bool Transform3f::bestFit (int npoints, const Vec3f points[], const Vec3f goals[], float *sqsum_out)
{
QS_DEF(Array<double>, X); //set of points
QS_DEF(Array<double>, Y); //set of goals
Matr3x3d R, RT, RTR, evectors_matrix;
//
Matr3x3d rotation;
double scale;
Vec3f translation;
//
bool res = 1;
Vec3f vec, tmp;
double cpoints[3] = {0.0}, cgoals[3] = {0.0}; // centroid of points, of goals
int i, j, k;
for (i = 0; i < npoints; i++)
{
cpoints[0] += points[i].x;
cpoints[1] += points[i].y;
cpoints[2] += points[i].z;
cgoals[0] += goals[i].x;
cgoals[1] += goals[i].y;
cgoals[2] += goals[i].z;
}
for (i = 0; i < 3; i++)
{
cpoints[i] /= npoints;
cgoals[i] /= npoints;
}
X.resize(npoints * 3);
Y.resize(npoints * 3);
//move each set to origin
for (i = 0; i < npoints; i++)
{
X[i * 3 + 0] = points[i].x - cpoints[0];
X[i * 3 + 1] = points[i].y - cpoints[1];
X[i * 3 + 2] = points[i].z - cpoints[2];
Y[i * 3 + 0] = goals[i].x - cgoals[0];
Y[i * 3 + 1] = goals[i].y - cgoals[1];
Y[i * 3 + 2] = goals[i].z - cgoals[2];
}
if (npoints > 1)
{
/* compute R */
for (i = 0; i < 3; i++)
{
for (j = 0; j < 3; j++)
{
R.elements[i * 3 + j] = 0.0;
for (k = 0; k < npoints; k++)
{
R.elements[i * 3 + j] += Y[k * 3 + i] * X[k * 3 + j];
}
}
}
//Compute R^T * R
R.getTransposed(RT);
RT.matrixMatrixMultiply(R, RTR);
RTR.eigenSystem(evectors_matrix);
if (RTR.elements[0] > 2 * EPSILON)
{
float norm_b0,norm_b1,norm_b2;
Vec3f a0, a1, a2;
Vec3f b0, b1, b2;
a0.set((float)evectors_matrix.elements[0], (float)evectors_matrix.elements[3], (float)evectors_matrix.elements[6]);
a1.set((float)evectors_matrix.elements[1], (float)evectors_matrix.elements[4], (float)evectors_matrix.elements[7]);
a2.cross(a0, a1);
R.matrixVectorMultiply(a0, b0);
R.matrixVectorMultiply(a1, b1);
norm_b0 = b0.length();
norm_b1 = b1.length();
Line3f l1, l2;
float sqs1, sqs2;
l1.bestFit(npoints, points, &sqs1);
l2.bestFit(npoints, goals, &sqs2);
if( sqs1 < 2 * EPSILON && sqs2 < 2 * EPSILON)
{
Transform3f temp;
temp.rotationVecVec(l1.dir, l2.dir);
for (i = 0; i < 3; i++)
for (j = 0; j < 3; j++)
rotation.elements[i * 3 + j] = temp.elements[j * 4 + i];
}
else
{
b0.normalize();
b1.normalize();
b2.cross(b0, b1);
norm_b2 = b2.length();
evectors_matrix.elements[2] = a2.x;
evectors_matrix.elements[5] = a2.y;
evectors_matrix.elements[8] = a2.z;
evectors_matrix.transpose();
RTR.elements[0] = b0.x; RTR.elements[1] = b1.x; RTR.elements[2] = b2.x;
RTR.elements[3] = b0.y; RTR.elements[4] = b1.y; RTR.elements[5] = b2.y;
RTR.elements[6] = b0.z; RTR.elements[7] = b1.z; RTR.elements[8] = b2.z;
RTR.matrixMatrixMultiply(evectors_matrix, rotation);
}
}
else
{
res = 0;
}
}
else
{
res = 0;
}
if (!res)
{
rotation.identity();
}
//Calc scale
scale = 1.0;
if (res && npoints > 1)
{
float l1 = 0.0;
float l2 = 0.0;
Vec3f vx, vy;
for (i = 0; i < npoints; i++)
{
Vec3f vx((float)X[i * 3 + 0], (float)X[i * 3 + 1], (float)X[i * 3 + 2]);
Vec3f vy((float)Y[i * 3 + 0], (float)Y[i * 3 + 1], (float)Y[i * 3 + 2]);
rotation.matrixVectorMultiply(vx, vec);
l1 += Vec3f::dot(vy, vec);
l2 += Vec3f::dot(vec, vec);
}
scale = l1 / l2;
}
X.clear();
Y.clear();
//Calc translation
translation.set((float)cgoals[0], (float)cgoals[1], (float)cgoals[2]);
tmp = Vec3f((float)cpoints[0], (float)cpoints[1], (float)cpoints[2]);
rotation.matrixVectorMultiply(tmp, vec);
vec.scale((float)scale);
translation.sub(vec);
identity();
for (i = 0; i < 3; i++)
{
for (j = 0; j < 3; j++)
{
elements[i * 4 + j] = (float)rotation.elements[j * 3 + i];
}
}
elements[15] = 1.0f;
translate(translation);
for (i = 0; i < 3; i++)
{
for (j = 0; j < 3; j++)
{
elements[i * 4 + j] *= (float)scale;
}
}
//Deviation
if (sqsum_out)
{
*sqsum_out = 0;
float d = .0f;
for (i = 0; i < npoints; i++)
{
vec.pointTransformation(points[i], *this);
d = Vec3f::dist(vec, goals[i]);
*sqsum_out += d * d;
}
}
return true;
}
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;
}