/*************************************************************************
* *
* 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 "objects.h"
#include "joint.h"
#include <ode/config.h>
#include <ode/odemath.h>
#include <ode/rotation.h>
#include <ode/timer.h>
#include <ode/error.h>
#include <ode/matrix.h>
#include "lcp.h"
//****************************************************************************
// misc defines
#define FAST_FACTOR
//#define TIMING
#define ALLOCA dALLOCA16
//****************************************************************************
// debugging - comparison of various vectors and matrices produced by the
// slow and fast versions of the stepper.
//#define COMPARE_METHODS
#ifdef COMPARE_METHODS
#include "testing.h"
dMatrixComparison comparator;
#endif
//****************************************************************************
// special matrix multipliers
// this assumes the 4th and 8th rows of B and C are zero.
static void Multiply2_p8r (dReal *A, dReal *B, dReal *C,
int p, int r, int Askip)
{
int i,j;
dReal sum,*bb,*cc;
dIASSERT (p>0 && r>0 && A && B && C);
bb = B;
for (i=p; i; i--) {
cc = C;
for (j=r; j; j--) {
sum = bb[0]*cc[0];
sum += bb[1]*cc[1];
sum += bb[2]*cc[2];
sum += bb[4]*cc[4];
sum += bb[5]*cc[5];
sum += bb[6]*cc[6];
*(A++) = sum;
cc += 8;
}
A += Askip - r;
bb += 8;
}
}
// this assumes the 4th and 8th rows of B and C are zero.
static void MultiplyAdd2_p8r (dReal *A, dReal *B, dReal *C,
int p, int r, int Askip)
{
int i,j;
dReal sum,*bb,*cc;
dIASSERT (p>0 && r>0 && A && B && C);
bb = B;
for (i=p; i; i--) {
cc = C;
for (j=r; j; j--) {
sum = bb[0]*cc[0];
sum += bb[1]*cc[1];
sum += bb[2]*cc[2];
sum += bb[4]*cc[4];
sum += bb[5]*cc[5];
sum += bb[6]*cc[6];
*(A++) += sum;
cc += 8;
}
A += Askip - r;
bb += 8;
}
}
// this assumes the 4th and 8th rows of B are zero.
static void Multiply0_p81 (dReal *A, dReal *B, dReal *C, int p)
{
int i;
dIASSERT (p>0 && A && B && C);
dReal sum;
for (i=p; i; i--) {
sum = B[0]*C[0];
sum += B[1]*C[1];
sum += B[2]*C[2];
sum += B[4]*C[4];
sum += B[5]*C[5];
sum += B[6]*C[6];
*(A++) = sum;
B += 8;
}
}
// this assumes the 4th and 8th rows of B are zero.
static void MultiplyAdd0_p81 (dReal *A, dReal *B, dReal *C, int p)
{
int i;
dIASSERT (p>0 && A && B && C);
dReal sum;
for (i=p; i; i--) {
sum = B[0]*C[0];
sum += B[1]*C[1];
sum += B[2]*C[2];
sum += B[4]*C[4];
sum += B[5]*C[5];
sum += B[6]*C[6];
*(A++) += sum;
B += 8;
}
}
// this assumes the 4th and 8th rows of B are zero.
static void MultiplyAdd1_8q1 (dReal *A, dReal *B, dReal *C, int q)
{
int k;
dReal sum;
dIASSERT (q>0 && A && B && C);
sum = 0;
for (k=0; k<q; k++) sum += B[k*8] * C[k];
A[0] += sum;
sum = 0;
for (k=0; k<q; k++) sum += B[1+k*8] * C[k];
A[1] += sum;
sum = 0;
for (k=0; k<q; k++) sum += B[2+k*8] * C[k];
A[2] += sum;
sum = 0;
for (k=0; k<q; k++) sum += B[4+k*8] * C[k];
A[4] += sum;
sum = 0;
for (k=0; k<q; k++) sum += B[5+k*8] * C[k];
A[5] += sum;
sum = 0;
for (k=0; k<q; k++) sum += B[6+k*8] * C[k];
A[6] += sum;
}
// this assumes the 4th and 8th rows of B are zero.
static void Multiply1_8q1 (dReal *A, dReal *B, dReal *C, int q)
{
int k;
dReal sum;
dIASSERT (q>0 && A && B && C);
sum = 0;
for (k=0; k<q; k++) sum += B[k*8] * C[k];
A[0] = sum;
sum = 0;
for (k=0; k<q; k++) sum += B[1+k*8] * C[k];
A[1] = sum;
sum = 0;
for (k=0; k<q; k++) sum += B[2+k*8] * C[k];
A[2] = sum;
sum = 0;
for (k=0; k<q; k++) sum += B[4+k*8] * C[k];
A[4] = sum;
sum = 0;
for (k=0; k<q; k++) sum += B[5+k*8] * C[k];
A[5] = sum;
sum = 0;
for (k=0; k<q; k++) sum += B[6+k*8] * C[k];
A[6] = sum;
}
//****************************************************************************
// body rotation
// return sin(x)/x. this has a singularity at 0 so special handling is needed
// for small arguments.
static inline dReal sinc (dReal x)
{
// if |x| < 1e-4 then use a taylor series expansion. this two term expansion
// is actually accurate to one LS bit within this range if double precision
// is being used - so don't worry!
if (dFabs(x) < 1.0e-4) return REAL(1.0) - x*x*REAL(0.166666666666666666667);
else return dSin(x)/x;
}
// given a body b, apply its linear and angular rotation over the time
// interval h, thereby adjusting its position and orientation.
