FCL/sf/mw/classicui: comparison ode/src/joint.cpp

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--1:000000000000
+:2f259fa3e83a
+/*************************************************************************
+*                                                                       *
+* 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.                     *
+*                                                                       *
+*************************************************************************/
+/*
+design note: the general principle for giving a joint the option of connecting
+to the static environment (i.e. the absolute frame) is to check the second
+body (joint->node[1].body), and if it is zero then behave as if its body
+transform is the identity.
+*/
+#include <ode/ode.h>
+#include <ode/odemath.h>
+#include <ode/rotation.h>
+#include <ode/matrix.h>
+#include "joint.h"
+#define dCROSSMUL(a,op,b,c) \
+do { \
+(a)[0] op dMUL(REAL(0.5),(dMUL((b)[1],(c)[2]) - dMUL((b)[2],(c)[1]))); \
+(a)[1] op dMUL(REAL(0.5),(dMUL((b)[2],(c)[0]) - dMUL((b)[0],(c)[2]))); \
+(a)[2] op dMUL(REAL(0.5),(dMUL((b)[0],(c)[1]) - dMUL((b)[1],(c)[0]))); \
+} while(0)
+//****************************************************************************
+// externs
+// extern "C" void dBodyAddTorque (dBodyID, dReal fx, dReal fy, dReal fz);
+// extern "C" void dBodyAddForce (dBodyID, dReal fx, dReal fy, dReal fz);
+//****************************************************************************
+// utility
+// set three "ball-and-socket" rows in the constraint equation, and the
+// corresponding right hand side.
+static inline void setBall (dxJoint *joint, dxJoint::Info2 *info,
+			    dVector3 anchor1, dVector3 anchor2)
+{
+// anchor points in global coordinates with respect to body PORs.
+dVector3 a1,a2;
+int s = info->rowskip;
+// set jacobian
+info->J1l[0] = REAL(1.0);
+info->J1l[s+1] = REAL(1.0);
+info->J1l[2*s+2] = REAL(1.0);
+dMULTIPLY0_331 (a1,joint->node[0].body->posr.R,anchor1);
+dCROSSMAT (info->J1a,a1,s,-,+);
+if (joint->node[1].body) {
+info->J2l[0] = -REAL(1.0);
+info->J2l[s+1] = -REAL(1.0);
+info->J2l[2*s+2] = -REAL(1.0);
+dMULTIPLY0_331 (a2,joint->node[1].body->posr.R,anchor2);
+dCROSSMAT (info->J2a,a2,s,+,-);
+}
+// set right hand side
+dReal k = dMUL(info->fps,info->erp);
+if (joint->node[1].body) {
+for (int j=0; j<3; j++) {
+info->c[j] = dMUL(k,(a2[j] + joint->node[1].body->posr.pos[j] -
+			a1[j] - joint->node[0].body->posr.pos[j]));
+}
+}
+else {
+for (int j=0; j<3; j++) {
+info->c[j] = dMUL(k,(anchor2[j] - a1[j] -
+			joint->node[0].body->posr.pos[j]));
+}
+}
+}
+// this is like setBall(), except that `axis' is a unit length vector
+// (in global coordinates) that should be used for the first jacobian
+// position row (the other two row vectors will be derived from this).
+// `erp1' is the erp value to use along the axis.
+static inline void setBall2 (dxJoint *joint, dxJoint::Info2 *info,
+			    dVector3 anchor1, dVector3 anchor2,
+			    dVector3 axis, dReal erp1)
+{
+// anchor points in global coordinates with respect to body PORs.
+dVector3 a1,a2;
+int i,s = info->rowskip;
+// get vectors normal to the axis. in setBall() axis,q1,q2 is [1 0 0],
+// [0 1 0] and [0 0 1], which makes everything much easier.
+dVector3 q1,q2;
+dPlaneSpace (axis,q1,q2);
+// set jacobian
+for (i=0; i<3; i++) info->J1l[i] = axis[i];
+for (i=0; i<3; i++) info->J1l[s+i] = q1[i];
+for (i=0; i<3; i++) info->J1l[2*s+i] = q2[i];
+dMULTIPLY0_331 (a1,joint->node[0].body->posr.R,anchor1);
+dCROSS (info->J1a,=,a1,axis);
+dCROSS (info->J1a+s,=,a1,q1);
+dCROSS (info->J1a+2*s,=,a1,q2);
+if (joint->node[1].body) {
+for (i=0; i<3; i++) info->J2l[i] = -axis[i];
+for (i=0; i<3; i++) info->J2l[s+i] = -q1[i];
+for (i=0; i<3; i++) info->J2l[2*s+i] = -q2[i];
+dMULTIPLY0_331 (a2,joint->node[1].body->posr.R,anchor2);
+dCROSS (info->J2a,= -,a2,axis);
+dCROSS (info->J2a+s,= -,a2,q1);
+dCROSS (info->J2a+2*s,= -,a2,q2);
+}
+// set right hand side - measure error along (axis,q1,q2)
+dReal k1 = dMUL(info->fps,erp1);
+dReal k = dMUL(info->fps,info->erp);
+for (i=0; i<3; i++) a1[i] += joint->node[0].body->posr.pos[i];
+if (joint->node[1].body) {
+for (i=0; i<3; i++) a2[i] += joint->node[1].body->posr.pos[i];
+info->c[0] = dMUL(k1,(dDOT(axis,a2) - dDOT(axis,a1)));
+info->c[1] = dMUL(k,(dDOT(q1,a2) - dDOT(q1,a1)));
+info->c[2] = dMUL(k,(dDOT(q2,a2) - dDOT(q2,a1)));
+}
+else {
+info->c[0] = dMUL(k1,(dDOT(axis,anchor2) - dDOT(axis,a1)));
+info->c[1] = dMUL(k,(dDOT(q1,anchor2) - dDOT(q1,a1)));
+info->c[2] = dMUL(k,(dDOT(q2,anchor2) - dDOT(q2,a1)));
+}
+}
+// set three orientation rows in the constraint equation, and the
+// corresponding right hand side.
+static void setFixedOrientation(dxJoint *joint, dxJoint::Info2 *info, dQuaternion qrel, int start_row)
+{
+int s = info->rowskip;
+int start_index = start_row * s;
+// 3 rows to make body rotations equal
+info->J1a[start_index] = REAL(1.0);
+info->J1a[start_index + s + 1] = REAL(1.0);
+info->J1a[start_index + s*2+2] = REAL(1.0);
+if (joint->node[1].body) {
+info->J2a[start_index] = REAL(-1.0);
+info->J2a[start_index + s+1] = REAL(-1.0);
+info->J2a[start_index + s*2+2] = REAL(-1.0);
+}
+// compute the right hand side. the first three elements will result in
+// relative angular velocity of the two bodies - this is set to bring them
+// back into alignment. the correcting angular velocity is
+//   |angular_velocity| = angle/time = erp*theta / stepsize
+//                      = (erp*fps) * theta
+//    angular_velocity  = |angular_velocity| * u
+//                      = (erp*fps) * theta * u
+// where rotation along unit length axis u by theta brings body 2's frame
+// to qrel with respect to body 1's frame. using a small angle approximation
+// for sin(), this gives
+//    angular_velocity  = (erp*fps) * 2 * v
+// where the quaternion of the relative rotation between the two bodies is
+//    q = [cos(theta/2) sin(theta/2)*u] = [s v]
+// get qerr = relative rotation (rotation error) between two bodies
+dQuaternion qerr,e;
+if (joint->node[1].body) {
+dQuaternion qq;
+dQMultiply1 (qq,joint->node[0].body->q,joint->node[1].body->q);
+dQMultiply2 (qerr,qq,qrel);
+}
+else {
+dQMultiply3 (qerr,joint->node[0].body->q,qrel);
+}
+if (qerr[0] < 0) {
+qerr[1] = -qerr[1];		// adjust sign of qerr to make theta small
+qerr[2] = -qerr[2];
+qerr[3] = -qerr[3];
+}
+dMULTIPLY0_331 (e,joint->node[0].body->posr.R,qerr+1); // @@@ bad SIMD padding!
+dReal k = dMUL(info->fps,info->erp);
+info->c[start_row] = 2*dMUL(k,e[0]);
+info->c[start_row+1] = 2*dMUL(k,e[1]);
+info->c[start_row+2] = 2*dMUL(k,e[2]);
+}
+// compute anchor points relative to bodies
+static void setAnchors (dxJoint *j, dReal x, dReal y, dReal z,
+			dVector3 anchor1, dVector3 anchor2)
+{
+if (j->node[0].body) {
+dReal q[4];
+q[0] = x - j->node[0].body->posr.pos[0];
+q[1] = y - j->node[0].body->posr.pos[1];
+q[2] = z - j->node[0].body->posr.pos[2];
+q[3] = 0;
+dMULTIPLY1_331 (anchor1,j->node[0].body->posr.R,q);
+if (j->node[1].body) {
+q[0] = x - j->node[1].body->posr.pos[0];
+q[1] = y - j->node[1].body->posr.pos[1];
+q[2] = z - j->node[1].body->posr.pos[2];
+q[3] = 0;
+dMULTIPLY1_331 (anchor2,j->node[1].body->posr.R,q);
+}
+else {
+anchor2[0] = x;
+anchor2[1] = y;
+anchor2[2] = z;
+}
+}
+anchor1[3] = 0;
+anchor2[3] = 0;
+}
+// compute axes relative to bodies. either axis1 or axis2 can be 0.
+static void setAxes (dxJoint *j, dReal x, dReal y, dReal z,
+		     dVector3 axis1, dVector3 axis2)
+{
+if (j->node[0].body) {
+dReal q[4];
+q[0] = x;
+q[1] = y;
+q[2] = z;
+q[3] = 0;
+dNormalize3 (q);
+if (axis1) {
+dMULTIPLY1_331 (axis1,j->node[0].body->posr.R,q);
+axis1[3] = 0;
+}
+if (axis2) {
+if (j->node[1].body) {
+	dMULTIPLY1_331 (axis2,j->node[1].body->posr.R,q);
+}
+else {
+	axis2[0] = x;
+	axis2[1] = y;
+	axis2[2] = z;
+}
+axis2[3] = 0;
+}
+}
+}
+static void getAnchor (dxJoint *j, dVector3 result, dVector3 anchor1)
+{
+if (j->node[0].body) {
+dMULTIPLY0_331 (result,j->node[0].body->posr.R,anchor1);
+result[0] += j->node[0].body->posr.pos[0];
+result[1] += j->node[0].body->posr.pos[1];
+result[2] += j->node[0].body->posr.pos[2];
+}
+}
+static void getAnchor2 (dxJoint *j, dVector3 result, dVector3 anchor2)
+{
+if (j->node[1].body) {
+dMULTIPLY0_331 (result,j->node[1].body->posr.R,anchor2);
+result[0] += j->node[1].body->posr.pos[0];
+result[1] += j->node[1].body->posr.pos[1];
+result[2] += j->node[1].body->posr.pos[2];
+}
+else {
+result[0] = anchor2[0];
+result[1] = anchor2[1];
+result[2] = anchor2[2];
+}
+}
+static void getAxis (dxJoint *j, dVector3 result, dVector3 axis1)
+{
+if (j->node[0].body) {
+dMULTIPLY0_331 (result,j->node[0].body->posr.R,axis1);
+}
+}
+static void getAxis2 (dxJoint *j, dVector3 result, dVector3 axis2)
+{
+if (j->node[1].body) {
+dMULTIPLY0_331 (result,j->node[1].body->posr.R,axis2);
+}
+else {
+result[0] = axis2[0];
+result[1] = axis2[1];
+result[2] = axis2[2];
+}
+}
+static dReal getHingeAngleFromRelativeQuat (dQuaternion qrel, dVector3 axis)
+{
+// the angle between the two bodies is extracted from the quaternion that
+// represents the relative rotation between them. recall that a quaternion
+// q is:
+//    [s,v] = [ cos(theta/2) , sin(theta/2) * u ]
+// where s is a scalar and v is a 3-vector. u is a unit length axis and
+// theta is a rotation along that axis. we can get theta/2 by:
+//    theta/2 = atan2 ( sin(theta/2) , cos(theta/2) )
+// but we can't get sin(theta/2) directly, only its absolute value, i.e.:
+//    |v| = |sin(theta/2)| * |u|
+//        = |sin(theta/2)|
+// using this value will have a strange effect. recall that there are two
+// quaternion representations of a given rotation, q and -q. typically as
+// a body rotates along the axis it will go through a complete cycle using
+// one representation and then the next cycle will use the other
+// representation. this corresponds to u pointing in the direction of the
+// hinge axis and then in the opposite direction. the result is that theta
+// will appear to go "backwards" every other cycle. here is a fix: if u
+// points "away" from the direction of the hinge (motor) axis (i.e. more
+// than 90 degrees) then use -q instead of q. this represents the same
+// rotation, but results in the cos(theta/2) value being sign inverted.
+// extract the angle from the quaternion. cost2 = cos(theta/2),
+// sint2 = |sin(theta/2)|
+dReal cost2 = qrel[0];
+dReal sint2 = dSqrt (dMUL(qrel[1],qrel[1])+dMUL(qrel[2],qrel[2])+dMUL(qrel[3],qrel[3]));
+dReal theta = (dDOT(qrel+REAL(1.0),axis) >= 0) ?	// @@@ padding assumptions
+(2 * dArcTan2(sint2,cost2)) :		// if u points in direction of axis
+(2 * dArcTan2(sint2,-cost2));		// if u points in opposite direction
+// the angle we get will be between 0..2*pi, but we want to return angles
+// between -pi..pi
+if (theta > dPI) theta -= 2*dPI;
+// the angle we've just extracted has the wrong sign
+theta = -theta;
+return theta;
+}
+// given two bodies (body1,body2), the hinge axis that they are connected by
+// w.r.t. body1 (axis), and the initial relative orientation between them
+// (q_initial), return the relative rotation angle. the initial relative
+// orientation corresponds to an angle of zero. if body2 is 0 then measure the
+// angle between body1 and the static frame.
+//
+// this will not return the correct angle if the bodies rotate along any axis
+// other than the given hinge axis.
+static dReal getHingeAngle (dxBody *body1, dxBody *body2, dVector3 axis,
+			    dQuaternion q_initial)
+{
+// get qrel = relative rotation between the two bodies
+dQuaternion qrel;
+if (body2) {
+dQuaternion qq;
+dQMultiply1 (qq,body1->q,body2->q);
+dQMultiply2 (qrel,qq,q_initial);
+}
+else {
+// pretend body2->q is the identity
+dQMultiply3 (qrel,body1->q,q_initial);
+}
+return getHingeAngleFromRelativeQuat (qrel,axis);
+}
+//****************************************************************************
+// dxJointLimitMotor
+void dxJointLimitMotor::init (dxWorld *world)
+{
+vel = 0;
+fmax = 0;
+lostop = -dInfinity;
+histop = dInfinity;
+fudge_factor = REAL(1.0);
+normal_cfm = world->global_cfm;
+stop_erp = world->global_erp;
+stop_cfm = world->global_cfm;
+bounce = 0;
+limit = 0;
+limit_err = 0;
+}
+void dxJointLimitMotor::set (int num, dReal value)
+{
+switch (num) {
+case dParamLoStop:
+lostop = value;
+break;
+case dParamHiStop:
+histop = value;
+break;
+case dParamVel:
+vel = value;
+break;
+case dParamFMax:
+if (value >= 0) fmax = value;
+break;
+case dParamFudgeFactor:
+if (value >= 0 && value <= REAL(1.0)) fudge_factor = value;
+break;
+case dParamBounce:
+bounce = value;
+break;
+case dParamCFM:
+normal_cfm = value;
+break;
+case dParamStopERP:
+stop_erp = value;
+break;
+case dParamStopCFM:
+stop_cfm = value;
+break;
+}
+}
+dReal dxJointLimitMotor::get (int num)
+{
+switch (num) {
+case dParamLoStop: return lostop;
+case dParamHiStop: return histop;
+case dParamVel: return vel;
+case dParamFMax: return fmax;
+case dParamFudgeFactor: return fudge_factor;
+case dParamBounce: return bounce;
+case dParamCFM: return normal_cfm;
+case dParamStopERP: return stop_erp;
+case dParamStopCFM: return stop_cfm;
+default: return 0;
+}
+}
+int dxJointLimitMotor::testRotationalLimit (dReal angle)
+{
+if (angle <= lostop) {
+limit = 1;
+limit_err = angle - lostop;
+return 1;
+}
+else if (angle >= histop) {
+limit = 2;
+limit_err = angle - histop;
+return 1;
+}
+else {
+limit = 0;
+return 0;
+}
+}
+int dxJointLimitMotor::addLimot (dxJoint *joint,
+				 dxJoint::Info2 *info, int row,
+				 const dVector3 ax1, int rotational)
+{
+int srow = row * info->rowskip;
+// if the joint is powered, or has joint limits, add in the extra row
+int powered = fmax > 0;
+if (powered || limit) {
+dReal *J1 = rotational ? info->J1a : info->J1l;
+dReal *J2 = rotational ? info->J2a : info->J2l;
+J1[srow+0] = ax1[0];
+J1[srow+1] = ax1[1];
+J1[srow+2] = ax1[2];
+if (joint->node[1].body) {
+J2[srow+0] = -ax1[0];
+J2[srow+1] = -ax1[1];
+J2[srow+2] = -ax1[2];
+}
+// linear limot torque decoupling step:
+//
+// if this is a linear limot (e.g. from a slider), we have to be careful
+// that the linear constraint forces (+/- ax1) applied to the two bodies
+// do not create a torque couple. in other words, the points that the
+// constraint force is applied at must lie along the same ax1 axis.
