public static Line3d Line(this V3d[] points)
{
// compute covariance matrix of k closest points relative to centroid
var kk = points.Length;
// compute covariance matrix of k closest points relative to centroid
var c = V3d.Zero;
for (var j = 0; j < kk; j++)
{
c += points[j];
}
c /= kk;
var cvm = M33d.Zero;
for (var j = 0; j < kk; j++)
{
CovarianceMatrixExtensions.AddOuterProduct(ref cvm, points[j] - c);
}
cvm /= kk;
// solve eigensystem -> eigenvector with largest eigenvalue is best fit line
Eigensystems.Dsyevh3(cvm, out M33d q, out V3d w);
var n = ((w.X > w.Y) ? ((w.X > w.Z) ? q.C0 : q.C2) : ((w.Y > w.Z) ? q.C1 : q.C2));
return(new Line3d(c - n, c + n));
}
public static Plane3d Fit(this V3d[] points)
{
var kk = points.Length;
// compute covariance matrix of k closest points relative to centroid
var c = V3d.Zero;
for (var j = 0; j < kk; j++)
{
c += points[j];
}
c /= kk;
var cvm = M33d.Zero;
for (var j = 0; j < kk; j++)
{
CovarianceMatrixExtensions.AddOuterProduct(ref cvm, points[j] - c);
}
cvm /= kk;
// solve eigensystem -> eigenvector for smallest eigenvalue gives normal
Eigensystems.Dsyevh3(cvm, out M33d q, out V3d w);
var n = ((w.X < w.Y) ? ((w.X < w.Z) ? q.C0 : q.C2) : ((w.Y < w.Z) ? q.C1 : q.C2));
return(new Plane3d(n, c));
}