resubmitting ode

1 files changed, 4065 insertions, 0 deletions

diff --git a/libraries/ode-0.9/ode/src/joint.cpp b/libraries/ode-0.9/ode/src/joint.cpp
new file mode 100644
index 0000000..d83294b
--- /dev/null
+++ b/libraries/ode-0.9/ode/src/joint.cpp
@@ -0,0 +1,4065 @@
+/*************************************************************************
+ *                                                                       *
+ * 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"
+
+//****************************************************************************
+// 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] = 1;
+  info->J1l[s+1] = 1;
+  info->J1l[2*s+2] = 1;
+  dMULTIPLY0_331 (a1,joint->node[0].body->posr.R,anchor1);
+  dCROSSMAT (info->J1a,a1,s,-,+);
+  if (joint->node[1].body) {
+    info->J2l[0] = -1;
+    info->J2l[s+1] = -1;
+    info->J2l[2*s+2] = -1;
+    dMULTIPLY0_331 (a2,joint->node[1].body->posr.R,anchor2);
+    dCROSSMAT (info->J2a,a2,s,+,-);
+  }
+
+  // set right hand side
+  dReal k = info->fps * info->erp;
+  if (joint->node[1].body) {
+    for (int j=0; j<3; j++) {
+      info->c[j] = 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] = 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 = info->fps * erp1;
+  dReal k = 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] = k1 * (dDOT(axis,a2) - dDOT(axis,a1));
+    info->c[1] = k * (dDOT(q1,a2) - dDOT(q1,a1));
+    info->c[2] = k * (dDOT(q2,a2) - dDOT(q2,a1));
+  }
+  else {
+    info->c[0] = k1 * (dDOT(axis,anchor2) - dDOT(axis,a1));
+    info->c[1] = k * (dDOT(q1,anchor2) - dDOT(q1,a1));
+    info->c[2] = 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] = 1;
+  info->J1a[start_index + s + 1] = 1;
+  info->J1a[start_index + s*2+2] = 1;
+  if (joint->node[1].body) {
+    info->J2a[start_index] = -1;
+    info->J2a[start_index + s+1] = -1;
+    info->J2a[start_index + s*2+2] = -1;
+  }
+
+  // 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 = info->fps * info->erp;
+  info->c[start_row] = 2*k * e[0];
+  info->c[start_row+1] = 2*k * e[1];
+  info->c[start_row+2] = 2*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 (qrel[1]*qrel[1]+qrel[2]*qrel[2]+qrel[3]*qrel[3]);
+  dReal theta = (dDOT(qrel+1,axis) >= 0) ?      // @@@ padding assumptions
+    (2 * dAtan2(sint2,cost2)) :         // if u points in direction of axis
+    (2 * dAtan2(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 > M_PI) theta -= 2*M_PI;
+
+  // 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 = 1;
+  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 <= 1) 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,
+                                 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]=REAL(0.5)*(joint->node[1].body->posr.pos[0]-joint->node[0].body->posr.pos[0]);
+      c[1]=REAL(0.5)*(joint->node[1].body->posr.pos[1]-joint->node[0].body->posr.pos[1]);
+      c[2]=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,-fm*ax1[0],-fm*ax1[1],
+                          -fm*ax1[2]);
+          if (joint->node[1].body)
+            dBodyAddTorque (joint->node[1].body,fm*ax1[0],fm*ax1[1],fm*ax1[2]);
+        }
+        else {
+          dBodyAddForce (joint->node[0].body,-fm*ax1[0],-fm*ax1[1],-fm*ax1[2]);
+          if (joint->node[1].body) {
+            dBodyAddForce (joint->node[1].body,fm*ax1[0],fm*ax1[1],fm*ax1[2]);
+
+            // linear limot torque decoupling step: refer to above discussion
+            dBodyAddTorque (joint->node[0].body,-fm*ltd[0],-fm*ltd[1],
+                            -fm*ltd[2]);
+            dBodyAddTorque (joint->node[1].body,-fm*ltd[0],-fm*ltd[1],
+                            -fm*ltd[2]);
+          }
+        }
+      }
+    }
+
+    if (limit) {
+      dReal k = info->fps * stop_erp;
+      info->c[row] = -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] = 0;
+          info->hi[row] = dInfinity;
+        }
+        else {
+          // high limit
+          info->lo[row] = -dInfinity;
+          info->hi[row] = 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 = -bounce * vel;
+              if (newc > info->c[row]) info->c[row] = newc;
+            }
+          }
+          else {
+            // high limit - all those computations are reversed
+            if (vel > 0) {
+              dReal newc = -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);
+  j->erp = j->world->global_erp;
+  j->cfm = j->world->global_cfm;
+}
+
+
+static void ballGetInfo1 (dxJointBall *j, dxJoint::Info1 *info)
+{
+  info->m = 3;
+  info->nub = 3;
+}
+
+
+static void ballGetInfo2 (dxJointBall *joint, dxJoint::Info2 *info)
+{
+  info->erp = joint->erp;
+  info->cfm[0] = joint->cfm;
+  info->cfm[1] = joint->cfm;
+  info->cfm[2] = joint->cfm;
+  setBall (joint,info,joint->anchor1,joint->anchor2);
+}
+
+
+void dJointSetBallAnchor (dJointID j, dReal x, dReal y, dReal z)
+{
+  dxJointBall* joint = (dxJointBall*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(joint->vtable == &__dball_vtable,"joint is not a ball");
+  setAnchors (joint,x,y,z,joint->anchor1,joint->anchor2);
+}
+
+
+void dJointSetBallAnchor2 (dJointID j, dReal x, dReal y, dReal z)
+{
+  dxJointBall* joint = (dxJointBall*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(joint->vtable == &__dball_vtable,"joint is not a ball");
+  joint->anchor2[0] = x;
+  joint->anchor2[1] = y;
+  joint->anchor2[2] = z;
+  joint->anchor2[3] = 0;
+
+}
+
