/*************************************************************************
* *
* 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/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->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->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->pos[j] -
a1[j] - joint->node[0].body->pos[j]);
}
}
else {
for (int j=0; j<3; j++) {
info->c[j] = k * (anchor2[j] - a1[j] -
joint->node[0].body->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->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->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->pos[i];
if (joint->node[1].body) {
for (i=0; i<3; i++) a2[i] += joint->node[1].body->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->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->pos[0];
q[1] = y - j->node[0].body->pos[1];
q[2] = z - j->node[0].body->pos[2];
q[3] = 0;
dMULTIPLY1_331 (anchor1,j->node[0].body->R,q);
if (j->node[1].body) {
q[0] = x - j->node[1].body->pos[0];
q[1] = y - j->node[1].body->pos[1];
q[2] = z - j->node[1].body->pos[2];
q[3] = 0;
dMULTIPLY1_331 (anchor2,j->node[1].body->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->R,q);
axis1[3] = 0;
}
if (axis2) {
if (j->node[1].body) {
dMULTIPLY1_331 (axis2,j->node[1].body->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->R,anchor1);
result[0] += j->node[0].body->pos[0];
result[1] += j->node[0].body->pos[1];
result[2] += j->node[0].body->pos[2];
}
}
static void getAnchor2 (dxJoint *j, dVector3 result, dVector3 anchor2)
{
if (j->node[1].body) {
dMULTIPLY0_331 (result,j->node[1].body->R,anchor2);
result[0] += j->node[1].body->pos[0];
result[1] += j->node[1].body->pos[1];
result[2] += j->node[1].body->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->R,axis1);
}
}
static void getAxis2 (dxJoint *j, dVector3 result, dVector3 axis2)
{
if (j->node[1].body) {
dMULTIPLY0_331 (result,j->node[1].body->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:
if (value <= histop) lostop = value;
break;
case dParamHiStop:
if (value >= lostop) 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->pos[0]-joint->node[0].body->pos[0]);
c[1]=REAL(0.5)*(joint->node[1].body->pos[1]-joint->node[0].body->pos[1]);
c[2]=REAL(0.5)*(joint->node[1].body->pos[2]-joint->node[0].body->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) 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);
}
static void ballGetInfo1 (dxJointBall *j, dxJoint::Info1 *info)
{
info->m = 3;
info->nub = 3;
}
static void ballGetInfo2 (dxJointBall *joint, dxJoint::Info2 *info)
{
setBall (joint,info,joint->anchor1,joint->anchor2);
}
extern "C" void dJointSetBallAnchor (dxJointBall *joint,
dReal x, dReal y, dReal z)
{
dUASSERT(joint,"bad joint argument");
dUASSERT(joint->vtable == &__dball_vtable,"joint is not a ball");
setAnchors (joint,x,y,z,joint->anchor1,joint->anchor2);
}
extern "C" void dJointGetBallAnchor (dxJointBall *joint, dVector3 result)
{
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);
}
extern "C" void dJointGetBallAnchor2 (dxJointBall *joint, dVector3 result)
{
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);
}
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->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->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];
}
}
}
extern "C" void dJointSetHingeAnchor (dxJointHinge *joint,
dReal x, dReal y, dReal z)
{
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);
}
extern "C" void dJointSetHingeAxis (dxJointHinge *joint,
dReal x, dReal y, dReal z)
{
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);
}
extern "C" void dJointGetHingeAnchor (dxJointHinge *joint, dVector3 result)
{
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);
}
extern "C" void dJointGetHingeAnchor2 (dxJointHinge *joint, dVector3 result)
{
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);
}
extern "C" void dJointGetHingeAxis (dxJointHinge *joint, dVector3 result)
{
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);
}
extern "C" void dJointSetHingeParam (dxJointHinge *joint,
int parameter, dReal value)
{
dUASSERT(joint,"bad joint argument");
dUASSERT(joint->vtable == &__dhinge_vtable,"joint is not a hinge");
joint->limot.set (parameter,value);
}
extern "C" dReal dJointGetHingeParam (dxJointHinge *joint, int parameter)
