From f205de7847da7ae1c10212d82e7042d0100b4ce0 Mon Sep 17 00:00:00 2001
From: dan miller
Date: Fri, 19 Oct 2007 05:24:38 +0000
Subject: from the start... checking in ode-0.9

---
 libraries/ode-0.9/ode/src/quickstep.cpp | 880 ++++++++++++++++++++++++++++++++
 1 file changed, 880 insertions(+)
 create mode 100644 libraries/ode-0.9/ode/src/quickstep.cpp

(limited to 'libraries/ode-0.9/ode/src/quickstep.cpp')

diff --git a/libraries/ode-0.9/ode/src/quickstep.cpp b/libraries/ode-0.9/ode/src/quickstep.cpp
new file mode 100644
index 0000000..07aa9f7
--- /dev/null
+++ b/libraries/ode-0.9/ode/src/quickstep.cpp
@@ -0,0 +1,880 @@
+/*************************************************************************
+ *                                                                       *
+ * Open Dynamics Engine, Copyright (C) 2001-2003 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 <ode/misc.h>
+#include "lcp.h"
+#include "util.h"
+
+#define ALLOCA dALLOCA16
+
+typedef const dReal *dRealPtr;
+typedef dReal *dRealMutablePtr;
+#define dRealArray(name,n) dReal name[n];
+#define dRealAllocaArray(name,n) dReal *name = (dReal*) ALLOCA ((n)*sizeof(dReal));
+
+//***************************************************************************
+// configuration
+
+// for the SOR and CG methods:
+// uncomment the following line to use warm starting. this definitely
+// help for motor-driven joints. unfortunately it appears to hurt
+// with high-friction contacts using the SOR method. use with care
+
+//#define WARM_STARTING 1
+
+
+// for the SOR method:
+// uncomment the following line to determine a new constraint-solving
+// order for each iteration. however, the qsort per iteration is expensive,
+// and the optimal order is somewhat problem dependent.
+// @@@ try the leaf->root ordering.
+
+//#define REORDER_CONSTRAINTS 1
+
+
+// for the SOR method:
+// uncomment the following line to randomly reorder constraint rows
+// during the solution. depending on the situation, this can help a lot
+// or hardly at all, but it doesn't seem to hurt.
+
+#define RANDOMLY_REORDER_CONSTRAINTS 1
+
+//****************************************************************************
+// special matrix multipliers
+
+// multiply block of B matrix (q x 6) with 12 dReal per row with C vektor (q)
+static void Multiply1_12q1 (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*12] * C[k];
+  A[0] = sum;
+  sum = 0;
+  for (k=0; k<q; k++) sum += B[1+k*12] * C[k];
+  A[1] = sum;
+  sum = 0;
+  for (k=0; k<q; k++) sum += B[2+k*12] * C[k];
+  A[2] = sum;
+  sum = 0;
+  for (k=0; k<q; k++) sum += B[3+k*12] * C[k];
+  A[3] = sum;
+  sum = 0;
+  for (k=0; k<q; k++) sum += B[4+k*12] * C[k];
+  A[4] = sum;
+  sum = 0;
+  for (k=0; k<q; k++) sum += B[5+k*12] * C[k];
+  A[5] = sum;
+}
+
+//***************************************************************************
+// testing stuff
+
+#ifdef TIMING
+#define IFTIMING(x) x
+#else
+#define IFTIMING(x) /* */
+#endif
+
+//***************************************************************************
+// various common computations involving the matrix J
+
+// compute iMJ = inv(M)*J'
+
+static void compute_invM_JT (int m, dRealMutablePtr J, dRealMutablePtr iMJ, int *jb,
+	dxBody * const *body, dRealPtr invI)
+{
+	int i,j;
+	dRealMutablePtr iMJ_ptr = iMJ;
+	dRealMutablePtr J_ptr = J;
+	for (i=0; i<m; i++) {
+		int b1 = jb[i*2];
+		int b2 = jb[i*2+1];
+		dReal k = body[b1]->invMass;
+		for (j=0; j<3; j++) iMJ_ptr[j] = k*J_ptr[j];
+		dMULTIPLY0_331 (iMJ_ptr + 3, invI + 12*b1, J_ptr + 3);
+		if (b2 >= 0) {
+			k = body[b2]->invMass;
+			for (j=0; j<3; j++) iMJ_ptr[j+6] = k*J_ptr[j+6];
+			dMULTIPLY0_331 (iMJ_ptr + 9, invI + 12*b2, J_ptr + 9);
+		}
+		J_ptr += 12;
+		iMJ_ptr += 12;
+	}
+}
+
+
+// compute out = inv(M)*J'*in.