+void dJointGetBallAnchor (dJointID j, dVector3 result)
+{
+  dxJointBall* joint = (dxJointBall*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(result,"bad result argument");
+  dUASSERT(joint->vtable == &__dball_vtable,"joint is not a ball");
+  if (joint->flags & dJOINT_REVERSE)
+    getAnchor2 (joint,result,joint->anchor2);
+  else
+    getAnchor (joint,result,joint->anchor1);
+}
+
+
+void dJointGetBallAnchor2 (dJointID j, dVector3 result)
+{
+  dxJointBall* joint = (dxJointBall*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(result,"bad result argument");
+  dUASSERT(joint->vtable == &__dball_vtable,"joint is not a ball");
+  if (joint->flags & dJOINT_REVERSE)
+    getAnchor (joint,result,joint->anchor1);
+  else
+    getAnchor2 (joint,result,joint->anchor2);
+}
+
+
+void dxJointBall::set (int num, dReal value)
+{
+  switch (num) {
+  case dParamCFM:
+    cfm = value;
+    break;
+  case dParamERP:
+    erp = value;
+    break;
+  }
+}
+ 
+
+dReal dxJointBall::get (int num)
+{
+  switch (num) {
+  case dParamCFM:
+    return cfm;
+  case dParamERP:
+    return erp;
+  default:
+        return 0;
+  }
+}
+
+
+void dJointSetBallParam (dJointID j, int parameter, dReal value)
+{
+  dxJointBall* joint = (dxJointBall*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(joint->vtable == &__dball_vtable,"joint is not a ball joint");
+  joint->set (parameter,value);
+}
+
+
+dReal dJointGetBallParam (dJointID j, int parameter)
+{
+  dxJointBall* joint = (dxJointBall*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(joint->vtable == &__dball_vtable,"joint is not a ball joint");
+  return joint->get (parameter);
+}
+
+
+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] = 1;
+  dSetZero (j->axis2,4);
+  j->axis2[0] = 1;
+  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 >= -M_PI || j->limot.histop <= M_PI) &&
+       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 = info->fps * info->erp;
+  info->c[3] = k * dDOT(b,p);
+  info->c[4] = 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];
+    }
+  }
+}
+
+
+void dJointSetHingeAnchor (dJointID j, dReal x, dReal y, dReal z)
+{
+  dxJointHinge* joint = (dxJointHinge*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(joint->vtable == &__dhinge_vtable,"joint is not a hinge");
+  setAnchors (joint,x,y,z,joint->anchor1,joint->anchor2);
+  hingeComputeInitialRelativeRotation (joint);
+}
+
+
+void dJointSetHingeAnchorDelta (dJointID j, dReal x, dReal y, dReal z, dReal dx, dReal dy, dReal dz)
+{
+  dxJointHinge* joint = (dxJointHinge*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(joint->vtable == &__dhinge_vtable,"joint is not a hinge");
+
+  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] = 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);
+}
+
+
+
+void dJointSetHingeAxis (dJointID j, dReal x, dReal y, dReal z)
+{
+  dxJointHinge* joint = (dxJointHinge*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(joint->vtable == &__dhinge_vtable,"joint is not a hinge");
+  setAxes (joint,x,y,z,joint->axis1,joint->axis2);
+  hingeComputeInitialRelativeRotation (joint);
+}
+
+
+void dJointGetHingeAnchor (dJointID j, dVector3 result)
+{
+  dxJointHinge* joint = (dxJointHinge*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(result,"bad result argument");
+  dUASSERT(joint->vtable == &__dhinge_vtable,"joint is not a hinge");
+  if (joint->flags & dJOINT_REVERSE)
+    getAnchor2 (joint,result,joint->anchor2);
+  else
+    getAnchor (joint,result,joint->anchor1);
+}
+
+
+void dJointGetHingeAnchor2 (dJointID j, dVector3 result)
+{
+  dxJointHinge* joint = (dxJointHinge*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(result,"bad result argument");
+  dUASSERT(joint->vtable == &__dhinge_vtable,"joint is not a hinge");
+  if (joint->flags & dJOINT_REVERSE)
+    getAnchor (joint,result,joint->anchor1);
+  else
+    getAnchor2 (joint,result,joint->anchor2);
+}
+
+
+void dJointGetHingeAxis (dJointID j, dVector3 result)
+{
+  dxJointHinge* joint = (dxJointHinge*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(result,"bad result argument");
+  dUASSERT(joint->vtable == &__dhinge_vtable,"joint is not a hinge");
+  getAxis (joint,result,joint->axis1);
+}
+
+
+void dJointSetHingeParam (dJointID j, int parameter, dReal value)
+{
+  dxJointHinge* joint = (dxJointHinge*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(joint->vtable == &__dhinge_vtable,"joint is not a hinge");
+  joint->limot.set (parameter,value);
+}
+
+
+dReal dJointGetHingeParam (dJointID j, int parameter)
+{
+  dxJointHinge* joint = (dxJointHinge*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(joint->vtable == &__dhinge_vtable,"joint is not a hinge");
+  return joint->limot.get (parameter);
+}
+
+
+dReal dJointGetHingeAngle (dJointID j)
+{
+  dxJointHinge* joint = (dxJointHinge*)j;
+  dAASSERT(joint);
+  dUASSERT(joint->vtable == &__dhinge_vtable,"joint is not a hinge");
+  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;
+}
+
+
+dReal dJointGetHingeAngleRate (dJointID j)
+{
+  dxJointHinge* joint = (dxJointHinge*)j;
+  dAASSERT(joint);
+  dUASSERT(joint->vtable == &__dhinge_vtable,"joint is not a Hinge");
+  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;
+}
+
+
+void dJointAddHingeTorque (dJointID j, dReal torque)
+{
+  dxJointHinge* joint = (dxJointHinge*)j;
+  dVector3 axis;
+  dAASSERT(joint);
+  dUASSERT(joint->vtable == &__dhinge_vtable,"joint is not a Hinge");
