T0 * (r[Y]*r[Y] + r[Z]*r[Z]);
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J[Y][Y] -= T0 * (r[Z]*r[Z] + r[X]*r[X]);
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J[Z][Z] -= T0 * (r[X]*r[X] + r[Y]*r[Y]);
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J[X][Y] = J[Y][X] += T0 * r[X] * r[Y];
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J[Y][Z] = J[Z][Y] += T0 * r[Y] * r[Z];
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J[Z][X] = J[X][Z] += T0 * r[Z] * r[X];
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}
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// Calcola autovalori ed autovettori dell'inertia tensor.
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// Gli autovettori fanno una rotmatrix che se applicata mette l'oggetto secondo gli assi id minima/max inerzia.
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void InertiaTensorEigen(Matrix44<MESH::scalar_type> &EV, Point4<MESH::scalar_type> &ev )
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{
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Matrix44<MESH::scalar_type> it;
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InertiaTensor(it);
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Matrix44d EVd,ITd;ITd.Import(it);
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Point4d evd; evd.Import(ev);
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int n;
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ITd.Jacobi(evd,EVd,n);
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EV.Import(EVd);
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ev.Import(evd);
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}
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};
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#if 0
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/*
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============================================================================
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constants
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============================================================================
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*/
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#define MAX_VERTS 100 /* maximum number of polyhedral vertices */
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#define MAX_FACES 100 /* maximum number of polyhedral faces */
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#define MAX_POLYGON_SZ 10 /* maximum number of verts per polygonal face */
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#define X 0
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#define Y 1
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#define Z 2
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/*
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============================================================================
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macros
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============================================================================
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*/
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inline MESH:scalar_Type SQR(MESH:scalar_Type &x) const { return x*x;}
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inline MESH:scalar_Type CUBE(MESH:scalar_Type &x) const { return x*x*x;}
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//#define CUBE(x) ((x)*(x)*(x))
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/*
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============================================================================
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data structures
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============================================================================
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*/
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typedef struct {
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int numVerts;
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double norm[3];
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double w;
