void
NurbsTools::pca (const vector_vec2d &data, Eigen::Vector2d &mean, Eigen::Matrix2d &eigenvectors,
Eigen::Vector2d &eigenvalues)
{
if (data.empty ())
{
printf ("[NurbsTools::pca] Error, data is empty\n");
abort ();
}
mean = computeMean (data);
unsigned s = unsigned (data.size ());
Eigen::MatrixXd Q (2, s);
for (unsigned i = 0; i < s; i++)
Q.col (i) << (data[i] - mean);
Eigen::Matrix2d C = Q * Q.transpose ();
Eigen::SelfAdjointEigenSolver<Eigen::Matrix2d> eigensolver (C);
if (eigensolver.info () != Success)
{
printf ("[NurbsTools::pca] Can not find eigenvalues.\n");
abort ();
}
for (int i = 0; i < 2; ++i)
{
eigenvalues (i) = eigensolver.eigenvalues () (1 - i);
eigenvectors.col (i) = eigensolver.eigenvectors ().col (1 - i);
}
}
static void diagonalizeInertiaTensor( const Matrix3s& I, Matrix3s& R0, Vector3s& I0 )
{
// Inertia tensor should by symmetric
assert( ( I - I.transpose() ).lpNorm<Eigen::Infinity>() <= 1.0e-6 );
// Inertia tensor should have positive determinant
assert( I.determinant() > 0.0 );
// Compute the eigenvectors and eigenvalues of the input matrix
const Eigen::SelfAdjointEigenSolver<Matrix3s> es{ I };
// Check for errors
if( es.info() == Eigen::NumericalIssue )
{
std::cerr << "Warning, failed to compute eigenvalues of inertia tensor due to Eigen::NumericalIssue" << std::endl;
}
else if( es.info() == Eigen::NoConvergence )
{
std::cerr << "Warning, failed to compute eigenvalues of inertia tensor due to Eigen::NoConvergence" << std::endl;
}
else if( es.info() == Eigen::InvalidInput )
{
std::cerr << "Warning, failed to compute eigenvalues of inertia tensor due to Eigen::InvalidInput" << std::endl;
}
assert( es.info() == Eigen::Success );
// Save the eigenvectors and eigenvalues
I0 = es.eigenvalues();
assert( ( I0.array() > 0.0 ).all() );
assert( I0.x() <= I0.y() );
assert( I0.y() <= I0.z() );
R0 = es.eigenvectors();
assert( fabs( fabs( R0.determinant() ) - 1.0 ) <= 1.0e-6 );
// Ensure that we have an orientation preserving transform
if( R0.determinant() < 0.0 )
{
R0.col( 0 ) *= -1.0;
}
}
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);
}
}