44     void SpatialTransform(
const btMatrix3x3 &rotation_matrix,  
    51         top_out = rotation_matrix * top_in;
    52         bottom_out = -displacement.
cross(top_out) + rotation_matrix * bottom_in;
    56     void InverseSpatialTransform(
const btMatrix3x3 &rotation_matrix,
    63         top_out = rotation_matrix.
transpose() * top_in;
    64         bottom_out = rotation_matrix.
transpose() * (bottom_in + displacement.
cross(top_in));            
    72         return a_bottom.
dot(b_top) + a_top.
dot(b_bottom);
    75         void SpatialCrossProduct(
const btVector3 &a_top,
    82                 top_out = a_top.
cross(b_top);
    83                 bottom_out = a_bottom.
cross(b_top) + a_top.
cross(b_bottom);
   104         m_baseQuat(0, 0, 0, 1),
   106       m_baseInertia(inertia),
   108                 m_fixedBase(fixedBase),
   110                 m_canSleep(canSleep),
   112                 m_userObjectPointer(0),
   115                 m_linearDamping(0.04f),
   116                 m_angularDamping(0.04f),
   118                         m_maxAppliedImpulse(1000.f),
   119                 m_maxCoordinateVelocity(100.f),
   120                         m_hasSelfCollision(true),               
   125                 m_useGlobalVelocities(false),
   126                 m_internalNeedsJointFeedback(false)
   150                                                    const btVector3 &parentComToThisPivotOffset,
   151                            const btVector3 &thisPivotToThisComOffset, 
bool )
   155     m_links[i].m_inertiaLocal = inertia;
   157     m_links[i].m_zeroRotParentToThis = rotParentToThis;
   158         m_links[i].m_dVector = thisPivotToThisComOffset;
   159     m_links[i].m_eVector = parentComToThisPivotOffset;    
   167         m_links[i].updateCacheMultiDof();
   180                                const btVector3 &parentComToThisPivotOffset,
   181                                                            const btVector3 &thisPivotToThisComOffset,
   182                                                            bool disableParentCollision)
   188     m_links[i].m_inertiaLocal = inertia;
   190     m_links[i].m_zeroRotParentToThis = rotParentToThis;
   191     m_links[i].setAxisTop(0, 0., 0., 0.);
   192     m_links[i].setAxisBottom(0, jointAxis);
   193     m_links[i].m_eVector = parentComToThisPivotOffset;
   194         m_links[i].m_dVector = thisPivotToThisComOffset;
   195     m_links[i].m_cachedRotParentToThis = rotParentToThis;
   200         m_links[i].m_jointPos[0] = 0.f;
   201         m_links[i].m_jointTorque[0] = 0.f;
   203         if (disableParentCollision)
   207         m_links[i].updateCacheMultiDof();
   218                               const btVector3 &parentComToThisPivotOffset,
   219                               const btVector3 &thisPivotToThisComOffset,
   220                                                           bool disableParentCollision)
   226     m_links[i].m_inertiaLocal = inertia;
   228     m_links[i].m_zeroRotParentToThis = rotParentToThis;
   229     m_links[i].setAxisTop(0, jointAxis);
   230     m_links[i].setAxisBottom(0, jointAxis.
cross(thisPivotToThisComOffset));
   231     m_links[i].m_dVector = thisPivotToThisComOffset;
   232     m_links[i].m_eVector = parentComToThisPivotOffset;
   237         m_links[i].m_jointPos[0] = 0.f;
   238         m_links[i].m_jointTorque[0] = 0.f;
   240         if (disableParentCollision)
   243         m_links[i].updateCacheMultiDof();
   255                                                    const btVector3 &parentComToThisPivotOffset,
   256                                                    const btVector3 &thisPivotToThisComOffset,
   257                                                    bool disableParentCollision)
   264     m_links[i].m_inertiaLocal = inertia;
   266     m_links[i].m_zeroRotParentToThis = rotParentToThis;    
   267     m_links[i].m_dVector = thisPivotToThisComOffset;
   268     m_links[i].m_eVector = parentComToThisPivotOffset;    
   273         m_links[i].setAxisTop(0, 1.f, 0.f, 0.f);
   274         m_links[i].setAxisTop(1, 0.f, 1.f, 0.f);
   275         m_links[i].setAxisTop(2, 0.f, 0.f, 1.f);
   276         m_links[i].setAxisBottom(0, 
m_links[i].getAxisTop(0).cross(thisPivotToThisComOffset));
   277         m_links[i].setAxisBottom(1, 
m_links[i].getAxisTop(1).cross(thisPivotToThisComOffset));
   278         m_links[i].setAxisBottom(2, 
m_links[i].getAxisTop(2).cross(thisPivotToThisComOffset));
   283         if (disableParentCollision)
   286         m_links[i].updateCacheMultiDof();       
   297                                                    const btVector3 &parentComToThisComOffset,                                              
   298                                                    bool disableParentCollision)
   305     m_links[i].m_inertiaLocal = inertia;
   307     m_links[i].m_zeroRotParentToThis = rotParentToThis;    
   308         m_links[i].m_dVector.setZero();
   309     m_links[i].m_eVector = parentComToThisComOffset;
   312         btVector3 vecNonParallelToRotAxis(1, 0, 0);
   313         if(rotationAxis.