+// a torque couple will result in powered or limited slider-jointed free
+// bodies from gaining angular momentum.
+// the solution used here is to apply the constraint forces at the point
+// halfway between the body centers. there is no penalty (other than an
+// extra tiny bit of computation) in doing this adjustment. note that we
+// only need to do this if the constraint connects two bodies.
+dVector3 ltd = {};	// Linear Torque Decoupling vector (a torque)
+if (!rotational && joint->node[1].body) {
+dVector3 c;
+c[0]=dMUL(REAL(0.5),(joint->node[1].body->posr.pos[0]-joint->node[0].body->posr.pos[0]));
+c[1]=dMUL(REAL(0.5),(joint->node[1].body->posr.pos[1]-joint->node[0].body->posr.pos[1]));
+c[2]=dMUL(REAL(0.5),(joint->node[1].body->posr.pos[2]-joint->node[0].body->posr.pos[2]));
+dCROSS (ltd,=,c,ax1);
+info->J1a[srow+0] = ltd[0];
+info->J1a[srow+1] = ltd[1];
+info->J1a[srow+2] = ltd[2];
+info->J2a[srow+0] = ltd[0];
+info->J2a[srow+1] = ltd[1];
+info->J2a[srow+2] = ltd[2];
+}
+// if we're limited low and high simultaneously, the joint motor is
+// ineffective
+if (limit && (lostop == histop)) powered = 0;
+if (powered) {
+info->cfm[row] = normal_cfm;
+if (! limit) {
+	info->c[row] = vel;
+	info->lo[row] = -fmax;
+	info->hi[row] = fmax;
+}
+else {
+	// the joint is at a limit, AND is being powered. if the joint is
+	// being powered into the limit then we apply the maximum motor force
+	// in that direction, because the motor is working against the
+	// immovable limit. if the joint is being powered away from the limit
+	// then we have problems because actually we need *two* lcp
+	// constraints to handle this case. so we fake it and apply some
+	// fraction of the maximum force. the fraction to use can be set as
+	// a fudge factor.
+	dReal fm = fmax;
+	if ((vel > 0) || (vel==0 && limit==2)) fm = -fm;
+	// if we're powering away from the limit, apply the fudge factor
+	if ((limit==1 && vel > 0) || (limit==2 && vel < 0)) fm *= fudge_factor;
+	if (rotational) {
+	  dBodyAddTorque (joint->node[0].body,-dMUL(fm,ax1[0]),-dMUL(fm,ax1[1]),
+			  -dMUL(fm,ax1[2]));
+	  if (joint->node[1].body)
+	    dBodyAddTorque (joint->node[1].body,dMUL(fm,ax1[0]),dMUL(fm,ax1[1]),dMUL(fm,ax1[2]));
+	}
+	else {
+	  dBodyAddForce (joint->node[0].body,-dMUL(fm,ax1[0]),-dMUL(fm,ax1[1]),-dMUL(fm,ax1[2]));
+	  if (joint->node[1].body) {
+	    dBodyAddForce (joint->node[1].body,dMUL(fm,ax1[0]),dMUL(fm,ax1[1]),dMUL(fm,ax1[2]));
+	    // linear limot torque decoupling step: refer to above discussion
+	    dBodyAddTorque (joint->node[0].body,-dMUL(fm,ltd[0]),-dMUL(fm,ltd[1]),
+			    -dMUL(fm,ltd[2]));
+	    dBodyAddTorque (joint->node[1].body,-dMUL(fm,ltd[0]),-dMUL(fm,ltd[1]),
+			    -dMUL(fm,ltd[2]));
+	  }
+	}
+}
+}
+if (limit) {
+dReal k = dMUL(info->fps,stop_erp);
+info->c[row] = -dMUL(k,limit_err);
+info->cfm[row] = stop_cfm;
+if (lostop == histop) {
+	// limited low and high simultaneously
+	info->lo[row] = -dInfinity;
+	info->hi[row] = dInfinity;
+}
+else {
+	if (limit == 1) {
+	  // low limit
+	  info->lo[row] = REAL(0.0);
+	  info->hi[row] = dInfinity;
+	}
+	else {
+	  // high limit
+	  info->lo[row] = -dInfinity;
+	  info->hi[row] = REAL(0.0);
+	}
+	// deal with bounce
+	if (bounce > 0) {
+	  // calculate joint velocity
+	  dReal vel;
+	  if (rotational) {
+	    vel = dDOT(joint->node[0].body->avel,ax1);
+	    if (joint->node[1].body)
+	      vel -= dDOT(joint->node[1].body->avel,ax1);
+	  }
+	  else {
+	    vel = dDOT(joint->node[0].body->lvel,ax1);
+	    if (joint->node[1].body)
+	      vel -= dDOT(joint->node[1].body->lvel,ax1);
+	  }
+	  // only apply bounce if the velocity is incoming, and if the
+	  // resulting c[] exceeds what we already have.
+	  if (limit == 1) {
+	    // low limit
+	    if (vel < 0) {
+	      dReal newc = -dMUL(bounce,vel);
+	      if (newc > info->c[row]) info->c[row] = newc;
+	    }
+	  }
+	  else {
+	    // high limit - all those computations are reversed
+	    if (vel > 0) {
+	      dReal newc = -dMUL(bounce,vel);
+	      if (newc < info->c[row]) info->c[row] = newc;
+	    }
+	  }
+	}
+}
+}
+return 1;
+}
+else return 0;
+}
+//****************************************************************************
+// ball and socket
+static void ballInit (dxJointBall *j)
+{
+dSetZero (j->anchor1,4);
+dSetZero (j->anchor2,4);
+}
+static void ballGetInfo1 (dxJointBall */*j*/, dxJoint::Info1 *info)
+{
+info->m = 3;
+info->nub = 3;
+}
+static void ballGetInfo2 (dxJointBall *joint, dxJoint::Info2 *info)
+{
+setBall (joint,info,joint->anchor1,joint->anchor2);
+}
+EXPORT_C void dJointSetBallAnchor (dJointID j, dReal x, dReal y, dReal z)
+{
+dxJointBall* joint = (dxJointBall*)j;
+setAnchors (joint,x,y,z,joint->anchor1,joint->anchor2);
+}
+EXPORT_C void dJointSetBallAnchor2 (dJointID j, dReal x, dReal y, dReal z)
+{
+dxJointBall* joint = (dxJointBall*)j;
+joint->anchor2[0] = x;
+joint->anchor2[1] = y;
+joint->anchor2[2] = z;
+joint->anchor2[3] = 0;
+}
+EXPORT_C void dJointGetBallAnchor (dJointID j, dVector3 result)
+{
+dxJointBall* joint = (dxJointBall*)j;
+if (joint->flags & dJOINT_REVERSE)
+getAnchor2 (joint,result,joint->anchor2);
+else
+getAnchor (joint,result,joint->anchor1);
+}
+EXPORT_C void dJointGetBallAnchor2 (dJointID j, dVector3 result)
+{
+dxJointBall* joint = (dxJointBall*)j;
+if (joint->flags & dJOINT_REVERSE)
+getAnchor (joint,result,joint->anchor1);
+else
+getAnchor2 (joint,result,joint->anchor2);
+}
+dxJoint::Vtable __dball_vtable = {
+sizeof(dxJointBall),
+(dxJoint::init_fn*) ballInit,
+(dxJoint::getInfo1_fn*) ballGetInfo1,
+(dxJoint::getInfo2_fn*) ballGetInfo2,
+dJointTypeBall};
+//****************************************************************************
+// hinge
+static void hingeInit (dxJointHinge *j)
+{
+dSetZero (j->anchor1,4);
+dSetZero (j->anchor2,4);
+dSetZero (j->axis1,4);
+j->axis1[0] = REAL(1.0);
+dSetZero (j->axis2,4);
+j->axis2[0] = REAL(1.0);
+dSetZero (j->qrel,4);
+j->limot.init (j->world);
+}
+static void hingeGetInfo1 (dxJointHinge *j, dxJoint::Info1 *info)
+{
+info->nub = 5;
+// see if joint is powered
+if (j->limot.fmax > 0)
+info->m = 6;	// powered hinge needs an extra constraint row
+else info->m = 5;
+// see if we're at a joint limit.
+if ((j->limot.lostop >= -dPI || j->limot.histop <= dPI) &&
+j->limot.lostop <= j->limot.histop) {
+dReal angle = getHingeAngle (j->node[0].body,j->node[1].body,j->axis1,
+				 j->qrel);
+if (j->limot.testRotationalLimit (angle)) info->m = 6;
+}
+}
+static void hingeGetInfo2 (dxJointHinge *joint, dxJoint::Info2 *info)
+{
+// set the three ball-and-socket rows
+setBall (joint,info,joint->anchor1,joint->anchor2);
+// set the two hinge rows. the hinge axis should be the only unconstrained
+// rotational axis, the angular velocity of the two bodies perpendicular to
+// the hinge axis should be equal. thus the constraint equations are
+//    p*w1 - p*w2 = 0
+//    q*w1 - q*w2 = 0
+// where p and q are unit vectors normal to the hinge axis, and w1 and w2
+// are the angular velocity vectors of the two bodies.
+dVector3 ax1;  // length 1 joint axis in global coordinates, from 1st body
+dVector3 p,q;  // plane space vectors for ax1
+dMULTIPLY0_331 (ax1,joint->node[0].body->posr.R,joint->axis1);
+dPlaneSpace (ax1,p,q);
+int s3=3*info->rowskip;
+int s4=4*info->rowskip;
+info->J1a[s3+0] = p[0];
+info->J1a[s3+1] = p[1];
+info->J1a[s3+2] = p[2];
+info->J1a[s4+0] = q[0];
+info->J1a[s4+1] = q[1];
+info->J1a[s4+2] = q[2];
+if (joint->node[1].body) {
+info->J2a[s3+0] = -p[0];
+info->J2a[s3+1] = -p[1];
+info->J2a[s3+2] = -p[2];
+info->J2a[s4+0] = -q[0];
+info->J2a[s4+1] = -q[1];
+info->J2a[s4+2] = -q[2];
+}
+// compute the right hand side of the constraint equation. set relative
+// body velocities along p and q to bring the hinge back into alignment.
+// if ax1,ax2 are the unit length hinge axes as computed from body1 and
+// body2, we need to rotate both bodies along the axis u = (ax1 x ax2).
+// if `theta' is the angle between ax1 and ax2, we need an angular velocity
+// along u to cover angle erp*theta in one step :
+//   |angular_velocity| = angle/time = erp*theta / stepsize
+//                      = (erp*fps) * theta
+//    angular_velocity  = |angular_velocity| * (ax1 x ax2) / |ax1 x ax2|
+//                      = (erp*fps) * theta * (ax1 x ax2) / sin(theta)
+// ...as ax1 and ax2 are unit length. if theta is smallish,
+// theta ~= sin(theta), so
+//    angular_velocity  = (erp*fps) * (ax1 x ax2)
+// ax1 x ax2 is in the plane space of ax1, so we project the angular
+// velocity to p and q to find the right hand side.
+dVector3 ax2,b;
+if (joint->node[1].body) {
+dMULTIPLY0_331 (ax2,joint->node[1].body->posr.R,joint->axis2);
+}
+else {
+ax2[0] = joint->axis2[0];
+ax2[1] = joint->axis2[1];
+ax2[2] = joint->axis2[2];
+}
+dCROSS (b,=,ax1,ax2);
+dReal k = dMUL(info->fps,info->erp);
+info->c[3] = dMUL(k,dDOT(b,p));
+info->c[4] = dMUL(k,dDOT(b,q));
+// if the hinge is powered, or has joint limits, add in the stuff
+joint->limot.addLimot (joint,info,5,ax1,1);
+}
+// compute initial relative rotation body1 -> body2, or env -> body1
+static void hingeComputeInitialRelativeRotation (dxJointHinge *joint)
+{
+if (joint->node[0].body) {
+if (joint->node[1].body) {
+dQMultiply1 (joint->qrel,joint->node[0].body->q,joint->node[1].body->q);
+}
+else {
+// set joint->qrel to the transpose of the first body q
+joint->qrel[0] = joint->node[0].body->q[0];
+for (int i=1; i<4; i++) joint->qrel[i] = -joint->node[0].body->q[i];
+}
+}
+}
+EXPORT_C void dJointSetHingeAnchor (dJointID j, dReal x, dReal y, dReal z)
+{
+dxJointHinge* joint = (dxJointHinge*)j;
+setAnchors (joint,x,y,z,joint->anchor1,joint->anchor2);
+hingeComputeInitialRelativeRotation (joint);
+}
+EXPORT_C void dJointSetHingeAnchorDelta (dJointID j, dReal x, dReal y, dReal z, dReal dx, dReal dy, dReal dz)
+{
+dxJointHinge* joint = (dxJointHinge*)j;
+if (joint->node[0].body) {
+dReal q[4];
+q[0] = x - joint->node[0].body->posr.pos[0];
+q[1] = y - joint->node[0].body->posr.pos[1];
+q[2] = z - joint->node[0].body->posr.pos[2];
+q[3] = REAL(0.0);
+dMULTIPLY1_331 (joint->anchor1,joint->node[0].body->posr.R,q);
+if (joint->node[1].body) {
+q[0] = x - joint->node[1].body->posr.pos[0];
+q[1] = y - joint->node[1].body->posr.pos[1];
+q[2] = z - joint->node[1].body->posr.pos[2];
+q[3] = 0;
+dMULTIPLY1_331 (joint->anchor2,joint->node[1].body->posr.R,q);
+}
+else {
+// Move the relative displacement between the passive body and the
+//  anchor in the same direction as the passive body has just moved
+joint->anchor2[0] = x + dx;
+joint->anchor2[1] = y + dy;
+joint->anchor2[2] = z + dz;
+}
+}
+joint->anchor1[3] = 0;
+joint->anchor2[3] = 0;
+hingeComputeInitialRelativeRotation (joint);
+}
+EXPORT_C void dJointSetHingeAxis (dJointID j, dReal x, dReal y, dReal z)
+{
+dxJointHinge* joint = (dxJointHinge*)j;
+setAxes (joint,x,y,z,joint->axis1,joint->axis2);
+hingeComputeInitialRelativeRotation (joint);
+}
+EXPORT_C void dJointGetHingeAnchor (dJointID j, dVector3 result)
+{
+dxJointHinge* joint = (dxJointHinge*)j;
+if (joint->flags & dJOINT_REVERSE)
+getAnchor2 (joint,result,joint->anchor2);
+else
+getAnchor (joint,result,joint->anchor1);
+}
+EXPORT_C void dJointGetHingeAnchor2 (dJointID j, dVector3 result)
+{
+dxJointHinge* joint = (dxJointHinge*)j;
+if (joint->flags & dJOINT_REVERSE)
+getAnchor (joint,result,joint->anchor1);
+else
+getAnchor2 (joint,result,joint->anchor2);
+}
+EXPORT_C void dJointGetHingeAxis (dJointID j, dVector3 result)
+{
+dxJointHinge* joint = (dxJointHinge*)j;
+getAxis (joint,result,joint->axis1);
+}
+EXPORT_C void dJointSetHingeParam (dJointID j, int parameter, dReal value)
+{
+dxJointHinge* joint = (dxJointHinge*)j;
+joint->limot.set (parameter,value);
+}
+EXPORT_C dReal dJointGetHingeParam (dJointID j, int parameter)
+{
+dxJointHinge* joint = (dxJointHinge*)j;
+return joint->limot.get (parameter);
+}
+EXPORT_C dReal dJointGetHingeAngle (dJointID j)
+{
+dxJointHinge* joint = (dxJointHinge*)j;
+if (joint->node[0].body) {
+dReal ang = getHingeAngle (joint->node[0].body,joint->node[1].body,joint->axis1,
+			  joint->qrel);
+	if (joint->flags & dJOINT_REVERSE)
+	   return -ang;
+	else
+	   return ang;
+}
+else return 0;
+}
+EXPORT_C dReal dJointGetHingeAngleRate (dJointID j)
+{
+dxJointHinge* joint = (dxJointHinge*)j;
+if (joint->node[0].body) {
+dVector3 axis;
+dMULTIPLY0_331 (axis,joint->node[0].body->posr.R,joint->axis1);
+dReal rate = dDOT(axis,joint->node[0].body->avel);
+if (joint->node[1].body) rate -= dDOT(axis,joint->node[1].body->avel);
+if (joint->flags & dJOINT_REVERSE) rate = - rate;
+return rate;
+}
+else return 0;
+}
+EXPORT_C void dJointAddHingeTorque (dJointID j, dReal torque)
+{
+dxJointHinge* joint = (dxJointHinge*)j;
+dVector3 axis;
+if (joint->flags & dJOINT_REVERSE)
+torque = -torque;
+getAxis (joint,axis,joint->axis1);
+axis[0] = dMUL(axis[0],torque);
+axis[1] = dMUL(axis[1],torque);
+axis[2] = dMUL(axis[2],torque);
+if (joint->node[0].body != 0)
+dBodyAddTorque (joint->node[0].body, axis[0], axis[1], axis[2]);
+if (joint->node[1].body != 0)
+dBodyAddTorque(joint->node[1].body, -axis[0], -axis[1], -axis[2]);
+}
+dxJoint::Vtable __dhinge_vtable = {
+sizeof(dxJointHinge),
+(dxJoint::init_fn*) hingeInit,
+(dxJoint::getInfo1_fn*) hingeGetInfo1,
+(dxJoint::getInfo2_fn*) hingeGetInfo2,
+dJointTypeHinge};
+//****************************************************************************
+// slider
+static void sliderInit (dxJointSlider *j)
+{
+dSetZero (j->axis1,4);
+j->axis1[0] = REAL(1.0);
+dSetZero (j->qrel,4);
+dSetZero (j->offset,4);
+j->limot.init (j->world);
+}
+EXPORT_C dReal dJointGetSliderPosition (dJointID j)
+{
+dxJointSlider* joint = (dxJointSlider*)j;
+// get axis1 in global coordinates
+dVector3 ax1,q;
+dMULTIPLY0_331 (ax1,joint->node[0].body->posr.R,joint->axis1);
+if (joint->node[1].body) {
+// get body2 + offset point in global coordinates
+dMULTIPLY0_331 (q,joint->node[1].body->posr.R,joint->offset);
+for (int i=0; i<3; i++) q[i] = joint->node[0].body->posr.pos[i] - q[i] -
+			      joint->node[1].body->posr.pos[i];
+}
+else {
+for (int i=0; i<3; i++) q[i] = joint->node[0].body->posr.pos[i] -
+			      joint->offset[i];
+}
+return dDOT(ax1,q);
+}
+EXPORT_C dReal dJointGetSliderPositionRate (dJointID j)
+{
+dxJointSlider* joint = (dxJointSlider*)j;
+// get axis1 in global coordinates
+dVector3 ax1;
+dMULTIPLY0_331 (ax1,joint->node[0].body->posr.R,joint->axis1);
+if (joint->node[1].body) {
+return dDOT(ax1,joint->node[0].body->lvel) -
+dDOT(ax1,joint->node[1].body->lvel);
+}
+else {
+return dDOT(ax1,joint->node[0].body->lvel);
+}
+}
+static void sliderGetInfo1 (dxJointSlider *j, dxJoint::Info1 *info)
+{
+info->nub = 5;
+// see if joint is powered
+if (j->limot.fmax > 0)
+info->m = 6;	// powered slider needs an extra constraint row
+else info->m = 5;
+// see if we're at a joint limit.