static inline void moveAndRotateBody (dxBody *b, dReal h)
{
int j;
// handle linear velocity
for (j=0; j<3; j++) b->pos[j] += h * b->lvel[j];
if (b->flags & dxBodyFlagFiniteRotation) {
dVector3 irv; // infitesimal rotation vector
dQuaternion q; // quaternion for finite rotation
if (b->flags & dxBodyFlagFiniteRotationAxis) {
// split the angular velocity vector into a component along the finite
// rotation axis, and a component orthogonal to it.
dVector3 frv,irv; // finite rotation vector
dReal k = dDOT (b->finite_rot_axis,b->avel);
frv[0] = b->finite_rot_axis[0] * k;
frv[1] = b->finite_rot_axis[1] * k;
frv[2] = b->finite_rot_axis[2] * k;
irv[0] = b->avel[0] - frv[0];
irv[1] = b->avel[1] - frv[1];
irv[2] = b->avel[2] - frv[2];
// make a rotation quaternion q that corresponds to frv * h.
// compare this with the full-finite-rotation case below.
h *= REAL(0.5);
dReal theta = k * h;
q[0] = dCos(theta);
dReal s = sinc(theta) * h;
q[1] = frv[0] * s;
q[2] = frv[1] * s;
q[3] = frv[2] * s;
}
else {
// make a rotation quaternion q that corresponds to w * h
dReal wlen = dSqrt (b->avel[0]*b->avel[0] + b->avel[1]*b->avel[1] +
b->avel[2]*b->avel[2]);
h *= REAL(0.5);
dReal theta = wlen * h;
q[0] = dCos(theta);
dReal s = sinc(theta) * h;
q[1] = b->avel[0] * s;
q[2] = b->avel[1] * s;
q[3] = b->avel[2] * s;
}
// do the finite rotation
dQuaternion q2;
dQMultiply0 (q2,q,b->q);
for (j=0; j<4; j++) b->q[j] = q2[j];
// do the infitesimal rotation if required
if (b->flags & dxBodyFlagFiniteRotationAxis) {
dReal dq[4];
dWtoDQ (irv,b->q,dq);
for (j=0; j<4; j++) b->q[j] += h * dq[j];
}
}
else {
// the normal way - do an infitesimal rotation
dReal dq[4];
dWtoDQ (b->avel,b->q,dq);
for (j=0; j<4; j++) b->q[j] += h * dq[j];
}
// normalize the quaternion and convert it to a rotation matrix
dNormalize4 (b->q);
dQtoR (b->q,b->R);
// notify all attached geoms that this body has moved
for (dxGeom *geom = b->geom; geom; geom = dGeomGetBodyNext (geom))
dGeomMoved (geom);
}
//****************************************************************************
// the slow, but sure way
// note that this does not do any joint feedback!
// given lists of bodies and joints that form an island, perform a first
// order timestep.
//
// `body' is the body array, `nb' is the size of the array.
// `_joint' is the body array, `nj' is the size of the array.
void dInternalStepIsland_x1 (dxWorld *world, dxBody * const *body, int nb,
dxJoint * const *_joint, int nj, dReal stepsize)
{
int i,j,k;
int n6 = 6*nb;
# ifdef TIMING
dTimerStart("preprocessing");
# endif
// number all bodies in the body list - set their tag values
for (i=0; i<nb; i++) body[i]->tag = i;
// make a local copy of the joint array, because we might want to modify it.
// (the "dxJoint *const*" declaration says we're allowed to modify the joints
// but not the joint array, because the caller might need it unchanged).
dxJoint **joint = (dxJoint**) ALLOCA (nj * sizeof(dxJoint*));
memcpy (joint,_joint,nj * sizeof(dxJoint*));
// for all bodies, compute the inertia tensor and its inverse in the global
// frame, and compute the rotational force and add it to the torque
// accumulator.
// @@@ check computation of rotational force.
dReal *I = (dReal*) ALLOCA (3*nb*4 * sizeof(dReal));
dReal *invI = (dReal*) ALLOCA (3*nb*4 * sizeof(dReal));
//dSetZero (I,3*nb*4);
//dSetZero (invI,3*nb*4);
for (i=0; i<nb; i++) {
dReal tmp[12];
// compute inertia tensor in global frame
dMULTIPLY2_333 (tmp,body[i]->mass.I,body[i]->R);
dMULTIPLY0_333 (I+i*12,body[i]->R,tmp);
// compute inverse inertia tensor in global frame
dMULTIPLY2_333 (tmp,body[i]->invI,body[i]->R);
dMULTIPLY0_333 (invI+i*12,body[i]->R,tmp);
// compute rotational force
dMULTIPLY0_331 (tmp,I+i*12,body[i]->avel);
dCROSS (body[i]->tacc,-=,body[i]->avel,tmp);
}
// add the gravity force to all bodies
for (i=0; i<nb; i++) {
if ((body[i]->flags & dxBodyNoGravity)==0) {
body[i]->facc[0] += body[i]->mass.mass * world->gravity[0];
body[i]->facc[1] += body[i]->mass.mass * world->gravity[1];
body[i]->facc[2] += body[i]->mass.mass * world->gravity[2];
}
}
// get m = total constraint dimension, nub = number of unbounded variables.
// create constraint offset array and number-of-rows array for all joints.
// the constraints are re-ordered as follows: the purely unbounded
// constraints, the mixed unbounded + LCP constraints, and last the purely
// LCP constraints.
