void
dxJointTransmission::getInfo2( dReal worldFPS,
dReal /*worldERP*/,
const Info2Descr* info )
{
dVector3 a[2], n[2], l[2], r[2], c[2], s, t, O, d, z, u, v;
dReal theta, delta, nn, na_0, na_1, cosphi, sinphi, m;
const dReal *p[2], *omega[2];
int i;
// Transform all needed quantities to the global frame.
for (i = 0 ; i < 2 ; i += 1) {
dBodyGetRelPointPos(node[i].body,
anchors[i][0], anchors[i][1], anchors[i][2],
a[i]);
dBodyVectorToWorld(node[i].body, axes[i][0], axes[i][1], axes[i][2],
n[i]);
p[i] = dBodyGetPosition(node[i].body);
omega[i] = dBodyGetAngularVel(node[i].body);
}
if (update) {
// Make sure both gear reference frames end up with the same
// handedness.
if (dCalcVectorDot3(n[0], n[1]) < 0) {
dNegateVector3(axes[0]);
dNegateVector3(n[0]);
}
}
// Calculate the mesh geometry based on the current mode.
switch (mode) {
case dTransmissionParallelAxes:
// Simply calculate the contact point as the point on the
// baseline that will yield the correct ratio.
dIASSERT (ratio > 0);
dSubtractVectors3(d, a[1], a[0]);
dAddScaledVectors3(c[0], a[0], d, 1, ratio / (1 + ratio));
dCopyVector3(c[1], c[0]);
dNormalize3(d);
for (i = 0 ; i < 2 ; i += 1) {
dCalcVectorCross3(l[i], d, n[i]);
}
break;
case dTransmissionIntersectingAxes:
// Calculate the line of intersection between the planes of the
// gears.
dCalcVectorCross3(l[0], n[0], n[1]);
dCopyVector3(l[1], l[0]);
nn = dCalcVectorDot3(n[0], n[1]);
dIASSERT(fabs(nn) != 1);
na_0 = dCalcVectorDot3(n[0], a[0]);
na_1 = dCalcVectorDot3(n[1], a[1]);
dAddScaledVectors3(O, n[0], n[1],
(na_0 - na_1 * nn) / (1 - nn * nn),
(na_1 - na_0 * nn) / (1 - nn * nn));
// Find the contact point as:
//
// c = ((r_a - O) . l) l + O
//
// where r_a the anchor point of either gear and l, O the tangent
// line direction and origin.
for (i = 0 ; i < 2 ; i += 1) {
dSubtractVectors3(d, a[i], O);
m = dCalcVectorDot3(d, l[i]);
dAddScaledVectors3(c[i], O, l[i], 1, m);
}
break;
case dTransmissionChainDrive:
dSubtractVectors3(d, a[0], a[1]);
m = dCalcVectorLength3(d);
dIASSERT(m > 0);
// Caclulate the angle of the contact point relative to the
// baseline.
cosphi = clamp((radii[1] - radii[0]) / m, REAL(-1.0), REAL(1.0)); // Force into range to fix possible computation errors
sinphi = dSqrt (REAL(1.0) - cosphi * cosphi);
dNormalize3(d);
for (i = 0 ; i < 2 ; i += 1) {
// Calculate the contact radius in the local reference
// frame of the chain. This has axis x pointing along the
// baseline, axis y pointing along the sprocket axis and
// the remaining axis normal to both.
u[0] = radii[i] * cosphi;
u[1] = 0;
u[2] = radii[i] * sinphi;
// Transform the contact radius into the global frame.
dCalcVectorCross3(z, d, n[i]);
v[0] = dCalcVectorDot3(d, u);
v[1] = dCalcVectorDot3(n[i], u);
v[2] = dCalcVectorDot3(z, u);
// Finally calculate contact points and l.
dAddVectors3(c[i], a[i], v);
dCalcVectorCross3(l[i], v, n[i]);
dNormalize3(l[i]);
// printf ("%d: %f, %f, %f\n",
// i, l[i][0], l[i][1], l[i][2]);
}
break;
}
if (update) {
// We need to calculate an initial reference frame for each
// wheel which we can measure the current phase against. This
// frame will have the initial contact radius as the x axis,
// the wheel axis as the z axis and their cross product as the
// y axis.