+j->limot.limit = 0;
+if ((j->limot.lostop > -dInfinity || j->limot.histop < dInfinity) &&
+j->limot.lostop <= j->limot.histop) {
+// measure joint position
+dReal pos = dJointGetSliderPosition (j);
+if (pos <= j->limot.lostop) {
+j->limot.limit = 1;
+j->limot.limit_err = pos - j->limot.lostop;
+info->m = 6;
+}
+else if (pos >= j->limot.histop) {
+j->limot.limit = 2;
+j->limot.limit_err = pos - j->limot.histop;
+info->m = 6;
+}
+}
+}
+static void sliderGetInfo2 (dxJointSlider *joint, dxJoint::Info2 *info)
+{
+int i,s = info->rowskip;
+int s3=3*s,s4=4*s;
+// pull out pos and R for both bodies. also get the `connection'
+// vector pos2-pos1.
+dReal *pos1,*pos2,*R1,*R2;
+dVector3 c;
+pos1 = joint->node[0].body->posr.pos;
+R1 = joint->node[0].body->posr.R;
+if (joint->node[1].body) {
+pos2 = joint->node[1].body->posr.pos;
+R2 = joint->node[1].body->posr.R;
+for (i=0; i<3; i++) c[i] = pos2[i] - pos1[i];
+}
+else {
+pos2 = 0;
+R2 = 0;
+}
+// 3 rows to make body rotations equal
+setFixedOrientation(joint, info, joint->qrel, 0);
+// remaining two rows. we want: vel2 = vel1 + w1 x c ... but this would
+// result in three equations, so we project along the planespace vectors
+// so that sliding along the slider axis is disregarded. for symmetry we
+// also substitute (w1+w2)/2 for w1, as w1 is supposed to equal w2.
+dVector3 ax1;	// joint axis in global coordinates (unit length)
+dVector3 p,q;	// plane space of ax1
+dMULTIPLY0_331 (ax1,R1,joint->axis1);
+dPlaneSpace (ax1,p,q);
+if (joint->node[1].body) {
+dVector3 tmp;
+dCROSSMUL (tmp, = ,c,p);
+for (i=0; i<3; i++) info->J1a[s3+i] = tmp[i];
+for (i=0; i<3; i++) info->J2a[s3+i] = tmp[i];
+dCROSSMUL (tmp, = ,c,q);
+for (i=0; i<3; i++) info->J1a[s4+i] = tmp[i];
+for (i=0; i<3; i++) info->J2a[s4+i] = tmp[i];
+for (i=0; i<3; i++) info->J2l[s3+i] = -p[i];
+for (i=0; i<3; i++) info->J2l[s4+i] = -q[i];
+}
+for (i=0; i<3; i++) info->J1l[s3+i] = p[i];
+for (i=0; i<3; i++) info->J1l[s4+i] = q[i];
+// compute last two elements of right hand side. we want to align the offset
+// point (in body 2's frame) with the center of body 1.
+dReal k = dMUL(info->fps,info->erp);
+if (joint->node[1].body) {
+dVector3 ofs;		// offset point in global coordinates
+dMULTIPLY0_331 (ofs,R2,joint->offset);
+for (i=0; i<3; i++) c[i] += ofs[i];
+info->c[3] = dMUL(k,dDOT(p,c));
+info->c[4] = dMUL(k,dDOT(q,c));
+}
+else {
+dVector3 ofs;		// offset point in global coordinates
+for (i=0; i<3; i++) ofs[i] = joint->offset[i] - pos1[i];
+info->c[3] = dMUL(k,dDOT(p,ofs));
+info->c[4] = dMUL(k,dDOT(q,ofs));
+}
+// if the slider is powered, or has joint limits, add in the extra row
+joint->limot.addLimot (joint,info,5,ax1,0);
+}
+EXPORT_C void dJointSetSliderAxis (dJointID j, dReal x, dReal y, dReal z)
+{
+dxJointSlider* joint = (dxJointSlider*)j;
+int i;
+setAxes (joint,x,y,z,joint->axis1,0);
+// compute initial relative rotation body1 -> body2, or env -> body1
+// also compute center of body1 w.r.t body 2
+if (joint->node[1].body) {
+dQMultiply1 (joint->qrel,joint->node[0].body->q,joint->node[1].body->q);
+dVector3 c;
+for (i=0; i<3; i++)
+c[i] = joint->node[0].body->posr.pos[i] - joint->node[1].body->posr.pos[i];
+dMULTIPLY1_331 (joint->offset,joint->node[1].body->posr.R,c);
+}
+else {
+// set joint->qrel to the transpose of the first body's q
+joint->qrel[0] = joint->node[0].body->q[0];
+for (i=1; i<4; i++) joint->qrel[i] = -joint->node[0].body->q[i];
+for (i=0; i<3; i++) joint->offset[i] = joint->node[0].body->posr.pos[i];
+}
+}
+EXPORT_C void dJointSetSliderAxisDelta (dJointID j, dReal x, dReal y, dReal z, dReal dx, dReal dy, dReal dz)
+{
+dxJointSlider* joint = (dxJointSlider*)j;
+int i;
+setAxes (joint,x,y,z,joint->axis1,0);
+// compute initial relative rotation body1 -> body2, or env -> body1
+// also compute center of body1 w.r.t body 2
+if (joint->node[1].body) {
+dQMultiply1 (joint->qrel,joint->node[0].body->q,joint->node[1].body->q);
+dVector3 c;
+for (i=0; i<3; i++)
+c[i] = joint->node[0].body->posr.pos[i] - joint->node[1].body->posr.pos[i];
+dMULTIPLY1_331 (joint->offset,joint->node[1].body->posr.R,c);
+}
+else {
+// set joint->qrel to the transpose of the first body's q
+joint->qrel[0] = joint->node[0].body->q[0];
+for (i=1; i<4; i++)
+joint->qrel[i] = -joint->node[0].body->q[i];
+joint->offset[0] = joint->node[0].body->posr.pos[0] + dx;
+joint->offset[1] = joint->node[0].body->posr.pos[1] + dy;
+joint->offset[2] = joint->node[0].body->posr.pos[2] + dz;
+}
+}
+EXPORT_C void dJointGetSliderAxis (dJointID j, dVector3 result)
+{
+dxJointSlider* joint = (dxJointSlider*)j;
+getAxis (joint,result,joint->axis1);
+}
+EXPORT_C void dJointSetSliderParam (dJointID j, int parameter, dReal value)
+{
+dxJointSlider* joint = (dxJointSlider*)j;
+joint->limot.set (parameter,value);
+}
+EXPORT_C dReal dJointGetSliderParam (dJointID j, int parameter)
+{
+dxJointSlider* joint = (dxJointSlider*)j;
+return joint->limot.get (parameter);
+}
+EXPORT_C void dJointAddSliderForce (dJointID j, dReal force)
+{
+dxJointSlider* joint = (dxJointSlider*)j;
+dVector3 axis;
+if (joint->flags & dJOINT_REVERSE)
+force -= force;
+getAxis (joint,axis,joint->axis1);
+axis[0] = dMUL(axis[0],force);
+axis[1] = dMUL(axis[1],force);
+axis[2] = dMUL(axis[2],force);
+if (joint->node[0].body != 0)
+dBodyAddForce (joint->node[0].body,axis[0],axis[1],axis[2]);
+if (joint->node[1].body != 0)
+dBodyAddForce(joint->node[1].body, -axis[0], -axis[1], -axis[2]);
+if (joint->node[0].body != 0 && joint->node[1].body != 0) {
+// linear torque decoupling:
+// we have to compensate the torque, that this slider force may generate
+// if body centers are not aligned along the slider axis
+dVector3 ltd; // Linear Torque Decoupling vector (a torque)
+dVector3 c;
+c[0]=dMUL(REAL(0.5),(joint->node[1].body->posr.pos[0]-joint->node[0].body->posr.pos[0]));
+c[1]=dMUL(REAL(0.5),(joint->node[1].body->posr.pos[1]-joint->node[0].body->posr.pos[1]));
+c[2]=dMUL(REAL(0.5),(joint->node[1].body->posr.pos[2]-joint->node[0].body->posr.pos[2]));
+dCROSS (ltd,=,c,axis);
+dBodyAddTorque (joint->node[0].body,ltd[0],ltd[1], ltd[2]);
+dBodyAddTorque (joint->node[1].body,ltd[0],ltd[1], ltd[2]);
+}
+}
+dxJoint::Vtable __dslider_vtable = {
+sizeof(dxJointSlider),
+(dxJoint::init_fn*) sliderInit,
+(dxJoint::getInfo1_fn*) sliderGetInfo1,
+(dxJoint::getInfo2_fn*) sliderGetInfo2,
+dJointTypeSlider};
+//****************************************************************************
+// contact
+static void contactInit (dxJointContact */*j*/)
+{
+}
+static void contactGetInfo1 (dxJointContact *j, dxJoint::Info1 *info)
+{
+// make sure mu's >= 0, then calculate number of constraint rows and number
+// of unbounded rows.
+int m = 1, nub=0;
+if (j->contact.surface.mu < 0) j->contact.surface.mu = 0;
+if (j->contact.surface.mode & dContactMu2) {
+if (j->contact.surface.mu > 0) m++;
+if (j->contact.surface.mu2 < 0) j->contact.surface.mu2 = 0;
+if (j->contact.surface.mu2 > 0) m++;
+if (j->contact.surface.mu  == dInfinity) nub ++;
+if (j->contact.surface.mu2 == dInfinity) nub ++;
+}
+else {
+if (j->contact.surface.mu > REAL(0.0)) m += 2;
+if (j->contact.surface.mu == dInfinity) nub += 2;
+}
+j->the_m = m;
+info->m = m;
+info->nub = nub;
+}
+static void contactGetInfo2 (dxJointContact *j, dxJoint::Info2 *info)
+{
+int s = info->rowskip;
+int s2 = 2*s;
+// get normal, with sign adjusted for body1/body2 polarity
+dVector3 normal;
+if (j->flags & dJOINT_REVERSE) {
+normal[0] = - j->contact.geom.normal[0];
+normal[1] = - j->contact.geom.normal[1];
+normal[2] = - j->contact.geom.normal[2];
+}
+else {
+normal[0] = j->contact.geom.normal[0];
+normal[1] = j->contact.geom.normal[1];
+normal[2] = j->contact.geom.normal[2];
+}
+normal[3] = 0;	// @@@ hmmm
+// c1,c2 = contact points with respect to body PORs
+dVector3 c1,c2 = {};
+c1[0] = j->contact.geom.pos[0] - j->node[0].body->posr.pos[0];
+c1[1] = j->contact.geom.pos[1] - j->node[0].body->posr.pos[1];
+c1[2] = j->contact.geom.pos[2] - j->node[0].body->posr.pos[2];
+// set jacobian for normal
+info->J1l[0] = normal[0];
+info->J1l[1] = normal[1];
+info->J1l[2] = normal[2];
+dCROSS (info->J1a,=,c1,normal);
+if (j->node[1].body) {
+c2[0] = j->contact.geom.pos[0] - j->node[1].body->posr.pos[0];
+c2[1] = j->contact.geom.pos[1] - j->node[1].body->posr.pos[1];
+c2[2] = j->contact.geom.pos[2] - j->node[1].body->posr.pos[2];
+info->J2l[0] = -normal[0];
+info->J2l[1] = -normal[1];
+info->J2l[2] = -normal[2];
+dCROSS (info->J2a,= -,c2,normal);
+}
+// set right hand side and cfm value for normal
+dReal erp = info->erp;
+if (j->contact.surface.mode & dContactSoftERP)
+erp = j->contact.surface.soft_erp;
+dReal k = dMUL(info->fps,erp);
+dReal depth = j->contact.geom.depth - j->world->contactp.min_depth;
+if (depth < 0) depth = 0;
+const dReal maxvel = j->world->contactp.max_vel;
+info->c[0] = dMUL(k,depth);
+if (info->c[0] > maxvel)
+info->c[0] = maxvel;
+if (j->contact.surface.mode & dContactSoftCFM)
+info->cfm[0] = j->contact.surface.soft_cfm;
+// deal with bounce
+if (j->contact.surface.mode & dContactBounce) {
+// calculate outgoing velocity (-ve for incoming contact)
+dReal outgoing = dDOT(info->J1l,j->node[0].body->lvel) +
+dDOT(info->J1a,j->node[0].body->avel);
+if (j->node[1].body) {
+outgoing += dDOT(info->J2l,j->node[1].body->lvel) +
+	dDOT(info->J2a,j->node[1].body->avel);
+}
+// only apply bounce if the outgoing velocity is greater than the
+// threshold, and if the resulting c[0] exceeds what we already have.
+if (j->contact.surface.bounce_vel >= 0 &&
+	(-outgoing) > j->contact.surface.bounce_vel) {
+dReal newc = - dMUL(j->contact.surface.bounce,outgoing);
+if (newc > info->c[0]) info->c[0] = newc;
+}
+}
+// set LCP limits for normal
+info->lo[0] = 0;
+info->hi[0] = dInfinity;
+// now do jacobian for tangential forces
+dVector3 t1,t2;	// two vectors tangential to normal
+// first friction direction
+if (j->the_m >= 2) {
+if (j->contact.surface.mode & dContactFDir1) {	// use fdir1 ?