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int verts[MAX_POLYGON_SZ];
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struct polyhedron *poly;
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} FACE;
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typedef struct polyhedron {
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int numVerts, numFaces;
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double verts[MAX_VERTS][3];
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FACE faces[MAX_FACES];
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} POLYHEDRON;
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/*
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============================================================================
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globals
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============================================================================
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*/
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static int A; /* alpha */
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static int B; /* beta */
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static int C; /* gamma */
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/* projection integrals */
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static double P1, Pa, Pb, Paa, Pab, Pbb, Paaa, Paab, Pabb, Pbbb;
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/* face integrals */
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static double Fa, Fb, Fc, Faa, Fbb, Fcc, Faaa, Fbbb, Fccc, Faab, Fbbc, Fcca;
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/* volume integrals */
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static double T0, T1[3], T2[3], TP[3];
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/*
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============================================================================
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read in a polyhedron
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============================================================================
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*/
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void readPolyhedron(char *name, POLYHEDRON *p)
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{
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FILE *fp;
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char line[200], *c;
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int i, j, n;
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double dx1, dy1, dz1, dx2, dy2, dz2, nx, ny, nz, len;
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FACE *f;
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if (!(fp = fopen(name, "r"))) {
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printf("i/o error\n");
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exit(1);
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}
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fscanf(fp, "%d", &p->numVerts);
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printf("Reading in %d vertices\n", p->numVerts);
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for (i = 0; i < p->numVerts; i++)
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fscanf(fp, "%lf %lf %lf",
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&p->verts[i][X], &p->verts[i][Y], &p->verts[i][Z]);
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fscanf(fp, "%d", &p->numFaces);
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printf("Reading in %d faces\n", p->numFaces);
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for (i = 0; i < p->numFaces; i++) {
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f = &p->faces[i];
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f->poly = p;
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fscanf(fp, "%d", &f->numVerts);
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for (j = 0; j < f->numVerts; j++) fscanf(fp, "%d", &f->verts[j]);
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/* compute face normal and offset w from first 3 vertices */