for (i = 0 ; i < 2 ; i += 1) {
dSubtractVectors3 (r[i], c[i], a[i]);
radii[i] = dCalcVectorLength3(r[i]);
dIASSERT(radii[i] > 0);
dBodyVectorFromWorld(node[i].body, r[i][0], r[i][1], r[i][2],
reference[i]);
dNormalize3(reference[i]);
dCopyVector3(reference[i] + 8, axes[i]);
dCalcVectorCross3(reference[i] + 4, reference[i] + 8, reference[i]);
// printf ("%f\n", dDOT(r[i], n[i]));
// printf ("(%f, %f, %f,\n %f, %f, %f,\n %f, %f, %f)\n",
// reference[i][0],reference[i][1],reference[i][2],
// reference[i][4],reference[i][5],reference[i][6],
// reference[i][8],reference[i][9],reference[i][10]);
radii[i] = radii[i];
phase[i] = 0;
}
ratio = radii[0] / radii[1];
update = 0;
}
for (i = 0 ; i < 2 ; i += 1) {
dReal phase_hat;
dSubtractVectors3 (r[i], c[i], a[i]);
// Transform the (global) contact radius into the gear's
// reference frame.
dBodyVectorFromWorld (node[i].body, r[i][0], r[i][1], r[i][2], s);
dMultiply0_331(t, reference[i], s);
// Now simply calculate its angle on the plane relative to the
// x-axis which is the initial contact radius. This will be
// an angle between -pi and pi that is coterminal with the
// actual phase of the wheel. To find the real phase we
// estimate it by adding omega * dt to the old phase and then
// find the closest angle to that, that is coterminal to
// theta.
theta = atan2(t[1], t[0]);
phase_hat = phase[i] + dCalcVectorDot3(omega[i], n[i]) / worldFPS;
if (phase_hat > M_PI_2) {
if (theta < 0) {
theta += (dReal)(2 * M_PI);
}
theta += (dReal)(floor(phase_hat / (2 * M_PI)) * (2 * M_PI));
} else if (phase_hat < -M_PI_2) {
if (theta > 0) {
theta -= (dReal)(2 * M_PI);
}
theta += (dReal)(ceil(phase_hat / (2 * M_PI)) * (2 * M_PI));
}
if (phase_hat - theta > M_PI) {
phase[i] = theta + (dReal)(2 * M_PI);
} else if (phase_hat - theta < -M_PI) {
phase[i] = theta - (dReal)(2 * M_PI);
} else {
phase[i] = theta;
}
dIASSERT(fabs(phase_hat - phase[i]) < M_PI);
}
// Calculate the phase error. Depending on the mode the condition
// is that the distances traveled by each contact point must be
// either equal (chain and sprockets) or opposite (gears).
if (mode == dTransmissionChainDrive) {
delta = (dCalcVectorLength3(r[0]) * phase[0] -
dCalcVectorLength3(r[1]) * phase[1]);
} else {
delta = (dCalcVectorLength3(r[0]) * phase[0] +
dCalcVectorLength3(r[1]) * phase[1]);
}
// When in chain mode a torque reversal, signified by the change
// in sign of the wheel phase difference, has the added effect of
// switching the active chain branch. We must therefore reflect
// the contact points and tangents across the baseline.
if (mode == dTransmissionChainDrive && delta < 0) {
dVector3 d;
dSubtractVectors3(d, a[0], a[1]);
for (i = 0 ; i < 2 ; i += 1) {
dVector3 nn;
dReal a;
dCalcVectorCross3(nn, n[i], d);
a = dCalcVectorDot3(nn, nn);
dIASSERT(a > 0);
dAddScaledVectors3(c[i], c[i], nn,
1, -2 * dCalcVectorDot3(c[i], nn) / a);
dAddScaledVectors3(l[i], l[i], nn,
-1, 2 * dCalcVectorDot3(l[i], nn) / a);
}
}
// Do not add the constraint if there's backlash and we're in the
// backlash gap.