+t1[0] = j->contact.fdir1[0];
+t1[1] = j->contact.fdir1[1];
+t1[2] = j->contact.fdir1[2];
+dCROSS (t2,=,normal,t1);
+}
+else {
+dPlaneSpace (normal,t1,t2);
+}
+info->J1l[s+0] = t1[0];
+info->J1l[s+1] = t1[1];
+info->J1l[s+2] = t1[2];
+dCROSS (info->J1a+s,=,c1,t1);
+if (j->node[1].body) {
+info->J2l[s+0] = -t1[0];
+info->J2l[s+1] = -t1[1];
+info->J2l[s+2] = -t1[2];
+dCROSS (info->J2a+s,= -,c2,t1);
+}
+// set right hand side
+if (j->contact.surface.mode & dContactMotion1) {
+info->c[1] = j->contact.surface.motion1;
+}
+// set LCP bounds and friction index. this depends on the approximation
+// mode
+info->lo[1] = -j->contact.surface.mu;
+info->hi[1] = j->contact.surface.mu;
+if (j->contact.surface.mode & dContactApprox1_1) info->findex[1] = 0;
+// set slip (constraint force mixing)
+if (j->contact.surface.mode & dContactSlip1)
+info->cfm[1] = j->contact.surface.slip1;
+}
+// second friction direction
+if (j->the_m >= 3) {
+info->J1l[s2+0] = t2[0];
+info->J1l[s2+1] = t2[1];
+info->J1l[s2+2] = t2[2];
+dCROSS (info->J1a+s2,=,c1,t2);
+if (j->node[1].body) {
+info->J2l[s2+0] = -t2[0];
+info->J2l[s2+1] = -t2[1];
+info->J2l[s2+2] = -t2[2];
+dCROSS (info->J2a+s2,= -,c2,t2);
+}
+// set right hand side
+if (j->contact.surface.mode & dContactMotion2) {
+info->c[2] = j->contact.surface.motion2;
+}
+// set LCP bounds and friction index. this depends on the approximation
+// mode
+if (j->contact.surface.mode & dContactMu2) {
+info->lo[2] = -j->contact.surface.mu2;
+info->hi[2] = j->contact.surface.mu2;
+}
+else {
+info->lo[2] = -j->contact.surface.mu;
+info->hi[2] = j->contact.surface.mu;
+}
+if (j->contact.surface.mode & dContactApprox1_2) info->findex[2] = 0;
+// set slip (constraint force mixing)
+if (j->contact.surface.mode & dContactSlip2)
+info->cfm[2] = j->contact.surface.slip2;
+}
+}
+dxJoint::Vtable __dcontact_vtable = {
+sizeof(dxJointContact),
+(dxJoint::init_fn*) contactInit,
+(dxJoint::getInfo1_fn*) contactGetInfo1,
+(dxJoint::getInfo2_fn*) contactGetInfo2,
+dJointTypeContact};
+//****************************************************************************
+// hinge 2. note that this joint must be attached to two bodies for it to work
+static dReal measureHinge2Angle (dxJointHinge2 *joint)
+{
+dVector3 a1,a2;
+dMULTIPLY0_331 (a1,joint->node[1].body->posr.R,joint->axis2);
+dMULTIPLY1_331 (a2,joint->node[0].body->posr.R,a1);
+dReal x = dDOT(joint->v1,a2);
+dReal y = dDOT(joint->v2,a2);
+return -dArcTan2 (y,x);
+}
+static void hinge2Init (dxJointHinge2 *j)
+{
+dSetZero (j->anchor1,4);
+dSetZero (j->anchor2,4);
+dSetZero (j->axis1,4);
+j->axis1[0] = REAL(1.0);
+dSetZero (j->axis2,4);
+j->axis2[1] = REAL(1.0);
+j->c0 = 0;
+j->s0 = 0;
+dSetZero (j->v1,4);
+j->v1[0] = REAL(1.0);
+dSetZero (j->v2,4);
+j->v2[1] = REAL(1.0);
+j->limot1.init (j->world);
+j->limot2.init (j->world);
+j->susp_erp = j->world->global_erp;
+j->susp_cfm = j->world->global_cfm;
+j->flags |= dJOINT_TWOBODIES;
+}
+static void hinge2GetInfo1 (dxJointHinge2 *j, dxJoint::Info1 *info)
+{
+info->m = 4;
+info->nub = 4;
+// see if we're powered or at a joint limit for axis 1
+int atlimit=0;
+if ((j->limot1.lostop >= -dPI || j->limot1.histop <= dPI) &&
+j->limot1.lostop <= j->limot1.histop) {
+dReal angle = measureHinge2Angle (j);
+if (j->limot1.testRotationalLimit (angle)) atlimit = 1;
+}
+if (atlimit || j->limot1.fmax > 0) info->m++;
+// see if we're powering axis 2 (we currently never limit this axis)
+j->limot2.limit = 0;
+if (j->limot2.fmax > 0) info->m++;
+}
+// macro that computes ax1,ax2 = axis 1 and 2 in global coordinates (they are
+// relative to body 1 and 2 initially) and then computes the constrained
+// rotational axis as the cross product of ax1 and ax2.
+// the sin and cos of the angle between axis 1 and 2 is computed, this comes
+// from dot and cross product rules.
+#define HINGE2_GET_AXIS_INFO(axis,sin_angle,cos_angle) \
+dVector3 ax1,ax2; \
+dMULTIPLY0_331 (ax1,joint->node[0].body->posr.R,joint->axis1); \
+dMULTIPLY0_331 (ax2,joint->node[1].body->posr.R,joint->axis2); \
+dCROSS (axis,=,ax1,ax2); \
+sin_angle = dSqrt (dMUL(axis[0],axis[0]) + dMUL(axis[1],axis[1]) + dMUL(axis[2],axis[2])); \
+cos_angle = dDOT (ax1,ax2);
+static void hinge2GetInfo2 (dxJointHinge2 *joint, dxJoint::Info2 *info)
+{
+// get information we need to set the hinge row
+dReal s,c;
+dVector3 q;
+HINGE2_GET_AXIS_INFO (q,s,c);
+dNormalize3 (q);		// @@@ quicker: divide q by s ?
+// set the three ball-and-socket rows (aligned to the suspension axis ax1)
+setBall2 (joint,info,joint->anchor1,joint->anchor2,ax1,joint->susp_erp);
+// set the hinge row
+int s3=3*info->rowskip;
+info->J1a[s3+0] = q[0];
+info->J1a[s3+1] = q[1];
+info->J1a[s3+2] = q[2];
+if (joint->node[1].body) {
+info->J2a[s3+0] = -q[0];
+info->J2a[s3+1] = -q[1];
+info->J2a[s3+2] = -q[2];
+}
+// compute the right hand side for the constrained rotational DOF.
+// axis 1 and axis 2 are separated by an angle `theta'. the desired
+// separation angle is theta0. sin(theta0) and cos(theta0) are recorded
+// in the joint structure. the correcting angular velocity is:
+//   |angular_velocity| = angle/time = erp*(theta0-theta) / stepsize
+//                      = (erp*fps) * (theta0-theta)
+// (theta0-theta) can be computed using the following small-angle-difference
+// approximation:
+//   theta0-theta ~= tan(theta0-theta)
+//                 = sin(theta0-theta)/cos(theta0-theta)
+//                 = (c*s0 - s*c0) / (c*c0 + s*s0)
+//                 = c*s0 - s*c0         assuming c*c0 + s*s0 ~= 1
+// where c = cos(theta), s = sin(theta)
+//       c0 = cos(theta0), s0 = sin(theta0)
+dReal k = dMUL(info->fps,info->erp);
+info->c[3] = dMUL(k,(dMUL(joint->c0,s) - dMUL(joint->s0,c)));
+// if the axis1 hinge is powered, or has joint limits, add in more stuff
+int row = 4 + joint->limot1.addLimot (joint,info,4,ax1,1);
+// if the axis2 hinge is powered, add in more stuff
+joint->limot2.addLimot (joint,info,row,ax2,1);
+// set parameter for the suspension
+info->cfm[0] = joint->susp_cfm;
+}
+// compute vectors v1 and v2 (embedded in body1), used to measure angle
+// between body 1 and body 2
+static void makeHinge2V1andV2 (dxJointHinge2 *joint)
+{
+if (joint->node[0].body) {
+// get axis 1 and 2 in global coords
+dVector3 ax1,ax2,v;
+dMULTIPLY0_331 (ax1,joint->node[0].body->posr.R,joint->axis1);
+dMULTIPLY0_331 (ax2,joint->node[1].body->posr.R,joint->axis2);
+// don't do anything if the axis1 or axis2 vectors are zero or the same
+if ((ax1[0]==0 && ax1[1]==0 && ax1[2]==0 ||
+	(ax2[0]==0) && ax2[1]==0 && ax2[2]==0) ||
+	(ax1[0]==ax2[0] && ax1[1]==ax2[1] && ax1[2]==ax2[2])) return;
+// modify axis 2 so it's perpendicular to axis 1
+dReal k = dDOT(ax1,ax2);
+for (int i=0; i<3; i++) ax2[i] -= dMUL(k,ax1[i]);
+dNormalize3 (ax2);
+// make v1 = modified axis2, v2 = axis1 x (modified axis2)
+dCROSS (v,=,ax1,ax2);
+dMULTIPLY1_331 (joint->v1,joint->node[0].body->posr.R,ax2);
+dMULTIPLY1_331 (joint->v2,joint->node[0].body->posr.R,v);
+}
+}
+EXPORT_C void dJointSetHinge2Anchor (dJointID j, dReal x, dReal y, dReal z)
+{
+dxJointHinge2* joint = (dxJointHinge2*)j;
+setAnchors (joint,x,y,z,joint->anchor1,joint->anchor2);
+makeHinge2V1andV2 (joint);
+}
+EXPORT_C void dJointSetHinge2Axis1 (dJointID j, dReal x, dReal y, dReal z)
+{
+dxJointHinge2* joint = (dxJointHinge2*)j;
+if (joint->node[0].body) {
+dReal q[4];
+q[0] = x;
+q[1] = y;
+q[2] = z;
+q[3] = 0;
+dNormalize3 (q);
+dMULTIPLY1_331 (joint->axis1,joint->node[0].body->posr.R,q);
+joint->axis1[3] = 0;
+// compute the sin and cos of the angle between axis 1 and axis 2
+dVector3 ax;
+HINGE2_GET_AXIS_INFO(ax,joint->s0,joint->c0);
+}
+makeHinge2V1andV2 (joint);
+}
+EXPORT_C void dJointSetHinge2Axis2 (dJointID j, dReal x, dReal y, dReal z)
+{
+dxJointHinge2* joint = (dxJointHinge2*)j;
+if (joint->node[1].body) {
+dReal q[4];
+q[0] = x;
+q[1] = y;
+q[2] = z;
+q[3] = 0;
+dNormalize3 (q);
+dMULTIPLY1_331 (joint->axis2,joint->node[1].body->posr.R,q);
+joint->axis1[3] = 0;
+// compute the sin and cos of the angle between axis 1 and axis 2
+dVector3 ax;
+HINGE2_GET_AXIS_INFO(ax,joint->s0,joint->c0);
+}
+makeHinge2V1andV2 (joint);
+}
+EXPORT_C void dJointSetHinge2Param (dJointID j, int parameter, dReal value)
+{
+dxJointHinge2* joint = (dxJointHinge2*)j;
+if ((parameter & 0xff00) == 0x100) {
+joint->limot2.set (parameter & 0xff,value);
+}
+else {
+if (parameter == dParamSuspensionERP) joint->susp_erp = value;
+else if (parameter == dParamSuspensionCFM) joint->susp_cfm = value;
+else joint->limot1.set (parameter,value);
+}
+}
+EXPORT_C void dJointGetHinge2Anchor (dJointID j, dVector3 result)
+{
+dxJointHinge2* joint = (dxJointHinge2*)j;
+if (joint->flags & dJOINT_REVERSE)
+getAnchor2 (joint,result,joint->anchor2);
+else
+getAnchor (joint,result,joint->anchor1);
+}
+EXPORT_C void dJointGetHinge2Anchor2 (dJointID j, dVector3 result)
+{
+dxJointHinge2* joint = (dxJointHinge2*)j;
+if (joint->flags & dJOINT_REVERSE)
+getAnchor (joint,result,joint->anchor1);
+else
+getAnchor2 (joint,result,joint->anchor2);
+}
+EXPORT_C void dJointGetHinge2Axis1 (dJointID j, dVector3 result)
+{
+dxJointHinge2* joint = (dxJointHinge2*)j;
+if (joint->node[0].body) {
+dMULTIPLY0_331 (result,joint->node[0].body->posr.R,joint->axis1);
+}
+}
+EXPORT_C void dJointGetHinge2Axis2 (dJointID j, dVector3 result)
+{
+dxJointHinge2* joint = (dxJointHinge2*)j;
+if (joint->node[1].body) {
+dMULTIPLY0_331 (result,joint->node[1].body->posr.R,joint->axis2);
+}
+}
+EXPORT_C dReal dJointGetHinge2Param (dJointID j, int parameter)
+{
+dxJointHinge2* joint = (dxJointHinge2*)j;
+if ((parameter & 0xff00) == 0x100) {
+return joint->limot2.get (parameter & 0xff);
+}
+else {
+if (parameter == dParamSuspensionERP) return joint->susp_erp;
+else if (parameter == dParamSuspensionCFM) return joint->susp_cfm;
+else return joint->limot1.get (parameter);
+}
+}
+EXPORT_C dReal dJointGetHinge2Angle1 (dJointID j)
+{
+dxJointHinge2* joint = (dxJointHinge2*)j;
+if (joint->node[0].body) return measureHinge2Angle (joint);
+else return 0;
+}
+EXPORT_C dReal dJointGetHinge2Angle1Rate (dJointID j)
+{
+dxJointHinge2* joint = (dxJointHinge2*)j;
+if (joint->node[0].body) {
+dVector3 axis;
+dMULTIPLY0_331 (axis,joint->node[0].body->posr.R,joint->axis1);
+dReal rate = dDOT(axis,joint->node[0].body->avel);
+if (joint->node[1].body) rate -= dDOT(axis,joint->node[1].body->avel);
+return rate;
+}
+else return 0;
+}
+EXPORT_C dReal dJointGetHinge2Angle2Rate (dJointID j)
+{
+dxJointHinge2* joint = (dxJointHinge2*)j;
+if (joint->node[0].body && joint->node[1].body) {
+dVector3 axis;
+dMULTIPLY0_331 (axis,joint->node[1].body->posr.R,joint->axis2);
+dReal rate = dDOT(axis,joint->node[0].body->avel);
+if (joint->node[1].body) rate -= dDOT(axis,joint->node[1].body->avel);
+return rate;
+}
+else return 0;
+}
+EXPORT_C void dJointAddHinge2Torques (dJointID j, dReal torque1, dReal torque2)
+{
+dxJointHinge2* joint = (dxJointHinge2*)j;
+dVector3 axis1, axis2;
+if (joint->node[0].body && joint->node[1].body) {
+dMULTIPLY0_331 (axis1,joint->node[0].body->posr.R,joint->axis1);
+dMULTIPLY0_331 (axis2,joint->node[1].body->posr.R,joint->axis2);
+axis1[0] = dMUL(axis1[0],torque1) + dMUL(axis2[0],torque2);
+axis1[1] = dMUL(axis1[1],torque1) + dMUL(axis2[1],torque2);
+axis1[2] = dMUL(axis1[2],torque1) + dMUL(axis2[2],torque2);
+dBodyAddTorque (joint->node[0].body,axis1[0],axis1[1],axis1[2]);
+dBodyAddTorque(joint->node[1].body, -axis1[0], -axis1[1], -axis1[2]);
+}
+}
+dxJoint::Vtable __dhinge2_vtable = {
+sizeof(dxJointHinge2),
+(dxJoint::init_fn*) hinge2Init,
+(dxJoint::getInfo1_fn*) hinge2GetInfo1,
+(dxJoint::getInfo2_fn*) hinge2GetInfo2,
+dJointTypeHinge2};
+//****************************************************************************
+// universal
+// I just realized that the universal joint is equivalent to a hinge 2 joint with
+// perfectly stiff suspension.  By comparing the hinge 2 implementation to
+// the universal implementation, you may be able to improve this
+// implementation (or, less likely, the hinge2 implementation).
+static void universalInit (dxJointUniversal *j)
+{
+dSetZero (j->anchor1,4);
+dSetZero (j->anchor2,4);
+dSetZero (j->axis1,4);
+j->axis1[0] = REAL(1.0);
+dSetZero (j->axis2,4);
+j->axis2[1] = REAL(1.0);
+dSetZero(j->qrel1,4);
+dSetZero(j->qrel2,4);
+j->limot1.init (j->world);
+j->limot2.init (j->world);
+}
+static void getUniversalAxes(dxJointUniversal *joint, dVector3 ax1, dVector3 ax2)
+{
+// This says "ax1 = joint->node[0].body->posr.R * joint->axis1"
+dMULTIPLY0_331 (ax1,joint->node[0].body->posr.R,joint->axis1);
+if (joint->node[1].body) {
+dMULTIPLY0_331 (ax2,joint->node[1].body->posr.R,joint->axis2);
+}
+else {
+ax2[0] = joint->axis2[0];
+ax2[1] = joint->axis2[1];
+ax2[2] = joint->axis2[2];
+}
+}
+static void getUniversalAngles(dxJointUniversal *joint, dReal *angle1, dReal *angle2)
+{
+if (joint->node[0].body)
+{
+// length 1 joint axis in global coordinates, from each body
+dVector3 ax1, ax2;
+dMatrix3 R;
+dQuaternion qcross, qq, qrel;
+getUniversalAxes (joint,ax1,ax2);
+// It should be possible to get both angles without explicitly
+// constructing the rotation matrix of the cross.  Basically,
+// orientation of the cross about axis1 comes from body 2,
+// about axis 2 comes from body 1, and the perpendicular
+// axis can come from the two bodies somehow.  (We don't really
+// want to assume it's 90 degrees, because in general the
+// constraints won't be perfectly satisfied, or even very well
+// satisfied.)
+//
+// However, we'd need a version of getHingeAngleFromRElativeQuat()
+// that CAN handle when its relative quat is rotated along a direction
+// other than the given axis.  What I have here works,
+// although it's probably much slower than need be.
+dRFrom2Axes (R, ax1[0], ax1[1], ax1[2], ax2[0], ax2[1], ax2[2]);
+dRtoQ (R, qcross);
+// This code is essentialy the same as getHingeAngle(), see the comments
+// there for details.
+// get qrel = relative rotation between node[0] and the cross
+dQMultiply1 (qq, joint->node[0].body->q, qcross);
+dQMultiply2 (qrel, qq, joint->qrel1);
+*angle1 = getHingeAngleFromRelativeQuat(qrel, joint->axis1);
+// This is equivalent to
+// dRFrom2Axes(R, ax2[0], ax2[1], ax2[2], ax1[0], ax1[1], ax1[2]);
+// You see that the R is constructed from the same 2 axis as for angle1
+// but the first and second axis are swapped.
