void Vec3f::rotate (const Vec3f &around, float angle)
{
Transform3f matr;
matr.rotation(around.x, around.y, around.z, angle);
transformVector(matr);
}
CMUK_ERROR_CODE cmuk::computeFootIK( LegIndex leg,
const vec3f& pos,
vec3f* q_bent_forward,
vec3f* q_bent_rearward ) const {
if ((int)leg < 0 || (int)leg >= NUM_LEGS) {
return CMUK_BAD_LEG_INDEX;
} else if (!q_bent_forward || !q_bent_rearward) {
return CMUK_INSUFFICIENT_ARGUMENTS;
}
debug << "*** computing IK...\n";
int hipflags = 0;
// subtract off hip position
vec3f p = pos - jo(_kc, leg, HIP_RX_OFFSET, _centeredFootIK);
vec3f orig = pos;
// get dist from hip rx joint to y rotation plane
const float& d = jo(_kc, leg, HIP_RY_OFFSET, _centeredFootIK)[1];
// get the squared length of the distance on the plane
float yz = p[1]*p[1] + p[2]*p[2];
// alpha is the angle of the foot in the YZ plane with respect to the Y axis
float alpha = atan2(p[2], p[1]);
// h is the distance of foot from hip in YZ plane
float h = sqrt(yz);
// beta is the angle between the foot-hip vector (projected in YZ
// plane) and the top hip link.
float cosbeta = d / h;
debug << "p = " << p << ", d = " << d << ", yz = " << yz << "\nalpha = " << alpha << ", h = " << h << ", cosbeta=" << cosbeta << "\n";
if (fabs(cosbeta) > 1) {
debug << "violated triangle inequality when calculating hip_rx_angle!\n" ;
if (fabs(cosbeta) - 1 > 1e-4) {
hipflags = hipflags | IK_UPPER_DISTANCE;
}
cosbeta = (cosbeta < 0) ? -1 : 1;
if (yz < 1e-4) {
p[1] = d;
p[2] = 0;
} else {
float scl = fabs(d) / h;
p[1] *= scl;
p[2] *= scl;
orig = p + jo(_kc, leg, HIP_RX_OFFSET, _centeredFootIK);
}
}
float beta = acos(cosbeta);
// Now compute the two possible hip angles
float hip_rx_angles[2], badness[2];
int flags[2];
flags[0] = hipflags;
flags[1] = hipflags;
hip_rx_angles[0] = fix_angle(alpha - beta, -M_PI, M_PI);
hip_rx_angles[1] = fix_angle(alpha + beta, -M_PI, M_PI);
const float& min = jl(_kc, leg, HIP_RX, 0);
const float& max = jl(_kc, leg, HIP_RX, 1);
// See how badly we violate the joint limits for this hip angles
for (int i=0; i<2; ++i) {
float& angle = hip_rx_angles[i];
badness[i] = fabs(compute_badness(angle, min, max));
if (badness[i]) { flags[i] = flags[i] | IK_UPPER_ANGLE_RANGE; }
}
// Put the least bad (and smallest) hip angle first
bool swap = false;
if ( badness[1] <= badness[0] ) {
// We want the less bad solution for hip angle
swap = true;
} else if (badness[0] == 0 && badness[1] == 0) {
// We want the solution for hip angle that leaves the hip up.
if ((leg == FL || leg == HL) && hip_rx_angles[0] > hip_rx_angles[1]) {
swap = true;
} else if ((leg == FR || leg == HR) && hip_rx_angles[0] < hip_rx_angles[1]) {
swap = true;
}
}
if (swap) {
std::swap(hip_rx_angles[0], hip_rx_angles[1]);
std::swap(badness[0], badness[1]);
std::swap(flags[0], flags[1]);
}
int hip_solution_cnt = 2;
if (badness[0] == 0 && badness[1] != 0) {
hip_solution_cnt = 1;
}
debug << "hip_rx_angles[0]=" << hip_rx_angles[0]
<< ", badness=" << badness[0]
<< ", flags=" << flags[0] << "\n";
debug << "hip_rx_angles[1]=" << hip_rx_angles[1]
<< ", badness=" << badness[1]
<< ", flags=" << flags[1] << "\n";
debug << "hip_solution_cnt = " << hip_solution_cnt << "\n";
vec3f qfwd[2], qrear[2];
for (int i=0; i<hip_solution_cnt; ++i) {
debug << "** computing ll solution " << (i+1) << " of " << (hip_solution_cnt) << "\n";
float hip_rx = hip_rx_angles[i];
// now make inv. transform to get rid of hip rotation
Transform3f tx = Transform3f::rx(hip_rx, jo(_kc, leg, HIP_RX_OFFSET, _centeredFootIK));
vec3f ptx = tx.transformInv(orig);
debug << "tx=[" << tx.translation() << ", " << tx.rotation() << "], ptx = " << ptx << "\n";
// calculate lengths for cosine law
float l1sqr = ol2(_kc, leg, KNEE_RY_OFFSET, _centeredFootIK);
float l2sqr = ol2(_kc, leg, FOOT_OFFSET, _centeredFootIK);
float l1 = ol(_kc, leg, KNEE_RY_OFFSET, _centeredFootIK);
float l2 = ol(_kc, leg, FOOT_OFFSET, _centeredFootIK);
float ksqr = ptx[0]*ptx[0] + ptx[2]*ptx[2];
float k = sqrt(ksqr);
debug << "l1=" << l1 << ", l2=" << l2 << ", k=" << k << "\n";
// check triangle inequality
if (k > l1 + l2) {
debug << "oops, violated the triangle inequality for lower segments: "
<< "k = " << k << ", "
<< "l1 + l2 = " << l1 + l2 << "\n";
if (k - (l1 + l2) > 1e-4) {
flags[i] = flags[i] | IK_LOWER_DISTANCE;
}
k = l1 + l2;
ksqr = k * k;
}
// 2*theta is the acute angle formed by the spread
// of the two hip rotations...