+
+static void multiply_invM_JT (int m, int nb, dRealMutablePtr iMJ, int *jb,
+	dRealMutablePtr in, dRealMutablePtr out)
+{
+	int i,j;
+	dSetZero (out,6*nb);
+	dRealPtr iMJ_ptr = iMJ;
+	for (i=0; i<m; i++) {
+		int b1 = jb[i*2];
+		int b2 = jb[i*2+1];
+		dRealMutablePtr out_ptr = out + b1*6;
+		for (j=0; j<6; j++) out_ptr[j] += iMJ_ptr[j] * in[i];
+		iMJ_ptr += 6;
+		if (b2 >= 0) {
+			out_ptr = out + b2*6;
+			for (j=0; j<6; j++) out_ptr[j] += iMJ_ptr[j] * in[i];
+		}
+		iMJ_ptr += 6;
+	}
+}
+
+
+// compute out = J*in.
+
+static void multiply_J (int m, dRealMutablePtr J, int *jb,
+	dRealMutablePtr in, dRealMutablePtr out)
+{
+	int i,j;
+	dRealPtr J_ptr = J;
+	for (i=0; i<m; i++) {
+		int b1 = jb[i*2];
+		int b2 = jb[i*2+1];
+		dReal sum = 0;
+		dRealMutablePtr in_ptr = in + b1*6;
+		for (j=0; j<6; j++) sum += J_ptr[j] * in_ptr[j];
+		J_ptr += 6;
+		if (b2 >= 0) {
+			in_ptr = in + b2*6;
+			for (j=0; j<6; j++) sum += J_ptr[j] * in_ptr[j];
+		}
+		J_ptr += 6;
+		out[i] = sum;
+	}
+}
+
+
+// compute out = (J*inv(M)*J' + cfm)*in.
+// use z as an nb*6 temporary.
+
+static void multiply_J_invM_JT (int m, int nb, dRealMutablePtr J, dRealMutablePtr iMJ, int *jb,
+	dRealPtr cfm, dRealMutablePtr z, dRealMutablePtr in, dRealMutablePtr out)
+{
+	multiply_invM_JT (m,nb,iMJ,jb,in,z);
+	multiply_J (m,J,jb,z,out);
+
+	// add cfm
+	for (int i=0; i<m; i++) out[i] += cfm[i] * in[i];
+}
+
+//***************************************************************************
+// conjugate gradient method with jacobi preconditioner
+// THIS IS EXPERIMENTAL CODE that doesn't work too well, so it is ifdefed out.
+//
+// adding CFM seems to be critically important to this method.
+
+#if 0
+
+static inline dReal dot (int n, dRealPtr x, dRealPtr y)
+{
+	dReal sum=0;
+	for (int i=0; i<n; i++) sum += x[i]*y[i];
+	return sum;
+}
+
+
+// x = y + z*alpha
+
+static inline void add (int n, dRealMutablePtr x, dRealPtr y, dRealPtr z, dReal alpha)
+{
+	for (int i=0; i<n; i++) x[i] = y[i] + z[i]*alpha;
+}
+
+
+static void CG_LCP (int m, int nb, dRealMutablePtr J, int *jb, dxBody * const *body,
+	dRealPtr invI, dRealMutablePtr lambda, dRealMutablePtr fc, dRealMutablePtr b,
+	dRealMutablePtr lo, dRealMutablePtr hi, dRealPtr cfm, int *findex,
+	dxQuickStepParameters *qs)
+{
+	int i,j;
+	const int num_iterations = qs->num_iterations;
+
+	// precompute iMJ = inv(M)*J'
+	dRealAllocaArray (iMJ,m*12);
+	compute_invM_JT (m,J,iMJ,jb,body,invI);
+
+	dReal last_rho = 0;
+	dRealAllocaArray (r,m);
+	dRealAllocaArray (z,m);
+	dRealAllocaArray (p,m);
+	dRealAllocaArray (q,m);
+
+	// precompute 1 / diagonals of A
+	dRealAllocaArray (Ad,m);
+	dRealPtr iMJ_ptr = iMJ;
+	dRealPtr J_ptr = J;
+	for (i=0; i<m; i++) {
+		dReal sum = 0;
+		for (j=0; j<6; j++) sum += iMJ_ptr[j] * J_ptr[j];
+		if (jb[i*2+1] >= 0) {
+			for (j=6; j<12; j++) sum += iMJ_ptr[j] * J_ptr[j];
+		}
+		iMJ_ptr += 12;
+		J_ptr += 12;
+		Ad[i] = REAL(1.0) / (sum + cfm[i]);
+	}
+
+#ifdef WARM_STARTING