+// So we can take the first R and rapply a rotation to it.
+// The rotation is around the axis between the 2 axes (ax1 and ax2).
+// We do a rotation of 180deg.
+dQuaternion qcross2;
+// Find the vector between ax1 and ax2 (i.e. in the middle)
+// We need to turn around this vector by 180deg
+// The 2 axes should be normalize so to find the vector between the 2.
+// Add and devide by 2 then normalize or simply normalize
+//    ax2
+//    ^
+//    |
+//    |
+///   *------------> ax1
+//    We want the vector a 45deg
+//
+// N.B. We don't need to normalize the ax1 and ax2 since there are
+//      normalized when we set them.
+// We set the quaternion q = [cos(theta), dir*sin(theta)] = [w, x, y, Z]
+qrel[0] = 0;                // equivalent to cos(Pi/2)
+qrel[1] = ax1[0] + ax2[0];  // equivalent to x*sin(Pi/2); since sin(Pi/2) = 1
+qrel[2] = ax1[1] + ax2[1];
+qrel[3] = ax1[2] + ax2[2];
+dReal l = dRecip(dSqrt(dMUL(qrel[1],qrel[1]) + dMUL(qrel[2],qrel[2]) + dMUL(qrel[3],qrel[3])));
+qrel[1] = dMUL(qrel[1],l);
+qrel[2] = dMUL(qrel[2],l);
+qrel[3] = dMUL(qrel[3],l);
+dQMultiply0 (qcross2, qrel, qcross);
+if (joint->node[1].body) {
+dQMultiply1 (qq, joint->node[1].body->q, qcross2);
+dQMultiply2 (qrel, qq, joint->qrel2);
+}
+else {
+// pretend joint->node[1].body->q is the identity
+dQMultiply2 (qrel, qcross2, joint->qrel2);
+}
+*angle2 = - getHingeAngleFromRelativeQuat(qrel, joint->axis2);
+}
+else
+{
+*angle1 = 0;
+*angle2 = 0;
+}
+}
+static dReal getUniversalAngle1(dxJointUniversal *joint)
+{
+if (joint->node[0].body) {
+// length 1 joint axis in global coordinates, from each body
+dVector3 ax1, ax2;
+dMatrix3 R;
+dQuaternion qcross, qq, qrel;
+getUniversalAxes (joint,ax1,ax2);
+// It should be possible to get both angles without explicitly
+// constructing the rotation matrix of the cross.  Basically,
+// orientation of the cross about axis1 comes from body 2,
+// about axis 2 comes from body 1, and the perpendicular
+// axis can come from the two bodies somehow.  (We don't really
+// want to assume it's 90 degrees, because in general the
+// constraints won't be perfectly satisfied, or even very well
+// satisfied.)
+//
+// However, we'd need a version of getHingeAngleFromRElativeQuat()
+// that CAN handle when its relative quat is rotated along a direction
+// other than the given axis.  What I have here works,
+// although it's probably much slower than need be.
+dRFrom2Axes(R, ax1[0], ax1[1], ax1[2], ax2[0], ax2[1], ax2[2]);
+dRtoQ (R,qcross);
+// This code is essential the same as getHingeAngle(), see the comments
+// there for details.
+// get qrel = relative rotation between node[0] and the cross
+dQMultiply1 (qq,joint->node[0].body->q,qcross);
+dQMultiply2 (qrel,qq,joint->qrel1);
+return getHingeAngleFromRelativeQuat(qrel, joint->axis1);
+}
+return 0;
+}
+static dReal getUniversalAngle2(dxJointUniversal *joint)
+{
+if (joint->node[0].body) {
+// length 1 joint axis in global coordinates, from each body
+dVector3 ax1, ax2;
+dMatrix3 R;
+dQuaternion qcross, qq, qrel;
+getUniversalAxes (joint,ax1,ax2);
+// It should be possible to get both angles without explicitly
+// constructing the rotation matrix of the cross.  Basically,
+// orientation of the cross about axis1 comes from body 2,
+// about axis 2 comes from body 1, and the perpendicular
+// axis can come from the two bodies somehow.  (We don't really
+// want to assume it's 90 degrees, because in general the
+// constraints won't be perfectly satisfied, or even very well
+// satisfied.)
+//
+// However, we'd need a version of getHingeAngleFromRElativeQuat()
+// that CAN handle when its relative quat is rotated along a direction
+// other than the given axis.  What I have here works,
+// although it's probably much slower than need be.
+dRFrom2Axes(R, ax2[0], ax2[1], ax2[2], ax1[0], ax1[1], ax1[2]);
+dRtoQ(R, qcross);
+if (joint->node[1].body) {
+dQMultiply1 (qq, joint->node[1].body->q, qcross);
+dQMultiply2 (qrel,qq,joint->qrel2);
+}
+else {
+// pretend joint->node[1].body->q is the identity
+dQMultiply2 (qrel,qcross, joint->qrel2);
+}
+return - getHingeAngleFromRelativeQuat(qrel, joint->axis2);
+}
+return 0;
+}
+static void universalGetInfo1 (dxJointUniversal *j, dxJoint::Info1 *info)
+{
+info->nub = 4;
+info->m = 4;
+// see if we're powered or at a joint limit.
+bool constraint1 = j->limot1.fmax > 0;
+bool constraint2 = j->limot2.fmax > 0;
+bool limiting1 = (j->limot1.lostop >= -dPI || j->limot1.histop <= dPI) &&
+j->limot1.lostop <= j->limot1.histop;
+bool limiting2 = (j->limot2.lostop >= -dPI || j->limot2.histop <= dPI) &&
+j->limot2.lostop <= j->limot2.histop;
+// We need to call testRotationLimit() even if we're motored, since it
+// records the result.
+if (limiting1 || limiting2) {
+dReal angle1, angle2;
+getUniversalAngles (j, &angle1, &angle2);
+if (limiting1 && j->limot1.testRotationalLimit (angle1)) constraint1 = true;
+if (limiting2 && j->limot2.testRotationalLimit (angle2)) constraint2 = true;
+}
+if (constraint1)
+info->m++;
+if (constraint2)
+info->m++;
+}
+static void universalGetInfo2 (dxJointUniversal *joint, dxJoint::Info2 *info)
+{
+// set the three ball-and-socket rows
+setBall (joint,info,joint->anchor1,joint->anchor2);
+// set the universal joint row. the angular velocity about an axis
+// perpendicular to both joint axes should be equal. thus the constraint
+// equation is
+//    p*w1 - p*w2 = 0
+// where p is a vector normal to both joint axes, and w1 and w2
+// are the angular velocity vectors of the two bodies.
+// length 1 joint axis in global coordinates, from each body
+dVector3 ax1, ax2;
+dVector3 ax2_temp;
+// length 1 vector perpendicular to ax1 and ax2. Neither body can rotate
+// about this.
+dVector3 p;
+dReal k;
+getUniversalAxes(joint, ax1, ax2);
+k = dDOT(ax1, ax2);
+ax2_temp[0] = ax2[0] - dMUL(k,ax1[0]);
+ax2_temp[1] = ax2[1] - dMUL(k,ax1[1]);
+ax2_temp[2] = ax2[2] - dMUL(k,ax1[2]);
+dCROSS(p, =, ax1, ax2_temp);
+dNormalize3(p);
+int s3=3*info->rowskip;
+info->J1a[s3+0] = p[0];
+info->J1a[s3+1] = p[1];
+info->J1a[s3+2] = p[2];
+if (joint->node[1].body) {
+info->J2a[s3+0] = -p[0];
+info->J2a[s3+1] = -p[1];
+info->J2a[s3+2] = -p[2];
+}
+// compute the right hand side of the constraint equation. set relative
+// body velocities along p to bring the axes back to perpendicular.
+// If ax1, ax2 are unit length joint axes as computed from body1 and
+// body2, we need to rotate both bodies along the axis p.  If theta
+// is the angle between ax1 and ax2, we need an angular velocity
+// along p to cover the angle erp * (theta - Pi/2) in one step:
+//
+//   |angular_velocity| = angle/time = erp*(theta - Pi/2) / stepsize
+//                      = (erp*fps) * (theta - Pi/2)
+//
+// if theta is close to Pi/2,
+// theta - Pi/2 ~= cos(theta), so
+//    |angular_velocity|  ~= (erp*fps) * (ax1 dot ax2)
+info->c[3] = dMUL(info->fps,dMUL(info->erp,- dDOT(ax1, ax2)));
+// if the first angle is powered, or has joint limits, add in the stuff
+int row = 4 + joint->limot1.addLimot (joint,info,4,ax1,1);
+// if the second angle is powered, or has joint limits, add in more stuff
+joint->limot2.addLimot (joint,info,row,ax2,1);
+}
+static void universalComputeInitialRelativeRotations (dxJointUniversal *joint)
+{
+if (joint->node[0].body) {
+dVector3 ax1, ax2;
+dMatrix3 R;
+dQuaternion qcross;
+getUniversalAxes(joint, ax1, ax2);
+// Axis 1.
+dRFrom2Axes(R, ax1[0], ax1[1], ax1[2], ax2[0], ax2[1], ax2[2]);
+dRtoQ(R, qcross);
+dQMultiply1 (joint->qrel1, joint->node[0].body->q, qcross);
+// Axis 2.
+dRFrom2Axes(R, ax2[0], ax2[1], ax2[2], ax1[0], ax1[1], ax1[2]);
+dRtoQ(R, qcross);
+if (joint->node[1].body) {
+dQMultiply1 (joint->qrel2, joint->node[1].body->q, qcross);
+}
+else {
+// set joint->qrel to qcross
+for (int i=0; i<4; i++) joint->qrel2[i] = qcross[i];
+}
+}
+}
+EXPORT_C void dJointSetUniversalAnchor (dJointID j, dReal x, dReal y, dReal z)
+{
+dxJointUniversal* joint = (dxJointUniversal*)j;
+setAnchors (joint,x,y,z,joint->anchor1,joint->anchor2);
+universalComputeInitialRelativeRotations(joint);
+}
+EXPORT_C void dJointSetUniversalAxis1 (dJointID j, dReal x, dReal y, dReal z)
+{
+dxJointUniversal* joint = (dxJointUniversal*)j;
+if (joint->flags & dJOINT_REVERSE)
+setAxes (joint,x,y,z,NULL,joint->axis2);
+else
+setAxes (joint,x,y,z,joint->axis1,NULL);
+universalComputeInitialRelativeRotations(joint);
+}
+EXPORT_C void dJointSetUniversalAxis2 (dJointID j, dReal x, dReal y, dReal z)
+{
+dxJointUniversal* joint = (dxJointUniversal*)j;
+if (joint->flags & dJOINT_REVERSE)
+setAxes (joint,x,y,z,joint->axis1,NULL);
+else
+setAxes (joint,x,y,z,NULL,joint->axis2);
+universalComputeInitialRelativeRotations(joint);
+}
+EXPORT_C void dJointGetUniversalAnchor (dJointID j, dVector3 result)
+{
+dxJointUniversal* joint = (dxJointUniversal*)j;
+if (joint->flags & dJOINT_REVERSE)
+getAnchor2 (joint,result,joint->anchor2);
+else
+getAnchor (joint,result,joint->anchor1);
+}
+EXPORT_C void dJointGetUniversalAnchor2 (dJointID j, dVector3 result)
+{
+dxJointUniversal* joint = (dxJointUniversal*)j;
+if (joint->flags & dJOINT_REVERSE)
+getAnchor (joint,result,joint->anchor1);
+else
+getAnchor2 (joint,result,joint->anchor2);
+}
+EXPORT_C void dJointGetUniversalAxis1 (dJointID j, dVector3 result)
+{
+dxJointUniversal* joint = (dxJointUniversal*)j;
+if (joint->flags & dJOINT_REVERSE)
+getAxis2 (joint,result,joint->axis2);
+else
+getAxis (joint,result,joint->axis1);
+}
+EXPORT_C void dJointGetUniversalAxis2 (dJointID j, dVector3 result)
+{
+dxJointUniversal* joint = (dxJointUniversal*)j;
+if (joint->flags & dJOINT_REVERSE)
+getAxis (joint,result,joint->axis1);
+else
+getAxis2 (joint,result,joint->axis2);
+}
+EXPORT_C void dJointSetUniversalParam (dJointID j, int parameter, dReal value)
+{
+dxJointUniversal* joint = (dxJointUniversal*)j;
+if ((parameter & 0xff00) == 0x100) {
+joint->limot2.set (parameter & 0xff,value);
+}
+else {
+joint->limot1.set (parameter,value);
+}
+}
+EXPORT_C dReal dJointGetUniversalParam (dJointID j, int parameter)
+{
+dxJointUniversal* joint = (dxJointUniversal*)j;
+if ((parameter & 0xff00) == 0x100) {
+return joint->limot2.get (parameter & 0xff);
+}
+else {
+return joint->limot1.get (parameter);
+}
+}
+EXPORT_C void dJointGetUniversalAngles (dJointID j, dReal *angle1, dReal *angle2)
+{
+dxJointUniversal* joint = (dxJointUniversal*)j;
+if (joint->flags & dJOINT_REVERSE)
+return getUniversalAngles (joint, angle2, angle1);
+else
+return getUniversalAngles (joint, angle1, angle2);
+}
+EXPORT_C dReal dJointGetUniversalAngle1 (dJointID j)
+{
+dxJointUniversal* joint = (dxJointUniversal*)j;
+if (joint->flags & dJOINT_REVERSE)
+return getUniversalAngle2 (joint);
+else
+return getUniversalAngle1 (joint);
+}
+EXPORT_C dReal dJointGetUniversalAngle2 (dJointID j)
+{
+dxJointUniversal* joint = (dxJointUniversal*)j;
+if (joint->flags & dJOINT_REVERSE)
+return getUniversalAngle1 (joint);
+else
+return getUniversalAngle2 (joint);
+}
+EXPORT_C dReal dJointGetUniversalAngle1Rate (dJointID j)
+{
+dxJointUniversal* joint = (dxJointUniversal*)j;
+if (joint->node[0].body) {
+dVector3 axis;
+if (joint->flags & dJOINT_REVERSE)
+getAxis2 (joint,axis,joint->axis2);
+else
+getAxis (joint,axis,joint->axis1);
+dReal rate = dDOT(axis, joint->node[0].body->avel);
+if (joint->node[1].body) rate -= dDOT(axis, joint->node[1].body->avel);
+return rate;
+}
+return 0;
+}
+EXPORT_C dReal dJointGetUniversalAngle2Rate (dJointID j)
+{
+dxJointUniversal* joint = (dxJointUniversal*)j;
+if (joint->node[0].body) {
+dVector3 axis;
+if (joint->flags & dJOINT_REVERSE)
+getAxis (joint,axis,joint->axis1);
+else
+getAxis2 (joint,axis,joint->axis2);
+dReal rate = dDOT(axis, joint->node[0].body->avel);
+if (joint->node[1].body) rate -= dDOT(axis, joint->node[1].body->avel);
+return rate;
+}
+return 0;
+}
+EXPORT_C void dJointAddUniversalTorques (dJointID j, dReal torque1, dReal torque2)
+{
+dxJointUniversal* joint = (dxJointUniversal*)j;
+dVector3 axis1, axis2;
+if (joint->flags & dJOINT_REVERSE) {
+dReal temp = torque1;
+torque1 = - torque2;
+torque2 = - temp;
+}
+getAxis (joint,axis1,joint->axis1);
+getAxis2 (joint,axis2,joint->axis2);
+axis1[0] = dMUL(axis1[0],torque1) + dMUL(axis2[0],torque2);
+axis1[1] = dMUL(axis1[1],torque1) + dMUL(axis2[1],torque2);
+axis1[2] = dMUL(axis1[2],torque1) + dMUL(axis2[2],torque2);
+if (joint->node[0].body != 0)
+dBodyAddTorque (joint->node[0].body,axis1[0],axis1[1],axis1[2]);
+if (joint->node[1].body != 0)
+dBodyAddTorque(joint->node[1].body, -axis1[0], -axis1[1], -axis1[2]);
+}
+dxJoint::Vtable __duniversal_vtable = {
+sizeof(dxJointUniversal),
+(dxJoint::init_fn*) universalInit,
+(dxJoint::getInfo1_fn*) universalGetInfo1,
+(dxJoint::getInfo2_fn*) universalGetInfo2,
+dJointTypeUniversal};
+//****************************************************************************
+// Prismatic and Rotoide
+static void PRInit (dxJointPR *j)
+{
+// Default Position
+// Z^
+//  | Body 1       P      R          Body2
+//  |+---------+   _      _         +-----------+
+//  ||         |----|----(_)--------+           |
+//  |+---------+   -                +-----------+
+//  |
+// X.-----------------------------------------> Y
+// N.B. X is comming out of the page
+dSetZero (j->anchor2,4);
+dSetZero (j->axisR1,4);
+j->axisR1[0] = REAL(1.0);
+dSetZero (j->axisR2,4);
+j->axisR2[0] = REAL(1.0);
+dSetZero (j->axisP1,4);
+j->axisP1[1] = REAL(1.0);
+dSetZero (j->qrel,4);
+dSetZero (j->offset,4);
+j->limotR.init (j->world);
+j->limotP.init (j->world);
+}
+EXPORT_C dReal dJointGetPRPosition (dJointID j)
+{
+dxJointPR* joint = (dxJointPR*)j;
+dVector3 q;
+// get the offset in global coordinates
+dMULTIPLY0_331 (q,joint->node[0].body->posr.R,joint->offset);
+if (joint->node[1].body) {
+dVector3 anchor2;
+// get the anchor2 in global coordinates
+dMULTIPLY0_331 (anchor2,joint->node[1].body->posr.R,joint->anchor2);
+q[0] = ( (joint->node[0].body->posr.pos[0] + q[0]) -
+(joint->node[1].body->posr.pos[0] + anchor2[0]) );
+q[1] = ( (joint->node[0].body->posr.pos[1] + q[1]) -
+(joint->node[1].body->posr.pos[1] + anchor2[1]) );
+q[2] = ( (joint->node[0].body->posr.pos[2] + q[2]) -
+(joint->node[1].body->posr.pos[2] + anchor2[2]) );
+}
+else {
+//N.B. When there is no body 2 the joint->anchor2 is already in
+//     global coordinates
+q[0] = ( (joint->node[0].body->posr.pos[0] + q[0]) -
+(joint->anchor2[0]) );
+q[1] = ( (joint->node[0].body->posr.pos[1] + q[1]) -
+(joint->anchor2[1]) );
+q[2] = ( (joint->node[0].body->posr.pos[2] + q[2]) -
+(joint->anchor2[2]) );
+}
+dVector3 axP;
+// get prismatic axis in global coordinates
+dMULTIPLY0_331 (axP,joint->node[0].body->posr.R,joint->axisP1);
+return dDOT(axP, q);
+}
+EXPORT_C dReal dJointGetPRPositionRate (dJointID j)
+{
+dxJointPR* joint = (dxJointPR*)j;
+if (joint->node[0].body) {
+		// We want to find the rate of change of the prismatic part of the joint
+		// We can find it by looking at the speed difference between body1 and the
+		// anchor point.
