void
GlobalOptimization::setCommonBoundary (const vector_vec3d &boundary, const vector_vec2i &nurbs_indices)
{
if (boundary.empty () || boundary.size () != nurbs_indices.size ())
{
printf ("[GlobalOptimization::setCommonBoundary] Error, common boundary empty or size does not match.\n");
return;
}
}
void
NurbsTools::pca (const vector_vec3d &data, ON_3dVector &mean, Eigen::Matrix3d &eigenvectors,
Eigen::Vector3d &eigenvalues)
{
if (data.empty ())
{
printf ("[NurbsTools::pca] Error, data is empty\n");
abort ();
}
mean = computeMean (data);
unsigned s = data.size ();
ON_Matrix Q(3, s);
for (unsigned i = 0; i < s; i++) {
Q[0][i] = data[i].x - mean.x;
Q[1][i] = data[i].y - mean.y;
Q[2][i] = data[i].z - mean.z;
}
ON_Matrix Qt = Q;
Qt.Transpose();
ON_Matrix oC;
oC.Multiply(Q,Qt);
Eigen::Matrix3d C(3,3);
for (unsigned i = 0; i < 3; i++) {
for (unsigned j = 0; j < 3; j++) {
C(i,j) = oC[i][j];
}
}
Eigen::SelfAdjointEigenSolver < Eigen::Matrix3d > eigensolver (C);
if (eigensolver.info () != Eigen::Success)
{
printf ("[NurbsTools::pca] Can not find eigenvalues.\n");
abort ();
}
for (int i = 0; i < 3; ++i)
{
eigenvalues (i) = eigensolver.eigenvalues () (2 - i);
if (i == 2)
eigenvectors.col (2) = eigenvectors.col (0).cross (eigenvectors.col (1));
else
eigenvectors.col (i) = eigensolver.eigenvectors ().col (2 - i);
}
}
unsigned
NurbsTools::getClosestPoint (const Eigen::Vector3d &p, const vector_vec3d &data)
{
if (data.empty ())
throw std::runtime_error ("[NurbsTools::getClosestPoint(2d)] Data empty.\n");
size_t idx = 0;
double dist2 (DBL_MAX);
for (size_t i = 0; i < data.size (); i++)
{
double d2 = (data[i] - p).squaredNorm ();
if (d2 < dist2)
{
idx = i;
dist2 = d2;
}
}
return idx;
}
unsigned
NurbsTools::getClosestPoint (const ON_3dPoint &p, const vector_vec3d &data)
{
if (data.empty ())
throw std::runtime_error ("[NurbsTools::getClosestPoint(2d)] Data empty.\n");
unsigned idx (0);
double dist2 (DBL_MAX);
for (unsigned i = 0; i < data.size (); i++)
{
ON_3dVector v = (data[i] - p);
double d2 = ON_DotProduct(v, v); // Was the squaredNorm in Eigen
if (d2 < dist2)
{
idx = i;
dist2 = d2;
}
}
return idx;
}
void
NurbsTools::pca (const vector_vec3d &data, Eigen::Vector3d &mean, Eigen::Matrix3d &eigenvectors,
Eigen::Vector3d &eigenvalues)
{
if (data.empty ())
{
printf ("[NurbsTools::pca] Error, data is empty\n");
abort ();
}
mean = computeMean (data);
unsigned s = unsigned (data.size ());
Eigen::MatrixXd Q (3, s);
for (unsigned i = 0; i < s; i++)
Q.col (i) << (data[i] - mean);
Eigen::Matrix3d C = Q * Q.transpose ();
Eigen::SelfAdjointEigenSolver<Eigen::Matrix3d> eigensolver (C);
if (eigensolver.info () != Success)
{
printf ("[NurbsTools::pca] Can not find eigenvalues.\n");
abort ();
}
for (int i = 0; i < 3; ++i)
{
eigenvalues (i) = eigensolver.eigenvalues () (2 - i);
if (i == 2)
eigenvectors.col (2) = eigenvectors.col (0).cross (eigenvectors.col (1));
else
eigenvectors.col (i) = eigensolver.eigenvectors ().col (2 - i);
}
}
ON_NurbsCurve
FittingCurve::initNurbsCurvePCA (int order, const vector_vec3d &data, int ncps, double rf)
{
if (data.empty ())
printf ("[FittingCurve::initNurbsCurvePCA] Warning, no boundary parameters available\n");
Eigen::Vector3d mean;
Eigen::Matrix3d eigenvectors;
Eigen::Vector3d eigenvalues;
unsigned s = unsigned (data.size ());
NurbsTools::pca (data, mean, eigenvectors, eigenvalues);
eigenvalues = eigenvalues / s; // seems that the eigenvalues are dependent on the number of points (???)
double r = rf * sqrt (eigenvalues (0));
if (ncps < 2 * order)
ncps = 2 * order;
ON_NurbsCurve nurbs = ON_NurbsCurve (3, false, order, ncps);
nurbs.MakePeriodicUniformKnotVector (1.0 / (ncps - order + 1));
double dcv = (2.0 * M_PI) / (ncps - order + 1);
Eigen::Vector3d cv, cv_t;
for (int j = 0; j < ncps; j++)
{
cv (0) = r * sin (dcv * j);
cv (1) = r * cos (dcv * j);
cv (2) = 0.0;
cv_t = eigenvectors * cv + mean;
nurbs.SetCV (j, ON_3dPoint (cv_t (0), cv_t (1), cv_t (2)));
}
return nurbs;
}