+	// compute residual r = b - A*lambda
+	multiply_J_invM_JT (m,nb,J,iMJ,jb,cfm,fc,lambda,r);
+	for (i=0; i<m; i++) r[i] = b[i] - r[i];
+#else
+	dSetZero (lambda,m);
+	memcpy (r,b,m*sizeof(dReal));		// residual r = b - A*lambda
+#endif
+
+	for (int iteration=0; iteration < num_iterations; iteration++) {
+		for (i=0; i<m; i++) z[i] = r[i]*Ad[i];	// z = inv(M)*r
+		dReal rho = dot (m,r,z);		// rho = r'*z
+
+		// @@@
+		// we must check for convergence, otherwise rho will go to 0 if
+		// we get an exact solution, which will introduce NaNs into the equations.
+		if (rho < 1e-10) {
+			printf ("CG returned at iteration %d\n",iteration);
+			break;
+		}
+
+		if (iteration==0) {
+			memcpy (p,z,m*sizeof(dReal));	// p = z
+		}
+		else {
+			add (m,p,z,p,rho/last_rho);	// p = z + (rho/last_rho)*p
+		}
+
+		// compute q = (J*inv(M)*J')*p
+		multiply_J_invM_JT (m,nb,J,iMJ,jb,cfm,fc,p,q);
+
+		dReal alpha = rho/dot (m,p,q);		// alpha = rho/(p'*q)
+		add (m,lambda,lambda,p,alpha);		// lambda = lambda + alpha*p
+		add (m,r,r,q,-alpha);			// r = r - alpha*q
+		last_rho = rho;
+	}
+
+	// compute fc = inv(M)*J'*lambda
+	multiply_invM_JT (m,nb,iMJ,jb,lambda,fc);
+
+#if 0
+	// measure solution error
+	multiply_J_invM_JT (m,nb,J,iMJ,jb,cfm,fc,lambda,r);
+	dReal error = 0;
+	for (i=0; i<m; i++) error += dFabs(r[i] - b[i]);
+	printf ("lambda error = %10.6e\n",error);
+#endif
+}
+
+#endif
+
+//***************************************************************************
+// SOR-LCP method
+
+// nb is the number of bodies in the body array.
+// J is an m*12 matrix of constraint rows
+// jb is an array of first and second body numbers for each constraint row
+// invI is the global frame inverse inertia for each body (stacked 3x3 matrices)
+//
+// this returns lambda and fc (the constraint force).
+// note: fc is returned as inv(M)*J'*lambda, the constraint force is actually J'*lambda
+//
+// b, lo and hi are modified on exit
+
+
+struct IndexError {
+	dReal error;		// error to sort on
+	int findex;
+	int index;		// row index
+};
+
+
+#ifdef REORDER_CONSTRAINTS
+
+static int compare_index_error (const void *a, const void *b)
+{
+	const IndexError *i1 = (IndexError*) a;
+	const IndexError *i2 = (IndexError*) b;
+	if (i1->findex < 0 && i2->findex >= 0) return -1;
+	if (i1->findex >= 0 && i2->findex < 0) return 1;
+	if (i1->error < i2->error) return -1;
+	if (i1->error > i2->error) return 1;
+	return 0;
+}
+
+#endif
+
+
+static void SOR_LCP (int m, int nb, dRealMutablePtr J, int *jb, dxBody * const *body,
+	dRealPtr invI, dRealMutablePtr lambda, dRealMutablePtr fc, dRealMutablePtr b,
+	dRealMutablePtr lo, dRealMutablePtr hi, dRealPtr cfm, int *findex,
+	dxQuickStepParameters *qs)
+{
+	const int num_iterations = qs->num_iterations;
+	const dReal sor_w = qs->w;		// SOR over-relaxation parameter
+
+	int i,j;
+
+#ifdef WARM_STARTING
+	// for warm starting, this seems to be necessary to prevent
+	// jerkiness in motor-driven joints. i have no idea why this works.
