public void Rescale()
{
Center();
Matrix <double> A = PositionMatrix();
Matrix <double> cov = 1.0f / ((float)A.RowCount) * A.Transpose() * A;
Evd <double> eigen = cov.Evd();
MathNet.Numerics.LinearAlgebra.Vector <System.Numerics.Complex> eigenvals = eigen.EigenValues;
double l1 = eigenvals[0].Real; //1 / Math.Sqrt(eigenvals[0].Real);
double l2 = eigenvals[1].Real; //1 / Math.Sqrt(eigenvals[1].Real);
double l3 = eigenvals[2].Real; // / Math.Sqrt(eigenvals[2].Real);
Debug.Log("l1: " + l1 + ", l2: " + l2 + ", l3: " + l3);
double vol = l1 * l2 * l3;
double max = eigenvals.AbsoluteMaximum().Real;
Debug.Log("max=" + max);
//double det = cov.Determinant();
A = A / Math.Sqrt(max) * 0.2;
Debug.Log(A);
//Debug.Log("determinant:");
for (int i = 0; i < A.RowCount; i++)
{
poses_[i].Translation = new Vector3((float)A[i, 0], (float)A[i, 1], (float)A[i, 2]);
}
/* Matrix<double> A = PositionMatrix();
* Matrix<double> cov = 1.0f / ((float)A.RowCount ) *A.Transpose() * A;
*
*
* Debug.Log(cov.ToString());
* Evd<double> eigen = cov.Evd();
* Matrix<double> m = eigen.EigenVectors;
* Matrix<double> points = m * A * m.Inverse();
*
* points = points * cov.Determinant() / 10;
* points = m * points * m.Inverse();
* for (int i = 0; i < points.RowCount; i++)
* {
* poses_[i].Translation =new Vector3((float)points[i, 0], (float)points[i, 1], (float)points[i, 2]);
* }*/
/*double det = cov.Determinant();
* cov_rotated = cov_rotated / det;
* Matrix<double> cov_recovered = m * cov_rotated * m.Inverse();*/
//Debug.Log(cov_recovered.ToString());
}