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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>
#define _I(i,j) I[(i)*4+(j)]
// return 1 if ok, 0 if bad
static int checkMass (dMass *m)
{
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 (int i=0; i<12; 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;
checkMass (m);
}
void dMassSetSphere (dMass *m, dReal density, dReal radius)
{
dAASSERT (m);
dMassSetZero (m);
m->mass = (REAL(4.0)/REAL(3.0)) * M_PI * radius*radius*radius * density;
dReal II = REAL(0.4) * m->mass * radius*radius;
m->_I(0,0) = II;
m->_I(1,1) = II;
m->_I(2,2) = II;
# ifndef dNODEBUG
checkMass (m);
# endif
}
void dMassSetCappedCylinder (dMass *m, dReal density, int direction,
dReal a, dReal b)
{
dReal M1,M2,Ia,Ib;
dAASSERT (m);
dUASSERT (direction >= 1 && direction <= 3,"bad direction number");
dMassSetZero (m);
M1 = M_PI*a*a*b*density; // cylinder mass
M2 = (REAL(4.0)/REAL(3.0))*M_PI*a*a*a*density; // total cap mass
m->mass = M1+M2;
Ia = M1*(REAL(0.25)*a*a + (REAL(1.0)/REAL(12.0))*b*b) +
M2*(REAL(0.4)*a*a + REAL(0.5)*b*b);
Ib = (M1*REAL(0.5) + M2*REAL(0.4))*a*a;
m->_I(0,0) = Ia;
m->_I(1,1) = Ia;
m->_I(2,2) = Ia;
m->_I(direction-1,direction-1) = Ib;
# ifndef dNODEBUG
checkMass (m);
# endif
}
void dMassSetBox (dMass *m, dReal density,
dReal lx, dReal ly, dReal lz)
{
dAASSERT (m);
dMassSetZero (m);
dReal M = lx*ly*lz*density;
m->mass = M;
m->_I(0,0) = M/REAL(12.0) * (ly*ly + lz*lz);
m->_I(1,1) = M/REAL(12.0) * (lx*lx + lz*lz);
m->_I(2,2) = M/REAL(12.0) * (lx*lx + ly*ly);
# ifndef dNODEBUG
checkMass (m);
# endif
}
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
checkMass (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
checkMass (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
checkMass (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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