+	for (i=0; i<m; i++) lambda[i] *= 0.9;
+#else
+	dSetZero (lambda,m);
+#endif
+
+#ifdef REORDER_CONSTRAINTS
+	// the lambda computed at the previous iteration.
+	// this is used to measure error for when we are reordering the indexes.
+	dRealAllocaArray (last_lambda,m);
+#endif
+
+	// a copy of the 'hi' vector in case findex[] is being used
+	dRealAllocaArray (hicopy,m);
+	memcpy (hicopy,hi,m*sizeof(dReal));
+
+	// precompute iMJ = inv(M)*J'
+	dRealAllocaArray (iMJ,m*12);
+	compute_invM_JT (m,J,iMJ,jb,body,invI);
+
+	// compute fc=(inv(M)*J')*lambda. we will incrementally maintain fc
+	// as we change lambda.
+#ifdef WARM_STARTING
+	multiply_invM_JT (m,nb,iMJ,jb,lambda,fc);
+#else
+	dSetZero (fc,nb*6);
+#endif
+
+	// precompute 1 / diagonals of A
+	dRealAllocaArray (Ad,m);
+	dRealPtr iMJ_ptr = iMJ;
+	dRealMutablePtr J_ptr = J;
+	for (i=0; i<m; i++) {
+		dReal sum = 0;
+		for (j=0; j<6; j++) sum += iMJ_ptr[j] * J_ptr[j];
+		if (jb[i*2+1] >= 0) {
+			for (j=6; j<12; j++) sum += iMJ_ptr[j] * J_ptr[j];
+		}
+		iMJ_ptr += 12;
+		J_ptr += 12;
+		Ad[i] = sor_w / (sum + cfm[i]);
+	}
+
+	// scale J and b by Ad
+	J_ptr = J;
+	for (i=0; i<m; i++) {
+		for (j=0; j<12; j++) {
+			J_ptr[0] *= Ad[i];
+			J_ptr++;
+		}
+		b[i] *= Ad[i];
+
+		// scale Ad by CFM. N.B. this should be done last since it is used above
+		Ad[i] *= cfm[i];
+	}
+
+	// order to solve constraint rows in
+	IndexError *order = (IndexError*) ALLOCA (m*sizeof(IndexError));
+
+#ifndef REORDER_CONSTRAINTS
+	// make sure constraints with findex < 0 come first.
+	j=0;
+	int k=1;
+
+	// Fill the array from both ends
+	for (i=0; i<m; i++)
+		if (findex[i] < 0)
+			order[j++].index = i; // Place them at the front
+		else
+			order[m-k++].index = i; // Place them at the end
+
+	dIASSERT ((j+k-1)==m); // -1 since k was started at 1 and not 0
+#endif
+
+	for (int iteration=0; iteration < num_iterations; iteration++) {
+
+#ifdef REORDER_CONSTRAINTS
+		// constraints with findex < 0 always come first.
+		if (iteration < 2) {
+			// for the first two iterations, solve the constraints in
+			// the given order
+			for (i=0; i<m; i++) {
+				order[i].error = i;
+				order[i].findex = findex[i];
+				order[i].index = i;
+			}
+		}
+		else {
+			// sort the constraints so that the ones converging slowest
+			// get solved last. use the absolute (not relative) error.