+		// r will be used to find the distance between body1 and the anchor point
+		dVector3 r;
+		if (joint->node[1].body) {
+			// Find joint->anchor2 in global coordinates
+			dVector3 anchor2;
+			dMULTIPLY0_331 (anchor2,joint->node[1].body->posr.R,joint->anchor2);
+			r[0] = joint->node[0].body->posr.pos[0] - anchor2[0];
+			r[1] = joint->node[0].body->posr.pos[1] - anchor2[1];
+			r[2] = joint->node[0].body->posr.pos[2] - anchor2[2];
+		}
+		else {
+			//N.B. When there is no body 2 the joint->anchor2 is already in
+			//     global coordinates
+			r[0] = joint->node[0].body->posr.pos[0] - joint->anchor2[0];
+			r[1] = joint->node[0].body->posr.pos[1] - joint->anchor2[1];
+			r[2] = joint->node[0].body->posr.pos[2] - joint->anchor2[2];
+		}
+		// The body1 can have velocity coming from the rotation of
+		// the rotoide axis. We need to remove this.
+		// Take only the angular rotation coming from the rotation
+		// of the rotoide articulation
+		// N.B. Body1 and Body2 should have the same rotation along axis
+		//      other than the rotoide axis.
+		dVector3 angular;
+		dMULTIPLY0_331 (angular,joint->node[0].body->posr.R,joint->axisR1);
+		dReal omega = dDOT(angular, joint->node[0].body->avel);
+		angular[0] = dMUL(angular[0],omega);
+		angular[1] = dMUL(angular[1],omega);
+		angular[2] = dMUL(angular[2],omega);
+		// Find the contribution of the angular rotation to the linear speed
+		// N.B. We do vel = r X w instead of vel = w x r to have vel negative
+		//      since we want to remove it from the linear velocity of the body
+		dVector3 lvel1;
+		dCROSS(lvel1, =, r, angular);
+		lvel1[0] += joint->node[0].body->lvel[0];
+		lvel1[1] += joint->node[0].body->lvel[1];
+		lvel1[2] += joint->node[0].body->lvel[2];
+		// Since we want rate of change along the prismatic axis
+		// get axisP1 in global coordinates and get the component
+		// along this axis only
+		dVector3 axP1;
+		dMULTIPLY0_331 (axP1,joint->node[0].body->posr.R,joint->axisP1);
+		return dDOT(axP1, lvel1);
+	}
+	return REAL(0.0);
+}
+static void PRGetInfo1 (dxJointPR *j, dxJoint::Info1 *info)
+{
+info->m = 4;
+info->nub = 4;
+bool added = false;
+added = false;
+// see if the prismatic articulation is powered
+if (j->limotP.fmax > 0)
+{
+added = true;
+(info->m)++;  // powered needs an extra constraint row
+}
+// see if we're at a joint limit.
+j->limotP.limit = 0;
+if ((j->limotP.lostop > -dInfinity || j->limotP.histop < dInfinity) &&
+j->limotP.lostop <= j->limotP.histop) {
+// measure joint position
+dReal pos = dJointGetPRPosition (j);
+if (pos <= j->limotP.lostop) {
+j->limotP.limit = 1;
+j->limotP.limit_err = pos - j->limotP.lostop;
+if (!added)
+(info->m)++;
+}
+if (pos >= j->limotP.histop) {
+j->limotP.limit = 2;
+j->limotP.limit_err = pos - j->limotP.histop;
+if (!added)
+(info->m)++;
+}
+}
+}
+static void PRGetInfo2 (dxJointPR *joint, dxJoint::Info2 *info)
+{
+int s = info->rowskip;
+int s2= 2*s;
+int s3= 3*s;
+int s4= 4*s;
+dReal k = dMUL(info->fps,info->erp);
+dVector3 q;  // plane space of axP and after that axR
+// pull out pos and R for both bodies. also get the `connection'
+// vector pos2-pos1.
+dReal *pos1,*pos2 = 0,*R1,*R2 = 0;
+pos1 = joint->node[0].body->posr.pos;
+R1 = joint->node[0].body->posr.R;
+if (joint->node[1].body) {
+pos2 = joint->node[1].body->posr.pos;
+R2 = joint->node[1].body->posr.R;
+}
+else {
+//     pos2 = 0; // N.B. We can do that to be safe but it is no necessary
+//     R2 = 0;   // N.B. We can do that to be safe but it is no necessary
+}
+dVector3 axP; // Axis of the prismatic joint in global frame
+dMULTIPLY0_331 (axP, R1, joint->axisP1);
+// distance between the body1 and the anchor2 in global frame
+// Calculated in the same way as the offset
+dVector3 dist;
+if (joint->node[1].body)
+{
+dMULTIPLY0_331 (dist, R2, joint->anchor2);
+dist[0] += pos2[0] - pos1[0];
+dist[1] += pos2[1] - pos1[1];
+dist[2] += pos2[2] - pos1[2];
+}
+else {
+dist[0] = joint->anchor2[0] - pos1[0];
+dist[1] = joint->anchor2[1] - pos1[1];
+dist[2] = joint->anchor2[2] - pos1[2];
+}
+// ======================================================================
+// Work on the Rotoide part (i.e. row 0, 1 and maybe 4 if rotoide powered
+// Set the two rotoide rows. The rotoide axis should be the only unconstrained
+// rotational axis, the angular velocity of the two bodies perpendicular to
+// the rotoide axis should be equal. Thus the constraint equations are
+//    p*w1 - p*w2 = 0
+//    q*w1 - q*w2 = 0
+// where p and q are unit vectors normal to the rotoide axis, and w1 and w2
+// are the angular velocity vectors of the two bodies.
+dVector3 ax1;
+dMULTIPLY0_331 (ax1, joint->node[0].body->posr.R, joint->axisR1);
+dCROSS(q , =, ax1, axP);
+info->J1a[0] = axP[0];
+info->J1a[1] = axP[1];
+info->J1a[2] = axP[2];
+info->J1a[s+0] = q[0];
+info->J1a[s+1] = q[1];
+info->J1a[s+2] = q[2];
+if (joint->node[1].body) {
+info->J2a[0] = -axP[0];
+info->J2a[1] = -axP[1];
+info->J2a[2] = -axP[2];
+info->J2a[s+0] = -q[0];
+info->J2a[s+1] = -q[1];
+info->J2a[s+2] = -q[2];
+}
+// Compute the right hand side of the constraint equation set. Relative
+// body velocities along p and q to bring the rotoide back into alignment.
+// ax1,ax2 are the unit length rotoide axes of body1 and body2 in world frame.
+// We need to rotate both bodies along the axis u = (ax1 x ax2).
+// if `theta' is the angle between ax1 and ax2, we need an angular velocity
+// along u to cover angle erp*theta in one step :
+//   |angular_velocity| = angle/time = erp*theta / stepsize
+//                      = (erp*fps) * theta
+//    angular_velocity  = |angular_velocity| * (ax1 x ax2) / |ax1 x ax2|
+//                      = (erp*fps) * theta * (ax1 x ax2) / sin(theta)
+// ...as ax1 and ax2 are unit length. if theta is smallish,
+// theta ~= sin(theta), so
+//    angular_velocity  = (erp*fps) * (ax1 x ax2)
+// ax1 x ax2 is in the plane space of ax1, so we project the angular
+// velocity to p and q to find the right hand side.
+dVector3 ax2;
+if (joint->node[1].body) {
+dMULTIPLY0_331 (ax2, R2, joint->axisR2);
+}
+else {
+ax2[0] = joint->axisR2[0];
+ax2[1] = joint->axisR2[1];
+ax2[2] = joint->axisR2[2];
+}
+dVector3 b;
+dCROSS (b,=,ax1, ax2);
+info->c[0] = dMUL(k,dDOT(b, axP));
+info->c[1] = dMUL(k,dDOT(b, q));
+// ==========================
+// Work on the Prismatic part (i.e row 2,3 and 4 if only the prismatic is powered
+// or 5 if rotoide and prismatic powered
+// two rows. we want: vel2 = vel1 + w1 x c ... but this would
+// result in three equations, so we project along the planespace vectors
+// so that sliding along the prismatic axis is disregarded. for symmetry we
+// also substitute (w1+w2)/2 for w1, as w1 is supposed to equal w2.
+// p1 + R1 dist' = p2 + R2 anchor2' ## OLD ## p1 + R1 anchor1' = p2 + R2 dist'
+// v1 + w1 x R1 dist' + v_p = v2 + w2 x R2 anchor2'## OLD  v1 + w1 x R1 anchor1' = v2 + w2 x R2 dist' + v_p
+// v_p is speed of prismatic joint (i.e. elongation rate)
+// Since the constraints are perpendicular to v_p we have:
+// p dot v_p = 0 and q dot v_p = 0
+// ax1 dot ( v1 + w1 x dist = v2 + w2 x anchor2 )
+// q dot ( v1 + w1 x dist = v2 + w2 x anchor2 )
+// ==
+// ax1 . v1 + ax1 . w1 x dist = ax1 . v2 + ax1 . w2 x anchor2 ## OLD ## ax1 . v1 + ax1 . w1 x anchor1 = ax1 . v2 + ax1 . w2 x dist
+// since a . (b x c) = - b . (a x c) = - (a x c) . b
+// and a x b = - b x a
+// ax1 . v1 - ax1 x dist . w1 - ax1 . v2 - (- ax1 x anchor2 . w2) = 0
+// ax1 . v1 + dist x ax1 . w1 - ax1 . v2 - anchor2 x ax1 . w2 = 0
+// Coeff for 1er line of: J1l => ax1, J2l => -ax1
+// Coeff for 2er line of: J1l => q, J2l => -q
+// Coeff for 1er line of: J1a => dist x ax1, J2a => - anchor2 x ax1
+// Coeff for 2er line of: J1a => dist x q,   J2a => - anchor2 x q
+	dCROSS ((info->J1a)+s2, = , dist, ax1);
+	dCROSS ((info->J1a)+s3, = , dist, q);
+info->J1l[s2+0] = ax1[0];
+	info->J1l[s2+1] = ax1[1];
+	info->J1l[s2+2] = ax1[2];
+info->J1l[s3+0] = q[0];
+	info->J1l[s3+1] = q[1];
+	info->J1l[s3+2] = q[2];
+if (joint->node[1].body) {
+dVector3 anchor2;
+// Calculate anchor2 in world coordinate
+dMULTIPLY0_331 (anchor2, R2, joint->anchor2);
+		// ax2 x anchor2 instead of anchor2 x ax2 since we want the negative value
+		dCROSS ((info->J2a)+s2, = , ax2, anchor2); // since ax1 == ax2
+		// The cross product is in reverse order since we want the negative value
+		dCROSS ((info->J2a)+s3, = , q, anchor2);
+		info->J2l[s2+0] = -ax1[0];
+		info->J2l[s2+1] = -ax1[1];
+		info->J2l[s2+2] = -ax1[2];
+info->J2l[s3+0] = -q[0];
+		info->J2l[s3+1] = -q[1];
+		info->J2l[s3+2] = -q[2];
+}
+// We want to make correction for motion not in the line of the axisP
+// We calculate the displacement w.r.t. the anchor pt.
+//
+// compute the elements 2 and 3 of right hand side.
+// we want to align the offset point (in body 2's frame) with the center of body 1.
+// The position should be the same when we are not along the prismatic axis
+dVector3 err;
+dMULTIPLY0_331 (err, R1, joint->offset);
+err[0] += dist[0];
+err[1] += dist[1];
+err[2] += dist[2];
+info->c[2] = dMUL(k,dDOT(ax1, err));
+info->c[3] = dMUL(k,dDOT(q, err));
+// Here we can't use addLimot because of some assumption in the function
+int powered = joint->limotP.fmax > 0;
+if (powered || joint->limotP.limit) {
+info->J1l[s4+0] = axP[0];
+info->J1l[s4+1] = axP[1];
+info->J1l[s4+2] = axP[2];
+if (joint->node[1].body) {
+info->J2l[s4+0] = -axP[0];
+info->J2l[s4+1] = -axP[1];
+info->J2l[s4+2] = -axP[2];
+}
+// linear limot torque decoupling step:
+//
+// if this is a linear limot (e.g. from a slider), we have to be careful
+// that the linear constraint forces (+/- ax1) applied to the two bodies
+// do not create a torque couple. in other words, the points that the
+// constraint force is applied at must lie along the same ax1 axis.
+// a torque couple will result in powered or limited slider-jointed free
+// bodies from gaining angular momentum.
+// the solution used here is to apply the constraint forces at the point
+// halfway between the body centers. there is no penalty (other than an
+// extra tiny bit of computation) in doing this adjustment. note that we
+// only need to do this if the constraint connects two bodies.
+	dVector3 ltd = {};  // Linear Torque Decoupling vector (a torque)
+if (joint->node[1].body) {
+			dVector3 c;
+c[0]=dMUL(REAL(0.5),(joint->node[1].body->posr.pos[0]-joint->node[0].body->posr.pos[0]));
+c[1]=dMUL(REAL(0.5),(joint->node[1].body->posr.pos[1]-joint->node[0].body->posr.pos[1]));
+c[2]=dMUL(REAL(0.5),(joint->node[1].body->posr.pos[2]-joint->node[0].body->posr.pos[2]));
+			dReal val = dDOT(q, c);
+			c[0] -= dMUL(val,c[0]);
+			c[1] -= dMUL(val,c[1]);
+			c[2] -= dMUL(val,c[2]);
+dCROSS (ltd,=,c,axP);
+info->J1a[s4+0] = ltd[0];
+info->J1a[s4+1] = ltd[1];
+info->J1a[s4+2] = ltd[2];
+info->J2a[s4+0] = ltd[0];
+info->J2a[s4+1] = ltd[1];
+info->J2a[s4+2] = ltd[2];
+}
+// if we're limited low and high simultaneously, the joint motor is
+// ineffective
+if (joint->limotP.limit && (joint->limotP.lostop == joint->limotP.histop))
+powered = 0;
+int row = 4;
+if (powered) {
+info->cfm[row] = joint->limotP.normal_cfm;
+if (!joint->limotP.limit) {
+info->c[row] = joint->limotP.vel;
+info->lo[row] = -joint->limotP.fmax;
+info->hi[row] = joint->limotP.fmax;
+}
+else {
+// the joint is at a limit, AND is being powered. if the joint is
+// being powered into the limit then we apply the maximum motor force
+// in that direction, because the motor is working against the
+// immovable limit. if the joint is being powered away from the limit
+// then we have problems because actually we need *two* lcp
+// constraints to handle this case. so we fake it and apply some
+// fraction of the maximum force. the fraction to use can be set as
+// a fudge factor.