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dx1 = p->verts[f->verts[1]][X] - p->verts[f->verts[0]][X];
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dy1 = p->verts[f->verts[1]][Y] - p->verts[f->verts[0]][Y];
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dz1 = p->verts[f->verts[1]][Z] - p->verts[f->verts[0]][Z];
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dx2 = p->verts[f->verts[2]][X] - p->verts[f->verts[1]][X];
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dy2 = p->verts[f->verts[2]][Y] - p->verts[f->verts[1]][Y];
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dz2 = p->verts[f->verts[2]][Z] - p->verts[f->verts[1]][Z];
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nx = dy1 * dz2 - dy2 * dz1;
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ny = dz1 * dx2 - dz2 * dx1;
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nz = dx1 * dy2 - dx2 * dy1;
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len = sqrt(nx * nx + ny * ny + nz * nz);
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f->norm[X] = nx / len;
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f->norm[Y] = ny / len;
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f->norm[Z] = nz / len;
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f->w = - f->norm[X] * p->verts[f->verts[0]][X]
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- f->norm[Y] * p->verts[f->verts[0]][Y]
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- f->norm[Z] * p->verts[f->verts[0]][Z];
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}
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fclose(fp);
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}
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/*
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||||
============================================================================
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compute mass properties
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||||
============================================================================
|
||||
*/
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|
||||
/* compute various integrations over projection of face */
|
||||
void compProjectionIntegrals(FACE *f)
|
||||
{
|
||||
double a0, a1, da;
|
||||
double b0, b1, db;
|
||||
double a0_2, a0_3, a0_4, b0_2, b0_3, b0_4;
|
||||
double a1_2, a1_3, b1_2, b1_3;
|
||||
double C1, Ca, Caa, Caaa, Cb, Cbb, Cbbb;
|
||||
double Cab, Kab, Caab, Kaab, Cabb, Kabb;
|
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int i;
|
||||
|
||||
P1 = Pa = Pb = Paa = Pab = Pbb = Paaa = Paab = Pabb = Pbbb = 0.0;
|
||||
|
||||
for (i = 0; i < f->numVerts; i++) {
|
||||
a0 = f->poly->verts[f->verts[i]][A];
|
||||
b0 = f->poly->verts[f->verts[i]][B];
|
||||
a1 = f->poly->verts[f->verts[(i+1) % f->numVerts]][A];
|
||||
b1 = f->poly->verts[f->verts[(i+1) % f->numVerts]][B];
|
||||
da = a1 - a0;
|
||||
db = b1 - b0;
|
||||
a0_2 = a0 * a0; a0_3 = a0_2 * a0; a0_4 = a0_3 * a0;
|
||||
b0_2 = b0 * b0; b0_3 = b0_2 * b0; b0_4 = b0_3 * b0;
|
||||
a1_2 = a1 * a1; a1_3 = a1_2 * a1;
|
||||
b1_2 = b1 * b1; b1_3 = b1_2 * b1;
|
||||
|
||||
C1 = a1 + a0;
|
||||
Ca = a1*C1 + a0_2; Caa = a1*Ca + a0_3; Caaa = a1*Caa + a0_4;
|
||||
Cb = b1*(b1 + b0) + b0_2; Cbb = b1*Cb + b0_3; Cbbb = b1*Cbb + b0_4;
|
||||
Cab = 3*a1_2 + 2*a1*a0 + a0_2; Kab = a1_2 + 2*a1*a0 + 3*a0_2;
|
||||
Caab = a0*Cab + 4*a1_3; Kaab = a1*Kab + 4*a0_3;
|
||||
Cabb = 4*b1_3 + 3*b1_2*b0 + 2*b1*b0_2 + b0_3;
|
||||
Kabb = b1_3 + 2*b1_2*b0 + 3*b1*b0_2 + 4*b0_3;
|
||||
|
||||
P1 += db*C1;
|
||||
Pa += db*Ca;
|
||||
Paa += db*Caa;
|
||||
Paaa += db*Caaa;
|
||||
Pb += da*Cb;
|
||||
Pbb += da*Cbb;
|
||||
Pbbb += da*Cbbb;
|
||||
Pab += db*(b1*Cab + b0*Kab);
|
||||
Paab += db*(b1*Caab + b0*Kaab);
|
||||
Pabb += da*(a1*Cabb + a0*Kabb);
|
||||
}
|
||||
|
||||
P1 /= 2.0;
|
||||
Pa /= 6.0;
|
||||
Paa /= 12.0;
|
||||
Paaa /= 20.0;
|
||||
Pb /= -6.0;
|
||||
Pbb /= -12.0;
|
||||
Pbbb /= -20.0;
|
||||
Pab /= 24.0;
|
||||
Paab /= 60.0;
|
||||
Pabb /= -60.0;
|
||||
}
|
||||
|
||||
compFaceIntegrals(FACE *f)
|
||||
{
|
||||
double *n, w;
|
||||
double k1, k2, k3, k4;
|
||||
|
||||
compProjectionIntegrals(f);
|
||||
|
||||
w = f->w;
|
||||
n = f->norm;
|
||||