normalized().
dot(vecNonParallelToRotAxis) > 0.999)
   314                 vecNonParallelToRotAxis.
setValue(0, 1, 0);
   321         m_links[i].setAxisTop(0, n[0],n[1],n[2]);
   322         m_links[i].setAxisTop(1,0,0,0);
   323         m_links[i].setAxisTop(2,0,0,0);
   324         m_links[i].setAxisBottom(0,0,0,0);
   326         m_links[i].setAxisBottom(1,cr[0],cr[1],cr[2]);
   328         m_links[i].setAxisBottom(2,cr[0],cr[1],cr[2]);
   332         if (disableParentCollision)
   335         m_links[i].updateCacheMultiDof();
   362     return m_links[i].m_inertiaLocal;
   367     return m_links[i].m_jointPos[0];
   377         return &
m_links[i].m_jointPos[0];
   387         return &
m_links[i].m_jointPos[0];
   399     m_links[i].updateCacheMultiDof();
   404         for(
int pos = 0; pos < 
m_links[i].m_posVarCount; ++pos)
   405                 m_links[i].m_jointPos[pos] = q[pos];
   407     m_links[i].updateCacheMultiDof();
   417         for(
int dof = 0; dof < 
m_links[i].m_dofCount; ++dof)
   423     return m_links[i].m_cachedRVector;
   428     return m_links[i].m_cachedRotParentToThis;
   514     result.
setValue(frameInWorld0[0], frameInWorld1[0], frameInWorld2[0], frameInWorld0[1], frameInWorld1[1], frameInWorld2[1], frameInWorld0[2], frameInWorld1[2], frameInWorld2[2]);
   525     for (
int i = 0; i < num_links; ++i) {
   526         const int parent = 
m_links[i].m_parent;
   530                          omega[parent+1], vel[parent+1],
   531                          omega[i+1], vel[i+1]);
   551     for (
int i = 0; i < num_links; ++i) {
   552         result += 
m_links[i].m_mass * vel[i+1].dot(vel[i+1]);
   553         result += omega[i+1].dot(
m_links[i].m_inertiaLocal * omega[i+1]);
   556     return 0.5f * result;
   571     for (
int i = 0; i < num_links; ++i) {
   572         rot_from_world[i+1] = 
m_links[i].m_cachedRotParentToThis * rot_from_world[
m_links[i].m_parent+1];
   573         result += (
quatRotate(rot_from_world[i+1].
inverse() , (m_links[i].m_inertiaLocal * omega[i+1])));
   586         m_links[i].m_appliedConstraintForce.setValue(0, 0, 0);
   587         m_links[i].m_appliedConstraintTorque.setValue(0, 0, 0);
   597         m_links[i].m_appliedForce.setValue(0, 0, 0);
   598         m_links[i].m_appliedTorque.setValue(0, 0, 0);
   612     m_links[i].m_appliedForce += f;
   617     m_links[i].m_appliedTorque += t;
   622     m_links[i].m_appliedConstraintForce += f;
   627     m_links[i].m_appliedConstraintTorque += t;
   634     m_links[i].m_jointTorque[0] += Q;
   639         m_links[i].m_jointTorque[dof] += Q;
   644         for(
int dof = 0; dof < 
m_links[i].m_dofCount; ++dof)
   645                 m_links[i].m_jointTorque[dof] = Q[dof];
   650     return m_links[i].m_appliedForce;
   655     return m_links[i].m_appliedTorque;
   660     return m_links[i].m_jointTorque[0];
   665     return &
m_links[i].m_jointTorque[0];
   684                                                 row1[0],row1[1],row1[2],
   685                                                 row2[0],row2[1],row2[2]);
   689 #define vecMulVecTranspose(v0, v1Transposed) outerProduct(v0, v1Transposed)   696                                 bool isConstraintPass)
   729     scratch_v.
resize(8*num_links + 6);
   730     scratch_m.
resize(4*num_links + 4);
   738         v_ptr += num_links * 2 + 2;
   742         v_ptr += num_links * 2 + 2;
   746         v_ptr += num_links * 2;
   759         v_ptr += num_links * 2 + 2;
   779     btScalar * joint_accel = output + 6;
   789         spatVel[0].
setVector(rot_from_parent[0] * base_omega, rot_from_parent[0] * base_vel);
   800                 zeroAccSpatFrc[0].
setVector(-(rot_from_parent[0] * baseTorque), -(rot_from_parent[0] * baseForce));     
   803                 btScalar linDampMult = 1., angDampMult = 1.;
   804                 zeroAccSpatFrc[0].
addVector(angDampMult * 
m_baseInertia * spatVel[0].getAngular() * (DAMPING_K1_ANGULAR + DAMPING_K2_ANGULAR * spatVel[0].getAngular().safeNorm()),
   805                                                                    linDampMult * 
m_baseMass * spatVel[0].getLinear() * (DAMPING_K1_LINEAR + DAMPING_K2_LINEAR * spatVel[0].getLinear().safeNorm()));
   812                 zeroAccSpatFrc[0].
