Hi,

It's been ages, but I'm trying to finish porting Avogadro to Eigen3. Benoit wrote some nice code to rotate a molecule (basically a 3D point cloud) using the best-fit hyperplane:

Vector3d ** atomPositions = new Vector3d*[nAtoms];
// Calculate the center of the molecule too
foreach (Atom *atom, m_atomList) {
Vector3d *pos = &(*m_atomPos)[atom->id()];
d->center += *pos;
atomPositions[i++] = pos;
}
d->center /= static_cast<double>(nAtoms);
Eigen::Hyperplane<double, 3> planeCoeffs;
Eigen::fitHyperplane(numAtoms(), atomPositions, &planeCoeffs);
delete[] atomPositions;
d->normalVector = planeCoeffs.normal();

Is there already some easy migration path for this (i.e., fitting a Hyperplane from a set of points)?

Thanks,
-Geoff

The main problem of the deprecated fitHyperplane function was that its API was not generic enough. Anyway, hyperplane fitting is not complicated:

Code: Select all

Matrix3Xf points = ...;
Vector3f mean = points.rowwise().mean();
Matrix3Xf centered_points = points.colwise()-mean();
Matrix3f cov = centered_points * centered_points.transpose();
SelfAdjointEigenSolver<Matrix3f> eig(cov);
HyperPlane3f plane(mean, eig.eigenvectors()(0));


You can also directly use eig.eigenvectors() as a 3x3 rotation matrix to align your molecule.

If the data are too far away from the origin, you also directly compute the covariance matrix as follows:

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Matrix3f cov = points * points.transpose();
cov  =- points.cols() * mean * mean.transpose();