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bluecore/ode/src/mass.cpp

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/*************************************************************************
* *
* Open Dynamics Engine, Copyright (C) 2001,2002 Russell L. Smith. *
* All rights reserved. Email: russ@q12.org Web: www.q12.org *
* *
* This library is free software; you can redistribute it and/or *
* modify it under the terms of EITHER: *
* (1) The GNU Lesser General Public License as published by the Free *
* Software Foundation; either version 2.1 of the License, or (at *
* your option) any later version. The text of the GNU Lesser *
* General Public License is included with this library in the *
* file LICENSE.TXT. *
* (2) The BSD-style license that is included with this library in *
* the file LICENSE-BSD.TXT. *
* *
* This library is distributed in the hope that it will be useful, *
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the files *
* LICENSE.TXT and LICENSE-BSD.TXT for more details. *
* *
*************************************************************************/
#include <ode/config.h>
#include <ode/mass.h>
#include <ode/odemath.h>
#include <ode/matrix.h>
// Local dependencies
#include "collision_kernel.h"
#define SQR(x) ((x)*(x)) //!< Returns x square
#define CUBE(x) ((x)*(x)*(x)) //!< Returns x cube
#define _I(i,j) I[(i)*4+(j)]
// return 1 if ok, 0 if bad
int dMassCheck (const dMass *m)
{
int i;
if (m->mass <= 0) {
dDEBUGMSG ("mass must be > 0");
return 0;
}
if (!dIsPositiveDefinite (m->I,3)) {
dDEBUGMSG ("inertia must be positive definite");
return 0;
}
// verify that the center of mass position is consistent with the mass
// and inertia matrix. this is done by checking that the inertia around
// the center of mass is also positive definite. from the comment in
// dMassTranslate(), if the body is translated so that its center of mass
// is at the point of reference, then the new inertia is:
// I + mass*crossmat(c)^2
// note that requiring this to be positive definite is exactly equivalent
// to requiring that the spatial inertia matrix
// [ mass*eye(3,3) M*crossmat(c)^T ]
// [ M*crossmat(c) I ]
// is positive definite, given that I is PD and mass>0. see the theorem
// about partitioned PD matrices for proof.
dMatrix3 I2,chat;
dSetZero (chat,12);
dCROSSMAT (chat,m->c,4,+,-);
dMULTIPLY0_333 (I2,chat,chat);
for (i=0; i<3; i++) I2[i] = m->I[i] + m->mass*I2[i];
for (i=4; i<7; i++) I2[i] = m->I[i] + m->mass*I2[i];
for (i=8; i<11; i++) I2[i] = m->I[i] + m->mass*I2[i];
if (!dIsPositiveDefinite (I2,3)) {
dDEBUGMSG ("center of mass inconsistent with mass parameters");
return 0;
}
return 1;
}
void dMassSetZero (dMass *m)
{
dAASSERT (m);
m->mass = REAL(0.0);
dSetZero (m->c,sizeof(m->c) / sizeof(dReal));
dSetZero (m->I,sizeof(m->I) / sizeof(dReal));
}
void dMassSetParameters (dMass *m, dReal themass,
dReal cgx, dReal cgy, dReal cgz,
dReal I11, dReal I22, dReal I33,
dReal I12, dReal I13, dReal I23)
{
dAASSERT (m);
dMassSetZero (m);
m->mass = themass;
m->c[0] = cgx;
m->c[1] = cgy;
m->c[2] = cgz;
m->_I(0,0) = I11;
m->_I(1,1) = I22;
m->_I(2,2) = I33;
m->_I(0,1) = I12;
m->_I(0,2) = I13;
m->_I(1,2) = I23;
m->_I(1,0) = I12;
m->_I(2,0) = I13;
m->_I(2,1) = I23;
dMassCheck (m);
}
void dMassSetSphere (dMass *m, dReal density, dReal radius)
{
dMassSetSphereTotal (m, (REAL(4.0)/REAL(3.0)) * M_PI *
radius*radius*radius * density, radius);
}