addLinear(
m_baseMass * spatVel[0].getAngular().cross(spatVel[0].getLinear()));
   828     rot_from_world[0] = rot_from_parent[0];
   831     for (
int i = 0; i < num_links; ++i) {               
   832         const int parent = 
m_links[i].m_parent;
   834         rot_from_world[i+1] = rot_from_parent[i+1] * rot_from_world[parent+1];
   837                 fromWorld.
m_rotMat = rot_from_world[i+1];
   838                 fromParent.
transform(spatVel[parent+1], spatVel[i+1]);
   846                         for(
int dof = 0; dof < 
m_links[i].m_dofCount; ++dof)            
   850                         spatVel[i+1] += spatJointVel;
   864                 spatVel[i+1].
cross(spatJointVel, spatCoriolisAcc[i]);           
   869                 btVector3 linkAppliedForce = isConstraintPass? 
m_links[i].m_appliedConstraintForce : 
m_links[i].m_appliedForce;
   870                 btVector3 linkAppliedTorque =isConstraintPass ? 
m_links[i].m_appliedConstraintTorque : 
m_links[i].m_appliedTorque;
   872                 zeroAccSpatFrc[i+1].
setVector(-(rot_from_world[i+1] * linkAppliedTorque), -(rot_from_world[i+1] * linkAppliedForce ));
   877                         b3Printf(
"stepVelocitiesMultiDof zeroAccSpatFrc[%d] linear:%f,%f,%f, angular:%f,%f,%f",
   879                         zeroAccSpatFrc[i+1].m_topVec[0],
   880                         zeroAccSpatFrc[i+1].m_topVec[1],
   881                         zeroAccSpatFrc[i+1].m_topVec[2],
   883                         zeroAccSpatFrc[i+1].m_bottomVec[0],
   884                         zeroAccSpatFrc[i+1].m_bottomVec[1],
   885                         zeroAccSpatFrc[i+1].m_bottomVec[2]);
   890                 btScalar linDampMult = 1., angDampMult = 1.;
   891                 zeroAccSpatFrc[i+1].
addVector(angDampMult * 
m_links[i].m_inertiaLocal * spatVel[i+1].getAngular() * (DAMPING_K1_ANGULAR + DAMPING_K2_ANGULAR * spatVel[i+1].getAngular().safeNorm()),
   892                                                                          linDampMult * 
m_links[i].m_mass * spatVel[i+1].getLinear() * (DAMPING_K1_LINEAR + DAMPING_K2_LINEAR * spatVel[i+1].getLinear().safeNorm()));
   903                                                                                                 0, 
m_links[i].m_inertiaLocal[1], 0,
   904                                                                                                 0, 0, 
m_links[i].m_inertiaLocal[2])
   909                         zeroAccSpatFrc[i+1].
addAngular(spatVel[i+1].getAngular().cross(
m_links[i].m_inertiaLocal * spatVel[i+1].getAngular()));                 
   911                 zeroAccSpatFrc[i+1].
addLinear(
m_links[i].m_mass * spatVel[i+1].getAngular().cross(spatVel[i+1].getLinear()));
   932     for (
int i = num_links - 1; i >= 0; --i)
   934                 const int parent = 
m_links[i].m_parent;
   937                 for(
int dof = 0; dof < 
m_links[i].m_dofCount; ++dof)
   941                         hDof = spatInertia[i+1] * m_links[i].m_axes[dof];
   943                         Y[m_links[i].m_dofOffset + dof] = m_links[i].m_jointTorque[dof]
   944                         - m_links[i].m_axes[dof].dot(zeroAccSpatFrc[i+1])
   945                         - spatCoriolisAcc[i].
dot(hDof)
   949                 for(
int dof = 0; dof < 
m_links[i].m_dofCount; ++dof)
   952                         for(
int dof2 = 0; dof2 < m_links[i].m_dofCount; ++dof2)
   955                                 D_row[dof2] = m_links[i].m_axes[dof].dot(hDof2);
   965                                 invDi[0] = 1.0f / D[0];
   975                                 for(
int row = 0; row < 3; ++row)
   977                                         for(
int col = 0; col < 3; ++col)
   979                                                 invDi[row * 3 + col] = invD3x3[row][col];
   992                 for(
int dof = 0; dof < 
m_links[i].m_dofCount; ++dof)
   994                         spatForceVecTemps[dof].
setZero();
   996                         for(
int dof2 = 0; dof2 < 
m_links[i].m_dofCount; ++dof2)
  1000                                 spatForceVecTemps[dof] += hDof2 * invDi[dof2 * m_links[i].m_dofCount + dof];
  1004                 dyadTemp = spatInertia[i+1];
  1007                 for(
int dof = 0; dof < 
m_links[i].m_dofCount; ++dof)
  1016                 for(
int dof = 0; dof < 
m_links[i].m_dofCount; ++dof)
  1018                         invD_times_Y[dof] = 0.f;
  1020                         for(
int dof2 = 0; dof2 < 
m_links[i].m_dofCount; ++dof2)
  1022                                 invD_times_Y[dof] += invDi[dof * 
m_links[i].m_dofCount + dof2] * Y[
m_links[i].m_dofOffset + dof2];                              
  1026                 spatForceVecTemps[0] = zeroAccSpatFrc[i+1] + spatInertia[i+1] * spatCoriolisAcc[i];             
  1028                 for(
int dof = 0; dof < 
m_links[i].m_dofCount; ++dof)
  1032                         spatForceVecTemps[0] += hDof * invD_times_Y[dof];                       
  1037                 zeroAccSpatFrc[parent+1] += spatForceVecTemps[1];
  1061                 spatAcc[0] = -result;
  1066     for (
int i = 0; i < num_links; ++i) 
  1074         const int parent = 
m_links[i].m_parent;
  1077                 fromParent.