if (backlash == 0 || fabs(delta) > backlash) {
// The constraint is satisfied iff the absolute velocity of the
// contact point projected onto the tangent of the wheels is equal
// for both gears. This velocity can be calculated as:
//
// u = v + omega x r_c
//
// The constraint therefore becomes:
// (v_1 + omega_1 x r_c1) . l = (v_2 + omega_2 x r_c2) . l <=>
// (v_1 . l + (r_c1 x l) . omega_1 = v_2 . l + (r_c2 x l) . omega_2
for (i = 0 ; i < 2 ; i += 1) {
dSubtractVectors3 (r[i], c[i], p[i]);
}
dCalcVectorCross3(info->J1a, r[0], l[0]);
dCalcVectorCross3(info->J2a, l[1], r[1]);
dCopyVector3(info->J1l, l[0]);
dCopyNegatedVector3(info->J2l, l[1]);
if (delta > 0) {
if (backlash > 0) {
info->lo[0] = -dInfinity;
info->hi[0] = 0;
}
info->c[0] = -worldFPS * erp * (delta - backlash);
} else {
if (backlash > 0) {
info->lo[0] = 0;
info->hi[0] = dInfinity;
}
info->c[0] = -worldFPS * erp * (delta + backlash);
}
}
info->cfm[0] = cfm;
// printf ("%f, %f, %f, %f, %f\n", delta, phase[0], phase[1], -phase[1] / phase[0], ratio);
// Cache the contact point (in world coordinates) to avoid
// recalculation if requested by the user.
dCopyVector3(contacts[0], c[0]);
dCopyVector3(contacts[1], c[1]);
}
void
dxJointPU::getInfo2( dReal worldFPS, dReal worldERP,
int rowskip, dReal *J1, dReal *J2,
int pairskip, dReal *pairRhsCfm, dReal *pairLoHi,
int *findex )
{
const dReal k = worldFPS * worldERP;
// ======================================================================
// The angular constraint
//
dVector3 ax1, ax2; // Global axes of rotation
getAxis(this, ax1, axis1);
getAxis2(this,ax2, axis2);
dVector3 uniPerp; // Axis perpendicular to axes of rotation
dCalcVectorCross3(uniPerp,ax1,ax2);
dNormalize3( uniPerp );
dCopyVector3( J1 + GI2__JA_MIN, uniPerp );
dxBody *body1 = node[1].body;
if ( body1 ) {
dCopyNegatedVector3( J2 + GI2__JA_MIN , uniPerp );
}
// Corrective velocity attempting to keep uni axes perpendicular
dReal val = dCalcVectorDot3( ax1, ax2 );
// Small angle approximation :
// theta = asin(val)
// theta is approximately val when val is near zero.
pairRhsCfm[GI2_RHS] = -k * val;
// ==========================================================================
// Handle axes orthogonal to the prismatic
dVector3 an1, an2; // Global anchor positions
dVector3 axP, sep; // Prismatic axis and separation vector
getAnchor(this, an1, anchor1);
getAnchor2(this, an2, anchor2);
if (flags & dJOINT_REVERSE) {
getAxis2(this, axP, axisP1);
} else {
getAxis(this, axP, axisP1);
}
dSubtractVectors3(sep, an2, an1);
dVector3 p, q;
dPlaneSpace(axP, p, q);
dCopyVector3( J1 + rowskip + GI2__JL_MIN, p );
dCopyVector3( J1 + 2 * rowskip + GI2__JL_MIN, q );
// Make the anchors be body local
// Aliasing isn't a problem here.
dSubtractVectors3(an1, an1, node[0].body->posr.pos);
dCalcVectorCross3( J1 + rowskip + GI2__JA_MIN, an1, p );
dCalcVectorCross3( J1 + 2 * rowskip + GI2__JA_MIN, an1, q );
if (body1) {
dCopyNegatedVector3( J2 + rowskip + GI2__JL_MIN, p );
dCopyNegatedVector3( J2 + 2 * rowskip + GI2__JL_MIN, q );
dSubtractVectors3(an2, an2, body1->posr.pos);
dCalcVectorCross3( J2 + rowskip + GI2__JA_MIN, p, an2 );
dCalcVectorCross3( J2 + 2 * rowskip + GI2__JA_MIN, q, an2 );
}
pairRhsCfm[pairskip + GI2_RHS] = k * dCalcVectorDot3( p, sep );
pairRhsCfm[2 * pairskip + GI2_RHS] = k * dCalcVectorDot3( q, sep );
// ==========================================================================
// Handle the limits/motors
