// vector _y as user input
public static void ComputePCATransf(List <Point3D> _points, Vector3D v_correction, out Matrix3D trWC2LC, out Matrix3D trLC2WC)
{
trWC2LC = Matrix3D.Identity;
trLC2WC = Matrix3D.Identity;
if (_points == null || _points.Count < 1 || v_correction == null)
{
return;
}
Point3D pivot;
Vector3D vec0, vec1, vec2;
GeometryTransf.CalculatePCA(_points, out pivot, out vec0, out vec1, out vec2);
// detect which base vector is closest to the correction vector
v_correction.Normalize();
double angle0 = Vector3D.DotProduct(v_correction, vec0);
double angle1 = Vector3D.DotProduct(v_correction, vec1);
double angle2 = Vector3D.DotProduct(v_correction, vec2);
Vector3D vec_to_rotate = vec2;
if (Math.Abs(angle0) < Math.Abs(angle1) && Math.Abs(angle0) < Math.Abs(angle2))
{
vec_to_rotate = (angle0 > 0) ? vec0 : -vec0;
}
else if (Math.Abs(angle1) < Math.Abs(angle0) && Math.Abs(angle1) < Math.Abs(angle2))
{
vec_to_rotate = (angle1 > 0) ? vec1 : -vec1;
}
else
{
vec_to_rotate = (angle2 > 0) ? vec2 : -vec2;
}
// correct by user-defined vector
Matrix3D R = GeometryTransf.AlingVector(v_correction, vec_to_rotate);
Vector3D vec0_r = R.Transform(vec0);
Vector3D vec1_r = R.Transform(vec1);
Vector3D vec2_r = R.Transform(vec2);
// debug
List <Vector3D> ucs_1 = new List <Vector3D> {
vec0, vec1, vec2, v_correction
};
List <Vector3D> ucs_2 = new List <Vector3D> {
vec0_r, vec1_r, vec2_r
};
string ucs_1_str = GeometryTransf.VectorListToString(ucs_1);
string ucs_2_str = GeometryTransf.VectorListToString(ucs_2);
// debug
// calculate the transforms WITH CORRECTION
trWC2LC = GeometryTransf.GetTransformWC2LC(pivot, vec0_r, vec1_r, vec2_r);
trLC2WC = GeometryTransf.GetTransformLC2WC(pivot, vec0_r, vec1_r, vec2_r);
}
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 = GeometryTransf.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));
}
public static void ComputePCATransf(List <Point3D> _points, out Matrix3D trWC2LC, out Matrix3D trLC2WC)
{
trWC2LC = Matrix3D.Identity;
trLC2WC = Matrix3D.Identity;
if (_points == null || _points.Count < 1)
{
return;
}
Point3D pivot;
Vector3D vec0, vec1, vec2;
GeometryTransf.CalculatePCA(_points, out pivot, out vec0, out vec1, out vec2);
// calculate the transforms
trWC2LC = GeometryTransf.GetTransformWC2LC(pivot, vec0, vec1, vec2);
trLC2WC = GeometryTransf.GetTransformLC2WC(pivot, vec0, vec1, vec2);
}