transform(spatAcc[parent+1], spatAcc[i+1]);
  1079                 for(
int dof = 0; dof < 
m_links[i].m_dofCount; ++dof)
  1083                         Y_minus_hT_a[dof] = Y[m_links[i].m_dofOffset + dof] - spatAcc[i+1].
dot(hDof);                   
  1090                 spatAcc[i+1] += spatCoriolisAcc[i];             
  1092                 for(
int dof = 0; dof < 
m_links[i].m_dofCount; ++dof)            
  1093                         spatAcc[i+1] += 
m_links[i].m_axes[dof] * joint_accel[
m_links[i].m_dofOffset + dof];
  1095                 if (
m_links[i].m_jointFeedback)
  1099                         btVector3 angularBotVec = (spatInertia[i+1]*spatAcc[i+1]+zeroAccSpatFrc[i+1]).m_bottomVec;
  1100                         btVector3 linearTopVec = (spatInertia[i+1]*spatAcc[i+1]+zeroAccSpatFrc[i+1]).m_topVec;
  1107                                  angularBotVec = angularBotVec - linearTopVec.
cross(
m_links[i].m_dVector);
  1113                                 if (isConstraintPass)
  1115  m_links[i].m_jointFeedback->m_reactionForces.m_bottomVec += 
m_links[i].m_cachedWorldTransform.getBasis()*angularBotVec;
  1116                                         m_links[i].m_jointFeedback->m_reactionForces.m_topVec += 
m_links[i].m_cachedWorldTransform.getBasis()*linearTopVec;
  1119                                         m_links[i].m_jointFeedback->m_reactionForces.m_bottomVec = 
m_links[i].m_cachedWorldTransform.getBasis()*angularBotVec;
  1120                                         m_links[i].m_jointFeedback->m_reactionForces.m_topVec = 
m_links[i].m_cachedWorldTransform.getBasis()*linearTopVec;
  1124                                 if (isConstraintPass)
  1126                                           m_links[i].m_jointFeedback->m_reactionForces.m_bottomVec += angularBotVec;                        
  1127                                 m_links[i].m_jointFeedback->m_reactionForces.m_topVec += linearTopVec;
  1132                                 m_links[i].m_jointFeedback->m_reactionForces.m_bottomVec = angularBotVec;
  1133                                 m_links[i].m_jointFeedback->m_reactionForces.m_topVec = linearTopVec;
  1142         output[0] = omegadot_out[0];
  1143         output[1] = omegadot_out[1];
  1144         output[2] = omegadot_out[2];
  1147         output[3] = vdot_out[0];
  1148         output[4] = vdot_out[1];
  1149         output[5] = vdot_out[2];
  1171         if (!isConstraintPass)
  1207                 for (
int i = 0; i < num_links; ++i) 
  1209                         const int parent = 
m_links[i].m_parent;
  1214                         fromWorld.
m_rotMat = rot_from_world[i+1];                       
  1217                         fromParent.
transform(spatVel[parent+1], spatVel[i+1]);
  1225                         for(
int dof = 0; dof < 
m_links[i].m_dofCount; ++dof)            
  1229                         spatVel[i+1] += spatJointVel;
  1258                         for (
int i=0;i<6;i++)
  1271                 btMatrix3x3 invI_lower_right = (invI_upper_left).transpose();
  1280                   btVector3 vtop = invI_upper_left*rhs_top;
  1282                   tmp = invIupper_right * rhs_bot;
  1284                   btVector3 vbot = invI_lower_left*rhs_top;
  1285                   tmp = invI_lower_right * rhs_bot;
  1287                   result[0] = vtop[0];
  1288                   result[1] = vtop[1];
  1289                   result[2] = vtop[2];
  1290                   result[3] = vbot[0];
  1291                   result[4] = vbot[1];
  1292                   result[5] = vbot[2];
  1322                 btMatrix3x3 invI_lower_right = (invI_upper_left).transpose();
  1346         for (
int row = 0; row < rowsA; row++)
  1348                 for (
int col = 0; col < colsB; col++)
  1350                         pC[row * colsB + col] = 0.f;
  1351                         for (
int inner = 0; inner < rowsB; inner++)
  1353                                 pC[row * colsB + col] += pA[row * colsA + inner] * pB[col + inner * colsB];
  1368     scratch_v.
resize(4*num_links + 4);      
  1375         v_ptr += num_links * 2 + 2;
  1384         v_ptr += num_links * 2 + 2;
  1409                 fromParent.
m_rotMat = rot_from_parent[0];
  1412     for (
int i = 0; i < num_links; ++i) 
  1414                 zeroAccSpatFrc[i+1].