+dReal fm = joint->limotP.fmax;
+dReal vel = joint->limotP.vel;
+int limit = joint->limotP.limit;
+if ((vel > 0) || (vel==0 && limit==2)) fm = -fm;
+// if we're powering away from the limit, apply the fudge factor
+if ((limit==1 && vel > 0) || (limit==2 && vel < 0))
+fm = dMUL(fm,joint->limotP.fudge_factor);
+dBodyAddForce (joint->node[0].body,-dMUL(fm,axP[0]),-dMUL(fm,axP[1]),-dMUL(fm,axP[2]));
+				if (joint->node[1].body) {
+					dBodyAddForce (joint->node[1].body,dMUL(fm,axP[0]),dMUL(fm,axP[1]),dMUL(fm,axP[2]));
+					// linear limot torque decoupling step: refer to above discussion
+					dBodyAddTorque (joint->node[0].body,-dMUL(fm,ltd[0]),-dMUL(fm,ltd[1]),
+													-dMUL(fm,ltd[2]));
+					dBodyAddTorque (joint->node[1].body,-dMUL(fm,ltd[0]),-dMUL(fm,ltd[1]),
+													-dMUL(fm,ltd[2]));
+				}
+}
+}
+		if (joint->limotP.limit) {
+dReal k = dMUL(info->fps,joint->limotP.stop_erp);
+info->c[row] = -dMUL(k,joint->limotP.limit_err);
+info->cfm[row] = joint->limotP.stop_cfm;
+if (joint->limotP.lostop == joint->limotP.histop) {
+				// limited low and high simultaneously
+				info->lo[row] = -dInfinity;
+				info->hi[row] = dInfinity;
+}
+else {
+if (joint->limotP.limit == 1) {
+					// low limit
+					info->lo[row] = 0;
+					info->hi[row] = dInfinity;
+				}
+				else {
+					// high limit
+					info->lo[row] = -dInfinity;
+					info->hi[row] = 0;
+				}
+				// deal with bounce
+if (joint->limotP.bounce > 0) {
+					// calculate joint velocity
+dReal vel;
+vel = dDOT(joint->node[0].body->lvel, axP);
+if (joint->node[1].body)
+vel -= dDOT(joint->node[1].body->lvel, axP);
+					// only apply bounce if the velocity is incoming, and if the
+					// resulting c[] exceeds what we already have.
+if (joint->limotP.limit == 1) {
+						// low limit
+						if (vel < 0) {
+dReal newc = -dMUL(joint->limotP.bounce,vel);
+							if (newc > info->c[row]) info->c[row] = newc;
+						}
+					}
+					else {
+						// high limit - all those computations are reversed
+						if (vel > 0) {
+dReal newc = -dMUL(joint->limotP.bounce,vel);
+							if (newc < info->c[row]) info->c[row] = newc;
+						}
+					}
+				}
+}
+}
+}
+}
+// compute initial relative rotation body1 -> body2, or env -> body1
+static void PRComputeInitialRelativeRotation (dxJointPR *joint)
+{
+if (joint->node[0].body) {
+if (joint->node[1].body) {
+dQMultiply1 (joint->qrel,joint->node[0].body->q,joint->node[1].body->q);
+}
+else {
+// set joint->qrel to the transpose of the first body q
+joint->qrel[0] = joint->node[0].body->q[0];
+for (int i=1; i<4; i++) joint->qrel[i] = -joint->node[0].body->q[i];
+// WARNING do we need the - in -joint->node[0].body->q[i]; or not
+}
+}
+}
+EXPORT_C void dJointSetPRAnchor (dJointID j, dReal x, dReal y, dReal z)
+{
+dxJointPR* joint = (dxJointPR*)j;
+dVector3 dummy;
+setAnchors (joint,x,y,z,dummy,joint->anchor2);
+}
+EXPORT_C void dJointSetPRAxis1 (dJointID j, dReal x, dReal y, dReal z)
+{
+dxJointPR* joint = (dxJointPR*)j;
+//int i;
+setAxes (joint,x,y,z,joint->axisP1, 0);
+PRComputeInitialRelativeRotation (joint);
+// compute initial relative rotation body1 -> body2, or env -> body1
+// also compute distance between anchor of body1 w.r.t center of body 2
+dVector3 c;
+if (joint->node[1].body) {
+dVector3 anchor2;
+dMULTIPLY0_331 (anchor2,joint->node[1].body->posr.R, joint->anchor2);
+c[0] = ( joint->node[1].body->posr.pos[0] + anchor2[0] -
+joint->node[0].body->posr.pos[0] );
+c[1] = ( joint->node[1].body->posr.pos[1] + anchor2[1] -
+joint->node[0].body->posr.pos[1] );
+c[2] = ( joint->node[1].body->posr.pos[2] + anchor2[2] -
+joint->node[0].body->posr.pos[2] );
+}
+else if (joint->node[0].body) {
+c[0] = joint->anchor2[0] - joint->node[0].body->posr.pos[0];
+c[1] = joint->anchor2[1] - joint->node[0].body->posr.pos[1];
+c[2] = joint->anchor2[2] - joint->node[0].body->posr.pos[2];
+}
+	else
+	{
+joint->offset[0] = joint->anchor2[0];
+		joint->offset[1] = joint->anchor2[1];
+		joint->offset[2] = joint->anchor2[2];
+		return;
+	}
+dMULTIPLY1_331 (joint->offset,joint->node[0].body->posr.R,c);
+}
+EXPORT_C void dJointSetPRAxis2 (dJointID j, dReal x, dReal y, dReal z)
+{
+dxJointPR* joint = (dxJointPR*)j;
+setAxes (joint,x,y,z,joint->axisR1,joint->axisR2);
+PRComputeInitialRelativeRotation (joint);
+}
+EXPORT_C void dJointSetPRParam (dJointID j, int parameter, dReal value)
+{
+dxJointPR* joint = (dxJointPR*)j;
+if ((parameter & 0xff00) == 0x100) {
+joint->limotR.set (parameter,value);
+}
+else {
+joint->limotP.set (parameter & 0xff,value);
+}
+}
+EXPORT_C void dJointGetPRAnchor (dJointID j, dVector3 result)
+{
+dxJointPR* joint = (dxJointPR*)j;
+if (joint->node[1].body)
+getAnchor2 (joint,result,joint->anchor2);
+else
+{
+result[0] = joint->anchor2[0];
+result[1] = joint->anchor2[1];
+result[2] = joint->anchor2[2];
+}
+}
+EXPORT_C void dJointGetPRAxis1 (dJointID j, dVector3 result)
+{
+dxJointPR* joint = (dxJointPR*)j;
+getAxis(joint, result, joint->axisP1);
+}
+EXPORT_C void dJointGetPRAxis2 (dJointID j, dVector3 result)
+{
+dxJointPR* joint = (dxJointPR*)j;
+getAxis(joint, result, joint->axisR1);
+}
+EXPORT_C dReal dJointGetPRParam (dJointID j, int parameter)
+{
+dxJointPR* joint = (dxJointPR*)j;
+if ((parameter & 0xff00) == 0x100) {
+return joint->limotR.get (parameter & 0xff);
+}
+	else {
+		return joint->limotP.get (parameter);
+	}
+}
+EXPORT_C void dJointAddPRTorque (dJointID j, dReal torque)
+{
+dxJointPR* joint = (dxJointPR*)j;
+dVector3 axis;
+if (joint->flags & dJOINT_REVERSE)
+torque = -torque;
+getAxis (joint,axis,joint->axisR1);
+axis[0] = dMUL(axis[0],torque);
+axis[1] = dMUL(axis[1],torque);
+axis[2] = dMUL(axis[2],torque);
+if (joint->node[0].body != 0)
+dBodyAddTorque (joint->node[0].body, axis[0], axis[1], axis[2]);
+if (joint->node[1].body != 0)
+dBodyAddTorque(joint->node[1].body, -axis[0], -axis[1], -axis[2]);
+}
+dxJoint::Vtable __dPR_vtable = {
+sizeof(dxJointPR),
+(dxJoint::init_fn*) PRInit,
+(dxJoint::getInfo1_fn*) PRGetInfo1,
+(dxJoint::getInfo2_fn*) PRGetInfo2,
+dJointTypePR
+};
+//****************************************************************************
+// angular motor
+static void amotorInit (dxJointAMotor *j)
+{
+int i;
+j->num = 0;
+j->mode = dAMotorUser;
+for (i=0; i<3; i++) {
+j->rel[i] = 0;
+dSetZero (j->axis[i],4);
+j->limot[i].init (j->world);
+j->angle[i] = 0;
+}
+dSetZero (j->reference1,4);
+dSetZero (j->reference2,4);
+}
+// compute the 3 axes in global coordinates
+static void amotorComputeGlobalAxes (dxJointAMotor *joint, dVector3 ax[3])
+{
+if (joint->mode == dAMotorEuler) {
+// special handling for euler mode
+dMULTIPLY0_331 (ax[0],joint->node[0].body->posr.R,joint->axis[0]);
+if (joint->node[1].body) {
+dMULTIPLY0_331 (ax[2],joint->node[1].body->posr.R,joint->axis[2]);
+}
+else {
+ax[2][0] = joint->axis[2][0];
+ax[2][1] = joint->axis[2][1];
+ax[2][2] = joint->axis[2][2];
+}
+dCROSS (ax[1],=,ax[2],ax[0]);
+dNormalize3 (ax[1]);
+}
+else {
+for (int i=0; i < joint->num; i++) {
+if (joint->rel[i] == 1) {
+	// relative to b1
+	dMULTIPLY0_331 (ax[i],joint->node[0].body->posr.R,joint->axis[i]);
+}
+else if (joint->rel[i] == 2) {
+	// relative to b2
+	if (joint->node[1].body) {   // jds: don't assert, just ignore
+	        dMULTIPLY0_331 (ax[i],joint->node[1].body->posr.R,joint->axis[i]);
+}
+}
+else {
+	// global - just copy it
+	ax[i][0] = joint->axis[i][0];
+	ax[i][1] = joint->axis[i][1];
+	ax[i][2] = joint->axis[i][2];
+}
+}
+}
+}
+static void amotorComputeEulerAngles (dxJointAMotor *joint, dVector3 ax[3])
+{
+// assumptions:
+//   global axes already calculated --> ax
+//   axis[0] is relative to body 1 --> global ax[0]
+//   axis[2] is relative to body 2 --> global ax[2]
+//   ax[1] = ax[2] x ax[0]
+//   original ax[0] and ax[2] are perpendicular
+//   reference1 is perpendicular to ax[0] (in body 1 frame)
+//   reference2 is perpendicular to ax[2] (in body 2 frame)
+//   all ax[] and reference vectors are unit length
+// calculate references in global frame
+dVector3 ref1,ref2;
+dMULTIPLY0_331 (ref1,joint->node[0].body->posr.R,joint->reference1);
+if (joint->node[1].body) {
+dMULTIPLY0_331 (ref2,joint->node[1].body->posr.R,joint->reference2);
+}
+else {
+ref2[0] = joint->reference2[0];
+ref2[1] = joint->reference2[1];
+ref2[2] = joint->reference2[2];
+}
+// get q perpendicular to both ax[0] and ref1, get first euler angle
+dVector3 q;
+dCROSS (q,=,ax[0],ref1);
+joint->angle[0] = -dArcTan2 (dDOT(ax[2],q),dDOT(ax[2],ref1));
+// get q perpendicular to both ax[0] and ax[1], get second euler angle
+dCROSS (q,=,ax[0],ax[1]);
+joint->angle[1] = -dArcTan2 (dDOT(ax[2],ax[0]),dDOT(ax[2],q));
+// get q perpendicular to both ax[1] and ax[2], get third euler angle
+dCROSS (q,=,ax[1],ax[2]);
+joint->angle[2] = -dArcTan2 (dDOT(ref2,ax[1]), dDOT(ref2,q));
+}
+// set the reference vectors as follows:
+//   * reference1 = current axis[2] relative to body 1
+//   * reference2 = current axis[0] relative to body 2
+// this assumes that:
+//    * axis[0] is relative to body 1
+//    * axis[2] is relative to body 2
+static void amotorSetEulerReferenceVectors (dxJointAMotor *j)
+{
+if (j->node[0].body && j->node[1].body) {
+dVector3 r;		// axis[2] and axis[0] in global coordinates
+dMULTIPLY0_331 (r,j->node[1].body->posr.R,j->axis[2]);
+dMULTIPLY1_331 (j->reference1,j->node[0].body->posr.R,r);
+dMULTIPLY0_331 (r,j->node[0].body->posr.R,j->axis[0]);
+dMULTIPLY1_331 (j->reference2,j->node[1].body->posr.R,r);
+}
+else {   // jds
+// else if (j->node[0].body) {
+// dMULTIPLY1_331 (j->reference1,j->node[0].body->posr.R,j->axis[2]);
+// dMULTIPLY0_331 (j->reference2,j->node[0].body->posr.R,j->axis[0]);
+// We want to handle angular motors attached to passive geoms
+dVector3 r;		// axis[2] and axis[0] in global coordinates
+r[0] = j->axis[2][0]; r[1] = j->axis[2][1]; r[2] = j->axis[2][2]; r[3] = j->axis[2][3];
+dMULTIPLY1_331 (j->reference1,j->node[0].body->posr.R,r);
+dMULTIPLY0_331 (r,j->node[0].body->posr.R,j->axis[0]);
+j->reference2[0] += r[0]; j->reference2[1] += r[1];
+j->reference2[2] += r[2]; j->reference2[3] += r[3];
+}
+}
+static void amotorGetInfo1 (dxJointAMotor *j, dxJoint::Info1 *info)
+{
+info->m = 0;
+info->nub = 0;
+// compute the axes and angles, if in euler mode
+if (j->mode == dAMotorEuler) {
+dVector3 ax[3];
+amotorComputeGlobalAxes (j,ax);
+amotorComputeEulerAngles (j,ax);
+}
+// see if we're powered or at a joint limit for each axis
+for (int i=0; i < j->num; i++) {
+if (j->limot[i].testRotationalLimit (j->angle[i]) ||
+	j->limot[i].fmax > 0) {
+info->m++;
+}
+}
+}
+static void amotorGetInfo2 (dxJointAMotor *joint, dxJoint::Info2 *info)
+{
+int i;
+// compute the axes (if not global)
+dVector3 ax[3];
+amotorComputeGlobalAxes (joint,ax);
+// in euler angle mode we do not actually constrain the angular velocity
+// along the axes axis[0] and axis[2] (although we do use axis[1]) :
+//
+//    to get			constrain w2-w1 along		...not
+//    ------			---------------------		------
+//    d(angle[0])/dt = 0	ax[1] x ax[2]			ax[0]
+//    d(angle[1])/dt = 0	ax[1]
+//    d(angle[2])/dt = 0	ax[0] x ax[1]			ax[2]
+//
+// constraining w2-w1 along an axis 'a' means that a'*(w2-w1)=0.
+// to prove the result for angle[0], write the expression for angle[0] from
+// GetInfo1 then take the derivative. to prove this for angle[2] it is
+// easier to take the euler rate expression for d(angle[2])/dt with respect
+// to the components of w and set that to 0.