+
+  if (joint->flags & dJOINT_REVERSE)
+    torque = -torque;
+
+  getAxis (joint,axis,joint->axis1);
+  axis[0] *= torque;
+  axis[1] *= torque;
+  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] = 1;
+  dSetZero (j->qrel,4);
+  dSetZero (j->offset,4);
+  j->limot.init (j->world);
+}
+
+
+dReal dJointGetSliderPosition (dJointID j)
+{
+  dxJointSlider* joint = (dxJointSlider*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(joint->vtable == &__dslider_vtable,"joint is not a slider");
+
+  // 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);
+}
+
+
+dReal dJointGetSliderPositionRate (dJointID j)
+{
+  dxJointSlider* joint = (dxJointSlider*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(joint->vtable == &__dslider_vtable,"joint is not a slider");
+
+  // 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;
+    dCROSS (tmp, = REAL(0.5) * ,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];
+    dCROSS (tmp, = REAL(0.5) * ,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 = 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] = k * dDOT(p,c);
+    info->c[4] = 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] = k * dDOT(p,ofs);
+    info->c[4] = 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);
+}
+
+
+void dJointSetSliderAxis (dJointID j, dReal x, dReal y, dReal z)
+{
+  dxJointSlider* joint = (dxJointSlider*)j;
+  int i;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(joint->vtable == &__dslider_vtable,"joint is not a slider");
+  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];
+  }
+}
+
+
+void dJointSetSliderAxisDelta (dJointID j, dReal x, dReal y, dReal z, dReal dx, dReal dy, dReal dz)
+{
+  dxJointSlider* joint = (dxJointSlider*)j;
+  int i;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(joint->vtable == &__dslider_vtable,"joint is not a slider");
+  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;
+  }
+}
+
+
+
+void dJointGetSliderAxis (dJointID j, dVector3 result)
+{
+  dxJointSlider* joint = (dxJointSlider*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(result,"bad result argument");
+  dUASSERT(joint->vtable == &__dslider_vtable,"joint is not a slider");
+  getAxis (joint,result,joint->axis1);
+}
+
+
+void dJointSetSliderParam (dJointID j, int parameter, dReal value)
+{
+  dxJointSlider* joint = (dxJointSlider*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(joint->vtable == &__dslider_vtable,"joint is not a slider");
+  joint->limot.set (parameter,value);
+}
+
+
+dReal dJointGetSliderParam (dJointID j, int parameter)
+{
+  dxJointSlider* joint = (dxJointSlider*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(joint->vtable == &__dslider_vtable,"joint is not a slider");
+  return joint->limot.get (parameter);
+}
+
+
+void dJointAddSliderForce (dJointID j, dReal force)
+{
+  dxJointSlider* joint = (dxJointSlider*)j;
+  dVector3 axis;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(joint->vtable == &__dslider_vtable,"joint is not a slider");
+
+  if (joint->flags & dJOINT_REVERSE)
+    force -= force;
+
+  getAxis (joint,axis,joint->axis1);
+  axis[0] *= force;
+  axis[1] *= force;
+  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]=REAL(0.5)*(joint->node[1].body->posr.pos[0]-joint->node[0].body->posr.pos[0]);
+    c[1]=REAL(0.5)*(joint->node[1].body->posr.pos[1]-joint->node[0].body->posr.pos[1]);
+    c[2]=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)
+{
+  // default frictionless contact. hmmm, this info gets overwritten straight
+  // away anyway, so why bother?
+#if 0 /* so don't bother ;) */
+  j->contact.surface.mode = 0;
+  j->contact.surface.mu = 0;
+  dSetZero (j->contact.geom.pos,4);
+  dSetZero (j->contact.geom.normal,4);
+  j->contact.geom.depth = 0;
+#endif
+}
+
+
+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 > 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 = 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] = 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 = - 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 -dAtan2 (y,x);
+}
+
+
+static void hinge2Init (dxJointHinge2 *j)
+{
+  dSetZero (j->anchor1,4);
+  dSetZero (j->anchor2,4);
+  dSetZero (j->axis1,4);
+  j->axis1[0] = 1;
+  dSetZero (j->axis2,4);
+  j->axis2[1] = 1;
+  j->c0 = 0;
+  j->s0 = 0;
+
+  dSetZero (j->v1,4);
+  j->v1[0] = 1;
+  dSetZero (j->v2,4);
+  j->v2[1] = 1;
+
+  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 >= -M_PI || j->limot1.histop <= M_PI) &&
+      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 (axis[0]*axis[0] + axis[1]*axis[1] + 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 = info->fps * info->erp;
+  info->c[3] = k * (joint->c0 * s - 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] -= 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);
+  }
+}
+
+
+void dJointSetHinge2Anchor (dJointID j, dReal x, dReal y, dReal z)
+{
+  dxJointHinge2* joint = (dxJointHinge2*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(joint->vtable == &__dhinge2_vtable,"joint is not a hinge2");
+  setAnchors (joint,x,y,z,joint->anchor1,joint->anchor2);
+  makeHinge2V1andV2 (joint);
+}
+
+
+void dJointSetHinge2Axis1 (dJointID j, dReal x, dReal y, dReal z)
+{
+  dxJointHinge2* joint = (dxJointHinge2*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(joint->vtable == &__dhinge2_vtable,"joint is not a hinge2");
+  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);