setZero();
  1419     for (
int i = num_links - 1; i >= 0; --i)
  1421                 const int parent = 
m_links[i].m_parent;
  1424                 for(
int dof = 0; dof < 
m_links[i].m_dofCount; ++dof)
  1426                         Y[
m_links[i].m_dofOffset + dof] = force[6 + m_links[i].m_dofOffset + dof]
  1427                                                                                         - m_links[i].m_axes[dof].dot(zeroAccSpatFrc[i+1])
  1431                 btVector3 in_top, in_bottom, out_top, out_bottom;
  1434                 for(
int dof = 0; dof < 
m_links[i].m_dofCount; ++dof)
  1436                         invD_times_Y[dof] = 0.f;
  1438                         for(
int dof2 = 0; dof2 < 
m_links[i].m_dofCount; ++dof2)
  1440                                 invD_times_Y[dof] += invDi[dof * 
m_links[i].m_dofCount + dof2] * Y[
m_links[i].m_dofOffset + dof2];                              
  1445                 spatForceVecTemps[0] = zeroAccSpatFrc[i+1];
  1447                 for(
int dof = 0; dof < 
m_links[i].m_dofCount; ++dof)
  1451                         spatForceVecTemps[0] += hDof * invD_times_Y[dof];               
  1457                 zeroAccSpatFrc[parent+1] += spatForceVecTemps[1];
  1461     btScalar * joint_accel = output + 6;
  1474                 spatAcc[0] = -result;
  1479     for (
int i = 0; i < num_links; ++i)
  1481         const int parent = 
m_links[i].m_parent;
  1484                 fromParent.
transform(spatAcc[parent+1], spatAcc[i+1]);
  1486                 for(
int dof = 0; dof < 
m_links[i].m_dofCount; ++dof)
  1490                         Y_minus_hT_a[dof] = Y[m_links[i].m_dofOffset + dof] - spatAcc[i+1].
dot(hDof);
  1496                 for(
int dof = 0; dof < 
m_links[i].m_dofCount; ++dof)            
  1497                         spatAcc[i+1] += 
m_links[i].m_axes[dof] * joint_accel[
m_links[i].m_dofOffset + dof];      
  1503         output[0] = omegadot_out[0];
  1504         output[1] = omegadot_out[1];
  1505         output[2] = omegadot_out[2];
  1509         output[3] = vdot_out[0];
  1510         output[4] = vdot_out[1];
  1511         output[5] = vdot_out[2];
  1534         pBasePos[0] += dt * pBaseVel[0];
  1535         pBasePos[1] += dt * pBaseVel[1];
  1536         pBasePos[2] += dt * pBaseVel[2];
  1566                                 axis   = angvel*( 
btScalar(0.5)*dt-(dt*dt*dt)*(
btScalar(0.020833333333))*fAngle*fAngle );
  1590         btQuaternion baseQuat; baseQuat.
setValue(pBaseQuat[0], pBaseQuat[1], pBaseQuat[2], pBaseQuat[3]);
  1591         btVector3 baseOmega; baseOmega.
setValue(pBaseOmega[0], pBaseOmega[1], pBaseOmega[2]);
  1592         pQuatUpdateFun(baseOmega, baseQuat, 
true, dt);
  1593         pBaseQuat[0] = baseQuat.
x();
  1594         pBaseQuat[1] = baseQuat.
y();
  1595         pBaseQuat[2] = baseQuat.
z();
  1596         pBaseQuat[3] = baseQuat.
w();
  1609     for (
int i = 0; i < num_links; ++i) 
  1614                 switch(
m_links[i].m_jointType)
  1620                                 pJointPos[0] += dt * jointVel;
  1625                                 btVector3 jointVel; jointVel.
setValue(pJointVel[0], pJointVel[1], pJointVel[2]);
  1626                                 btQuaternion jointOri; jointOri.
setValue(pJointPos[0], pJointPos[1], pJointPos[2], pJointPos[3]);
  1627                                 pQuatUpdateFun(jointVel, jointOri, 
false, dt);
  1628                                 pJointPos[0] = jointOri.
x(); pJointPos[1] = jointOri.
y(); pJointPos[2] = jointOri.
z(); pJointPos[3] = jointOri.
w();
  1637                                 pJointPos[1] += 
m_links[i].getAxisBottom(1).dot(no_q0_coors_qd1qd2) * dt;
  1638                                 pJointPos[2] += 
m_links[i].getAxisBottom(2).dot(no_q0_coors_qd1qd2) * dt;
  1648                 m_links[i].updateCacheMultiDof(pq);
  1651                         pq += 
m_links[i].m_posVarCount;
  1669     scratch_v.
resize(3*num_links + 3);                  
  1670     scratch_m.
resize(num_links + 1);
  1673     btVector3 * p_minus_com_local = v_ptr; v_ptr += num_links + 1;
  1674     btVector3 * n_local_lin = v_ptr; v_ptr += num_links + 1;
  1675         btVector3 * n_local_ang = v_ptr; v_ptr += num_links + 1;
  1678     scratch_r.
resize(m_dofCount);
  1679     btScalar * results = m_dofCount > 0 ? &scratch_r[0] : 0;
  1684         const btVector3 &normal_lin_world = normal_lin;                                                 
  1685         const btVector3 &normal_ang_world = normal_ang;
  1691     omega_coeffs_world = p_minus_com_world.
