source: code/branches/ode/ode-0.9/ode/src/mass.cpp @ 216

/*************************************************************************
 *                                                                       *
 * 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];

        // Added to address SF bug 1729095
        dMassTranslate( m, T1[0] / T0,  T1[1] / T0,  T1[2] / T0 );

# ifndef dNODEBUG
        dMassCheck (m);
# endif
}


void dMassSetTrimeshTotal( dMass *m, dReal total_mass, dGeomID g)
{
  dAASSERT( m );
  dUASSERT( g && g->type == dTriMeshClass, "argument not a trimesh" );
  dMassSetTrimesh( m, 1.0, g );
  dMassAdjust( m, total_mass );
}

#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];
}