//
// joints with m=0 are inactive and are removed from the joints array
// entirely, so that the code that follows does not consider them.
int m = 0;
dxJoint::Info1 *info = (dxJoint::Info1*) ALLOCA (nj*sizeof(dxJoint::Info1));
int *ofs = (int*) ALLOCA (nj*sizeof(int));
for (i=0, j=0; j<nj; j++) { // i=dest, j=src
joint[j]->vtable->getInfo1 (joint[j],info+i);
dIASSERT (info[i].m >= 0 && info[i].m <= 6 &&
info[i].nub >= 0 && info[i].nub <= info[i].m);
if (info[i].m > 0) {
joint[i] = joint[j];
i++;
}
}
nj = i;
// the purely unbounded constraints
for (i=0; i<nj; i++) if (info[i].nub == info[i].m) {
ofs[i] = m;
m += info[i].m;
}
int nub = m;
// the mixed unbounded + LCP constraints
for (i=0; i<nj; i++) if (info[i].nub > 0 && info[i].nub < info[i].m) {
ofs[i] = m;
m += info[i].m;
}
// the purely LCP constraints
for (i=0; i<nj; i++) if (info[i].nub == 0) {
ofs[i] = m;
m += info[i].m;
}
// create (6*nb,6*nb) inverse mass matrix `invM', and fill it with mass
// parameters
# ifdef TIMING
dTimerNow ("create mass matrix");
# endif
int nskip = dPAD (n6);
dReal *invM = (dReal*) ALLOCA (n6*nskip*sizeof(dReal));
dSetZero (invM,n6*nskip);
for (i=0; i<nb; i++) {
dReal *MM = invM+(i*6)*nskip+(i*6);
MM[0] = body[i]->invMass;
MM[nskip+1] = body[i]->invMass;
MM[2*nskip+2] = body[i]->invMass;
MM += 3*nskip+3;
for (j=0; j<3; j++) for (k=0; k<3; k++) {
MM[j*nskip+k] = invI[i*12+j*4+k];
}
}
// assemble some body vectors: fe = external forces, v = velocities
dReal *fe = (dReal*) ALLOCA (n6 * sizeof(dReal));
dReal *v = (dReal*) ALLOCA (n6 * sizeof(dReal));
//dSetZero (fe,n6);
//dSetZero (v,n6);
for (i=0; i<nb; i++) {
for (j=0; j<3; j++) fe[i*6+j] = body[i]->facc[j];
for (j=0; j<3; j++) fe[i*6+3+j] = body[i]->tacc[j];
for (j=0; j<3; j++) v[i*6+j] = body[i]->lvel[j];
for (j=0; j<3; j++) v[i*6+3+j] = body[i]->avel[j];
}
// this will be set to the velocity update
dReal *vnew = (dReal*) ALLOCA (n6 * sizeof(dReal));
dSetZero (vnew,n6);
// if there are constraints, compute cforce
if (m > 0) {
// create a constraint equation right hand side vector `c', a constraint
// force mixing vector `cfm', and LCP low and high bound vectors, and an
// 'findex' vector.
dReal *c = (dReal*) ALLOCA (m*sizeof(dReal));
dReal *cfm = (dReal*) ALLOCA (m*sizeof(dReal));
dReal *lo = (dReal*) ALLOCA (m*sizeof(dReal));
dReal *hi = (dReal*) ALLOCA (m*sizeof(dReal));
int *findex = (int*) alloca (m*sizeof(int));
dSetZero (c,m);
dSetValue (cfm,m,world->global_cfm);
dSetValue (lo,m,-dInfinity);
dSetValue (hi,m, dInfinity);
for (i=0; i<m; i++) findex[i] = -1;
// create (m,6*nb) jacobian mass matrix `J', and fill it with constraint
// data. also fill the c vector.
# ifdef TIMING
dTimerNow ("create J");
# endif
dReal *J = (dReal*) ALLOCA (m*nskip*sizeof(dReal));
dSetZero (J,m*nskip);
dxJoint::Info2 Jinfo;
Jinfo.rowskip = nskip;
Jinfo.fps = dRecip(stepsize);
Jinfo.erp = world->global_erp;
for (i=0; i<nj; i++) {
Jinfo.J1l = J + nskip*ofs[i] + 6*joint[i]->node[0].body->tag;
Jinfo.J1a = Jinfo.J1l + 3;
if (joint[i]->node[1].body) {
Jinfo.J2l = J + nskip*ofs[i] + 6*joint[i]->node[1].body->tag;
Jinfo.J2a = Jinfo.J2l + 3;
}
else {
Jinfo.J2l = 0;
Jinfo.J2a = 0;
}
Jinfo.c = c + ofs[i];
Jinfo.cfm = cfm + ofs[i];
Jinfo.lo = lo + ofs[i];
Jinfo.hi = hi + ofs[i];
Jinfo.findex = findex + ofs[i];
joint[i]->vtable->getInfo2 (joint[i],&Jinfo);
// adjust returned findex values for global index numbering
for (j=0; j<info[i].m; j++) {
if (findex[ofs[i] + j] >= 0) findex[ofs[i] + j] += ofs[i];
}
}
// compute A = J*invM*J'
# ifdef TIMING
dTimerNow ("compute A");
# endif
dReal *JinvM = (dReal*) ALLOCA (m*nskip*sizeof(dReal));
//dSetZero (JinvM,m*nskip);
dMultiply0 (JinvM,J,invM,m,n6,n6);
int mskip = dPAD(m);
dReal *A = (dReal*) ALLOCA (m*mskip*sizeof(dReal));
//dSetZero (A,m*mskip);
dMultiply2 (A,JinvM,J,m,n6,m);
// add cfm to the diagonal of A
for (i=0; i<m; i++) A[i*mskip+i] += cfm[i] * Jinfo.fps;
# ifdef COMPARE_METHODS
comparator.nextMatrix (A,m,m,1,"A");
# endif
// compute `rhs', the right hand side of the equation J*a=c
# ifdef TIMING
dTimerNow ("compute rhs");
# endif
dReal *tmp1 = (dReal*) ALLOCA (n6 * sizeof(dReal));
//dSetZero (tmp1,n6);
dMultiply0 (tmp1,invM,fe,n6,n6,1);
for (i=0; i<n6; i++) tmp1[i] += v[i]/stepsize;
dReal *rhs = (dReal*) ALLOCA (m * sizeof(dReal));
//dSetZero (rhs,m);
dMultiply0 (rhs,J,tmp1,m,n6,1);
for (i=0; i<m; i++) rhs[i] = c[i]/stepsize - rhs[i];
# ifdef COMPARE_METHODS
comparator.nextMatrix (c,m,1,0,"c");
comparator.nextMatrix (rhs,m,1,0,"rhs");
# endif
// solve the LCP problem and get lambda.