cross(normal_lin_world);
  1692         jac[0] = omega_coeffs_world[0] + normal_ang_world[0];
  1693         jac[1] = omega_coeffs_world[1] + normal_ang_world[1];
  1694         jac[2] = omega_coeffs_world[2] + normal_ang_world[2];
  1696     jac[3] = normal_lin_world[0];
  1697     jac[4] = normal_lin_world[1];
  1698     jac[5] = normal_lin_world[2];
  1701         p_minus_com_local[0] = rot_from_world[0] * p_minus_com_world;
  1702     n_local_lin[0] = rot_from_world[0] * normal_lin_world;
  1703         n_local_ang[0] = rot_from_world[0] * normal_ang_world;
  1712     if (num_links > 0 && link > -1) {
  1719         for (
int i = 0; i < num_links; ++i) {
  1722             const int parent = 
m_links[i].m_parent;
  1724             rot_from_world[i+1] = mtx * rot_from_world[parent+1];
  1726             n_local_lin[i+1] = mtx * n_local_lin[parent+1];
  1727                         n_local_ang[i+1] = mtx * n_local_ang[parent+1];
  1728             p_minus_com_local[i+1] = mtx * p_minus_com_local[parent+1] - 
m_links[i].m_cachedRVector;
  1731                         switch(
m_links[i].m_jointType)
  1735                                         results[
m_links[i].m_dofOffset] = n_local_lin[i+1].dot(m_links[i].getAxisTop(0).cross(p_minus_com_local[i+1]) + m_links[i].getAxisBottom(0));
  1736                                         results[m_links[i].m_dofOffset] += n_local_ang[i+1].dot(m_links[i].getAxisTop(0));
  1741                                         results[
m_links[i].m_dofOffset] = n_local_lin[i+1].dot(m_links[i].getAxisBottom(0));
  1746                                         results[
m_links[i].m_dofOffset + 0] = n_local_lin[i+1].dot(m_links[i].getAxisTop(0).cross(p_minus_com_local[i+1]) + m_links[i].getAxisBottom(0));
  1747                                         results[m_links[i].m_dofOffset + 1] = n_local_lin[i+1].dot(m_links[i].getAxisTop(1).cross(p_minus_com_local[i+1]) + m_links[i].getAxisBottom(1));
  1748                                         results[m_links[i].m_dofOffset + 2] = n_local_lin[i+1].dot(m_links[i].getAxisTop(2).cross(p_minus_com_local[i+1]) + m_links[i].getAxisBottom(2));
  1750                                         results[m_links[i].m_dofOffset + 0] += n_local_ang[i+1].dot(m_links[i].getAxisTop(0));
  1751                                         results[m_links[i].m_dofOffset + 1] += n_local_ang[i+1].dot(m_links[i].getAxisTop(1));
  1752                                         results[m_links[i].m_dofOffset + 2] += n_local_ang[i+1].dot(m_links[i].getAxisTop(2));
  1758                                         results[
m_links[i].m_dofOffset + 0] = n_local_lin[i+1].dot(m_links[i].getAxisTop(0).cross(p_minus_com_local[i+1]));
  1759                                         results[m_links[i].m_dofOffset + 1] = n_local_lin[i+1].dot(m_links[i].getAxisBottom(1));
  1760                                         results[m_links[i].m_dofOffset + 2] = n_local_lin[i+1].dot(m_links[i].getAxisBottom(2));
  1775                         for(
int dof = 0; dof < 
m_links[link].m_dofCount; ++dof)
  1777                                 jac[6 + 
m_links[link].m_dofOffset + dof] = results[m_links[link].m_dofOffset + dof];
  1781                         link = 
m_links[link].m_parent;
  1816     if (motion < SLEEP_EPSILON) {
  1839         for (
int i = 0; i < num_links; ++i) 
  1846         world_to_local.
resize(nLinks+1);
  1847         local_origin.
resize(nLinks+1);
  1864                 btScalar quat[4]={-world_to_local[index].x(),-world_to_local[index].y(),-world_to_local[index].z(),world_to_local[index].w()};
  1887                 btScalar quat[4]={-world_to_local[0].x(),-world_to_local[0].y(),-world_to_local[0].z(),world_to_local[0].w()};
  1917                         btScalar quat[4]={-world_to_local[index].x(),-world_to_local[index].y(),-world_to_local[index].z(),world_to_local[index].w()};
  1944                         if (mbd->m_baseName)
  1950                 if (mbd->m_numLinks)
  1953                         int numElem = mbd->m_numLinks;
  1956                         for (
int i=0;i<numElem;i++,memPtr++)
  1983                                 for (
int posvar = 0; posvar < numPosVar;posvar++)
  1992                                         if (memPtr->m_linkName)
  2000                                         if (memPtr->m_jointName)
 
void setupPlanar(int i, btScalar mass, const btVector3 &inertia, int parent, const btQuaternion &rotParentToThis, const btVector3 &rotationAxis, const btVector3 &parentComToThisComOffset, bool disableParentCollision=false)
const btScalar & x() const
Return the x value. 