+dVector3 *axptr[3];
+axptr[0] = &ax[0];
+axptr[1] = &ax[1];
+axptr[2] = &ax[2];
+dVector3 ax0_cross_ax1;
+dVector3 ax1_cross_ax2;
+if (joint->mode == dAMotorEuler) {
+dCROSS (ax0_cross_ax1,=,ax[0],ax[1]);
+axptr[2] = &ax0_cross_ax1;
+dCROSS (ax1_cross_ax2,=,ax[1],ax[2]);
+axptr[0] = &ax1_cross_ax2;
+}
+int row=0;
+for (i=0; i < joint->num; i++) {
+row += joint->limot[i].addLimot (joint,info,row,*(axptr[i]),1);
+}
+}
+EXPORT_C void dJointSetAMotorNumAxes (dJointID j, int num)
+{
+dxJointAMotor* joint = (dxJointAMotor*)j;
+if (joint->mode == dAMotorEuler) {
+joint->num = 3;
+}
+else {
+if (num < 0) num = 0;
+if (num > 3) num = 3;
+joint->num = num;
+}
+}
+EXPORT_C void dJointSetAMotorAxis (dJointID j, int anum, int rel, dReal x, dReal y, dReal z)
+{
+dxJointAMotor* joint = (dxJointAMotor*)j;
+if (anum < 0) anum = 0;
+if (anum > 2) anum = 2;
+// adjust rel to match the internal body order
+if (!joint->node[1].body && rel==2) rel = 1;
+joint->rel[anum] = rel;
+// x,y,z is always in global coordinates regardless of rel, so we may have
+// to convert it to be relative to a body
+dVector3 r;
+r[0] = x;
+r[1] = y;
+r[2] = z;
+r[3] = 0;
+if (rel > 0) {
+if (rel==1) {
+dMULTIPLY1_331 (joint->axis[anum],joint->node[0].body->posr.R,r);
+}
+else {
+// don't assert; handle the case of attachment to a bodiless geom
+if (joint->node[1].body) {   // jds
+dMULTIPLY1_331 (joint->axis[anum],joint->node[1].body->posr.R,r);
+}
+else {
+	joint->axis[anum][0] = r[0]; joint->axis[anum][1] = r[1];
+	joint->axis[anum][2] = r[2]; joint->axis[anum][3] = r[3];
+}
+}
+}
+else {
+joint->axis[anum][0] = r[0];
+joint->axis[anum][1] = r[1];
+joint->axis[anum][2] = r[2];
+}
+dNormalize3 (joint->axis[anum]);
+if (joint->mode == dAMotorEuler) amotorSetEulerReferenceVectors (joint);
+}
+EXPORT_C void dJointSetAMotorAngle (dJointID j, int anum, dReal angle)
+{
+dxJointAMotor* joint = (dxJointAMotor*)j;
+if (joint->mode == dAMotorUser) {
+if (anum < 0) anum = 0;
+if (anum > 3) anum = 3;
+joint->angle[anum] = angle;
+}
+}
+EXPORT_C void dJointSetAMotorParam (dJointID j, int parameter, dReal value)
+{
+dxJointAMotor* joint = (dxJointAMotor*)j;
+int anum = parameter >> 8;
+if (anum < 0) anum = 0;
+if (anum > 2) anum = 2;
+parameter &= 0xff;
+joint->limot[anum].set (parameter, value);
+}
+EXPORT_C void dJointSetAMotorMode (dJointID j, int mode)
+{
+dxJointAMotor* joint = (dxJointAMotor*)j;
+joint->mode = mode;
+if (joint->mode == dAMotorEuler) {
+joint->num = 3;
+amotorSetEulerReferenceVectors (joint);
+}
+}
+EXPORT_C int dJointGetAMotorNumAxes (dJointID j)
+{
+dxJointAMotor* joint = (dxJointAMotor*)j;
+return joint->num;
+}
+EXPORT_C void dJointGetAMotorAxis (dJointID j, int anum, dVector3 result)
+{
+dxJointAMotor* joint = (dxJointAMotor*)j;
+if (anum < 0) anum = 0;
+if (anum > 2) anum = 2;
+if (joint->rel[anum] > 0) {
+if (joint->rel[anum]==1) {
+dMULTIPLY0_331 (result,joint->node[0].body->posr.R,joint->axis[anum]);
+}
+else {
+if (joint->node[1].body) {   // jds
+dMULTIPLY0_331 (result,joint->node[1].body->posr.R,joint->axis[anum]);
+}
+else {
+	result[0] = joint->axis[anum][0]; result[1] = joint->axis[anum][1];
+	result[2] = joint->axis[anum][2]; result[3] = joint->axis[anum][3];
+}
+}
+}
+else {
+result[0] = joint->axis[anum][0];
+result[1] = joint->axis[anum][1];
+result[2] = joint->axis[anum][2];
+}
+}
+EXPORT_C int dJointGetAMotorAxisRel (dJointID j, int anum)
+{
+dxJointAMotor* joint = (dxJointAMotor*)j;
+if (anum < 0) anum = 0;
+if (anum > 2) anum = 2;
+return joint->rel[anum];
+}
+EXPORT_C dReal dJointGetAMotorAngle (dJointID j, int anum)
+{
+dxJointAMotor* joint = (dxJointAMotor*)j;
+if (anum < 0) anum = 0;
+if (anum > 3) anum = 3;
+return joint->angle[anum];
+}
+EXPORT_C dReal dJointGetAMotorAngleRate (dJointID /*j*/, int /*anum*/)
+{
+// @@@
+return 0;
+}
+EXPORT_C dReal dJointGetAMotorParam (dJointID j, int parameter)
+{
+dxJointAMotor* joint = (dxJointAMotor*)j;
+int anum = parameter >> 8;
+if (anum < 0) anum = 0;
+if (anum > 2) anum = 2;
+parameter &= 0xff;
+return joint->limot[anum].get (parameter);
+}
+EXPORT_C int dJointGetAMotorMode (dJointID j)
+{
+dxJointAMotor* joint = (dxJointAMotor*)j;
+return joint->mode;
+}
+EXPORT_C void dJointAddAMotorTorques (dJointID j, dReal torque1, dReal torque2, dReal torque3)
+{
+dxJointAMotor* joint = (dxJointAMotor*)j;
+dVector3 axes[3];
+if (joint->num == 0)
+return;
+amotorComputeGlobalAxes (joint,axes);
+axes[0][0] = dMUL(axes[0][0],torque1);
+axes[0][1] = dMUL(axes[0][1],torque1);
+axes[0][2] = dMUL(axes[0][2],torque1);
+if (joint->num >= 2) {
+axes[0][0] += dMUL(axes[1][0],torque2);
+axes[0][1] += dMUL(axes[1][1],torque2);
+axes[0][2] += dMUL(axes[1][2],torque2);
+if (joint->num >= 3) {
+axes[0][0] += dMUL(axes[2][0],torque3);
+axes[0][1] += dMUL(axes[2][1],torque3);
+axes[0][2] += dMUL(axes[2][2],torque3);
+}
+}
+if (joint->node[0].body != 0)
+dBodyAddTorque (joint->node[0].body,axes[0][0],axes[0][1],axes[0][2]);
+if (joint->node[1].body != 0)
+dBodyAddTorque(joint->node[1].body, -axes[0][0], -axes[0][1], -axes[0][2]);
+}
+dxJoint::Vtable __damotor_vtable = {
+sizeof(dxJointAMotor),
+(dxJoint::init_fn*) amotorInit,
+(dxJoint::getInfo1_fn*) amotorGetInfo1,
+(dxJoint::getInfo2_fn*) amotorGetInfo2,
+dJointTypeAMotor};
+//****************************************************************************
+// lmotor joint
+static void lmotorInit (dxJointLMotor *j)
+{
+int i;
+j->num = 0;
+for (i=0;i<3;i++) {
+dSetZero(j->axis[i],4);
+j->limot[i].init(j->world);
+}
+}
+static void lmotorComputeGlobalAxes (dxJointLMotor *joint, dVector3 ax[3])
+{
+for (int i=0; i< joint->num; i++) {
+if (joint->rel[i] == 1) {
+dMULTIPLY0_331 (ax[i],joint->node[0].body->posr.R,joint->axis[i]);
+}
+else if (joint->rel[i] == 2) {
+if (joint->node[1].body) {   // jds: don't assert, just ignore
+dMULTIPLY0_331 (ax[i],joint->node[1].body->posr.R,joint->axis[i]);
+}
+} else {
+ax[i][0] = joint->axis[i][0];
+ax[i][1] = joint->axis[i][1];
+ax[i][2] = joint->axis[i][2];
+}
+}
+}
+static void lmotorGetInfo1 (dxJointLMotor *j, dxJoint::Info1 *info)
+{
+info->m = 0;
+info->nub = 0;
+for (int i=0; i < j->num; i++) {
+if (j->limot[i].fmax > 0) {
+info->m++;
+}
+}
+}
+static void lmotorGetInfo2 (dxJointLMotor *joint, dxJoint::Info2 *info)
+{
+int row=0;
+dVector3 ax[3];
+lmotorComputeGlobalAxes(joint, ax);
+for (int i=0;i<joint->num;i++) {
+row += joint->limot[i].addLimot(joint,info,row,ax[i], 0);
+}
+}
+EXPORT_C void dJointSetLMotorAxis (dJointID j, int anum, int rel, dReal x, dReal y, dReal z)
+{
+dxJointLMotor* joint = (dxJointLMotor*)j;
+//for now we are ignoring rel!
+if (anum < 0) anum = 0;
+if (anum > 2) anum = 2;
+if (!joint->node[1].body && rel==2) rel = 1; //ref 1
+joint->rel[anum] = rel;
+dVector3 r;
+r[0] = x;
+r[1] = y;
+r[2] = z;
+r[3] = 0;
+if (rel > 0) {
+if (rel==1) {
+dMULTIPLY1_331 (joint->axis[anum],joint->node[0].body->posr.R,r);
+	} else {
+	  //second body has to exists thanks to ref 1 line
+dMULTIPLY1_331 (joint->axis[anum],joint->node[1].body->posr.R,r);
+	}
+} else {
+joint->axis[anum][0] = r[0];
+joint->axis[anum][1] = r[1];
+joint->axis[anum][2] = r[2];
+}
+dNormalize3 (joint->axis[anum]);
+}
+EXPORT_C void dJointSetLMotorNumAxes (dJointID j, int num)
+{
+dxJointLMotor* joint = (dxJointLMotor*)j;
+if (num < 0) num = 0;
+if (num > 3) num = 3;
+joint->num = num;
+}
+EXPORT_C void dJointSetLMotorParam (dJointID j, int parameter, dReal value)
+{
+dxJointLMotor* joint = (dxJointLMotor*)j;
+int anum = parameter >> 8;
+if (anum < 0) anum = 0;
+if (anum > 2) anum = 2;
+parameter &= 0xff;
+joint->limot[anum].set (parameter, value);
+}
+EXPORT_C int dJointGetLMotorNumAxes (dJointID j)
+{
+dxJointLMotor* joint = (dxJointLMotor*)j;
+return joint->num;
+}
+EXPORT_C void dJointGetLMotorAxis (dJointID j, int anum, dVector3 result)
+{
+dxJointLMotor* joint = (dxJointLMotor*)j;
+if (anum < 0) anum = 0;
+if (anum > 2) anum = 2;
+result[0] = joint->axis[anum][0];
+result[1] = joint->axis[anum][1];
+result[2] = joint->axis[anum][2];
+}
+EXPORT_C dReal dJointGetLMotorParam (dJointID j, int parameter)
+{
+dxJointLMotor* joint = (dxJointLMotor*)j;
+int anum = parameter >> 8;
+if (anum < 0) anum = 0;
+if (anum > 2) anum = 2;
+parameter &= 0xff;
+return joint->limot[anum].get (parameter);
+}
+dxJoint::Vtable __dlmotor_vtable = {
+sizeof(dxJointLMotor),
+	(dxJoint::init_fn*) lmotorInit,
+	(dxJoint::getInfo1_fn*) lmotorGetInfo1,
+	(dxJoint::getInfo2_fn*) lmotorGetInfo2,
+	dJointTypeLMotor
+};
+//****************************************************************************
+// fixed joint
+static void fixedInit (dxJointFixed *j)
+{
+dSetZero (j->offset,4);
+dSetZero (j->qrel,4);
+}
+static void fixedGetInfo1 (dxJointFixed */*j*/, dxJoint::Info1 *info)
+{
+info->m = 6;
+info->nub = 6;
+}
+static void fixedGetInfo2 (dxJointFixed *joint, dxJoint::Info2 *info)
+{
+int s = info->rowskip;
+// Three rows for orientation
+setFixedOrientation(joint, info, joint->qrel, 3);
+// Three rows for position.
+// set jacobian
+info->J1l[0] = REAL(1.0);
+info->J1l[s+1] = REAL(1.0);
+info->J1l[2*s+2] = REAL(1.0);
+dVector3 ofs;
+dMULTIPLY0_331 (ofs,joint->node[0].body->posr.R,joint->offset);
+if (joint->node[1].body) {
+dCROSSMAT (info->J1a,ofs,s,+,-);
+info->J2l[0] = REAL(-1.0);
+info->J2l[s+1] = REAL(-1.0);
+info->J2l[2*s+2] = REAL(-1.0);
+}
+// set right hand side for the first three rows (linear)
+dReal k = dMUL(info->fps,info->erp);
+if (joint->node[1].body) {
+for (int j=0; j<3; j++)
+info->c[j] = dMUL(k,(joint->node[1].body->posr.pos[j] -
+			joint->node[0].body->posr.pos[j] + ofs[j]));
+}
+else {
+for (int j=0; j<3; j++)
+info->c[j] = dMUL(k,(joint->offset[j] - joint->node[0].body->posr.pos[j]));
+}
+}
+EXPORT_C void dJointSetFixed (dJointID j)
+{
+dxJointFixed* joint = (dxJointFixed*)j;
+int i;
+// This code is taken from sJointSetSliderAxis(), we should really put the
+// common code in its own function.
+// compute the offset between the bodies
+if (joint->node[0].body) {
+if (joint->node[1].body) {
+dQMultiply1 (joint->qrel,joint->node[0].body->q,joint->node[1].body->q);
+dReal ofs[4];
+for (i=0; i<4; i++) ofs[i] = joint->node[0].body->posr.pos[i];
+for (i=0; i<4; i++) ofs[i] -= joint->node[1].body->posr.pos[i];
+dMULTIPLY1_331 (joint->offset,joint->node[0].body->posr.R,ofs);
+}
+else {
+// set joint->qrel to the transpose of the first body's q
+joint->qrel[0] = joint->node[0].body->q[0];
+for (i=1; i<4; i++) joint->qrel[i] = -joint->node[0].body->q[i];
+for (i=0; i<4; i++) joint->offset[i] = joint->node[0].body->posr.pos[i];
+}
+}
+}
+dxJoint::Vtable __dfixed_vtable = {
+sizeof(dxJointFixed),
+(dxJoint::init_fn*) fixedInit,
+(dxJoint::getInfo1_fn*) fixedGetInfo1,
+(dxJoint::getInfo2_fn*) fixedGetInfo2,
+dJointTypeFixed};
+//****************************************************************************
+// null joint
+static void nullGetInfo1 (dxJointNull */*j*/, dxJoint::Info1 *info)
+{
+info->m = 0;
+info->nub = 0;
+}
+static void nullGetInfo2 (dxJointNull */*joint*/, dxJoint::Info2 */*info*/)
+{
+}
+dxJoint::Vtable __dnull_vtable = {
+sizeof(dxJointNull),
+(dxJoint::init_fn*) 0,
+(dxJoint::getInfo1_fn*) nullGetInfo1,
+(dxJoint::getInfo2_fn*) nullGetInfo2,
+dJointTypeNull};
+/*
+This code is part of the Plane2D ODE joint
+by psero@gmx.de
+Wed Apr 23 18:53:43 CEST 2003
+Add this code to the file: ode/src/joint.cpp
+*/
+# define        VoXYZ(v1, o1, x, y, z) \
+( \
+(v1)[0] o1 (x), \
+(v1)[1] o1 (y), \
+(v1)[2] o1 (z)  \
+)
+static const dReal   Midentity[3][3] =
+{
+{   REAL(1.0),  0,  0   },
+{   0,  REAL(1.0),  0   },
+{   0,  0,  REAL(1.0),  }
+};
+static void     plane2dInit (dxJointPlane2D *j)
+/*********************************************/
+{
+/* MINFO ("plane2dInit ()"); */
+j->motor_x.init (j->world);
+j->motor_y.init (j->world);
+j->motor_angle.init (j->world);
+}
+static void     plane2dGetInfo1 (dxJointPlane2D *j, dxJoint::Info1 *info)
+/***********************************************************************/
+{
+/* MINFO ("plane2dGetInfo1 ()"); */
+info->nub = 3;
+info->m = 3;
+if (j->motor_x.fmax > 0)
+j->row_motor_x = info->m ++;
+if (j->motor_y.fmax > 0)
+j->row_motor_y = info->m ++;
+if (j->motor_angle.fmax > 0)
+j->row_motor_angle = info->m ++;
+}
+static void     plane2dGetInfo2 (dxJointPlane2D *joint, dxJoint::Info2 *info)
+/***************************************************************************/
+{
+int         r0 = 0,
+r1 = info->rowskip,
+r2 = 2 * r1;
+dReal       eps = dMUL(info->fps,info->erp);
+/* MINFO ("plane2dGetInfo2 ()"); */
+/*
+v = v1, w = omega1
+(v2, omega2 not important (== static environment))
+constraint equations:
+xz = 0
+wx = 0
+wy = 0
+<=> ( 0 0 1 ) (vx)   ( 0 0 0 ) (wx)   ( 0 )
+( 0 0 0 ) (vy) + ( 1 0 0 ) (wy) = ( 0 )
+( 0 0 0 ) (vz)   ( 0 1 0 ) (wz)   ( 0 )
+J1/J1l           Omega1/J1a
+*/
+// fill in linear and angular coeff. for left hand side:
+VoXYZ (&info->J1l[r0], =, 0, 0, REAL(1.0));
+VoXYZ (&info->J1l[r1], =, 0, 0, 0);
+VoXYZ (&info->J1l[r2], =, 0, 0, 0);
+VoXYZ (&info->J1a[r0], =, 0, 0, 0);
+VoXYZ (&info->J1a[r1], =, REAL(1.0), 0, 0);
+VoXYZ (&info->J1a[r2], =, 0, REAL(1.0), 0);
+// error correction (against drift):
+// a) linear vz, so that z (== pos[2]) == 0
+info->c[0] = dMUL(eps,-joint->node[0].body->posr.pos[2]);
+// if the slider is powered, or has joint limits, add in the extra row:
+if (joint->row_motor_x > 0)
+joint->motor_x.addLimot (
+joint, info, joint->row_motor_x, Midentity[0], 0);
+if (joint->row_motor_y > 0)
+joint->motor_y.addLimot (
+joint, info, joint->row_motor_y, Midentity[1], 0);
+if (joint->row_motor_angle > 0)
+joint->motor_angle.addLimot (
+joint, info, joint->row_motor_angle, Midentity[2], 1);
+}
+dxJoint::Vtable __dplane2d_vtable =
+{
+sizeof (dxJointPlane2D),
+(dxJoint::init_fn*) plane2dInit,
+(dxJoint::getInfo1_fn*) plane2dGetInfo1,
+(dxJoint::getInfo2_fn*) plane2dGetInfo2,
+dJointTypePlane2D
+};
+EXPORT_C void dJointSetPlane2DXParam (dxJoint *joint,
+int parameter, dReal value)
+{
+	dxJointPlane2D* joint2d = (dxJointPlane2D*)( joint );
+	joint2d->motor_x.set (parameter, value);
+}
+EXPORT_C void dJointSetPlane2DYParam (dxJoint *joint,
+int parameter, dReal value)
+{
+	dxJointPlane2D* joint2d = (dxJointPlane2D*)( joint );
+	joint2d->motor_y.set (parameter, value);
+}
+EXPORT_C void dJointSetPlane2DAngleParam (dxJoint *joint,
+int parameter, dReal value)
+{
+	dxJointPlane2D* joint2d = (dxJointPlane2D*)( joint );
+	joint2d->motor_angle.set (parameter, value);
+}