+			for (i=0; i<m; i++) {
+				dReal v1 = dFabs (lambda[i]);
+				dReal v2 = dFabs (last_lambda[i]);
+				dReal max = (v1 > v2) ? v1 : v2;
+				if (max > 0) {
+					//@@@ relative error: order[i].error = dFabs(lambda[i]-last_lambda[i])/max;
+					order[i].error = dFabs(lambda[i]-last_lambda[i]);
+				}
+				else {
+					order[i].error = dInfinity;
+				}
+				order[i].findex = findex[i];
+				order[i].index = i;
+			}
+		}
+		qsort (order,m,sizeof(IndexError),&compare_index_error);
+
+		//@@@ potential optimization: swap lambda and last_lambda pointers rather
+		//    than copying the data. we must make sure lambda is properly
+		//    returned to the caller
+		memcpy (last_lambda,lambda,m*sizeof(dReal));
+#endif
+#ifdef RANDOMLY_REORDER_CONSTRAINTS
+		if ((iteration & 7) == 0) {
+			for (i=1; i<m; ++i) {
+				IndexError tmp = order[i];
+				int swapi = dRandInt(i+1);
+				order[i] = order[swapi];
+				order[swapi] = tmp;
+			}
+		}
+#endif
+
+		for (int i=0; i<m; i++) {
+			// @@@ potential optimization: we could pre-sort J and iMJ, thereby
+			//     linearizing access to those arrays. hmmm, this does not seem
+			//     like a win, but we should think carefully about our memory
+			//     access pattern.
+
+			int index = order[i].index;
+			J_ptr = J + index*12;
+			iMJ_ptr = iMJ + index*12;
+
+			// set the limits for this constraint. note that 'hicopy' is used.
+			// this is the place where the QuickStep method differs from the
+			// direct LCP solving method, since that method only performs this
+			// limit adjustment once per time step, whereas this method performs
+			// once per iteration per constraint row.
+			// the constraints are ordered so that all lambda[] values needed have
+			// already been computed.
+			if (findex[index] >= 0) {
+				hi[index] = dFabs (hicopy[index] * lambda[findex[index]]);
+				lo[index] = -hi[index];
+			}
+
+			int b1 = jb[index*2];
+			int b2 = jb[index*2+1];
+			dReal delta = b[index] - lambda[index]*Ad[index];
+			dRealMutablePtr fc_ptr = fc + 6*b1;
+
+			// @@@ potential optimization: SIMD-ize this and the b2 >= 0 case
+			delta -=fc_ptr[0] * J_ptr[0] + fc_ptr[1] * J_ptr[1] +
+				fc_ptr[2] * J_ptr[2] + fc_ptr[3] * J_ptr[3] +
+				fc_ptr[4] * J_ptr[4] + fc_ptr[5] * J_ptr[5];
+			// @@@ potential optimization: handle 1-body constraints in a separate
+			//     loop to avoid the cost of test & jump?
+			if (b2 >= 0) {
+				fc_ptr = fc + 6*b2;
+				delta -=fc_ptr[0] * J_ptr[6] + fc_ptr[1] * J_ptr[7] +
+					fc_ptr[2] * J_ptr[8] + fc_ptr[3] * J_ptr[9] +
+					fc_ptr[4] * J_ptr[10] + fc_ptr[5] * J_ptr[11];
+			}
+
+			// compute lambda and clamp it to [lo,hi].
+			// @@@ potential optimization: does SSE have clamping instructions
+			//     to save test+jump penalties here?
+			dReal new_lambda = lambda[index] + delta;
+			if (new_lambda < lo[index]) {
+				delta = lo[index]-lambda[index];
+				lambda[index] = lo[index];
+			}
+			else if (new_lambda > hi[index]) {
+				delta = hi[index]-lambda[index];
+				lambda[index] = hi[index];
+			}
+			else {
+				lambda[index] = new_lambda;
+			}
+
+			//@@@ a trick that may or may not help
+			//dReal ramp = (1-((dReal)(iteration+1)/(dReal)num_iterations));
+			//delta *= ramp;
+
+			// update fc.
+			// @@@ potential optimization: SIMD for this and the b2 >= 0 case
+			fc_ptr = fc + 6*b1;
+			fc_ptr[0] += delta * iMJ_ptr[0];
+			fc_ptr[1] += delta * iMJ_ptr[1];
+			fc_ptr[2] += delta * iMJ_ptr[2];
+			fc_ptr[3] += delta * iMJ_ptr[3];
+			fc_ptr[4] += delta * iMJ_ptr[4];
+			fc_ptr[5] += delta * iMJ_ptr[5];
+			// @@@ potential optimization: handle 1-body constraints in a separate
+			//     loop to avoid the cost of test & jump?