void solveImatrix(const btVector3 &rhs_top, const btVector3 &rhs_bot, float result[6]) const
btQuaternion m_zeroRotParentToThis
void clearConstraintForces()
void setupRevolute(int linkIndex, btScalar mass, const btVector3 &inertia, int parentIndex, const btQuaternion &rotParentToThis, const btVector3 &jointAxis, const btVector3 &parentComToThisPivotOffset, const btVector3 &thisPivotToThisComOffset, bool disableParentCollision=false)
const btVector3 & getBasePos() const
btVector3 localPosToWorld(int i, const btVector3 &vec) const
btAlignedObjectArray< btMatrix3x3 > m_matrixBuf
void setupFixed(int linkIndex, btScalar mass, const btVector3 &inertia, int parent, const btQuaternion &rotParentToThis, const btVector3 &parentComToThisPivotOffset, const btVector3 &thisPivotToThisComOffset, bool deprecatedDisableParentCollision=true)
const btMultiBodyLinkCollider * getBaseCollider() const
void setValue(const btScalar &_x, const btScalar &_y, const btScalar &_z)
const btVector3 & getLinear() const
const btVector3 & getAxisTop(int dof) const
These spatial algebra classes are used for btMultiBody, see BulletDynamics/Featherstone. 
#define btMultiBodyLinkDataName
btScalar btSin(btScalar x)
void stepPositionsMultiDof(btScalar dt, btScalar *pq=0, btScalar *pqd=0)
eFeatherstoneJointType m_jointType
class btMultiBodyLinkCollider * m_collider
void compTreeLinkVelocities(btVector3 *omega, btVector3 *vel) const
bool gDisableDeactivation
void computeAccelerationsArticulatedBodyAlgorithmMultiDof(btScalar dt, btAlignedObjectArray< btScalar > &scratch_r, btAlignedObjectArray< btVector3 > &scratch_v, btAlignedObjectArray< btMatrix3x3 > &scratch_m, bool isConstraintPass=false)
virtual void * getUniquePointer(void *oldPtr)=0
bool gJointFeedbackInWorldSpace
todo: determine if we need these options. If so, make a proper API, otherwise delete those globals ...
void setupSpherical(int linkIndex, btScalar mass, const btVector3 &inertia, int parent, const btQuaternion &rotParentToThis, const btVector3 &parentComToThisPivotOffset, const btVector3 &thisPivotToThisComOffset, bool disableParentCollision=false)
void addLinkConstraintForce(int i, const btVector3 &f)
const btQuaternion & getWorldToBaseRot() const
btMatrix3x3 m_cachedInertiaLowerRight
btScalar * getJointVelMultiDof(int i)
void addLinkForce(int i, const btVector3 &f)
void addLinear(const btVector3 &linear)
btVector3 worldPosToLocal(int i, const btVector3 &vec) const
bool gJointFeedbackInJointFrame
void calcAccelerationDeltasMultiDof(const btScalar *force, btScalar *output, btAlignedObjectArray< btScalar > &scratch_r, btAlignedObjectArray< btVector3 > &scratch_v) const
void setJointPosMultiDof(int i, btScalar *q)
void symmetricSpatialOuterProduct(const SpatialVectorType &a, const SpatialVectorType &b, btSymmetricSpatialDyad &out)
void updateCollisionObjectWorldTransforms(btAlignedObjectArray< btQuaternion > &scratch_q, btAlignedObjectArray< btVector3 > &scratch_m)
btVector3 m_baseConstraintTorque
#define btCollisionObjectData
void applyDeltaVeeMultiDof(const btScalar *delta_vee, btScalar multiplier)
btQuaternion inverse(const btQuaternion &q)
Return the inverse of a quaternion. 
const btVector3 & getLinkTorque(int i) const
btAlignedObjectArray< btScalar > m_deltaV
btVector3 getBaseOmega() const
btMatrix3x3 outerProduct(const btVector3 &v0, const btVector3 &v1)
const btVector3 & getAxisBottom(int dof) const
void clearForcesAndTorques()
btVector3 quatRotate(const btQuaternion &rotation, const btVector3 &v)
btVector3 normalized() const
Return a normalized version of this vector. 
btMatrix3x3 transpose() const
Return the transpose of the matrix. 
btVector3 getColumn(int i) const
Get a column of the matrix as a vector. 
void addAngular(const btVector3 &angular)
void addLinkConstraintTorque(int i, const btVector3 &t)
btMatrix3x3 localFrameToWorld(int i, const btMatrix3x3 &mat) const
void forwardKinematics(btAlignedObjectArray< btQuaternion > &scratch_q, btAlignedObjectArray< btVector3 > &scratch_m)
virtual int calculateSerializeBufferSize() const
btMatrix3x3 m_cachedInertiaTopLeft
void setupPrismatic(int i, btScalar mass, const btVector3 &inertia, int parent, const btQuaternion &rotParentToThis, const btVector3 &jointAxis, const btVector3 &parentComToThisPivotOffset, const btVector3 &thisPivotToThisComOffset, bool disableParentCollision)
btScalar m_jointTorque[6]
const btVector3 & getBaseInertia() const
const btQuaternion & getParentToLocalRot(int i) const
btTransform getBaseWorldTransform() const
const btVector3 & getLinear() const
const btScalar & x() const
Return the x value. 
void setVector(const btVector3 &angular, const btVector3 &linear)
btMatrix3x3 m_cachedInertiaLowerLeft
btScalar getBaseMass() const
btQuaternion & normalize()
Normalize the quaternion Such that x^2 + y^2 + z^2 +w^2 = 1. 