void dMassSetSphereTotal (dMass *m, dReal total_mass, dReal radius)
{
dAASSERT (m);
dMassSetZero (m);
m->mass = total_mass;
dReal II = REAL(0.4) * total_mass * radius*radius;
m->_I(0,0) = II;
m->_I(1,1) = II;
m->_I(2,2) = II;
# ifndef dNODEBUG
dMassCheck (m);
# endif
}
void dMassSetCapsule (dMass *m, dReal density, int direction,
dReal radius, dReal length)
{
dReal M1,M2,Ia,Ib;
dAASSERT (m);
dUASSERT (direction >= 1 && direction <= 3,"bad direction number");
dMassSetZero (m);
M1 = M_PI*radius*radius*length*density; // cylinder mass
M2 = (REAL(4.0)/REAL(3.0))*M_PI*radius*radius*radius*density; // total cap mass
m->mass = M1+M2;
Ia = M1*(REAL(0.25)*radius*radius + (REAL(1.0)/REAL(12.0))*length*length) +
M2*(REAL(0.4)*radius*radius + REAL(0.375)*radius*length + REAL(0.25)*length*length);
Ib = (M1*REAL(0.5) + M2*REAL(0.4))*radius*radius;
m->_I(0,0) = Ia;
m->_I(1,1) = Ia;
m->_I(2,2) = Ia;
m->_I(direction-1,direction-1) = Ib;
# ifndef dNODEBUG
dMassCheck (m);
# endif
}
void dMassSetCapsuleTotal (dMass *m, dReal total_mass, int direction,
dReal a, dReal b)
{
dMassSetCapsule (m, 1.0, direction, a, b);
dMassAdjust (m, total_mass);
}
void dMassSetCylinder (dMass *m, dReal density, int direction,
dReal radius, dReal length)
{
dMassSetCylinderTotal (m, M_PI*radius*radius*length*density,
direction, radius, length);
}
void dMassSetCylinderTotal (dMass *m, dReal total_mass, int direction,
dReal radius, dReal length)
{
dReal r2,I;
dAASSERT (m);
dUASSERT (direction >= 1 && direction <= 3,"bad direction number");
dMassSetZero (m);
r2 = radius*radius;
m->mass = total_mass;
I = total_mass*(REAL(0.25)*r2 + (REAL(1.0)/REAL(12.0))*length*length);
m->_I(0,0) = I;
m->_I(1,1) = I;
m->_I(2,2) = I;
m->_I(direction-1,direction-1) = total_mass*REAL(0.5)*r2;
# ifndef dNODEBUG
dMassCheck (m);
# endif
}
void dMassSetBox (dMass *m, dReal density,
dReal lx, dReal ly, dReal lz)
{
dMassSetBoxTotal (m, lx*ly*lz*density, lx, ly, lz);
}
void dMassSetBoxTotal (dMass *m, dReal total_mass,
dReal lx, dReal ly, dReal lz)
{
dAASSERT (m);
dMassSetZero (m);
m->mass = total_mass;
m->_I(0,0) = total_mass/REAL(12.0) * (ly*ly + lz*lz);
m->_I(1,1) = total_mass/REAL(12.0) * (lx*lx + lz*lz);
m->_I(2,2) = total_mass/REAL(12.0) * (lx*lx + ly*ly);
# ifndef dNODEBUG
dMassCheck (m);
# endif
}
#if dTRIMESH_ENABLED
/*
* dMassSetTrimesh, implementation by Gero Mueller.
* Based on Brian Mirtich, "Fast and Accurate Computation of
* Polyhedral Mass Properties," journal of graphics tools, volume 1,
* number 2, 1996.
*/
void dMassSetTrimesh( dMass *m, dReal density, dGeomID g )
{
dAASSERT (m);
dUASSERT(g && g->type == dTriMeshClass, "argument not a trimesh");
dMassSetZero (m);
unsigned int triangles = dGeomTriMeshGetTriangleCount( g );
dReal nx, ny, nz;
unsigned int i, A, B, C;
// face integrals
dReal Fa, Fb, Fc, Faa, Fbb, Fcc, Faaa, Fbbb, Fccc, Faab, Fbbc, Fcca;
// projection integrals
dReal P1, Pa, Pb, Paa, Pab, Pbb, Paaa, Paab, Pabb, Pbbb;
dReal T0 = 0;
dReal T1[3] = {0., 0., 0.};
dReal T2[3] = {0., 0., 0.};
dReal TP[3] = {0., 0., 0.};
for( i = 0; i < triangles; i++ )
{
dVector3 v0, v1, v2;
dGeomTriMeshGetTriangle( g, i, &v0, &v1, &v2);
dVector3 n, a, b;
dOP( a, -, v1, v0 );
dOP( b, -, v2, v0 );
dCROSS( n, =, b, a );
nx = fabs(n[0]);
ny = fabs(n[1]);
nz = fabs(n[2]);
if( nx > ny && nx > nz )
C = 0;
else
C = (ny > nz) ? 1 : 2;
A = (C + 1) % 3;
B = (A + 1) % 3;
// calculate face integrals
{
dReal w;
dReal k1, k2, k3, k4;
//compProjectionIntegrals(f);