{
dUASSERT(joint,"bad joint argument");
dUASSERT(joint->vtable == &__dhinge_vtable,"joint is not a hinge");
return joint->limot.get (parameter);
}
extern "C" dReal dJointGetHingeAngle (dxJointHinge *joint)
{
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;
}
extern "C" dReal dJointGetHingeAngleRate (dxJointHinge *joint)
{
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->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;
}
extern "C" void dJointAddHingeTorque (dxJointHinge *joint, dReal torque)
{
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);
}
extern "C" dReal dJointGetSliderPosition (dxJointSlider *joint)
{
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->R,joint->axis1);
if (joint->node[1].body) {
// get body2 + offset point in global coordinates
dMULTIPLY0_331 (q,joint->node[1].body->R,joint->offset);
for (int i=0; i<3; i++) q[i] = joint->node[0].body->pos[i] - q[i] -
joint->node[1].body->pos[i];
}
else {
for (int i=0; i<3; i++) q[i] = joint->node[0].body->pos[i] -
joint->offset[i];
}
return dDOT(ax1,q);
}
extern "C" dReal dJointGetSliderPositionRate (dxJointSlider *joint)
{
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->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 s2=2*s,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->pos;
R1 = joint->node[0].body->R;
if (joint->node[1].body) {
pos2 = joint->node[1].body->pos;
R2 = joint->node[1].body->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->J2a[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->J2a[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);
}
extern "C" void dJointSetSliderAxis (dxJointSlider *joint,
dReal x, dReal y, dReal z)
{
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->pos[i] - joint->node[1].body->pos[i];
dMULTIPLY1_331 (joint->offset,joint->node[1].body->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->pos[i];
}
}
extern "C" void dJointGetSliderAxis (dxJointSlider *joint, dVector3 result)
{
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);
}
extern "C" void dJointSetSliderParam (dxJointSlider *joint,
int parameter, dReal value)
{
dUASSERT(joint,"bad joint argument");
dUASSERT(joint->vtable == &__dslider_vtable,"joint is not a slider");
joint->limot.set (parameter,value);
}
extern "C" dReal dJointGetSliderParam (dxJointSlider *joint, int parameter)
{
dUASSERT(joint,"bad joint argument");
dUASSERT(joint->vtable == &__dslider_vtable,"joint is not a slider");
return joint->limot.get (parameter);
}
extern "C" void dJointAddSliderForce (dxJointSlider *joint, dReal force)
{
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]);
}
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 i,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;
for (i=0; i<3; i++) c1[i] = j->contact.geom.pos[i] - j->node[0].body->pos[i];
// 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) {
for (i=0; i<3; i++) c2[i] = j->contact.geom.pos[i] -
j->node[1].body->pos[i];
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;
info->c[0] = k*j->contact.geom.depth;
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->R,joint->axis2);
dMULTIPLY1_331 (a2,joint->node[0].body->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->R,joint->axis1); \
dMULTIPLY0_331 (ax2,joint->node[1].body->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->R,joint->axis1);
dMULTIPLY0_331 (ax2,joint->node[1].body->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->R,ax2);
dMULTIPLY1_331 (joint->v2,joint->node[0].body->R,v);
}
}
extern "C" void dJointSetHinge2Anchor (dxJointHinge2 *joint,
dReal x, dReal y, dReal z)
{
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);
}
extern "C" void dJointSetHinge2Axis1 (dxJointHinge2 *joint,
dReal x, dReal y, dReal z)
{
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->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);
}
extern "C" void dJointSetHinge2Axis2 (dxJointHinge2 *joint,
dReal x, dReal y, dReal z)
{
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->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);
}
extern "C" void dJointSetHinge2Param (dxJointHinge2 *joint,
int parameter, dReal value)
{
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);
}
}
extern "C" void dJointGetHinge2Anchor (dxJointHinge2 *joint, dVector3 result)
{