btScalar getJointTorque(int i) const
void addLinkTorque(int i, const btVector3 &t)
const btVector3 & getAngular() const
btVector3 cross(const btVector3 &v) const
Return the cross product between this and another vector. 
btScalar dot(const btVector3 &v) const
Return the dot product. 
void setValue(const btScalar &_x, const btScalar &_y, const btScalar &_z)
Set x,y,z and zero w. 
void setLinear(const btVector3 &linear)
int getParent(int link_num) const
const btScalar & y() const
Return the y value. 
const btScalar & z() const
Return the z value. 
bool m_cachedInertiaValid
void addJointTorque(int i, btScalar Q)
void setValue(const btScalar &xx, const btScalar &xy, const btScalar &xz, const btScalar &yx, const btScalar &yy, const btScalar &yz, const btScalar &zx, const btScalar &zy, const btScalar &zz)
Set the values of the matrix explicitly (row major) 
virtual const char * serialize(void *dataBuffer, class btSerializer *serializer) const
fills the dataBuffer and returns the struct name (and 0 on failure) 
void setJointVel(int i, btScalar qdot)
const btScalar & z() const
Return the z value. 
void setAngular(const btVector3 &angular)
void setJointPos(int i, btScalar q)
void setWorldTransform(const btTransform &worldTrans)
void checkMotionAndSleepIfRequired(btScalar timestep)
btVector3 m_baseConstraintForce
const btMultibodyLink & getLink(int index) const
btVector3 can be used to represent 3D points and vectors. 
bool m_internalNeedsJointFeedback
the m_needsJointFeedback gets updated/computed during the stepVelocitiesMultiDof and it for internal ...
btMultiBody(int n_links, btScalar mass, const btVector3 &inertia, bool fixedBase, bool canSleep, bool deprecatedMultiDof=true)
int size() const
return the number of elements in the array 
void serialize(struct btVector3Data &dataOut) const
btAlignedObjectArray< btScalar > m_realBuf
void cross(const SpatialVectorType &b, SpatialVectorType &out) const
void setMatrix(const btMatrix3x3 &topLeftMat, const btMatrix3x3 &topRightMat, const btMatrix3x3 &bottomLeftMat)
btScalar dot(const btSpatialForceVector &b) const
virtual void finalizeChunk(btChunk *chunk, const char *structType, int chunkCode, void *oldPtr)=0
void updateLinksDofOffsets()
const btVector3 & getAngular() const
#define btMultiBodyDataName
#define btMultiBodyData
serialization data, don't change them if you are not familiar with the details of the serialization m...
bool m_useGlobalVelocities
btVector3 localDirToWorld(int i, const btVector3 &vec) const
virtual void serializeName(const char *ptr)=0
void resize(int newsize, const T &fillData=T())
void addJointTorqueMultiDof(int i, int dof, btScalar Q)
void mulMatrix(btScalar *pA, btScalar *pB, int rowsA, int colsA, int rowsB, int colsB, btScalar *pC) const
btScalar getJointPos(int i) const
btVector3 getAngularMomentum() const
const btVector3 & getLinkForce(int i) const
btMatrix3x3 m_bottomLeftMat
void setVector(const btVector3 &angular, const btVector3 &linear)
btAlignedObjectArray< btVector3 > m_vectorBuf
btTransform m_cachedWorldTransform
The btMatrix3x3 class implements a 3x3 rotation matrix, to perform linear algebra in combination with...
const btScalar & y() const
Return the y value. 
void fillConstraintJacobianMultiDof(int link, const btVector3 &contact_point, const btVector3 &normal_ang, const btVector3 &normal_lin, btScalar *jac, btAlignedObjectArray< btScalar > &scratch_r, btAlignedObjectArray< btVector3 > &scratch_v, btAlignedObjectArray< btMatrix3x3 > &scratch_m) const
void setJointVelMultiDof(int i, btScalar *qdot)
btScalar getLinkMass(int i) const
btScalar getKineticEnergy() const
virtual const char * findNameForPointer(const void *ptr) const =0
The btQuaternion implements quaternion to perform linear algebra rotations in combination with btMatr...
void addVector(const btVector3 &angular, const btVector3 &linear)
btScalar getJointVel(int i) const
btMatrix3x3 inverse() const
Return the inverse of the matrix. 
btVector3 worldDirToLocal(int i, const btVector3 &vec) const
btAlignedObjectArray< btMultibodyLink > m_links
btScalar * getJointTorqueMultiDof(int i)
#define btMultiBodyLinkData
const btScalar & w() const
Return the w value. 
void serialize(struct btQuaternionData &dataOut) const
btMatrix3x3 m_cachedInertiaTopRight
btScalar * getJointPosMultiDof(int i)
virtual btChunk * allocate(size_t size, int numElements)=0
const btVector3 & getLinkInertia(int i) const
const btVector3 & getRVector(int i) const
float btScalar
The btScalar type abstracts floating point numbers, to easily switch between double and single floati...
btScalar m_angularDamping
btScalar btCos(btScalar x)
btMatrix3x3 m_topRightMat
btScalar length() const
Return the length of the vector. 
const btVector3 getBaseVel() const