// this will destroy A but that's okay
# ifdef TIMING
dTimerNow ("solving LCP problem");
# endif
dReal *lambda = (dReal*) ALLOCA (m * sizeof(dReal));
dReal *residual = (dReal*) ALLOCA (m * sizeof(dReal));
dSolveLCP (m,A,lambda,rhs,residual,nub,lo,hi,findex);
// OLD WAY - direct factor and solve
//
// // factorize A (L*L'=A)
//# ifdef TIMING
// dTimerNow ("factorize A");
//# endif
// dReal *L = (dReal*) ALLOCA (m*mskip*sizeof(dReal));
// memcpy (L,A,m*mskip*sizeof(dReal));
// if (dFactorCholesky (L,m)==0) dDebug (0,"A is not positive definite");
//
// // compute lambda
//# ifdef TIMING
// dTimerNow ("compute lambda");
//# endif
// dReal *lambda = (dReal*) ALLOCA (m * sizeof(dReal));
// memcpy (lambda,rhs,m * sizeof(dReal));
// dSolveCholesky (L,lambda,m);
# ifdef COMPARE_METHODS
comparator.nextMatrix (lambda,m,1,0,"lambda");
# endif
// compute the velocity update `vnew'
# ifdef TIMING
dTimerNow ("compute velocity update");
# endif
dMultiply1 (tmp1,J,lambda,n6,m,1);
for (i=0; i<n6; i++) tmp1[i] += fe[i];
dMultiply0 (vnew,invM,tmp1,n6,n6,1);
for (i=0; i<n6; i++) vnew[i] = v[i] + stepsize*vnew[i];
// see if the constraint has worked: compute J*vnew and make sure it equals
// `c' (to within a certain tolerance).
# ifdef TIMING
dTimerNow ("verify constraint equation");
# endif
dMultiply0 (tmp1,J,vnew,m,n6,1);
dReal err = 0;
for (i=0; i<m; i++) err += dFabs(tmp1[i]-c[i]);
printf ("%.6e\n",err);
}
else {
// no constraints
dMultiply0 (vnew,invM,fe,n6,n6,1);
for (i=0; i<n6; i++) vnew[i] = v[i] + stepsize*vnew[i];
}
# ifdef COMPARE_METHODS
comparator.nextMatrix (vnew,n6,1,0,"vnew");
# endif
// apply the velocity update to the bodies
# ifdef TIMING
dTimerNow ("update velocity");
# endif
for (i=0; i<nb; i++) {
for (j=0; j<3; j++) body[i]->lvel[j] = vnew[i*6+j];
for (j=0; j<3; j++) body[i]->avel[j] = vnew[i*6+3+j];
}
// update the position and orientation from the new linear/angular velocity
// (over the given timestep)
# ifdef TIMING
dTimerNow ("update position");
# endif
for (i=0; i<nb; i++) moveAndRotateBody (body[i],stepsize);
# ifdef TIMING
dTimerNow ("tidy up");
# endif
// zero all force accumulators
for (i=0; i<nb; i++) {
body[i]->facc[0] = 0;
body[i]->facc[1] = 0;
body[i]->facc[2] = 0;
body[i]->facc[3] = 0;
body[i]->tacc[0] = 0;
body[i]->tacc[1] = 0;
body[i]->tacc[2] = 0;
body[i]->tacc[3] = 0;
}
# ifdef TIMING
dTimerEnd();
if (m > 0) dTimerReport (stdout,1);
# endif
}
//****************************************************************************
// an optimized version of dInternalStepIsland1()
void dInternalStepIsland_x2 (dxWorld *world, dxBody * const *body, int nb,
dxJoint * const *_joint, int nj, dReal stepsize)
{
int i,j,k;
# ifdef TIMING
dTimerStart("preprocessing");
# endif
dReal stepsize1 = dRecip(stepsize);
// number all bodies in the body list - set their tag values
for (i=0; i<nb; i++) body[i]->tag = i;
// make a local copy of the joint array, because we might want to modify it.
// (the "dxJoint *const*" declaration says we're allowed to modify the joints
// but not the joint array, because the caller might need it unchanged).
dxJoint **joint = (dxJoint**) ALLOCA (nj * sizeof(dxJoint*));
memcpy (joint,_joint,nj * sizeof(dxJoint*));
// for all bodies, compute the inertia tensor and its inverse in the global
// frame, and compute the rotational force and add it to the torque
// accumulator. I and invI are vertically stacked 3x4 matrices, one per body.