int currRowSkip = 3 * rowskip, currPairSkip = 3 * pairskip;
if (limot1.addLimot( this, worldFPS, J1 + currRowSkip, J2 + currRowSkip, pairRhsCfm + currPairSkip, pairLoHi + currPairSkip, ax1, 1 )) {
currRowSkip += rowskip; currPairSkip += pairskip;
}
if (limot2.addLimot( this, worldFPS, J1 + currRowSkip, J2 + currRowSkip, pairRhsCfm + currPairSkip, pairLoHi + currPairSkip, ax2, 1 )) {
currRowSkip += rowskip; currPairSkip += pairskip;
}
if ( body1 || (flags & dJOINT_REVERSE) == 0 ) {
limotP.addTwoPointLimot( this, worldFPS, J1 + currRowSkip, J2 + currRowSkip, pairRhsCfm + currPairSkip, pairLoHi + currPairSkip, axP, an1, an2 );
} else {
dNegateVector3(axP);
limotP.addTwoPointLimot ( this, worldFPS, J1 + currRowSkip, J2 + currRowSkip, pairRhsCfm + currPairSkip, pairLoHi + currPairSkip, axP, an1, an2 );
}
}
void
dxJointPU::getInfo2( dReal worldFPS, dReal worldERP, const Info2Descr *info )
{
const int s1 = info->rowskip;
const int s2 = 2 * s1;
const dReal k = worldFPS * worldERP;
// ======================================================================
// The angular constraint
//
dVector3 ax1, ax2; // Global axes of rotation
getAxis(this, ax1, axis1);
getAxis2(this,ax2, axis2);
dVector3 uniPerp; // Axis perpendicular to axes of rotation
dCalcVectorCross3(uniPerp,ax1,ax2);
dNormalize3( uniPerp );
dCopyVector3( info->J1a , uniPerp );
if ( node[1].body )
{
dCopyNegatedVector3( info->J2a , uniPerp );
}
// Corrective velocity attempting to keep uni axes perpendicular
dReal val = dCalcVectorDot3( ax1, ax2 );
// Small angle approximation :
// theta = asin(val)
// theta is approximately val when val is near zero.
info->c[0] = -k * val;
// ==========================================================================
// Handle axes orthogonal to the prismatic
dVector3 an1, an2; // Global anchor positions
dVector3 axP, sep; // Prismatic axis and separation vector
getAnchor(this,an1,anchor1);
getAnchor2(this,an2,anchor2);
if (flags & dJOINT_REVERSE) {
getAxis2(this, axP, axisP1);
} else {
getAxis(this, axP, axisP1);
}
dSubtractVectors3(sep,an2,an1);
dVector3 p,q;
dPlaneSpace(axP,p,q);
dCopyVector3(( info->J1l ) + s1, p );
dCopyVector3(( info->J1l ) + s2, q );
// Make the anchors be body local
// Aliasing isn't a problem here.
dSubtractVectors3(an1,an1,node[0].body->posr.pos);
dCalcVectorCross3(( info->J1a ) + s1, an1, p );
dCalcVectorCross3(( info->J1a ) + s2, an1, q );
if (node[1].body) {
dCopyNegatedVector3(( info->J2l ) + s1, p );
dCopyNegatedVector3(( info->J2l ) + s2, q );
dSubtractVectors3(an2,an2,node[1].body->posr.pos);
dCalcVectorCross3(( info->J2a ) + s1, p, an2 );
dCalcVectorCross3(( info->J2a ) + s2, q, an2 );
}
info->c[1] = k * dCalcVectorDot3( p, sep );
info->c[2] = k * dCalcVectorDot3( q, sep );
// ==========================================================================
// Handle the limits/motors
int row = 3 + limot1.addLimot( this, worldFPS, info, 3, ax1, 1 );
row += limot2.addLimot( this, worldFPS, info, row, ax2, 1 );
if ( node[1].body || !(flags & dJOINT_REVERSE) )
limotP.addTwoPointLimot( this, worldFPS, info, row, axP, an1, an2 );
else
{
axP[0] = -axP[0];
axP[1] = -axP[1];
axP[2] = -axP[2];
limotP.addTwoPointLimot ( this, worldFPS, info, row, axP, an1, an2 );
}
}
void
dxJointPU::getInfo2( dxJoint::Info2 *info )
{
const int s0 = 0;
const int s1 = info->rowskip;
const int s2 = 2 * s1;
const dReal k = info->fps * info->erp;
// pull out pos and R for both bodies. also get the `connection'
// vector pos2-pos1.