+			if (b2 >= 0) {
+				fc_ptr = fc + 6*b2;
+				fc_ptr[0] += delta * iMJ_ptr[6];
+				fc_ptr[1] += delta * iMJ_ptr[7];
+				fc_ptr[2] += delta * iMJ_ptr[8];
+				fc_ptr[3] += delta * iMJ_ptr[9];
+				fc_ptr[4] += delta * iMJ_ptr[10];
+				fc_ptr[5] += delta * iMJ_ptr[11];
+			}
+		}
+	}
+}
+
+
+void dxQuickStepper (dxWorld *world, dxBody * const *body, int nb,
+		     dxJoint * const *_joint, int nj, dReal stepsize)
+{
+	int i,j;
+	IFTIMING(dTimerStart("preprocessing");)
+
+	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).
+	//@@@ do we really need to do this? we'll be sorting constraint rows individually, not joints
+	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 a vertical stack of 3x4 matrices, one per body.
+	//dRealAllocaArray (I,3*4*nb);	// need to remember all I's for feedback purposes only
+	dRealAllocaArray (invI,3*4*nb);
+	for (i=0; i<nb; i++) {
+		dMatrix3 tmp;
+
+		// compute inverse inertia tensor in global frame
+		dMULTIPLY2_333 (tmp,body[i]->invI,body[i]->posr.R);
+		dMULTIPLY0_333 (invI+i*12,body[i]->posr.R,tmp);
+#ifdef dGYROSCOPIC
+		dMatrix3 I;
+		// compute inertia tensor in global frame
+		dMULTIPLY2_333 (tmp,body[i]->mass.I,body[i]->posr.R);
+		//dMULTIPLY0_333 (I+i*12,body[i]->posr.R,tmp);
+		dMULTIPLY0_333 (I,body[i]->posr.R,tmp);
+		// compute rotational force
+		//dMULTIPLY0_331 (tmp,I+i*12,body[i]->avel);
+		dMULTIPLY0_331 (tmp,I,body[i]->avel);
+		dCROSS (body[i]->tacc,-=,body[i]->avel,tmp);
+#endif
+	}
+
+	// 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 joint information (m = total constraint dimension, nub = number of unbounded variables).
+	// joints with m=0 are inactive and are removed from the joints array
+	// entirely, so that the code that follows does not consider them.
+	//@@@ do we really need to save all the info1's
+	dxJoint::Info1 *info = (dxJoint::Info1*) ALLOCA (nj*sizeof(dxJoint::Info1));
+	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;
+
+	// create the row offset array
+	int m = 0;
+	int *ofs = (int*) ALLOCA (nj*sizeof(int));
+	for (i=0; i<nj; i++) {
+		ofs[i] = m;
+		m += info[i].m;
+	}
+
+	// if there are constraints, compute the constraint force
+	dRealAllocaArray (J,m*12);
+	int *jb = (int*) ALLOCA (m*2*sizeof(int));
+	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.
+		dRealAllocaArray (c,m);
+		dRealAllocaArray (cfm,m);
+		dRealAllocaArray (lo,m);
+		dRealAllocaArray (hi,m);
+		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. an m*12 matrix will be created
+		// to store the two jacobian blocks from each constraint. it has this
+		// format:
+		//
+		//   l1 l1 l1 a1 a1 a1 l2 l2 l2 a2 a2 a2 \    .
+		//   l1 l1 l1 a1 a1 a1 l2 l2 l2 a2 a2 a2  }-- jacobian for joint 0, body 1 and body 2 (3 rows)
+		//   l1 l1 l1 a1 a1 a1 l2 l2 l2 a2 a2 a2 /
+		//   l1 l1 l1 a1 a1 a1 l2 l2 l2 a2 a2 a2 }--- jacobian for joint 1, body 1 and body 2 (3 rows)
+		//   etc...