// @@@ check computation of rotational force.
dReal *I = (dReal*) ALLOCA (3*nb*4 * sizeof(dReal));
dReal *invI = (dReal*) ALLOCA (3*nb*4 * sizeof(dReal));
//dSetZero (I,3*nb*4);
//dSetZero (invI,3*nb*4);
for (i=0; i<nb; i++) {
dReal tmp[12];
// compute inertia tensor in global frame
dMULTIPLY2_333 (tmp,body[i]->mass.I,body[i]->R);
dMULTIPLY0_333 (I+i*12,body[i]->R,tmp);
// compute inverse inertia tensor in global frame
dMULTIPLY2_333 (tmp,body[i]->invI,body[i]->R);
dMULTIPLY0_333 (invI+i*12,body[i]->R,tmp);
// compute rotational force
dMULTIPLY0_331 (tmp,I+i*12,body[i]->avel);
dCROSS (body[i]->tacc,-=,body[i]->avel,tmp);
}
// add the gravity force to all bodies
for (i=0; i<nb; i++) {
if ((body[i]->flags & dxBodyNoGravity)==0) {
body[i]->facc[0] += body[i]->mass.mass * world->gravity[0];
body[i]->facc[1] += body[i]->mass.mass * world->gravity[1];
body[i]->facc[2] += body[i]->mass.mass * world->gravity[2];
}
}
// get m = total constraint dimension, nub = number of unbounded variables.
// create constraint offset array and number-of-rows array for all joints.
// the constraints are re-ordered as follows: the purely unbounded
// constraints, the mixed unbounded + LCP constraints, and last the purely
// LCP constraints. this assists the LCP solver to put all unbounded
// variables at the start for a quick factorization.
//
// joints with m=0 are inactive and are removed from the joints array
// entirely, so that the code that follows does not consider them.
// also number all active joints in the joint list (set their tag values).
// inactive joints receive a tag value of -1.
int m = 0;
dxJoint::Info1 *info = (dxJoint::Info1*) ALLOCA (nj*sizeof(dxJoint::Info1));
int *ofs = (int*) ALLOCA (nj*sizeof(int));
for (i=0, j=0; j<nj; j++) { // i=dest, j=src
joint[j]->vtable->getInfo1 (joint[j],info+i);
dIASSERT (info[i].m >= 0 && info[i].m <= 6 &&
info[i].nub >= 0 && info[i].nub <= info[i].m);
if (info[i].m > 0) {
joint[i] = joint[j];
joint[i]->tag = i;
i++;
}
else {
joint[j]->tag = -1;
}
}
nj = i;
// the purely unbounded constraints
for (i=0; i<nj; i++) if (info[i].nub == info[i].m) {
ofs[i] = m;
m += info[i].m;
}
int nub = m;
// the mixed unbounded + LCP constraints
for (i=0; i<nj; i++) if (info[i].nub > 0 && info[i].nub < info[i].m) {
ofs[i] = m;
m += info[i].m;
}
// the purely LCP constraints
for (i=0; i<nj; i++) if (info[i].nub == 0) {
ofs[i] = m;
m += info[i].m;
}
// this will be set to the force due to the constraints
dReal *cforce = (dReal*) ALLOCA (nb*8 * sizeof(dReal));
dSetZero (cforce,nb*8);
// if there are constraints, compute cforce
if (m > 0) {
// create a constraint equation right hand side vector `c', a constraint
// force mixing vector `cfm', and LCP low and high bound vectors, and an
// 'findex' vector.
dReal *c = (dReal*) ALLOCA (m*sizeof(dReal));
dReal *cfm = (dReal*) ALLOCA (m*sizeof(dReal));
dReal *lo = (dReal*) ALLOCA (m*sizeof(dReal));
dReal *hi = (dReal*) ALLOCA (m*sizeof(dReal));
int *findex = (int*) alloca (m*sizeof(int));
dSetZero (c,m);
dSetValue (cfm,m,world->global_cfm);
dSetValue (lo,m,-dInfinity);
dSetValue (hi,m, dInfinity);
for (i=0; i<m; i++) findex[i] = -1;
// get jacobian data from constraints. a (2*m)x8 matrix will be created
// to store the two jacobian blocks from each constraint. it has this
// format:
//
// l l l 0 a a a 0 \ .
// l l l 0 a a a 0 }-- jacobian body 1 block for joint 0 (3 rows)
// l l l 0 a a a 0 /
// l l l 0 a a a 0 \ .
// l l l 0 a a a 0 }-- jacobian body 2 block for joint 0 (3 rows)
// l l l 0 a a a 0 /
// l l l 0 a a a 0 }--- jacobian body 1 block for joint 1 (1 row)
// l l l 0 a a a 0 }--- jacobian body 2 block for joint 1 (1 row)
// etc...