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);
}
extern "C" void dJointGetHinge2Anchor2 (dxJointHinge2 *joint, dVector3 result)
{
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);
}
extern "C" void dJointGetHinge2Axis1 (dxJointHinge2 *joint, dVector3 result)
{
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->R,joint->axis1);
}
}
extern "C" void dJointGetHinge2Axis2 (dxJointHinge2 *joint, dVector3 result)
{
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->R,joint->axis2);
}
}
extern "C" dReal dJointGetHinge2Param (dxJointHinge2 *joint, int parameter)
{
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);
}
}
extern "C" dReal dJointGetHinge2Angle1 (dxJointHinge2 *joint)
{
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;
}
extern "C" dReal dJointGetHinge2Angle1Rate (dxJointHinge2 *joint)
{
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->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;
}
extern "C" dReal dJointGetHinge2Angle2Rate (dxJointHinge2 *joint)
{
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->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;
}
extern "C" void dJointAddHinge2Torques (dxJointHinge2 *joint, dReal torque1, dReal torque2)
{
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->R,joint->axis1);
dMULTIPLY0_331 (axis2,joint->node[1].body->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->R * joint->axis1"
dMULTIPLY0_331 (ax1,joint->node[0].body->R,joint->axis1);
if (joint->node[1].body) {
dMULTIPLY0_331 (ax2,joint->node[1].body->R,joint->axis2);
}
else {
ax2[0] = joint->axis2[0];
ax2[1] = joint->axis2[1];
ax2[2] = joint->axis2[2];
}
}
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;
angle1 = getUniversalAngle1(j);
angle2 = getUniversalAngle2(j);
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];
}
}
}
extern "C" void dJointSetUniversalAnchor (dxJointUniversal *joint,
dReal x, dReal y, dReal z)
{
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);
}
extern "C" void dJointSetUniversalAxis1 (dxJointUniversal *joint,
dReal x, dReal y, dReal z)
{
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);
}
extern "C" void dJointSetUniversalAxis2 (dxJointUniversal *joint,
dReal x, dReal y, dReal z)
{
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);
}
extern "C" void dJointGetUniversalAnchor (dxJointUniversal *joint,
dVector3 result)
{
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);
}
extern "C" void dJointGetUniversalAnchor2 (dxJointUniversal *joint,
dVector3 result)
{
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);
}
extern "C" void dJointGetUniversalAxis1 (dxJointUniversal *joint,
dVector3 result)
{
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);
}
extern "C" void dJointGetUniversalAxis2 (dxJointUniversal *joint,
dVector3 result)
{
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);
}
extern "C" void dJointSetUniversalParam (dxJointUniversal *joint,
int parameter, dReal value)
{
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);
}
}
extern "C" dReal dJointGetUniversalParam (dxJointUniversal *joint, int parameter)
{
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);
}
}
extern "C" dReal dJointGetUniversalAngle1 (dxJointUniversal *joint)
{
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);
}
extern "C" dReal dJointGetUniversalAngle2 (dxJointUniversal *joint)
{
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);
}
extern "C" dReal dJointGetUniversalAngle1Rate (dxJointUniversal *joint)
{
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;
}
extern "C" dReal dJointGetUniversalAngle2Rate (dxJointUniversal *joint)
{
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;
}
extern "C" void dJointAddUniversalTorques (dxJointUniversal *joint, dReal torque1, dReal torque2)
{
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};
//****************************************************************************
// 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);
j->flags |= dJOINT_TWOBODIES;
}
// 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->R,joint->axis[0]);
dMULTIPLY0_331 (ax[2],joint->node[1].body->R,joint->axis[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->R,joint->axis[i]);
}
if (joint->rel[i] == 2) {
// relative to b2
dMULTIPLY0_331 (ax[i],joint->node[1].body->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->R,joint->reference1);