+		//
+		//   (lll) = linear jacobian data
+		//   (aaa) = angular jacobian data
+		//
+		IFTIMING (dTimerNow ("create J");)
+		dSetZero (J,m*12);
+		dxJoint::Info2 Jinfo;
+		Jinfo.rowskip = 12;
+		Jinfo.fps = stepsize1;
+		Jinfo.erp = world->global_erp;
+		int mfb = 0; // number of rows of Jacobian we will have to save for joint feedback
+		for (i=0; i<nj; i++) {
+			Jinfo.J1l = J + ofs[i]*12;
+			Jinfo.J1a = Jinfo.J1l + 3;
+			Jinfo.J2l = Jinfo.J1l + 6;
+			Jinfo.J2a = Jinfo.J1l + 9;
+			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];
+			}
+			if (joint[i]->feedback)
+				mfb += info[i].m;
+		}
+
+		// we need a copy of Jacobian for joint feedbacks
+		// because it gets destroyed by SOR solver
+		// instead of saving all Jacobian, we can save just rows
+		// for joints, that requested feedback (which is normaly much less)
+		dRealAllocaArray (Jcopy,mfb*12);
+		if (mfb > 0) {
+			mfb = 0;
+			for (i=0; i<nj; i++)
+				if (joint[i]->feedback) {
+					memcpy(Jcopy+mfb*12, J+ofs[i]*12, info[i].m*12*sizeof(dReal));
+					mfb += info[i].m;
+				}
+		}
+
+
+		// create an array of body numbers for each joint row
+		int *jb_ptr = jb;
+		for (i=0; i<nj; i++) {
+			int b1 = (joint[i]->node[0].body) ? (joint[i]->node[0].body->tag) : -1;
+			int b2 = (joint[i]->node[1].body) ? (joint[i]->node[1].body->tag) : -1;
+			for (j=0; j<info[i].m; j++) {
+				jb_ptr[0] = b1;
+				jb_ptr[1] = b2;
+				jb_ptr += 2;
+			}
+		}
+		dIASSERT (jb_ptr == jb+2*m);
+
+		// compute the right hand side `rhs'
+		IFTIMING (dTimerNow ("compute rhs");)
+		dRealAllocaArray (tmp1,nb*6);
+		// put v/h + invM*fe into tmp1
+		for (i=0; i<nb; i++) {
+			dReal body_invMass = body[i]->invMass;
+			for (j=0; j<3; j++) tmp1[i*6+j] = body[i]->facc[j] * body_invMass + body[i]->lvel[j] * stepsize1;
+			dMULTIPLY0_331 (tmp1 + i*6 + 3,invI + i*12,body[i]->tacc);
+			for (j=0; j<3; j++) tmp1[i*6+3+j] += body[i]->avel[j] * stepsize1;
+		}
+
+		// put J*tmp1 into rhs
+		dRealAllocaArray (rhs,m);
+		multiply_J (m,J,jb,tmp1,rhs);
+
+		// complete rhs
+		for (i=0; i<m; i++) rhs[i] = c[i]*stepsize1 - rhs[i];
+
+		// scale CFM
+		for (i=0; i<m; i++) cfm[i] *= stepsize1;
+
+		// load lambda from the value saved on the previous iteration
+		dRealAllocaArray (lambda,m);
+#ifdef WARM_STARTING
+		dSetZero (lambda,m);	//@@@ shouldn't be necessary
+		for (i=0; i<nj; i++) {
+			memcpy (lambda+ofs[i],joint[i]->lambda,info[i].m * sizeof(dReal));
+		}
+#endif
+
+		// solve the LCP problem and get lambda and invM*constraint_force
+		IFTIMING (dTimerNow ("solving LCP problem");)
+		dRealAllocaArray (cforce,nb*6);
+		SOR_LCP (m,nb,J,jb,body,invI,lambda,cforce,rhs,lo,hi,cfm,findex,&world->qs);
+
+#ifdef WARM_STARTING
+		// save lambda for the next iteration
+		//@@@ note that this doesn't work for contact joints yet, as they are
+		// recreated every iteration
+		for (i=0; i<nj; i++) {
+			memcpy (joint[i]->lambda,lambda+ofs[i],info[i].m * sizeof(dReal));
+		}
+#endif
+
+		// note that the SOR method overwrites rhs and J at this point, so
+		// they should not be used again.
+
+		// add stepsize * cforce to the body velocity
+		for (i=0; i<nb; i++) {
+			for (j=0; j<3; j++) body[i]->lvel[j] += stepsize * cforce[i*6+j];
+			for (j=0; j<3; j++) body[i]->avel[j] += stepsize * cforce[i*6+3+j];
+		}
+
+		// if joint feedback is requested, compute the constraint force.
+		// BUT: cforce is inv(M)*J'*lambda, whereas we want just J'*lambda,
+		// so we must compute M*cforce.
+		// @@@ if any joint has a feedback request we compute the entire
+		//     adjusted cforce, which is not the most efficient way to do it.