//
// (lll) = linear jacobian data
// (aaa) = angular jacobian data
//
# ifdef TIMING
dTimerNow ("create J");
# endif
dReal *J = (dReal*) ALLOCA (2*m*8*sizeof(dReal));
dSetZero (J,2*m*8);
dxJoint::Info2 Jinfo;
Jinfo.rowskip = 8;
Jinfo.fps = stepsize1;
Jinfo.erp = world->global_erp;
for (i=0; i<nj; i++) {
Jinfo.J1l = J + 2*8*ofs[i];
Jinfo.J1a = Jinfo.J1l + 4;
Jinfo.J2l = Jinfo.J1l + 8*info[i].m;
Jinfo.J2a = Jinfo.J2l + 4;
Jinfo.c = c + ofs[i];
Jinfo.cfm = cfm + ofs[i];
Jinfo.lo = lo + ofs[i];
Jinfo.hi = hi + ofs[i];
Jinfo.findex = findex + ofs[i];
joint[i]->vtable->getInfo2 (joint[i],&Jinfo);
// adjust returned findex values for global index numbering
for (j=0; j<info[i].m; j++) {
if (findex[ofs[i] + j] >= 0) findex[ofs[i] + j] += ofs[i];
}
}
// compute A = J*invM*J'. first compute JinvM = J*invM. this has the same
// format as J so we just go through the constraints in J multiplying by
// the appropriate scalars and matrices.
# ifdef TIMING
dTimerNow ("compute A");
# endif
dReal *JinvM = (dReal*) ALLOCA (2*m*8*sizeof(dReal));
dSetZero (JinvM,2*m*8);
for (i=0; i<nj; i++) {
int b = joint[i]->node[0].body->tag;
dReal body_invMass = body[b]->invMass;
dReal *body_invI = invI + b*12;
dReal *Jsrc = J + 2*8*ofs[i];
dReal *Jdst = JinvM + 2*8*ofs[i];
for (j=info[i].m-1; j>=0; j--) {
for (k=0; k<3; k++) Jdst[k] = Jsrc[k] * body_invMass;
dMULTIPLY0_133 (Jdst+4,Jsrc+4,body_invI);
Jsrc += 8;
Jdst += 8;
}
if (joint[i]->node[1].body) {
b = joint[i]->node[1].body->tag;
body_invMass = body[b]->invMass;
body_invI = invI + b*12;
for (j=info[i].m-1; j>=0; j--) {
for (k=0; k<3; k++) Jdst[k] = Jsrc[k] * body_invMass;
dMULTIPLY0_133 (Jdst+4,Jsrc+4,body_invI);
Jsrc += 8;
Jdst += 8;
}
}
}
// now compute A = JinvM * J'. A's rows and columns are grouped by joint,
// i.e. in the same way as the rows of J. block (i,j) of A is only nonzero
// if joints i and j have at least one body in common. this fact suggests
// the algorithm used to fill A:
//
// for b = all bodies
// n = number of joints attached to body b
// for i = 1..n
// for j = i+1..n
// ii = actual joint number for i
// jj = actual joint number for j
// // (ii,jj) will be set to all pairs of joints around body b
// compute blockwise: A(ii,jj) += JinvM(ii) * J(jj)'
//
// this algorithm catches all pairs of joints that have at least one body
// in common. it does not compute the diagonal blocks of A however -
// another similar algorithm does that.
int mskip = dPAD(m);
dReal *A = (dReal*) ALLOCA (m*mskip*sizeof(dReal));
dSetZero (A,m*mskip);
for (i=0; i<nb; i++) {
for (dxJointNode *n1=body[i]->firstjoint; n1; n1=n1->next) {
for (dxJointNode *n2=n1->next; n2; n2=n2->next) {
// get joint numbers and ensure ofs[j1] >= ofs[j2]
int j1 = n1->joint->tag;
int j2 = n2->joint->tag;
if (ofs[j1] < ofs[j2]) {
int tmp = j1;
j1 = j2;
j2 = tmp;
}
// if either joint was tagged as -1 then it is an inactive (m=0)
// joint that should not be considered
if (j1==-1 || j2==-1) continue;
// determine if body i is the 1st or 2nd body of joints j1 and j2
int jb1 = (joint[j1]->node[1].body == body[i]);
int jb2 = (joint[j2]->node[1].body == body[i]);
// jb1/jb2 must be 0 for joints with only one body
dIASSERT(joint[j1]->node[1].body || jb1==0);
dIASSERT(joint[j2]->node[1].body || jb2==0);
// set block of A
MultiplyAdd2_p8r (A + ofs[j1]*mskip + ofs[j2],
JinvM + 2*8*ofs[j1] + jb1*8*info[j1].m,
J + 2*8*ofs[j2] + jb2*8*info[j2].m,
info[j1].m,info[j2].m, mskip);
}
}
}
// compute diagonal blocks of A
for (i=0; i<nj; i++) {
Multiply2_p8r (A + ofs[i]*(mskip+1),
JinvM + 2*8*ofs[i],
J + 2*8*ofs[i],
info[i].m,info[i].m, mskip);
if (joint[i]->node[1].body) {
MultiplyAdd2_p8r (A + ofs[i]*(mskip+1),
JinvM + 2*8*ofs[i] + 8*info[i].m,
J + 2*8*ofs[i] + 8*info[i].m,
info[i].m,info[i].m, mskip);
}
}
// add cfm to the diagonal of A
for (i=0; i<m; i++) A[i*mskip+i] += cfm[i] * stepsize1;
# ifdef COMPARE_METHODS
comparator.nextMatrix (A,m,m,1,"A");
# endif
// compute the right hand side `rhs'
# ifdef TIMING
dTimerNow ("compute rhs");
# endif
dReal *tmp1 = (dReal*) ALLOCA (nb*8 * sizeof(dReal));
//dSetZero (tmp1,nb*8);
// put v/h + invM*fe into tmp1
for (i=0; i<nb; i++) {
dReal body_invMass = body[i]->invMass;
dReal *body_invI = invI + i*12;
for (j=0; j<3; j++) tmp1[i*8+j] = body[i]->facc[j] * body_invMass +
body[i]->lvel[j] * stepsize1;
dMULTIPLY0_331 (tmp1 + i*8 + 4,body_invI,body[i]->tacc);
for (j=0; j<3; j++) tmp1[i*8+4+j] += body[i]->avel[j] * stepsize1;
}
// put J*tmp1 into rhs
dReal *rhs = (dReal*) ALLOCA (m * sizeof(dReal));
//dSetZero (rhs,m);
for (i=0; i<nj; i++) {
dReal *JJ = J + 2*8*ofs[i];
Multiply0_p81 (rhs+ofs[i],JJ,
tmp1 + 8*joint[i]->node[0].body->tag, info[i].m);
if (joint[i]->node[1].body) {
MultiplyAdd0_p81 (rhs+ofs[i],JJ + 8*info[i].m,
tmp1 + 8*joint[i]->node[1].body->tag, info[i].m);
}
}
// complete rhs
for (i=0; i<m; i++) rhs[i] = c[i]*stepsize1 - rhs[i];
# ifdef COMPARE_METHODS
comparator.nextMatrix (c,m,1,0,"c");
comparator.nextMatrix (rhs,m,1,0,"rhs");
# endif
// solve the LCP problem and get lambda.