dReal *pos1, *pos2 = 0, *R1, *R2 = 0;
pos1 = node[0].body->posr.pos;
R1 = node[0].body->posr.R;
if ( node[1].body )
{
pos2 = node[1].body->posr.pos;
R2 = node[1].body->posr.R;
}
dVector3 axP; // Axis of the prismatic joint in global frame
dMultiply0_331( axP, R1, axisP1 );
// distance between the body1 and the anchor2 in global frame
// Calculated in the same way as the offset
dVector3 dist;
dVector3 wanchor2 = {0,0,0};
if ( node[1].body )
{
dMultiply0_331( wanchor2, R2, anchor2 );
dist[0] = wanchor2[0] + pos2[0] - pos1[0];
dist[1] = wanchor2[1] + pos2[1] - pos1[1];
dist[2] = wanchor2[2] + pos2[2] - pos1[2];
}
else
{
if (flags & dJOINT_REVERSE )
{
// Invert the sign of dist
dist[0] = pos1[0] - anchor2[0];
dist[1] = pos1[1] - anchor2[1];
dist[2] = pos1[2] - anchor2[2];
}
else
{
dist[0] = anchor2[0] - pos1[0];
dist[1] = anchor2[1] - pos1[1];
dist[2] = anchor2[2] - pos1[2];
}
}
dVector3 q; // Temporary axis vector
// Will be used at 2 places with 2 different meaning
// ======================================================================
// Work on the angular part (i.e. row 0)
//
// The axis perpendicular to both axis1 and axis2 should be the only unconstrained
// rotational axis, the angular velocity of the two bodies perpendicular to
// the rotoide axes should be equal. Thus the constraint equations are
// p*w1 - p*w2 = 0
// where p is a unit vector perpendicular to both axis1 and axis2
// and w1 and w2 are the angular velocity vectors of the two bodies.
dVector3 ax1, ax2;
getAxes( ax1, ax2 );
dReal val = dCalcVectorDot3( ax1, ax2 );
q[0] = ax2[0] - val * ax1[0];
q[1] = ax2[1] - val * ax1[1];
q[2] = ax2[2] - val * ax1[2];
dVector3 p;
dCalcVectorCross3( p, ax1, q );
dNormalize3( p );
// info->J1a[s0+i] = p[i];
dCopyVector3(( info->J1a ) + s0, p );
if ( node[1].body )
{
// info->J2a[s0+i] = -p[i];
dCopyNegatedVector3(( info->J2a ) + s0, p );
}
// 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[0] = k * - val;
// ==========================================================================
// Work on the linear part (i.e rows 1 and 2)
//
// 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 axisP is disregarded.
//
// p1 + R1 dist' = p2 + R2 anchor2'
// v1 + w1 x R1 dist' + v_p = v2 + w2 x R2 anchor2'
// v_p is speed of prismatic joint (i.e. elongation rate)
// Since the constraints are perpendicular to v_p we have:
// e1 dot v_p = 0 and e2 dot v_p = 0
// e1 dot ( v1 + w1 x dist = v2 + w2 x anchor2 )
// e2 dot ( v1 + w1 x dist = v2 + w2 x anchor2 )
// ==
// e1 . v1 + e1 . w1 x dist = e1 . v2 + e1 . w2 x anchor2
// since a . (b x c) = - b . (a x c) = - (a x c) . b
// and a x b = - b x a
// e1 . v1 - e1 x dist . w1 - e1 . v2 - (- e1 x anchor2 . w2) = 0
// e1 . v1 + dist x e1 . w1 - e1 . v2 - anchor2 x e1 . w2 = 0
// Coeff for 1er line of: J1l => e1, J2l => -e1
// Coeff for 2er line of: J1l => e2, J2l => -ax2
// Coeff for 1er line of: J1a => dist x e1, J2a => - anchor2 x e1
// Coeff for 2er line of: J1a => dist x e2, J2a => - anchor2 x e2
// e1 and e2 are perpendicular to axP
// so e1 = ax1 and e2 = ax1 x axP
// N.B. ax2 is not always perpendicular to axP since it is attached to body 2
dCalcVectorCross3( q , ax1, axP );
dMultiply0_331( axP, R1, axisP1 );
dCalcVectorCross3(( info->J1a ) + s1, dist, ax1 );
dCalcVectorCross3(( info->J1a ) + s2, dist, q );
// info->J1l[s1+i] = ax[i];
dCopyVector3(( info->J1l ) + s1, ax1 );
// info->J1l[s2+i] = q[i];
dCopyVector3(( info->J1l ) + s2, q );
if ( node[1].body )
{
// Calculate anchor2 in world coordinate
// q x anchor2 instead of anchor2 x q since we want the negative value
dCalcVectorCross3(( info->J2a ) + s1, ax1, wanchor2 );
// The cross product is in reverse order since we want the negative value
dCalcVectorCross3(( info->J2a ) + s2, q, wanchor2 );
// info->J2l[s1+i] = -ax1[i];
dCopyNegatedVector3(( info->J2l ) + s1, ax1 );