+		/*for (j=0; j<nj; j++) {
+			if (joint[j]->feedback) {
+				// compute adjusted cforce
+				for (i=0; i<nb; i++) {
+					dReal k = body[i]->mass.mass;
+					cforce [i*6+0] *= k;
+					cforce [i*6+1] *= k;
+					cforce [i*6+2] *= k;
+					dVector3 tmp;
+					dMULTIPLY0_331 (tmp, I + 12*i, cforce + i*6 + 3);
+					cforce [i*6+3] = tmp[0];
+					cforce [i*6+4] = tmp[1];
+					cforce [i*6+5] = tmp[2];
+				}
+				// compute feedback for this and all remaining joints
+				for (; j<nj; j++) {
+					dJointFeedback *fb = joint[j]->feedback;
+					if (fb) {
+						int b1 = joint[j]->node[0].body->tag;
+						memcpy (fb->f1,cforce+b1*6,3*sizeof(dReal));
+						memcpy (fb->t1,cforce+b1*6+3,3*sizeof(dReal));
+						if (joint[j]->node[1].body) {
+							int b2 = joint[j]->node[1].body->tag;
+							memcpy (fb->f2,cforce+b2*6,3*sizeof(dReal));
+							memcpy (fb->t2,cforce+b2*6+3,3*sizeof(dReal));
+						}
+					}
+				}
+			}
+		}*/
+
+		if (mfb > 0) {
+			// straightforward computation of joint constraint forces:
+			// multiply related lambdas with respective J' block for joints
+			// where feedback was requested
+			mfb = 0;
+			for (i=0; i<nj; i++) {
+				if (joint[i]->feedback) {
+					dJointFeedback *fb = joint[i]->feedback;
+					dReal data[6];
+					Multiply1_12q1 (data, Jcopy+mfb*12, lambda+ofs[i], info[i].m);
+					fb->f1[0] = data[0];
+					fb->f1[1] = data[1];
+					fb->f1[2] = data[2];
+					fb->t1[0] = data[3];
+					fb->t1[1] = data[4];
+					fb->t1[2] = data[5];
+					if (joint[i]->node[1].body)
+					{
+						Multiply1_12q1 (data, Jcopy+mfb*12+6, lambda+ofs[i], info[i].m);
+						fb->f2[0] = data[0];
+						fb->f2[1] = data[1];
+						fb->f2[2] = data[2];
+						fb->t2[0] = data[3];
+						fb->t2[1] = data[4];
+						fb->t2[2] = data[5];
+					}
+					mfb += info[i].m;
+				}
+			}
+		}
+	}
+
+	// compute the velocity update:
+	// add stepsize * invM * fe to the body velocity
+
+	IFTIMING (dTimerNow ("compute velocity update");)
+	for (i=0; i<nb; i++) {
+		dReal body_invMass = body[i]->invMass;
+		for (j=0; j<3; j++) body[i]->lvel[j] += stepsize * body_invMass * body[i]->facc[j];
+		for (j=0; j<3; j++) body[i]->tacc[j] *= stepsize;
+		dMULTIPLYADD0_331 (body[i]->avel,invI + i*12,body[i]->tacc);
+	}
+
+#if 0
+	// check that the updated velocity obeys the constraint (this check needs unmodified J)
+	dRealAllocaArray (vel,nb*6);
+	for (i=0; i<nb; i++) {
+		for (j=0; j<3; j++) vel[i*6+j] = body[i]->lvel[j];
+		for (j=0; j<3; j++) vel[i*6+3+j] = body[i]->avel[j];
+	}
+	dRealAllocaArray (tmp,m);
+	multiply_J (m,J,jb,vel,tmp);
+	dReal error = 0;
+	for (i=0; i<m; i++) error += dFabs(tmp[i]);
+	printf ("velocity error = %10.6e\n",error);
+#endif
+
+	// update the position and orientation from the new linear/angular velocity
+	// (over the given timestep)
+	IFTIMING (dTimerNow ("update position");)
+	for (i=0; i<nb; i++) dxStepBody (body[i],stepsize);
+
+	IFTIMING (dTimerNow ("tidy up");)
+
+	// zero all force accumulators
+	for (i=0; i<nb; i++) {
+		dSetZero (body[i]->facc,3);
+		dSetZero (body[i]->tacc,3);
+	}
+
+	IFTIMING (dTimerEnd();)
+	IFTIMING (if (m > 0) dTimerReport (stdout,1);)
+}
-- 
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