dMULTIPLY0_331 (ref2,joint->node[1].body->R,joint->reference2);
// 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->R,j->axis[2]);
dMULTIPLY1_331 (j->reference1,j->node[0].body->R,r);
dMULTIPLY0_331 (r,j->node[0].body->R,j->axis[0]);
dMULTIPLY1_331 (j->reference2,j->node[1].body->R,r);
}
}
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);
}
}
extern "C" void dJointSetAMotorNumAxes (dxJointAMotor *joint, int num)
{
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;
}
}
extern "C" void dJointSetAMotorAxis (dxJointAMotor *joint, int anum, int rel,
dReal x, dReal y, dReal z)
{
dAASSERT(joint && anum >= 0 && anum <= 2 && rel >= 0 && rel <= 2);
dUASSERT(joint->vtable == &__damotor_vtable,"joint is not an amotor");
if (anum < 0) anum = 0;
if (anum > 2) anum = 2;
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->R,r);
}
else {
dMULTIPLY1_331 (joint->axis[anum],joint->node[1].body->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]);
if (joint->mode == dAMotorEuler) amotorSetEulerReferenceVectors (joint);
}
extern "C" void dJointSetAMotorAngle (dxJointAMotor *joint, int anum,
dReal angle)
{
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;
}
}
extern "C" void dJointSetAMotorParam (dxJointAMotor *joint, int parameter,
dReal value)
{
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);
}
extern "C" void dJointSetAMotorMode (dxJointAMotor *joint, int mode)
{
dAASSERT(joint);
dUASSERT(joint->vtable == &__damotor_vtable,"joint is not an amotor");
joint->mode = mode;
if (joint->mode == dAMotorEuler) {
joint->num = 3;
amotorSetEulerReferenceVectors (joint);
}
}
extern "C" int dJointGetAMotorNumAxes (dxJointAMotor *joint)
{
dAASSERT(joint);
dUASSERT(joint->vtable == &__damotor_vtable,"joint is not an amotor");
return joint->num;
}
extern "C" void dJointGetAMotorAxis (dxJointAMotor *joint, int anum,
dVector3 result)
{
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->R,joint->axis[anum]);
}
else {
dMULTIPLY0_331 (result,joint->node[1].body->R,joint->axis[anum]);
}
}
else {
result[0] = joint->axis[anum][0];
result[1] = joint->axis[anum][1];
result[2] = joint->axis[anum][2];
}
}
extern "C" int dJointGetAMotorAxisRel (dxJointAMotor *joint, int anum)
{
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];
}
extern "C" dReal dJointGetAMotorAngle (dxJointAMotor *joint, int anum)
{
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];
}
extern "C" dReal dJointGetAMotorAngleRate (dxJointAMotor *joint, int anum)
{
// @@@
dDebug (0,"not yet implemented");
return 0;
}
extern "C" dReal dJointGetAMotorParam (dxJointAMotor *joint, int parameter)
{
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);
}
extern "C" int dJointGetAMotorMode (dxJointAMotor *joint)
{
dAASSERT(joint);
dUASSERT(joint->vtable == &__damotor_vtable,"joint is not an amotor");
return joint->mode;
}
extern "C" void dJointAddAMotorTorques (dxJointAMotor *joint, dReal torque1, dReal torque2, dReal torque3)
{
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][0] * torque2;
axes[0][2] += axes[1][0] * torque2;
if (joint->num >= 3) {
axes[0][0] += axes[2][0] * torque3;
axes[0][1] += axes[2][0] * torque3;
axes[0][2] += axes[2][0] * 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};
//****************************************************************************
// fixed joint
static void fixedInit (dxJointFixed *j)
{
dSetZero (j->offset,4);
dSetZero (j->qrel,4);
}
static void fixedGetInfo1 (dxJointFixed *j, dxJoint::Info1 *info)
{
info->m = 6;
info->nub = 6;
}
static void fixedGetInfo2 (dxJointFixed *joint, dxJoint::Info2 *info)
{
int s = info->rowskip;
// Three rows for orientation
setFixedOrientation(joint, info, joint->qrel, 3);
// Three rows for position.
// set jacobian
info->J1l[0] = 1;
info->J1l[s+1] = 1;
info->J1l[2*s+2] = 1;
dVector3 ofs;
dMULTIPLY0_331 (ofs,joint->node[0].body->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->pos[j] -
joint->node[0].body->pos[j] + ofs[j]);
}
else {
for (int j=0; j<3; j++)
info->c[j] = k * (joint->offset[j] - joint->node[0].body->pos[j]);
}
}
extern "C" void dJointSetFixed (dxJointFixed *joint)
{
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->pos[i];
for (i=0; i<4; i++) ofs[i] -= joint->node[1].body->pos[i];