+}
+
+
+void dJointSetHinge2Axis2 (dJointID j, dReal x, dReal y, dReal z)
+{
+  dxJointHinge2* joint = (dxJointHinge2*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(joint->vtable == &__dhinge2_vtable,"joint is not a hinge2");
+  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);
+}
+
+
+void dJointSetHinge2Param (dJointID j, int parameter, dReal value)
+{
+  dxJointHinge2* joint = (dxJointHinge2*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(joint->vtable == &__dhinge2_vtable,"joint is not a hinge2");
+  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);
+  }
+}
+
+
+void dJointGetHinge2Anchor (dJointID j, dVector3 result)
+{
+  dxJointHinge2* joint = (dxJointHinge2*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(result,"bad result argument");
+  dUASSERT(joint->vtable == &__dhinge2_vtable,"joint is not a hinge2");
+  if (joint->flags & dJOINT_REVERSE)
+    getAnchor2 (joint,result,joint->anchor2);
+  else
+    getAnchor (joint,result,joint->anchor1);
+}
+
+
+void dJointGetHinge2Anchor2 (dJointID j, dVector3 result)
+{
+  dxJointHinge2* joint = (dxJointHinge2*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(result,"bad result argument");
+  dUASSERT(joint->vtable == &__dhinge2_vtable,"joint is not a hinge2");
+  if (joint->flags & dJOINT_REVERSE)
+    getAnchor (joint,result,joint->anchor1);
+  else
+    getAnchor2 (joint,result,joint->anchor2);
+}
+
+
+void dJointGetHinge2Axis1 (dJointID j, dVector3 result)
+{
+  dxJointHinge2* joint = (dxJointHinge2*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(result,"bad result argument");
+  dUASSERT(joint->vtable == &__dhinge2_vtable,"joint is not a hinge2");
+  if (joint->node[0].body) {
+    dMULTIPLY0_331 (result,joint->node[0].body->posr.R,joint->axis1);
+  }
+}
+
+
+void dJointGetHinge2Axis2 (dJointID j, dVector3 result)
+{
+  dxJointHinge2* joint = (dxJointHinge2*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(result,"bad result argument");
+  dUASSERT(joint->vtable == &__dhinge2_vtable,"joint is not a hinge2");
+  if (joint->node[1].body) {
+    dMULTIPLY0_331 (result,joint->node[1].body->posr.R,joint->axis2);
+  }
+}
+
+
+dReal dJointGetHinge2Param (dJointID j, int parameter)
+{
+  dxJointHinge2* joint = (dxJointHinge2*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(joint->vtable == &__dhinge2_vtable,"joint is not a hinge2");
+  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);
+  }
+}
+
+
+dReal dJointGetHinge2Angle1 (dJointID j)
+{
+  dxJointHinge2* joint = (dxJointHinge2*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(joint->vtable == &__dhinge2_vtable,"joint is not a hinge2");
+  if (joint->node[0].body) return measureHinge2Angle (joint);
+  else return 0;
+}
+
+
+dReal dJointGetHinge2Angle1Rate (dJointID j)
+{
+  dxJointHinge2* joint = (dxJointHinge2*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(joint->vtable == &__dhinge2_vtable,"joint is not a hinge2");
+  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;
+}
+
+
+dReal dJointGetHinge2Angle2Rate (dJointID j)
+{
+  dxJointHinge2* joint = (dxJointHinge2*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(joint->vtable == &__dhinge2_vtable,"joint is not a hinge2");
+  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;
+}
+
+
+void dJointAddHinge2Torques (dJointID j, dReal torque1, dReal torque2)
+{
+  dxJointHinge2* joint = (dxJointHinge2*)j;
+  dVector3 axis1, axis2;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(joint->vtable == &__dhinge2_vtable,"joint is not a hinge2");
+
+  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] = axis1[0] * torque1 + axis2[0] * torque2;
+    axis1[1] = axis1[1] * torque1 + axis2[1] * torque2;
+    axis1[2] = axis1[2] * torque1 + 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] = 1;
+  dSetZero (j->axis2,4);
+  j->axis2[1] = 1;
+  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(sqrt(qrel[1]*qrel[1] + qrel[2]*qrel[2] + qrel[3]*qrel[3]));
+    qrel[1] *= l;
+    qrel[2] *= l;
+    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 >= -M_PI || j->limot1.histop <= M_PI) &&
+       j->limot1.lostop <= j->limot1.histop;
+  bool limiting2 = (j->limot2.lostop >= -M_PI || j->limot2.histop <= M_PI) &&
+       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] - k*ax1[0];
+  ax2_temp[1] = ax2[1] - k*ax1[1];
+  ax2_temp[2] = ax2[2] - 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] = info->fps * 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];
+    }
+  }
+}
+
+
+void dJointSetUniversalAnchor (dJointID j, dReal x, dReal y, dReal z)
+{
+  dxJointUniversal* joint = (dxJointUniversal*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(joint->vtable == &__duniversal_vtable,"joint is not a universal");
+  setAnchors (joint,x,y,z,joint->anchor1,joint->anchor2);
+  universalComputeInitialRelativeRotations(joint);
+}
+
+
+void dJointSetUniversalAxis1 (dJointID j, dReal x, dReal y, dReal z)
+{
+  dxJointUniversal* joint = (dxJointUniversal*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(joint->vtable == &__duniversal_vtable,"joint is not a universal");
+  if (joint->flags & dJOINT_REVERSE)
+    setAxes (joint,x,y,z,NULL,joint->axis2);
+  else
+    setAxes (joint,x,y,z,joint->axis1,NULL);
+  universalComputeInitialRelativeRotations(joint);
+}
+
+
+void dJointSetUniversalAxis2 (dJointID j, dReal x, dReal y, dReal z)
+{