// info->J2l[s2+i] = -ax1[i];
dCopyNegatedVector3(( info->J2l ) + s2, q );
}
// 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 1 and 2 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, anchor1 );
// err[i] = dist[i] - err[i];
dSubtractVectors3( err, dist, err );
info->c[1] = k * dCalcVectorDot3( ax1, err );
info->c[2] = k * dCalcVectorDot3( q, err );
int row = 3 + limot1.addLimot( this, info, 3, ax1, 1 );
row += limot2.addLimot( this, info, row, ax2, 1 );
if ( node[1].body || !(flags & dJOINT_REVERSE) )
limotP.addLimot( this, info, row, axP, 0 );
else
{
axP[0] = -axP[0];
axP[1] = -axP[1];
axP[2] = -axP[2];
limotP.addLimot ( this, info, row, axP, 0 );
}
}
void
dxJointUniversal::getInfo2( dReal worldFPS, dReal worldERP,
int rowskip, dReal *J1, dReal *J2,
int pairskip, dReal *pairRhsCfm, dReal *pairLoHi,
int *findex )
{
// set the three ball-and-socket rows
setBall( this, worldFPS, worldERP, rowskip, J1, J2, pairskip, pairRhsCfm, anchor1, 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;
// length 1 vector perpendicular to ax1 and ax2. Neither body can rotate
// about this.
dVector3 p;
// Since axis1 and axis2 may not be perpendicular
// we find a axis2_tmp which is really perpendicular to axis1
// and in the plane of axis1 and axis2
getAxes( ax1, ax2 );
dReal k = dCalcVectorDot3( ax1, ax2 );
dVector3 ax2_temp;
dAddVectorScaledVector3(ax2_temp, ax2, ax1, -k);
dCalcVectorCross3( p, ax1, ax2_temp );
dNormalize3( p );
int currRowSkip = 3 * rowskip;
{
dCopyVector3( J1 + currRowSkip + GI2__JA_MIN, p);
if ( node[1].body )
{
dCopyNegatedVector3( J2 + currRowSkip + GI2__JA_MIN, p);
}
}
// 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)
int currPairSkip = 3 * pairskip;
{
pairRhsCfm[currPairSkip + GI2_RHS] = worldFPS * worldERP * (-k);
}
currRowSkip += rowskip; currPairSkip += pairskip;
// if the first angle is powered, or has joint limits, add in the stuff
if (limot1.addLimot( this, worldFPS, J1 + currRowSkip, J2 + currRowSkip, pairRhsCfm + currPairSkip, pairLoHi + currPairSkip, ax1, 1 ))
{
currRowSkip += rowskip; currPairSkip += pairskip;
}
// if the second angle is powered, or has joint limits, add in more stuff
limot2.addLimot( this, worldFPS, J1 + currRowSkip, J2 + currRowSkip, pairRhsCfm + currPairSkip, pairLoHi + currPairSkip, ax2, 1 );
}
void
dxJointPR::getInfo2( dReal worldFPS, dReal worldERP,
int rowskip, dReal *J1, dReal *J2,
int pairskip, dReal *pairRhsCfm, dReal *pairLoHi,
int *findex )
{
dReal k = worldFPS * worldERP;
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 *pos2 = NULL, *R2 = NULL;
dReal *pos1 = node[0].body->posr.pos;
dReal *R1 = node[0].body->posr.R;
dxBody *body1 = node[1].body;
if ( body1 )
{
pos2 = body1->posr.pos;
R2 = body1->posr.R;
}
dVector3 axP; // Axis of the prismatic joint in global frame
dMultiply0_331( axP, R1, axisP1 );
// distance between the body1 and the anchor2 in global frame
// Calculated in the same way as the offset
dVector3 wanchor2 = {0, 0, 0}, dist;
if ( body1 )
{
// Calculate anchor2 in world coordinate
dMultiply0_331( wanchor2, R2, anchor2 );
dist[0] = wanchor2[0] + pos2[0] - pos1[0];
dist[1] = wanchor2[1] + pos2[1] - pos1[1];
dist[2] = wanchor2[2] + pos2[2] - pos1[2];
}
else
{
if ( (flags & dJOINT_REVERSE) != 0 )
{
dSubtractVectors3(dist, pos1, anchor2); // Invert the value
}
else
{
dSubtractVectors3(dist, anchor2, pos1); // Invert the value
}
}
// ======================================================================
// 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 ax2;
dVector3 ax1;
dMultiply0_331( ax1, R1, axisR1 );
dCalcVectorCross3( q , ax1, axP );
dCopyVector3(J1 + GI2__JA_MIN, axP);
if ( body1 )
{
dCopyNegatedVector3(J2 + GI2__JA_MIN, axP);
}
dCopyVector3(J1 + rowskip + GI2__JA_MIN, q);
if ( body1 )
{
dCopyNegatedVector3(J2 + rowskip + GI2__JA_MIN, q);
}
// 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.