dMULTIPLY1_331 (joint->offset,joint->node[0].body->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->pos[i];
}
}
}
dxJoint::Vtable __dfixed_vtable = {
sizeof(dxJointFixed),
(dxJoint::init_fn*) fixedInit,
(dxJoint::getInfo1_fn*) fixedGetInfo1,
(dxJoint::getInfo2_fn*) fixedGetInfo2,
dJointTypeFixed};
//****************************************************************************
// null joint
static void nullGetInfo1 (dxJointNull *j, dxJoint::Info1 *info)
{
info->m = 0;
info->nub = 0;
}
static void nullGetInfo2 (dxJointNull *joint, dxJoint::Info2 *info)
{
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};
/******************** breakable joint contribution ***********************/
extern "C" void dJointSetBreakable (dxJoint *joint, int b) {
dAASSERT(joint);
if (b) {
// we want this joint to be breakable but we must first check if it
// was already breakable
if (!joint->breakInfo) {
// allocate a dxJointBreakInfo struct
joint->breakInfo = new dxJointBreakInfo;
joint->breakInfo->flags = 0;
for (int i = 0; i < 3; i++) {
joint->breakInfo->b1MaxF[0] = 0;
joint->breakInfo->b1MaxT[0] = 0;
joint->breakInfo->b2MaxF[0] = 0;
joint->breakInfo->b2MaxT[0] = 0;
}
joint->breakInfo->callback = 0;
}
else {
// the joint was already breakable
return;
}
}
else {
// we want this joint to be unbreakable mut we must first check if
// it is alreay unbreakable
if (joint->breakInfo) {
// deallocate the dxJointBreakInfo struct
delete joint->breakInfo;
joint->breakInfo = 0;
}
else {
// the joint was already unbreakable
return;
}
}
}
extern "C" void dJointSetBreakCallback (dxJoint *joint, dJointBreakCallback *callbackFunc) {
dAASSERT(joint);
# ifndef dNODEBUG
// only works for a breakable joint
if (!joint->breakInfo) {
dDebug (0, "dJointSetBreakCallback called on unbreakable joint");
}
# endif
joint->breakInfo->callback = callbackFunc;
}
extern "C" void dJointSetBreakMode (dxJoint *joint, int mode) {
dAASSERT(joint);
# ifndef dNODEBUG
// only works for a breakable joint
if (!joint->breakInfo) {
dDebug (0, "dJointSetBreakMode called on unbreakable joint");
}
# endif
joint->breakInfo->flags = mode;
}
extern "C" int dJointGetBreakMode (dxJoint *joint) {
dAASSERT(joint);
# ifndef dNODEBUG
// only works for a breakable joint
if (!joint->breakInfo) {
dDebug (0, "dJointGetBreakMode called on unbreakable joint");
}
# endif
return joint->breakInfo->flags;
}
extern "C" void dJointSetBreakForce (dxJoint *joint, int body, dReal x, dReal y, dReal z) {
dAASSERT(joint);
# ifndef dNODEBUG
// only works for a breakable joint
if (!joint->breakInfo) {
dDebug (0, "dJointSetBreakForce called on unbreakable joint");
}
# endif
if (body) {
joint->breakInfo->b2MaxF[0] = x;
joint->breakInfo->b2MaxF[1] = y;
joint->breakInfo->b2MaxF[2] = z;
}
else {
joint->breakInfo->b1MaxF[0] = x;
joint->breakInfo->b1MaxF[1] = y;
joint->breakInfo->b1MaxF[2] = z;
}
}
extern "C" void dJointSetBreakTorque (dxJoint *joint, int body, dReal x, dReal y, dReal z) {
dAASSERT(joint);
# ifndef dNODEBUG
// only works for a breakable joint
if (!joint->breakInfo) {
dDebug (0, "dJointSetBreakTorque called on unbreakable joint");
}
# endif
if (body) {
joint->breakInfo->b2MaxT[0] = x;
joint->breakInfo->b2MaxT[1] = y;
joint->breakInfo->b2MaxT[2] = z;
}
else {
joint->breakInfo->b1MaxT[0] = x;
joint->breakInfo->b1MaxT[1] = y;
joint->breakInfo->b1MaxT[2] = z;
}
}
extern "C" int dJointIsBreakable (dxJoint *joint) {
dAASSERT(joint);
return joint->breakInfo != 0;
}
extern "C" void dJointGetBreakForce (dxJoint *joint, int body, dReal *force) {
dAASSERT(joint);
# ifndef dNODEBUG
// only works for a breakable joint
if (!joint->breakInfo) {
dDebug (0, "dJointGetBreakForce called on unbreakable joint");
}
# endif
if (body)
for (int i=0; i<3; i++) force[i]=joint->breakInfo->b2MaxF[i];
else
for (int i=0; i<3; i++) force[i]=joint->breakInfo->b1MaxF[i];
}
extern "C" void dJointGetBreakTorque (dxJoint *joint, int body, dReal *torque) {
dAASSERT(joint);
# ifndef dNODEBUG
// only works for a breakable joint
if (!joint->breakInfo) {
dDebug (0, "dJointGetBreakTorque called on unbreakable joint");
}
# endif
if (body)
for (int i=0; i<3; i++) torque[i]=joint->breakInfo->b2MaxT[i];
else
for (int i=0; i<3; i++) torque[i]=joint->breakInfo->b1MaxT[i];
}
/*************************************************************************/
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