+  dxJointUniversal* joint = (dxJointUniversal*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(joint->vtable == &__duniversal_vtable,"joint is not a universal");
+  if (joint->flags & dJOINT_REVERSE)
+    setAxes (joint,x,y,z,joint->axis1,NULL);
+  else
+    setAxes (joint,x,y,z,NULL,joint->axis2);
+  universalComputeInitialRelativeRotations(joint);
+}
+
+
+void dJointGetUniversalAnchor (dJointID j, dVector3 result)
+{
+  dxJointUniversal* joint = (dxJointUniversal*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(result,"bad result argument");
+  dUASSERT(joint->vtable == &__duniversal_vtable,"joint is not a universal");
+  if (joint->flags & dJOINT_REVERSE)
+    getAnchor2 (joint,result,joint->anchor2);
+  else
+    getAnchor (joint,result,joint->anchor1);
+}
+
+
+void dJointGetUniversalAnchor2 (dJointID j, dVector3 result)
+{
+  dxJointUniversal* joint = (dxJointUniversal*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(result,"bad result argument");
+  dUASSERT(joint->vtable == &__duniversal_vtable,"joint is not a universal");
+  if (joint->flags & dJOINT_REVERSE)
+    getAnchor (joint,result,joint->anchor1);
+  else
+    getAnchor2 (joint,result,joint->anchor2);
+}
+
+
+void dJointGetUniversalAxis1 (dJointID j, dVector3 result)
+{
+  dxJointUniversal* joint = (dxJointUniversal*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(result,"bad result argument");
+  dUASSERT(joint->vtable == &__duniversal_vtable,"joint is not a universal");
+  if (joint->flags & dJOINT_REVERSE)
+    getAxis2 (joint,result,joint->axis2);
+  else
+    getAxis (joint,result,joint->axis1);
+}
+
+
+void dJointGetUniversalAxis2 (dJointID j, dVector3 result)
+{
+  dxJointUniversal* joint = (dxJointUniversal*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(result,"bad result argument");
+  dUASSERT(joint->vtable == &__duniversal_vtable,"joint is not a universal");
+  if (joint->flags & dJOINT_REVERSE)
+    getAxis (joint,result,joint->axis1);
+  else
+    getAxis2 (joint,result,joint->axis2);
+}
+
+
+void dJointSetUniversalParam (dJointID j, int parameter, dReal value)
+{
+  dxJointUniversal* joint = (dxJointUniversal*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(joint->vtable == &__duniversal_vtable,"joint is not a universal");
+  if ((parameter & 0xff00) == 0x100) {
+    joint->limot2.set (parameter & 0xff,value);
+  }
+  else {
+    joint->limot1.set (parameter,value);
+  }
+}
+
+
+dReal dJointGetUniversalParam (dJointID j, int parameter)
+{
+  dxJointUniversal* joint = (dxJointUniversal*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(joint->vtable == &__duniversal_vtable,"joint is not a universal");
+  if ((parameter & 0xff00) == 0x100) {
+    return joint->limot2.get (parameter & 0xff);
+  }
+  else {
+    return joint->limot1.get (parameter);
+  }
+}
+
+void dJointGetUniversalAngles (dJointID j, dReal *angle1, dReal *angle2)
+{
+  dxJointUniversal* joint = (dxJointUniversal*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(joint->vtable == &__duniversal_vtable,"joint is not a universal");
+  if (joint->flags & dJOINT_REVERSE)
+    return getUniversalAngles (joint, angle2, angle1);
+  else
+    return getUniversalAngles (joint, angle1, angle2);
+}
+
+
+dReal dJointGetUniversalAngle1 (dJointID j)
+{
+  dxJointUniversal* joint = (dxJointUniversal*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(joint->vtable == &__duniversal_vtable,"joint is not a universal");
+  if (joint->flags & dJOINT_REVERSE)
+    return getUniversalAngle2 (joint);
+  else
+    return getUniversalAngle1 (joint);
+}
+
+
+dReal dJointGetUniversalAngle2 (dJointID j)
+{
+  dxJointUniversal* joint = (dxJointUniversal*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(joint->vtable == &__duniversal_vtable,"joint is not a universal");
+  if (joint->flags & dJOINT_REVERSE)
+    return getUniversalAngle1 (joint);
+  else
+    return getUniversalAngle2 (joint);
+}
+
+
+dReal dJointGetUniversalAngle1Rate (dJointID j)
+{
+  dxJointUniversal* joint = (dxJointUniversal*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(joint->vtable == &__duniversal_vtable,"joint is not a universal");
+
+  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;
+}
+
+
+dReal dJointGetUniversalAngle2Rate (dJointID j)
+{
+  dxJointUniversal* joint = (dxJointUniversal*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(joint->vtable == &__duniversal_vtable,"joint is not a universal");
+
+  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;
+}
+
+
+void dJointAddUniversalTorques (dJointID j, dReal torque1, dReal torque2)
+{
+  dxJointUniversal* joint = (dxJointUniversal*)j;
+  dVector3 axis1, axis2;
+  dAASSERT(joint);
+  dUASSERT(joint->vtable == &__duniversal_vtable,"joint is not a universal");
+
+  if (joint->flags & dJOINT_REVERSE) {
+    dReal temp = torque1;
+    torque1 = - torque2;
+    torque2 = - temp;
+  }
+
+  getAxis (joint,axis1,joint->axis1);
+  getAxis2 (joint,axis2,joint->axis2);
+  axis1[0] = axis1[0] * torque1 + axis2[0] * torque2;
+  axis1[1] = axis1[1] * torque1 + axis2[1] * torque2;
+  axis1[2] = axis1[2] * torque1 + 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] = 1;
+  dSetZero (j->axisR2,4);
+  j->axisR2[0] = 1;
+
+  dSetZero (j->axisP1,4);
+  j->axisP1[1] = 1;
+  dSetZero (j->qrel,4);
+  dSetZero (j->offset,4);
+
+  j->limotR.init (j->world);
+  j->limotP.init (j->world);
+}
+
+
+dReal dJointGetPRPosition (dJointID j)
+{
