/// <summary>
/// Returns true if a unique plane was found i.e. the given points are not coincident or colinear.
/// </summary>
/// <param name="points"></param>
/// <param name="start"></param>
/// <param name="direction"></param>
/// <param name="tolerance"></param>
/// <returns></returns>
public static bool FitLineToPoints(IEnumerable <Vector3d> points, Vector3d start, out Vector3d direction, double tolerance = D.ZeroTolerance)
{
// impl refs
// https://www.geometrictools.com/Documentation/LeastSquaresFitting.pdf
var covm = Matrix3d.CreateCovariance(points, start);
Matrix3d.Decompose.EigenSymmetric(ref covm, out Matrix3d vecs, out Vector3d vals, tolerance);
direction = vecs.Column0;
// Check for degeneracy -> if 1st eigenvalue is 0, then points are coincident
return(Math.Abs(vals.X) >= tolerance);
}
/// <summary>
/// Returns true if a unique plane was found i.e. the given points are not coincident or colinear.
/// </summary>
/// <param name="points"></param>
/// <param name="origin"></param>
/// <param name="normal"></param>
/// <param name="tolerance"></param>
/// <returns></returns>
public static bool FitPlaneToPoints(IEnumerable <Vector3d> points, Vector3d origin, out Vector3d normal, double tolerance = D.ZeroTolerance)
{
// impl refs
// https://www.geometrictools.com/Documentation/LeastSquaresFitting.pdf
// http://www.ilikebigbits.com/blog/2017/9/24/fitting-a-plane-to-noisy-points-in-3d
var covm = Matrix3d.CreateCovariance(points, origin);
Matrix3d.Decompose.EigenSymmetric(ref covm, out Matrix3d vecs, out Vector3d vals, tolerance);
normal = vecs.Column2;
// Check for degeneracy -> if 2nd eigenvalue is 0, the points are colinear at best
return(Math.Abs(vals.Y) >= tolerance);
}
/// <summary>
/// Returns 0 if the given points are coincident, 1 if they're colinear, 2 if they're coplanar, and 3 otherwise.
/// </summary>
/// <param name="points"></param>
/// <param name="origin"></param>
/// <param name="xAxis"></param>
/// <param name="yAxis"></param>
/// <param name="tolerance"></param>
/// <returns></returns>
public static int PrincipalComponentAnalysis(IEnumerable <Vector3d> points, out Vector3d origin, out Vector3d xAxis, out Vector3d yAxis, double tolerance = D.ZeroTolerance)
{
origin = points.Mean();
var covm = Matrix3d.CreateCovariance(points, origin);
Matrix3d.Decompose.EigenSymmetric(ref covm, out Matrix3d vecs, out Vector3d vals, tolerance);
xAxis = vecs.Column0;
yAxis = vecs.Column1;
return
(Math.Abs(vals.X) < tolerance ? 0 :
Math.Abs(vals.Y) < tolerance ? 1 :
Math.Abs(vals.Z) < tolerance ? 2 : 3);
}