// this will destroy A but that's okay
# ifdef TIMING
dTimerNow ("solving LCP problem");
# endif
dReal *lambda = (dReal*) ALLOCA (m * sizeof(dReal));
dReal *residual = (dReal*) ALLOCA (m * sizeof(dReal));
dSolveLCP (m,A,lambda,rhs,residual,nub,lo,hi,findex);
// OLD WAY - direct factor and solve
//
// // factorize A (L*L'=A)
//# ifdef TIMING
// dTimerNow ("factorize A");
//# endif
// dReal *L = (dReal*) ALLOCA (m*mskip*sizeof(dReal));
// memcpy (L,A,m*mskip*sizeof(dReal));
//# ifdef FAST_FACTOR
// dFastFactorCholesky (L,m); // does not report non positive definiteness
//# else
// if (dFactorCholesky (L,m)==0) dDebug (0,"A is not positive definite");
//# endif
//
// // compute lambda
//# ifdef TIMING
// dTimerNow ("compute lambda");
//# endif
// dReal *lambda = (dReal*) ALLOCA (m * sizeof(dReal));
// memcpy (lambda,rhs,m * sizeof(dReal));
// dSolveCholesky (L,lambda,m);
# ifdef COMPARE_METHODS
comparator.nextMatrix (lambda,m,1,0,"lambda");
# endif
// compute the constraint force `cforce'
# ifdef TIMING
dTimerNow ("compute constraint force");
# endif
// compute cforce = J'*lambda
for (i=0; i<nj; i++) {
dReal *JJ = J + 2*8*ofs[i];
dxBody* b1 = joint[i]->node[0].body;
dxBody* b2 = joint[i]->node[1].body;
dJointFeedback *fb = joint[i]->feedback;
/******************** breakable joint contribution ***********************/
// this saves us a few dereferences
dxJointBreakInfo *jBI = joint[i]->breakInfo;
// we need joint feedback if the joint is breakable or if the user
// requested feedback.
if (jBI||fb) {
// we need feedback on the amount of force that this joint is
// applying to the bodies. we use a slightly slower computation
// that splits out the force components and puts them in the
// feedback structure.
dJointFeedback temp_fb; // temporary storage for joint feedback
dReal data1[8],data2[8];
Multiply1_8q1 (data1, JJ, lambda+ofs[i], info[i].m);
dReal *cf1 = cforce + 8*b1->tag;
cf1[0] += (temp_fb.f1[0] = data1[0]);
cf1[1] += (temp_fb.f1[1] = data1[1]);
cf1[2] += (temp_fb.f1[2] = data1[2]);
cf1[4] += (temp_fb.t1[0] = data1[4]);
cf1[5] += (temp_fb.t1[1] = data1[5]);
cf1[6] += (temp_fb.t1[2] = data1[6]);
if (b2) {
Multiply1_8q1 (data2, JJ + 8*info[i].m, lambda+ofs[i], info[i].m);
dReal *cf2 = cforce + 8*b2->tag;
cf2[0] += (temp_fb.f2[0] = data2[0]);
cf2[1] += (temp_fb.f2[1] = data2[1]);
cf2[2] += (temp_fb.f2[2] = data2[2]);
cf2[4] += (temp_fb.t2[0] = data2[4]);
cf2[5] += (temp_fb.t2[1] = data2[5]);
cf2[6] += (temp_fb.t2[2] = data2[6]);
}
// if the user requested so we must copy the feedback information to
// the feedback struct that the user suplied.