+  dxJointPR* joint = (dxJointPR*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(joint->vtable == &__dPR_vtable,"joint is not a Prismatic and Rotoide");
+
+  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);
+}
+
+
+dReal dJointGetPRPositionRate (dJointID j)
+{
+  dxJointPR* joint = (dxJointPR*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(joint->vtable == &__dPR_vtable,"joint is not a Prismatic and Rotoide");
+
+  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] *= omega;
+                angular[1] *= omega;
+                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 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 = 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,*R1,*R2;
+  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] = k * dDOT(b, axP);
+  info->c[1] = 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] = k * dDOT(ax1, err);
+  info->c[3] = 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]=REAL(0.5)*(joint->node[1].body->posr.pos[0]-joint->node[0].body->posr.pos[0]);
+      c[1]=REAL(0.5)*(joint->node[1].body->posr.pos[1]-joint->node[0].body->posr.pos[1]);
+      c[2]=REAL(0.5)*(joint->node[1].body->posr.pos[2]-joint->node[0].body->posr.pos[2]);
+                        dReal val = dDOT(q, c);
+                        c[0] -= val * c[0];
+                        c[1] -= val * c[1];
+                        c[2] -= 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 *= joint->limotP.fudge_factor;
+
+
+        dBodyAddForce (joint->node[0].body,-fm*axP[0],-fm*axP[1],-fm*axP[2]);
+
+                                if (joint->node[1].body) {
+                                        dBodyAddForce (joint->node[1].body,fm*axP[0],fm*axP[1],fm*axP[2]);
+
+                                        // linear limot torque decoupling step: refer to above discussion
+                                        dBodyAddTorque (joint->node[0].body,-fm*ltd[0],-fm*ltd[1],
+                                                                                                        -fm*ltd[2]);
+                                        dBodyAddTorque (joint->node[1].body,-fm*ltd[0],-fm*ltd[1],
+                                                                                                        -fm*ltd[2]);
+                                }
+      }
+    }
+
+                if (joint->limotP.limit) {
+      dReal k = info->fps * joint->limotP.stop_erp;
+      info->c[row] = -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 = -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 = -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
+    }
+  }
+}
+
+void dJointSetPRAnchor (dJointID j, dReal x, dReal y, dReal z)
+{
+  dxJointPR* joint = (dxJointPR*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(joint->vtable == &__dPR_vtable,"joint is not a Prismatic and Rotoide");
+
+  dVector3 dummy;
+  setAnchors (joint,x,y,z,dummy,joint->anchor2);
+}
+
+
+void dJointSetPRAxis1 (dJointID j, dReal x, dReal y, dReal z)
+{
+  dxJointPR* joint = (dxJointPR*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(joint->vtable == &__dPR_vtable,"joint is not a  Prismatic and Rotoide");
+
+  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);
+}
+
+
+void dJointSetPRAxis2 (dJointID j, dReal x, dReal y, dReal z)
+{
+  dxJointPR* joint = (dxJointPR*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(joint->vtable == &__dPR_vtable,"joint is not a Prismatic and Rotoide");
+  setAxes (joint,x,y,z,joint->axisR1,joint->axisR2);
+  PRComputeInitialRelativeRotation (joint);
+}
+
+
+void dJointSetPRParam (dJointID j, int parameter, dReal value)
+{
+  dxJointPR* joint = (dxJointPR*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(joint->vtable == &__dPR_vtable,"joint is not a Prismatic and Rotoide");
+  if ((parameter & 0xff00) == 0x100) {
+    joint->limotR.set (parameter,value);
+  }
+  else {
+    joint->limotP.set (parameter & 0xff,value);
+  }
+}
+
+void dJointGetPRAnchor (dJointID j, dVector3 result)
+{
+  dxJointPR* joint = (dxJointPR*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(result,"bad result argument");
+  dUASSERT(joint->vtable == &__dPR_vtable,"joint is not a Prismatic and Rotoide");
+
+  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];
+  }
+
+}
+
+void dJointGetPRAxis1 (dJointID j, dVector3 result)
+{
+  dxJointPR* joint = (dxJointPR*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(result,"bad result argument");
+  dUASSERT(joint->vtable == &__dPR_vtable,"joint is not a Prismatic and Rotoide");
+  getAxis(joint, result, joint->axisP1);
+}
+
+void dJointGetPRAxis2 (dJointID j, dVector3 result)
+{
+  dxJointPR* joint = (dxJointPR*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(result,"bad result argument");
+  dUASSERT(joint->vtable == &__dPR_vtable,"joint is not a Prismatic and Rotoide");
+  getAxis(joint, result, joint->axisR1);
+}
+
+dReal dJointGetPRParam (dJointID j, int parameter)
+{
+  dxJointPR* joint = (dxJointPR*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(joint->vtable == &__dPR_vtable,"joint is not Prismatic and Rotoide");
+  if ((parameter & 0xff00) == 0x100) {
+    return joint->limotR.get (parameter & 0xff);
+  }
+        else {
+                return joint->limotP.get (parameter);
+        }
+}
+
+void dJointAddPRTorque (dJointID j, dReal torque)
+{
+  dxJointPR* joint = (dxJointPR*)j;
+  dVector3 axis;
+  dAASSERT(joint);