float costheta = (l1sqr + ksqr - l2sqr) / (2 * l1 * k);
if (fabs(costheta) > 1) {
debug << "costheta = " << costheta << " > 1\n";
if (fabs(costheta) - 1 > 1e-4) {
flags[i] = flags[i] | IK_LOWER_DISTANCE;
}
costheta = (costheta < 0) ? -1 : 1;
}
float theta = acos(costheta);
// gamma is the angle of the foot with respect to the z axis
float gamma = atan2(-ptx[0], -ptx[2]);
// hip angles are just offsets off of gamma now
float hip_ry_1 = gamma - theta;
float hip_ry_2 = gamma + theta;
// phi is the obtuse angle of the parallelogram
float cosphi = (l1sqr + l2sqr - ksqr) / (2 * l1 * l2);
if (fabs(cosphi) > 1) {
debug << "cosphi = " << cosphi << " > 1\n";
if (fabs(cosphi) - 1 > 1e-4) {
flags[i] = flags[i] | IK_LOWER_DISTANCE;
}
cosphi = (cosphi < 0) ? -1 : 1;
}
float phi = acos(cosphi);
// epsilon is the "error" caused by not having feet offset directly
// along the z-axis (if they were, epsilon would equal zero)
float epsilon = le(_kc, leg, _centeredFootIK);
// now we can directly solve for knee angles
float knee_ry_1 = M_PI - phi - epsilon;
float knee_ry_2 = -M_PI + phi - epsilon;
// now fill out angle structs and check limits
qfwd[i] = vec3f(hip_rx, hip_ry_1, knee_ry_1);
qrear[i] = vec3f(hip_rx, hip_ry_2, knee_ry_2);
debug << "before wrap, qfwd = " << qfwd[i] << "\n";
debug << "before wrap, qrear = " << qrear[i] << "\n";
check_wrap(_kc, qfwd[i], leg);
check_wrap(_kc, qrear[i], leg);
debug << "after wrap, qfwd = " << qfwd[i] << "\n";
debug << "after wrap, qrear = " << qrear[i] << "\n";
if (!check_limits(_kc, qfwd[i], leg)) {
debug << "violated limits forward!\n";
flags[i] = flags[i] | IK_LOWER_ANGLE_RANGE_FWD;
}
if (!check_limits(_kc, qrear[i], leg)) {
debug << "violated limits rearward!\n";
flags[i] = flags[i] | IK_LOWER_ANGLE_RANGE_REAR;
}
} // for each viable hip solution
int best = 0;
if (hip_solution_cnt == 2) {
if (howbad(flags[0]) > howbad(flags[1])) {
best = 1;
}
debug << "best overall solution is " << (best+1) << "\n";
}
*q_bent_forward = qfwd[best];
*q_bent_rearward = qrear[best];
return flags_to_errcode(flags[best]);
}
bool EdgeRotationMatcher::match (float rms_threshold, float eps)
{
if (cb_get_xyz == 0)
throw Error("cb_get_xyz not specified");
if (_subgraph.vertexCount() < 2 || _subgraph.edgeCount() < 1)
return true;
QS_DEF(Array<int>, in_cycle);
QS_DEF(Array<_DirEdge>, edge_queue);
QS_DEF(Array<int>, vertex_queue);
QS_DEF(Array<int>, states);
in_cycle.clear_resize(_subgraph.edgeEnd());
edge_queue.clear();
states.clear_resize(__max(_subgraph.edgeEnd(), _subgraph.vertexEnd() + 1));
int i, j, k, bottom;
// Find all subgraph bridges
SpanningTree spt(_subgraph, 0);
in_cycle.zerofill();
spt.markAllEdgesInCycles(in_cycle.ptr(), 1);
// Find the first bridge, put it to the queue 2 times
for (i = _subgraph.edgeBegin(); i < _subgraph.edgeEnd(); i = _subgraph.edgeNext(i))
if (!in_cycle[i] && (cb_can_rotate == 0 || cb_can_rotate(_subgraph, i)))
{
const Edge &edge = _subgraph.getEdge(i);
if (_mapping[edge.beg] < 0 || _mapping[edge.end] < 0)
continue;
edge_queue.push();
edge_queue.top().idx = i;
edge_queue.top().beg = edge.beg;
edge_queue.top().end = edge.end;
edge_queue.push();
edge_queue.top().idx = i;
edge_queue.top().beg = edge.end;
edge_queue.top().end = edge.beg;
break;
}
// If the queue is empty, then we have no bridge