if ( body1 )
{
dMultiply0_331( ax2, R2, axisR2 );
}
else
{
dCopyVector3(ax2, axisR2);
}
dVector3 b;
dCalcVectorCross3( b, ax1, ax2 );
pairRhsCfm[GI2_RHS] = k * dCalcVectorDot3( b, axP );
pairRhsCfm[pairskip + GI2_RHS] = k * dCalcVectorDot3( 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
int currRowSkip = 2 * rowskip;
{
dCopyVector3( J1 + currRowSkip + GI2__JL_MIN, ax1 );
dCalcVectorCross3( J1 + currRowSkip + GI2__JA_MIN, dist, ax1 );
if ( body1 )
{
dCopyNegatedVector3( J2 + currRowSkip + GI2__JL_MIN, ax1 );
// ax2 x anchor2 instead of anchor2 x ax2 since we want the negative value
dCalcVectorCross3( J2 + currRowSkip + GI2__JA_MIN, ax2, wanchor2 ); // since ax1 == ax2
}
}
currRowSkip += rowskip;
{
dCopyVector3( J1 + currRowSkip + GI2__JL_MIN, q );
dCalcVectorCross3(J1 + currRowSkip + GI2__JA_MIN, dist, q );
if ( body1 )
{
dCopyNegatedVector3( J2 + currRowSkip + GI2__JL_MIN, q);
// The cross product is in reverse order since we want the negative value
dCalcVectorCross3( J2 + currRowSkip + GI2__JA_MIN, q, wanchor2 );
}
}
// 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, offset );
dSubtractVectors3(err, dist, err);
int currPairSkip = 2 * pairskip;
{
pairRhsCfm[currPairSkip + GI2_RHS] = k * dCalcVectorDot3( ax1, err );
}
currPairSkip += pairskip;
{
pairRhsCfm[currPairSkip + GI2_RHS] = k * dCalcVectorDot3( q, err );
}
currRowSkip += rowskip; currPairSkip += pairskip;
if ( body1 || (flags & dJOINT_REVERSE) == 0 )
{
if (limotP.addLimot ( this, worldFPS, J1 + currRowSkip, J2 + currRowSkip, pairRhsCfm + currPairSkip, pairLoHi + currPairSkip, axP, 0 ))
{
currRowSkip += rowskip; currPairSkip += pairskip;
}
}
else
{
dVector3 rAxP;
dCopyNegatedVector3(rAxP, axP);
if (limotP.addLimot ( this, worldFPS, J1 + currRowSkip, J2 + currRowSkip, pairRhsCfm + currPairSkip, pairLoHi + currPairSkip, rAxP, 0 ))
{
currRowSkip += rowskip; currPairSkip += pairskip;
}
}
limotR.addLimot ( this, worldFPS, J1 + currRowSkip, J2 + currRowSkip, pairRhsCfm + currPairSkip, pairLoHi + currPairSkip, ax1, 1 );
}
void dxPlanarJoint::getInfo2(dReal worldFPS, dReal worldERP, const Info2Descr* info)
{
/* ====================================================================
* This joint restricts 2 rotational and 1 translational DOF.
*
* The 2 rotational constraints are essentially the same as in dxJointPiston, so the implementation here is mostly
* just a copy of them.
*
* The translational 1DOF constraint has not yet been implemented for any joint in ODE, so we'll talk more about it.
* It is similar to the constraints in a slider joint, but in this case we only want body2 to move the plane, and
* body1 anchor has no use in this case, too.
*
* We basically want to express the plane in body2 local coordinates (because it should move along with body2), and
* check, if body1 origin lies in the plane.
*
* Let's say n' is the plane normal in body2 coordinates and a' is the anchor point in body2 coordinates
* (with n, a, being the corresponding global variables).
* Further, let's call the global position of body1 p1, and similarly p2 for body2.
* Last, let's call body2 rotation matrix R2 (so that n = R2*n' and a = R2*a' + p2).