+  dUASSERT(joint->vtable == &__dPR_vtable,"joint is not a Prismatic and Rotoide");
+
+  if (joint->flags & dJOINT_REVERSE)
+    torque = -torque;
+
+  getAxis (joint,axis,joint->axisR1);
+  axis[0] *= torque;
+  axis[1] *= torque;
+  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] = -dAtan2 (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] = -dAtan2 (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] = -dAtan2 (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);
+  }
+}
+
+
+void dJointSetAMotorNumAxes (dJointID j, int num)
+{
+  dxJointAMotor* joint = (dxJointAMotor*)j;
+  dAASSERT(joint && num >= 0 && num <= 3);
+  dUASSERT(joint->vtable == &__damotor_vtable,"joint is not an amotor");
+  if (joint->mode == dAMotorEuler) {
+    joint->num = 3;
+  }
+  else {
+    if (num < 0) num = 0;
+    if (num > 3) num = 3;
+    joint->num = num;
+  }
+}
+
+
+void dJointSetAMotorAxis (dJointID j, int anum, int rel, dReal x, dReal y, dReal z)
+{
+  dxJointAMotor* joint = (dxJointAMotor*)j;
+  dAASSERT(joint && anum >= 0 && anum <= 2 && rel >= 0 && rel <= 2);
+  dUASSERT(joint->vtable == &__damotor_vtable,"joint is not an amotor");
+  dUASSERT(!(!joint->node[1].body &&  (joint->flags & dJOINT_REVERSE) && rel == 1),"no first body, can't set axis rel=1");
+  dUASSERT(!(!joint->node[1].body && !(joint->flags & dJOINT_REVERSE) && rel == 2),"no second body, can't set axis rel=2");
+  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);
+}
+
+
+void dJointSetAMotorAngle (dJointID j, int anum, dReal angle)
+{
+  dxJointAMotor* joint = (dxJointAMotor*)j;
+  dAASSERT(joint && anum >= 0 && anum < 3);
+  dUASSERT(joint->vtable == &__damotor_vtable,"joint is not an amotor");
+  if (joint->mode == dAMotorUser) {
+    if (anum < 0) anum = 0;
+    if (anum > 3) anum = 3;
+    joint->angle[anum] = angle;
+  }
+}
+
+
+void dJointSetAMotorParam (dJointID j, int parameter, dReal value)
+{
+  dxJointAMotor* joint = (dxJointAMotor*)j;
+  dAASSERT(joint);
+  dUASSERT(joint->vtable == &__damotor_vtable,"joint is not an amotor");
+  int anum = parameter >> 8;
+  if (anum < 0) anum = 0;
+  if (anum > 2) anum = 2;
+  parameter &= 0xff;
+  joint->limot[anum].set (parameter, value);
+}
+
+
+void dJointSetAMotorMode (dJointID j, int mode)
+{
+  dxJointAMotor* joint = (dxJointAMotor*)j;
+  dAASSERT(joint);
+  dUASSERT(joint->vtable == &__damotor_vtable,"joint is not an amotor");
+  joint->mode = mode;
+  if (joint->mode == dAMotorEuler) {
+    joint->num = 3;
+    amotorSetEulerReferenceVectors (joint);
+  }
+}
+
+
+int dJointGetAMotorNumAxes (dJointID j)
+{
+  dxJointAMotor* joint = (dxJointAMotor*)j;
+  dAASSERT(joint);
+  dUASSERT(joint->vtable == &__damotor_vtable,"joint is not an amotor");
+  return joint->num;
+}
+
+
+void dJointGetAMotorAxis (dJointID j, int anum, dVector3 result)
+{
+  dxJointAMotor* joint = (dxJointAMotor*)j;
+  dAASSERT(joint && anum >= 0 && anum < 3);
+  dUASSERT(joint->vtable == &__damotor_vtable,"joint is not an amotor");
+  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];
+  }
+}
+
+
+int dJointGetAMotorAxisRel (dJointID j, int anum)
+{
+  dxJointAMotor* joint = (dxJointAMotor*)j;
+  dAASSERT(joint && anum >= 0 && anum < 3);
+  dUASSERT(joint->vtable == &__damotor_vtable,"joint is not an amotor");
+  if (anum < 0) anum = 0;
+  if (anum > 2) anum = 2;
+  return joint->rel[anum];
+}
+
+
+dReal dJointGetAMotorAngle (dJointID j, int anum)
+{
+  dxJointAMotor* joint = (dxJointAMotor*)j;
+  dAASSERT(joint && anum >= 0 && anum < 3);
+  dUASSERT(joint->vtable == &__damotor_vtable,"joint is not an amotor");
+  if (anum < 0) anum = 0;
+  if (anum > 3) anum = 3;
+  return joint->angle[anum];
+}
+
+
+dReal dJointGetAMotorAngleRate (dJointID j, int anum)
+{
+  dxJointAMotor* joint = (dxJointAMotor*)j;
+  // @@@
+  dDebug (0,"not yet implemented");
+  return 0;
+}
+
+
+dReal dJointGetAMotorParam (dJointID j, int parameter)
+{
+  dxJointAMotor* joint = (dxJointAMotor*)j;
+  dAASSERT(joint);
+  dUASSERT(joint->vtable == &__damotor_vtable,"joint is not an amotor");
+  int anum = parameter >> 8;
+  if (anum < 0) anum = 0;
+  if (anum > 2) anum = 2;
+  parameter &= 0xff;
+  return joint->limot[anum].get (parameter);
+}
+
+
+int dJointGetAMotorMode (dJointID j)
+{
+  dxJointAMotor* joint = (dxJointAMotor*)j;
+  dAASSERT(joint);
+  dUASSERT(joint->vtable == &__damotor_vtable,"joint is not an amotor");
+  return joint->mode;
+}
+
+
+void dJointAddAMotorTorques (dJointID j, dReal torque1, dReal torque2, dReal torque3)
+{
+  dxJointAMotor* joint = (dxJointAMotor*)j;
+  dVector3 axes[3];
+  dAASSERT(joint);
+  dUASSERT(joint->vtable == &__damotor_vtable,"joint is not an amotor");
+
+  if (joint->num == 0)
+    return;
+  dUASSERT((joint->flags & dJOINT_REVERSE) == 0, "dJointAddAMotorTorques not yet implemented for reverse AMotor joints");
+
+  amotorComputeGlobalAxes (joint,axes);
+  axes[0][0] *= torque1;
+  axes[0][1] *= torque1;
+  axes[0][2] *= torque1;
+  if (joint->num >= 2) {
+    axes[0][0] += axes[1][0] * torque2;
+    axes[0][1] += axes[1][1] * torque2;
+    axes[0][2] += axes[1][2] * torque2;
+    if (joint->num >= 3) {
+      axes[0][0] += axes[2][0] * torque3;
+      axes[0][1] += axes[2][1] * torque3;
+      axes[0][2] += 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);
+  }
+}
+
+void dJointSetLMotorAxis (dJointID j, int anum, int rel, dReal x, dReal y, dReal z)
+{
+  dxJointLMotor* joint = (dxJointLMotor*)j;
+//for now we are ignoring rel!