k1 = 1 / n[C]; k2 = k1 * k1; k3 = k2 * k1; k4 = k3 * k1;
|
||||
|
||||
Fa = k1 * Pa;
|
||||
Fb = k1 * Pb;
|
||||
Fc = -k2 * (n[A]*Pa + n[B]*Pb + w*P1);
|
||||
|
||||
Faa = k1 * Paa;
|
||||
Fbb = k1 * Pbb;
|
||||
Fcc = k3 * (SQR(n[A])*Paa + 2*n[A]*n[B]*Pab + SQR(n[B])*Pbb
|
||||
+ w*(2*(n[A]*Pa + n[B]*Pb) + w*P1));
|
||||
|
||||
Faaa = k1 * Paaa;
|
||||
Fbbb = k1 * Pbbb;
|
||||
Fccc = -k4 * (CUBE(n[A])*Paaa + 3*SQR(n[A])*n[B]*Paab
|
||||
+ 3*n[A]*SQR(n[B])*Pabb + CUBE(n[B])*Pbbb
|
||||
+ 3*w*(SQR(n[A])*Paa + 2*n[A]*n[B]*Pab + SQR(n[B])*Pbb)
|
||||
+ w*w*(3*(n[A]*Pa + n[B]*Pb) + w*P1));
|
||||
|
||||
Faab = k1 * Paab;
|
||||
Fbbc = -k2 * (n[A]*Pabb + n[B]*Pbbb + w*Pbb);
|
||||
Fcca = k3 * (SQR(n[A])*Paaa + 2*n[A]*n[B]*Paab + SQR(n[B])*Pabb
|
||||
+ w*(2*(n[A]*Paa + n[B]*Pab) + w*Pa));
|
||||
}
|
||||
|
||||
void CompVolumeIntegrals(POLYHEDRON *p)
|
||||
{
|
||||
FACE *f;
|
||||
double nx, ny, nz;
|
||||
int i;
|
||||
|
||||
T0 = T1[X] = T1[Y] = T1[Z]
|
||||
= T2[X] = T2[Y] = T2[Z]
|
||||
= TP[X] = TP[Y] = TP[Z] = 0;
|
||||
|
||||
for (i = 0; i < p->numFaces; i++) {
|
||||
|
||||
f = &p->faces[i];
|
||||
|
||||
nx = fabs(f->norm[X]);
|
||||
ny = fabs(f->norm[Y]);
|
||||
nz = fabs(f->norm[Z]);
|
||||
if (nx > ny && nx > nz) C = X;
|
||||
else C = (ny > nz) ? Y : Z;
|
||||
A = (C + 1) % 3;
|
||||
B = (A + 1) % 3;
|
||||
|
||||
compFaceIntegrals(f);
|
||||
|
||||
T0 += f->norm[X] * ((A == X) ? Fa : ((B == X) ? Fb : Fc));
|
||||
|
||||
T1[A] += f->norm[A] * Faa;
|
||||
T1[B] += f->norm[B] * Fbb;
|
||||
T1[C] += f->norm[C] * Fcc;
|
||||
T2[A] += f->norm[A] * Faaa;
|
||||
T2[B] += f->norm[B] * Fbbb;
|
||||
T2[C] += f->norm[C] * Fccc;
|
||||
TP[A] += f->norm[A] * Faab;
|
||||
TP[B] += f->norm[B] * Fbbc;
|
||||
TP[C] += f->norm[C] * Fcca;
|
||||
}
|
||||
|
||||
T1[X] /= 2; T1[Y] /= 2; T1[Z] /= 2;
|
||||
T2[X] /= 3; T2[Y] /= 3; T2[Z] /= 3;
|
||||
TP[X] /= 2; TP[Y] /= 2; TP[Z] /= 2;
|
||||
}
|
||||
|
||||
|
||||
/*
|
||||
============================================================================
|
||||
main
|
||||
============================================================================
|
||||
*/
|
||||
|
||||
|
||||
int main(int argc, char *argv[])
|
||||
{
|
||||
POLYHEDRON p;
|
||||
double density, mass;
|
||||
double r[3]; /* center of mass */
|
||||
double J[3][3]; /* inertia tensor */
|
||||
|
||||
if (argc != 2) {
|
||||
printf("usage: %s <polyhedron geometry filename>\n", argv[0]);
|
||||
exit(0);
|
||||
}
|
||||
|
||||
readPolyhedron(argv[1], &p);
|
||||
|
||||
compVolumeIntegrals(&p);
|
||||
|
||||
|
||||
printf("\nT1 = %+20.6f\n\n", T0);
|
||||
|
||||
printf("Tx = %+20.6f\n", T1[X]);
|
||||
printf("Ty = %+20.6f\n", T1[Y]);
|
||||
printf("Tz = %+20.6f\n\n", T1[Z]);
|
||||
|
||||
printf("Txx = %+20.6f\n", T2[X]);
|
||||
printf("Tyy = %+20.6f\n", T2[Y]);
|
||||
printf("Tzz = %+20.6f\n\n", T2[Z]);
|
||||
|
||||
printf("Txy = %+20.6f\n", TP[X]);
|
||||
printf("Tyz = %+20.6f\n", TP[Y]);
|
||||
printf("Tzx = %+20.6f\n\n", TP[Z]);
|
||||
|
||||
density = 1.0; /* assume unit density */
|
||||
|
||||
mass = density * T0;
|
||||
|
||||
/* compute center of mass */
|
||||
r[X] = T1[X] / T0;
|
||||
r[Y] = T1[Y] / T0;
|
||||
r[Z] = T1[Z] / T0;
|
||||
|
||||
/* compute inertia tensor */
|
||||
J[X][X] = density * (T2[Y] + T2[Z]);
|
||||
J[Y][Y] = density * (T2[Z] + T2[X]);
|
||||
J[Z][Z] = density * (T2[X] + T2[Y]);
|
||||
J[X][Y] = J[Y][X] = - density * TP[X];
|
||||
J[Y][Z] = J[Z][Y] = - density * TP[Y];
|
||||
J[Z][X] = J[X][Z] = - density * TP[Z];
|
||||
|
||||
/* translate inertia tensor to center of mass */
|
||||
J[X][X] -= mass * (r[Y]*r[Y] + r[Z]*r[Z]);
|
||||
J[Y][Y] -= mass * (r[Z]*r[Z] + r[X]*r[X]);
|
||||
J[Z][Z] -= mass * (r[X]*r[X] + r[Y]*r[Y]);
|
||||
J[X][Y] = J[Y][X] += mass * r[X] * r[Y];
|
||||
J[Y][Z] = J[Z][Y] += mass * r[Y] * r[Z];
|
||||
J[Z][X] = J[X][Z] += mass * r[Z] * r[X];
|
||||
|
||||
printf("center of mass: (%+12.6f,%+12.6f,%+12.6f)\n\n", r[X], r[Y], r[Z]);
|
||||
|
||||
printf("inertia tensor with origin at c.o.m. :\n");
|
||||
printf("%+15.6f %+15.6f %+15.6f\n", J[X][X], J[X][Y], J[X][Z]);
|
||||
printf("%+15.6f %+15.6f %+15.6f\n", J[Y][X], J[Y][Y], J[Y][Z]);
|
||||
printf("%+15.6f %+15.6f %+15.6f\n", J[Z][X], J[Z][Y], J[Z][Z]);
|
||||
|
||||
}
|
||||
#endif
|
||||
Loading…
Reference in New Issue