if (edge_queue.size() == 0)
{
GraphAffineMatcher afm(_subgraph, _supergraph, _mapping);
afm.cb_get_xyz = cb_get_xyz;
return afm.match(rms_threshold);
}
float scale = 1.f;
// detect scaling factor by average bond length
if (equalize_edges)
{
float sum_sub = 0.f, sum_super = 0.f;
for (i = _subgraph.edgeBegin(); i < _subgraph.edgeEnd(); i = _subgraph.edgeNext(i))
{
const Edge &edge = _subgraph.getEdge(i);
Vec3f beg, end;
cb_get_xyz(_subgraph, edge.beg, beg);
cb_get_xyz(_subgraph, edge.end, end);
sum_sub += Vec3f::dist(beg, end);
}
for (i = _supergraph.edgeBegin(); i < _supergraph.edgeEnd(); i = _supergraph.edgeNext(i))
{
const Edge &edge = _supergraph.getEdge(i);
Vec3f beg, end;
cb_get_xyz(_supergraph, edge.beg, beg);
cb_get_xyz(_supergraph, edge.end, end);
sum_super += Vec3f::dist(beg, end);
}
if (sum_sub > EPSILON && sum_super > EPSILON)
{
sum_sub /= _subgraph.edgeCount();
sum_super /= _supergraph.edgeCount();
scale = sum_super / sum_sub;
}
}
// save vertex positions
QS_DEF(Array<Vec3f>, xyz_sub);
QS_DEF(Array<Vec3f>, xyz_super);
QS_DEF(Array<int>, xyzmap);
xyzmap.clear_resize(_supergraph.vertexEnd());
xyz_sub.clear();
xyz_super.clear();
for (i = _subgraph.vertexBegin(); i != _subgraph.vertexEnd();
i = _subgraph.vertexNext(i))
{
if (_mapping[i] < 0)
continue;
Vec3f &pos_sub = xyz_sub.push();
Vec3f &pos_super = xyz_super.push();
cb_get_xyz(_subgraph, i, pos_sub);
cb_get_xyz(_supergraph, _mapping[i], pos_super);
pos_sub.scale(scale);
xyzmap[_mapping[i]] = xyz_sub.size() - 1;
}
// Make queue of edges
states.zerofill();
bottom = 0;
while (edge_queue.size() != bottom)
{
// extract edge from queue
int edge_end = edge_queue[bottom].end;
int edge_idx = edge_queue[bottom].idx;
bottom++;
// mark it as 'completed'
states[edge_idx] = 2;
// look for neighbors
const Vertex &end_vertex = _subgraph.getVertex(edge_end);
for (i = end_vertex.neiBegin(); i != end_vertex.neiEnd(); i = end_vertex.neiNext(i))
{
int nei_edge_idx = end_vertex.neiEdge(i);
// check that neighbor have 'untouched' status
if (states[nei_edge_idx] != 0)
continue;
const Edge &nei_edge = _subgraph.getEdge(nei_edge_idx);
int other_end = nei_edge.findOtherEnd(edge_end);
if (_mapping[other_end] < 0)
continue;
// set status 'in process'
states[nei_edge_idx] = 1;
// push the neighbor edge to the queue
edge_queue.push();
edge_queue.top().idx = nei_edge_idx;
edge_queue.top().beg = edge_end;
edge_queue.top().end = other_end;
}
}
// do initial transform (impose first subgraph edge in the queue on corresponding one in the graph)
int beg2 = edge_queue[0].beg;
int end2 = edge_queue[0].end;
int beg1 = _mapping[beg2];
int end1 = _mapping[end2];
Vec3f g1_v1, g1_v2, g2_v1, g2_v2, diff1, diff2;
Transform3f matr;
cb_get_xyz(_supergraph, beg1, g1_v1);
cb_get_xyz(_supergraph, end1, g1_v2);
cb_get_xyz(_subgraph, beg2, g2_v1);
cb_get_xyz(_subgraph, end2, g2_v2);
g2_v1.scale(scale);
g2_v2.scale(scale);
diff1.diff(g1_v2, g1_v1);
diff2.diff(g2_v2, g2_v1);
matr.identity();
if (!matr.rotationVecVec(diff2, diff1))
throw Error("error calling RotationVecVec()");
matr.translateLocal(-g2_v1.x, -g2_v1.y, -g2_v1.z);
matr.translate(g1_v1);
for (k = 0; k < xyz_sub.size(); k++)
xyz_sub[k].transformPoint(matr);
// for all edges in queue that are subject to rotate...