+  dAASSERT(joint && anum >= 0 && anum <= 2 && rel >= 0 && rel <= 2);
+  dUASSERT(joint->vtable == &__dlmotor_vtable,"joint is not an lmotor");
+  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]);
+}
+
+void dJointSetLMotorNumAxes (dJointID j, int num)
+{
+  dxJointLMotor* joint = (dxJointLMotor*)j;
+  dAASSERT(joint && num >= 0 && num <= 3);
+  dUASSERT(joint->vtable == &__dlmotor_vtable,"joint is not an lmotor");
+  if (num < 0) num = 0;
+  if (num > 3) num = 3;
+  joint->num = num;
+}
+
+void dJointSetLMotorParam (dJointID j, int parameter, dReal value)
+{
+  dxJointLMotor* joint = (dxJointLMotor*)j;
+  dAASSERT(joint);
+  dUASSERT(joint->vtable == &__dlmotor_vtable,"joint is not an lmotor");
+  int anum = parameter >> 8;
+  if (anum < 0) anum = 0;
+  if (anum > 2) anum = 2;
+  parameter &= 0xff;
+  joint->limot[anum].set (parameter, value);
+}
+
+int dJointGetLMotorNumAxes (dJointID j)
+{
+  dxJointLMotor* joint = (dxJointLMotor*)j;
+  dAASSERT(joint);
+  dUASSERT(joint->vtable == &__dlmotor_vtable,"joint is not an lmotor");
+  return joint->num;
+}
+
+
+void dJointGetLMotorAxis (dJointID j, int anum, dVector3 result)
+{
+  dxJointLMotor* joint = (dxJointLMotor*)j;
+  dAASSERT(joint && anum >= 0 && anum < 3);
+  dUASSERT(joint->vtable == &__dlmotor_vtable,"joint is not an lmotor");
+  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];
+}
+
+dReal dJointGetLMotorParam (dJointID j, int parameter)
+{
+  dxJointLMotor* joint = (dxJointLMotor*)j;
+  dAASSERT(joint);
+  dUASSERT(joint->vtable == &__dlmotor_vtable,"joint is not an lmotor");
+  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);
+  j->erp = j->world->global_erp;
+  j->cfm = j->world->global_cfm;
+}
+
+
+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] = 1;
+  info->J1l[s+1] = 1;
+  info->J1l[2*s+2] = 1;
+
+  info->erp = joint->erp;
+  info->cfm[0] = joint->cfm;
+  info->cfm[1] = joint->cfm;
+  info->cfm[2] = joint->cfm;
+
+  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] = -1;
+    info->J2l[s+1] = -1;
+    info->J2l[2*s+2] = -1;
+  }
+
+  // set right hand side for the first three rows (linear)
+  dReal k = info->fps * info->erp;
+  if (joint->node[1].body) {
+    for (int j=0; j<3; j++)
+      info->c[j] = 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] = k * (joint->offset[j] - joint->node[0].body->posr.pos[j]);
+  }
+}
+
+
+void dJointSetFixed (dJointID j)
+{
+  dxJointFixed* joint = (dxJointFixed*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(joint->vtable == &__dfixed_vtable,"joint is not fixed");
+  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];
+    }
+  }
+}
+
+void dxJointFixed::set (int num, dReal value)
+{
+  switch (num) {
+  case dParamCFM:
+    cfm = value;
+    break;
+  case dParamERP:
+    erp = value;
+    break;
+  }
+}
+ 
+
+dReal dxJointFixed::get (int num)
+{
+  switch (num) {
+  case dParamCFM:
+    return cfm;
+  case dParamERP:
+    return erp;
+  default:
+        return 0;
+  }
+}
+
+
+void dJointSetFixedParam (dJointID j, int parameter, dReal value)
+{
+  dxJointFixed* joint = (dxJointFixed*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(joint->vtable == &__dfixed_vtable,"joint is not a fixed joint");
+  joint->set (parameter,value);
+}
+
+
+dReal dJointGetFixedParam (dJointID j, int parameter)
+{
+  dxJointFixed* joint = (dxJointFixed*)j;
+  dUASSERT(joint,"bad joint argument");
+  dUASSERT(joint->vtable == &__dfixed_vtable,"joint is not a fixed joint");
+  return joint->get (parameter);
+}
+
+
+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)
+{
+  dDebug (0,"this should never get called");
+}
+
+
+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 dReal   Midentity[3][3] =
+                {
+                    {   1,  0,  0   },
+                    {   0,  1,  0   },
+                    {   0,  0,  1,  }
+                };
+
+
+
+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 = 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, 1);
+    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], =, 1, 0, 0);
+    VoXYZ (&info->J1a[r2], =, 0, 1, 0);
+
+    // error correction (against drift):
+
+    // a) linear vz, so that z (== pos[2]) == 0
+    info->c[0] = eps * -joint->node[0].body->posr.pos[2];
+
+# if 0
+    // b) angular correction? -> left to application !!!
+    dReal       *body_z_axis = &joint->node[0].body->R[8];
+    info->c[1] = eps * +atan2 (body_z_axis[1], body_z_axis[2]); // wx error
+    info->c[2] = eps * -atan2 (body_z_axis[0], body_z_axis[2]); // wy error
+# endif
+
+    // 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
+};
+
+
+void dJointSetPlane2DXParam (dxJoint *joint,
+                      int parameter, dReal value)
+{
+        dUASSERT (joint, "bad joint argument");
+        dUASSERT (joint->vtable == &__dplane2d_vtable, "joint is not a plane2d");
+        dxJointPlane2D* joint2d = (dxJointPlane2D*)( joint );
+        joint2d->motor_x.set (parameter, value);
+}
+
+
+void dJointSetPlane2DYParam (dxJoint *joint,
+                      int parameter, dReal value)
+{
+        dUASSERT (joint, "bad joint argument");
+        dUASSERT (joint->vtable == &__dplane2d_vtable, "joint is not a plane2d");
+        dxJointPlane2D* joint2d = (dxJointPlane2D*)( joint );
+        joint2d->motor_y.set (parameter, value);
+}
+
+
+
+void dJointSetPlane2DAngleParam (dxJoint *joint,
+                      int parameter, dReal value)
+{
+        dUASSERT (joint, "bad joint argument");
+        dUASSERT (joint->vtable == &__dplane2d_vtable, "joint is not a plane2d");
+        dxJointPlane2D* joint2d = (dxJointPlane2D*)( joint );
+        joint2d->motor_angle.set (parameter, value);
+}
+
+
+