{
dReal a0, a1, da;
dReal b0, b1, db;
dReal a0_2, a0_3, a0_4, b0_2, b0_3, b0_4;
dReal a1_2, a1_3, b1_2, b1_3;
dReal C1, Ca, Caa, Caaa, Cb, Cbb, Cbbb;
dReal Cab, Kab, Caab, Kaab, Cabb, Kabb;
P1 = Pa = Pb = Paa = Pab = Pbb = Paaa = Paab = Pabb = Pbbb = 0.0;
for( int j = 0; j < 3; j++)
{
switch(j)
{
case 0:
a0 = v0[A];
b0 = v0[B];
a1 = v1[A];
b1 = v1[B];
break;
case 1:
a0 = v1[A];
b0 = v1[B];
a1 = v2[A];
b1 = v2[B];
break;
case 2:
a0 = v2[A];
b0 = v2[B];
a1 = v0[A];
b1 = v0[B];
break;
}
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;
}
w = - dDOT(n, v0);
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));
}
T0 += n[0] * ((A == 0) ? Fa : ((B == 0) ? Fb : Fc));
T1[A] += n[A] * Faa;
T1[B] += n[B] * Fbb;
T1[C] += n[C] * Fcc;
T2[A] += n[A] * Faaa;
T2[B] += n[B] * Fbbb;
T2[C] += n[C] * Fccc;
TP[A] += n[A] * Faab;
TP[B] += n[B] * Fbbc;
TP[C] += n[C] * Fcca;
}
T1[0] /= 2; T1[1] /= 2; T1[2] /= 2;
T2[0] /= 3; T2[1] /= 3; T2[2] /= 3;
TP[0] /= 2; TP[1] /= 2; TP[2] /= 2;
m->mass = density * T0;
m->_I(0,0) = density * (T2[1] + T2[2]);
m->_I(1,1) = density * (T2[2] + T2[0]);
m->_I(2,2) = density * (T2[0] + T2[1]);
m->_I(0,1) = - density * TP[0];
m->_I(1,0) = - density * TP[0];
m->_I(2,1) = - density * TP[1];
m->_I(1,2) = - density * TP[1];
m->_I(2,0) = - density * TP[2];
m->_I(0,2) = - density * TP[2];
# ifndef dNODEBUG
dMassCheck (m);
# endif
}
#endif // dTRIMESH_ENABLED
void dMassAdjust (dMass *m, dReal newmass)
{
dAASSERT (m);
dReal scale = newmass / m->mass;
m->mass = newmass;
for (int i=0; i<3; i++) for (int j=0; j<3; j++) m->_I(i,j) *= scale;
# ifndef dNODEBUG
dMassCheck (m);
# endif
}
void dMassTranslate (dMass *m, dReal x, dReal y, dReal z)
{
// if the body is translated by `a' relative to its point of reference,
// the new inertia about the point of reference is:
//
// I + mass*(crossmat(c)^2 - crossmat(c+a)^2)
//
// where c is the existing center of mass and I is the old inertia.
int i,j;
dMatrix3 ahat,chat,t1,t2;
dReal a[3];
dAASSERT (m);
// adjust inertia matrix
dSetZero (chat,12);
dCROSSMAT (chat,m->c,4,+,-);
a[0] = x + m->c[0];
a[1] = y + m->c[1];
a[2] = z + m->c[2];
dSetZero (ahat,12);
dCROSSMAT (ahat,a,4,+,-);
dMULTIPLY0_333 (t1,ahat,ahat);
dMULTIPLY0_333 (t2,chat,chat);
for (i=0; i<3; i++) for (j=0; j<3; j++)
m->_I(i,j) += m->mass * (t2[i*4+j]-t1[i*4+j]);
// ensure perfect symmetry
m->_I(1,0) = m->_I(0,1);
m->_I(2,0) = m->_I(0,2);
m->_I(2,1) = m->_I(1,2);
// adjust center of mass
m->c[0] += x;
m->c[1] += y;
m->c[2] += z;
# ifndef dNODEBUG
dMassCheck (m);
# endif
}
void dMassRotate (dMass *m, const dMatrix3 R)
{
// if the body is rotated by `R' relative to its point of reference,
// the new inertia about the point of reference is:
//
// R * I * R'
//
// where I is the old inertia.
dMatrix3 t1;
dReal t2[3];
dAASSERT (m);
// rotate inertia matrix
dMULTIPLY2_333 (t1,m->I,R);
dMULTIPLY0_333 (m->I,R,t1);
// ensure perfect symmetry
m->_I(1,0) = m->_I(0,1);
m->_I(2,0) = m->_I(0,2);
m->_I(2,1) = m->_I(1,2);
// rotate center of mass
dMULTIPLY0_331 (t2,R,m->c);
m->c[0] = t2[0];
m->c[1] = t2[1];
m->c[2] = t2[2];
# ifndef dNODEBUG
dMassCheck (m);
# endif
}
void dMassAdd (dMass *a, const dMass *b)
{
int i;
dAASSERT (a && b);
dReal denom = dRecip (a->mass + b->mass);
for (i=0; i<3; i++) a->c[i] = (a->c[i]*a->mass + b->c[i]*b->mass)*denom;
a->mass += b->mass;
for (i=0; i<12; i++) a->I[i] += b->I[i];
}
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