*
* The plane can then be expressed in global coordinates as:
* (n^ . x) - (n^ . a) = 0,
* where x is in global coordinates and ^ denotes vector/matrix transpose.
*
* Rewriting the equation using body2 local coordinates and setting x=p1, we get the constraint:
* (R2*n')^ * p1 - (R2*n')^ * (R2*a' + p2) = 0
* ...
* (n'^ * R2^ * p1) - (n'^ * R2^ * p2) - (n'^ * a') = 0
* (n^ * p1) - (n^ * p2) - (n'^ * a') = 0
*
* The part left to "=" will be the "c" on the RHS of the Jacobian equation (because it expresses
* the distance of p1 from the plane).
*
* Next, we need to take time derivative of the constraint to get the J1 and J2 parts.
* v1, v2, w1 and w2 denote the linear and angular velocities od body1 and body2.
* [a]x denotes the skew-symmetric cross-product matrix of vector a.
*
* d/dt [(n'^ * R2^ * p1) - (n'^ * R2^ * p2) - (n'^ * a') = 0] (n', a' are constant in time)
* n'^ * ((d/dt[R2^] * p1) + (R2^ * v1)) - n'^ * ((d/dt[R2^] * p2) + (R2^ * v2)) = 0
* n'^ * ((([w2]x R2)^ * p1) + (R2^ * v1)) - n'^ * ((([w2]x R2)^ * p2) + (R2^ * v2)) = 0
* ...
* n^*v1 - n^*v2 + [n]x (p1 - p2) . w2 = 0
* -n^*v1 + n^*v2 + [n]x (p2 - p1) . w2 = 0
*
* Thus we see that
* J1l = -n
* J2l = n
* J1a = 0
* J2a = [n]x (p2 - p1)
* c = eps * ( (n^ * p1) - (n^ * a) )
*
*/
const int row0Index = 0;
const int row1Index = info->rowskip;
const int row2Index = 2 * row1Index;
const dReal eps = worldFPS * worldERP;
dVector3 globalAxis1;
dBodyVectorToWorld(node[0].body, axis1[0], axis1[1], axis1[2], globalAxis1);
dVector3 globalAxis2;
dVector3 globalAnchor;
if (node[1].body) {
dBodyVectorToWorld(node[1].body, axis2[0], axis2[1], axis2[2], globalAxis2);
dBodyGetRelPointPos(node[1].body, anchor2[0], anchor2[1], anchor2[2], globalAnchor);
} else {
dCopyVector3(globalAxis2, axis2);
dCopyVector3(globalAnchor, anchor2);
}
///////////////////////////////////////////////////////
// Angular velocity constraints (2 rows)
//
// Refer to the piston joint source code for details.
///////////////////////////////////////////////////////
// Find the 2 direction vectors of the plane.
dVector3 p, q;
dPlaneSpace ( globalAxis2, p, q );
// LHS 0
dCopyNegatedVector3 (info->J1a + row0Index, p );
dCopyNegatedVector3 (info->J1a + row1Index, q );
// LHS 1
dCopyVector3 (info->J2a + row0Index, p );
dCopyVector3 (info->J2a + row1Index, q );
// RHS 0 & 1 (absolute errors of the axis direction computed by dot product of the desired and actual axis)
dVector3 b;
dCalcVectorCross3( b, globalAxis2, globalAxis1 );
info->c[0] = eps * dCalcVectorDot3 ( p, b );
info->c[1] = eps * dCalcVectorDot3 ( q, b );
//////////////////////////////////////////////////////////////////////////////////////////
// Linear velocity constraint (1 row, removes 1 translational DOF along the plane normal)
//
// Only body1 should be restricted by the plane, which is moved along with body2.
//////////////////////////////////////////////////////////////////////////////////////////
dVector3 body1Center;
dCopyVector3(body1Center, node[0].body->posr.pos);
dVector3 body2Center = {0, 0, 0};
if (node[1].body) {
dCopyVector3(body2Center, node[1].body->posr.pos);
}
// LHS 2
dCopyNegatedVector3(info->J1l + row2Index, globalAxis2);
dCopyVector3( info->J2l + row2Index, globalAxis2);
dVector3 body2_body1;
dSubtractVectors3(body2_body1, body2Center, body1Center);
dCalcVectorCross3(info->J2a + row2Index, globalAxis2, body2_body1);
// RHS 2 (distance of body1 center from the plane)
info->c[2] = eps * (dCalcVectorDot3(globalAxis2, body1Center) - dCalcVectorDot3(globalAxis2, globalAnchor));
}