for (i = 0; i < edge_queue.size(); i++)
{
int edge_beg = edge_queue[i].beg;
int edge_end = edge_queue[i].end;
int edge_idx = edge_queue[i].idx;
if (in_cycle[edge_idx])
continue;
if (cb_can_rotate != 0 && !cb_can_rotate(_subgraph, edge_idx))
continue;
// start BFS from the end of the edge
states.zerofill();
states[edge_end] = 1;
vertex_queue.clear();
vertex_queue.push(edge_end);
bottom = 0;
while (vertex_queue.size() != bottom)
{
// extract vertex from queue
const Vertex &vertex = _subgraph.getVertex(vertex_queue[bottom]);
states[vertex_queue[bottom]] = 2;
bottom++;
// look over neighbors
for (int j = vertex.neiBegin(); j != vertex.neiEnd(); j = vertex.neiNext(j))
{
int nei_idx = vertex.neiVertex(j);
if (nei_idx == edge_beg)
continue;
if (states[nei_idx] != 0)
continue;
states[nei_idx] = 1;
vertex_queue.push(nei_idx);
}
}
// now states[j] == 0 if j-th vertex shound not be moved
Vec3f edge_beg_pos, edge_end_pos, rot_axis;
// get rotation axis
edge_beg_pos.copy(xyz_sub[xyzmap[_mapping[edge_beg]]]);
edge_end_pos.copy(xyz_sub[xyzmap[_mapping[edge_end]]]);
rot_axis.diff(edge_end_pos, edge_beg_pos);
if (!rot_axis.normalize())
continue;
const Vertex &edge_end_vertex = _subgraph.getVertex(edge_end);
float max_sum_len = -1;
for (j = edge_end_vertex.neiBegin(); j != edge_end_vertex.neiEnd();
j = edge_end_vertex.neiNext(j))
{
int nei_idx_2 = edge_end_vertex.neiVertex(j);
int nei_idx_1 = _mapping[nei_idx_2];
if (nei_idx_2 == edge_beg)
continue;
if (nei_idx_1 == -1)
continue;
Vec3f nei1_pos;
Vec3f nei2_pos;
nei1_pos.copy(xyz_super[xyzmap[nei_idx_1]]);
nei2_pos.copy(xyz_sub[xyzmap[_mapping[nei_idx_2]]]);
nei1_pos.sub(edge_end_pos);
nei2_pos.sub(edge_end_pos);
float dot1 = Vec3f::dot(nei1_pos, rot_axis);
float dot2 = Vec3f::dot(nei2_pos, rot_axis);
nei1_pos.addScaled(rot_axis, -dot1);
nei2_pos.addScaled(rot_axis, -dot2);
if (max_sum_len > nei1_pos.length() + nei1_pos.length())
continue;
max_sum_len = nei1_pos.length() + nei1_pos.length();
if (!nei1_pos.normalize() || !nei2_pos.normalize())
continue;
double dp = Vec3f::dot(nei1_pos, nei2_pos);
if (dp > 1 - EPSILON)
dp = 1 - EPSILON;
if (dp < -1 + EPSILON)
dp = -1 + EPSILON;
double ang = acos(dp);
Vec3f cross;
cross.cross(nei1_pos, nei2_pos);
if (Vec3f::dot(cross, rot_axis) < 0)
ang = -ang;
matr.rotation(rot_axis.x, rot_axis.y, rot_axis.z, (float)ang);
matr.translateLocalInv(edge_end_pos);
matr.translate(edge_end_pos);
}
if (max_sum_len > 0)
{
for (j = _subgraph.vertexBegin(); j < _subgraph.vertexEnd(); j = _subgraph.vertexNext(j))
if (_mapping[j] >= 0 && states[j] != 0)
xyz_sub[xyzmap[_mapping[j]]].transformPoint(matr);
}
}
float sqsum = 0;
for (k = 0; k < xyz_sub.size(); k++)
sqsum += Vec3f::distSqr(xyz_sub[k], xyz_super[k]);
sqsum = sqrt(sqsum / xyz_sub.size());
if (sqsum > rms_threshold + eps)
return false;
return true;
}
