private static void CalculatePCA(List <Point3D> _points, out Point3D pivotO,
out Vector3D vecX, out Vector3D vecY, out Vector3D vecZ)
{
pivotO = new Point3D(0, 0, 0);
vecX = new Vector3D(0, 0, 0);
vecY = new Vector3D(0, 0, 0);
vecZ = new Vector3D(0, 0, 0);
if (_points == null || _points.Count < 1)
{
return;
}
Point3D pivot = GeometricTransforms.GetPivot(_points);
pivotO = new Point3D(pivot.X, pivot.Y, pivot.Z);
List <Vector3D> point_deviations = _points.Select(x => x - pivot).ToList();
int nrP = _points.Count;
#region COVARIANCE:Old
//// compute the covariance matrix
//double[] m = new double[3*nrP];
//for(int i = 0; i < nrP; i++)
//{
// m[i*3] = point_deviations[i].X;
// m[i*3 + 1] = point_deviations[i].Y;
// m[i*3 + 2] = point_deviations[i].Z;
//}
//MatrixNxN M = new MatrixNxN(nrP, 3, m);
//MatrixNxN MtxM = MatrixNxN.Squared(M);
//MtxM.Scale(1.0 / nrP);
#endregion
// compute the covariance matrix ...
// using 3rd party library DotNetMatrix
double[][] pd_as_array = new double[nrP][];
for (int i = 0; i < nrP; i++)
{
pd_as_array[i] = new double[] { point_deviations[i].X, point_deviations[i].Y, point_deviations[i].Z };
}
GeneralMatrix gm_M = new GeneralMatrix(pd_as_array);
GeneralMatrix gm_Mt = gm_M.Transpose();
GeneralMatrix gm_Msq = gm_Mt.Multiply(gm_M);
GeneralMatrix gm_Msqn = gm_Msq.Multiply(1.0 / nrP);
// extract the sorted Eigenvalues of the matrix...
// using 3rd party library DotNetMatrix
EigenvalueDecomposition decomp = gm_Msqn.Eigen();
GeneralMatrix gm_EVec = decomp.GetV();
double[] gm_EVal = decomp.RealEigenvalues;
// from smallest to largest eigenvalue
vecX = new Vector3D(gm_EVec.GetElement(0, 0), gm_EVec.GetElement(1, 0), gm_EVec.GetElement(2, 0));
vecY = new Vector3D(gm_EVec.GetElement(0, 1), gm_EVec.GetElement(1, 1), gm_EVec.GetElement(2, 1));
vecZ = new Vector3D(gm_EVec.GetElement(0, 2), gm_EVec.GetElement(1, 2), gm_EVec.GetElement(2, 2));
}