if (fb) {
// copy temp_fb to fb
fb->f1[0] = temp_fb.f1[0];
fb->f1[1] = temp_fb.f1[1];
fb->f1[2] = temp_fb.f1[2];
fb->t1[0] = temp_fb.t1[0];
fb->t1[1] = temp_fb.t1[1];
fb->t1[2] = temp_fb.t1[2];
if (b2) {
fb->f2[0] = temp_fb.f2[0];
fb->f2[1] = temp_fb.f2[1];
fb->f2[2] = temp_fb.f2[2];
fb->t2[0] = temp_fb.t2[0];
fb->t2[1] = temp_fb.t2[1];
fb->t2[2] = temp_fb.t2[2];
}
}
// if the joint is breakable we need to check the breaking conditions
if (jBI) {
dReal relCF1[3];
dReal relCT1[3];
// multiply the force and torque vectors by the rotation matrix of body 1
dMULTIPLY1_331 (&relCF1[0],b1->R,&temp_fb.f1[0]);
dMULTIPLY1_331 (&relCT1[0],b1->R,&temp_fb.t1[0]);
if (jBI->flags & dJOINT_BREAK_AT_B1_FORCE) {
// check if the force is to high
for (int i = 0; i < 3; i++) {
if (relCF1[i] > jBI->b1MaxF[i]) {
jBI->flags |= dJOINT_BROKEN;
goto doneCheckingBreaks;
}
}
}
if (jBI->flags & dJOINT_BREAK_AT_B1_TORQUE) {
// check if the torque is to high
for (int i = 0; i < 3; i++) {
if (relCT1[i] > jBI->b1MaxT[i]) {
jBI->flags |= dJOINT_BROKEN;
goto doneCheckingBreaks;
}
}
}
if (b2) {
dReal relCF2[3];
dReal relCT2[3];
// multiply the force and torque vectors by the rotation matrix of body 2
dMULTIPLY1_331 (&relCF2[0],b2->R,&temp_fb.f2[0]);
dMULTIPLY1_331 (&relCT2[0],b2->R,&temp_fb.t2[0]);
if (jBI->flags & dJOINT_BREAK_AT_B2_FORCE) {
// check if the force is to high
for (int i = 0; i < 3; i++) {
if (relCF2[i] > jBI->b2MaxF[i]) {
jBI->flags |= dJOINT_BROKEN;
goto doneCheckingBreaks;
}
}
}
if (jBI->flags & dJOINT_BREAK_AT_B2_TORQUE) {
// check if the torque is to high
for (int i = 0; i < 3; i++) {
if (relCT2[i] > jBI->b2MaxT[i]) {
jBI->flags |= dJOINT_BROKEN;
goto doneCheckingBreaks;
}
}
}
}
doneCheckingBreaks:
;
}
}
/*************************************************************************/
else {
// no feedback is required, let's compute cforce the faster way
MultiplyAdd1_8q1 (cforce + 8*b1->tag,JJ, lambda+ofs[i], info[i].m);
if (b2) {
MultiplyAdd1_8q1 (cforce + 8*b2->tag,
JJ + 8*info[i].m, lambda+ofs[i], info[i].m);
}
}
}
}
// compute the velocity update
# ifdef TIMING
dTimerNow ("compute velocity update");
# endif
// add fe to cforce
for (i=0; i<nb; i++) {
for (j=0; j<3; j++) cforce[i*8+j] += body[i]->facc[j];
for (j=0; j<3; j++) cforce[i*8+4+j] += body[i]->tacc[j];
}
// multiply cforce by stepsize
for (i=0; i < nb*8; i++) cforce[i] *= stepsize;
// add invM * cforce to the body velocity
for (i=0; i<nb; i++) {
dReal body_invMass = body[i]->invMass;
dReal *body_invI = invI + i*12;
for (j=0; j<3; j++) body[i]->lvel[j] += body_invMass * cforce[i*8+j];
dMULTIPLYADD0_331 (body[i]->avel,body_invI,cforce+i*8+4);
}
// update the position and orientation from the new linear/angular velocity
// (over the given timestep)
# ifdef TIMING
dTimerNow ("update position");
# endif
for (i=0; i<nb; i++) moveAndRotateBody (body[i],stepsize);
# ifdef COMPARE_METHODS
dReal *tmp_vnew = (dReal*) ALLOCA (nb*6*sizeof(dReal));
for (i=0; i<nb; i++) {
for (j=0; j<3; j++) tmp_vnew[i*6+j] = body[i]->lvel[j];
for (j=0; j<3; j++) tmp_vnew[i*6+3+j] = body[i]->avel[j];
}
comparator.nextMatrix (tmp_vnew,nb*6,1,0,"vnew");
# endif
# ifdef TIMING
dTimerNow ("tidy up");
# endif
// zero all force accumulators
for (i=0; i<nb; i++) {
body[i]->facc[0] = 0;
body[i]->facc[1] = 0;
body[i]->facc[2] = 0;
body[i]->facc[3] = 0;
body[i]->tacc[0] = 0;
body[i]->tacc[1] = 0;
body[i]->tacc[2] = 0;
body[i]->tacc[3] = 0;
}
# ifdef TIMING
dTimerEnd();
if (m > 0) dTimerReport (stdout,1);
# endif
}
//****************************************************************************
void dInternalStepIsland (dxWorld *world, dxBody * const *body, int nb,
dxJoint * const *joint, int nj, dReal stepsize)
{
# ifndef COMPARE_METHODS
dInternalStepIsland_x2 (world,body,nb,joint,nj,stepsize);
# endif
# ifdef COMPARE_METHODS
int i;
// save body state
dxBody *state = (dxBody*) ALLOCA (nb*sizeof(dxBody));
for (i=0; i<nb; i++) memcpy (state+i,body[i],sizeof(dxBody));
// take slow step
comparator.reset();
dInternalStepIsland_x1 (world,body,nb,joint,nj,stepsize);
comparator.end();
// restore state
for (i=0; i<nb; i++) memcpy (body[i],state+i,sizeof(dxBody));
// take fast step
dInternalStepIsland_x2 (world,body,nb,joint,nj,stepsize);
comparator.end();
//comparator.dump();
//_exit (1);
# endif
}
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