// 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;
GeometricTransforms.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 = GeometricTransforms.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 = GeometricTransforms.VectorListToString(ucs_1);
string ucs_2_str = GeometricTransforms.VectorListToString(ucs_2);
// debug
// calculate the transforms WITH CORRECTION
trWC2LC = GeometricTransforms.GetTransformWC2LC(pivot, vec0_r, vec1_r, vec2_r);
trLC2WC = GeometricTransforms.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 = 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));
}
public static void TestGeometricTransforms()
{
// get geometric properties of a reference object (e.g. BOX_01)
Matrix3D tr_WC2LC, tr_LC2WC;
GeometricTransforms.ComputePCATransf(GeometricTransforms.BOX_01, out tr_WC2LC, out tr_LC2WC);
List <Point3D> BOX_01_lc = GeometricTransforms.TransformBy(GeometricTransforms.BOX_01, tr_WC2LC);
string BOX_01_lc_str = GeometricTransforms.PointListToString(BOX_01_lc);
// position a new object (e.g. BOX_02_wc) relative to the one above
List <Point3D> BOX_02_wc = GeometricTransforms.TransformBy(GeometricTransforms.BOX_02_LC, tr_LC2WC);
string BOX_02_wc_str = GeometricTransforms.PointListToString(BOX_02_wc);
// test test
GeometricTransforms.ComputePCATransf(GeometricTransforms.OBJ_01, GeometricTransforms.OBJ_01_CORRECTION, out tr_WC2LC, out tr_LC2WC);
List <Point3D> OBJ_01_lc = GeometricTransforms.TransformBy(GeometricTransforms.OBJ_01, tr_WC2LC);
string OBJ_01_lc_str = GeometricTransforms.PointListToString(OBJ_01_lc);
}
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;
GeometricTransforms.CalculatePCA(_points, out pivot, out vec0, out vec1, out vec2);
// calculate the transforms
trWC2LC = GeometricTransforms.GetTransformWC2LC(pivot, vec0, vec1, vec2);
trLC2WC = GeometricTransforms.GetTransformLC2WC(pivot, vec0, vec1, vec2);
}
/// <summary>
/// <para>Calculates the local coordinate system based on the position on the editor canvas.</para>
/// <para>Calculates a simple path for edges which contains the ids of the start and end nodes in the first path entry.</para>
/// </summary>
private static void DeriveGeomPositionOutOfPlacementIn(Component.FlNetElement _nwe, System.Windows.Point _offset, double _scale, out Matrix3D ucs, out List <Point3D> path)
{
ucs = Matrix3D.Identity;
path = new List <Point3D>();
if (_nwe == null)
{
return;
}
Point3D pivot = new Point3D(0, 0, 0);
System.Windows.Point offset = new System.Windows.Point(_offset.X * _scale, _offset.Y * _scale);
List <Vector3D> axes = new List <Vector3D>(); // x, y, z
if (_nwe is Component.FlNetNode)
{
Component.FlNetNode node = _nwe as Component.FlNetNode;
if (!(node.IsValid))
{
return;
}
pivot.X = node.Position.X * _scale + offset.X;
pivot.Z = node.Position.Y * _scale + offset.Y;
axes.Add(new Vector3D(1, 0, 0));
axes.Add(new Vector3D(0, 0, 1));
axes.Add(new Vector3D(0, 1, 0));
}
else if (_nwe is Component.FlNetEdge)
{
Component.FlNetEdge edge = _nwe as Component.FlNetEdge;
if (!(edge.IsValid))
{
return;
}
pivot.X = edge.Start.Position.X * _scale + offset.X;
pivot.Z = edge.Start.Position.Y * _scale + offset.Y;
// the first entry in the path saves the ids of the start and end nodes to
// communicate connectivity to the GeometryViewer
long start_id = edge.Start.ID;
long end_id = edge.End.ID;
if (edge.Start is Component.FlowNetwork)
{
Component.FlowNetwork nw_start = edge.Start as Component.FlowNetwork;
Component.FlNetNode nN = nw_start.SortAndGetLastNode();
if (nN != null)
{
start_id = nN.ID;
}
}
if (edge.End is Component.FlowNetwork)
{
Component.FlowNetwork nw_end = edge.End as Component.FlowNetwork;
Component.FlNetNode n1 = nw_end.SortAndGetFirstNode();
if (n1 != null)
{
end_id = n1.ID;
}
}
path.Add(new Point3D(start_id, end_id, -1));
path.Add(new Point3D(edge.Start.Position.X * _scale + offset.X, 0, edge.Start.Position.Y * _scale + offset.Y));
path.Add(new Point3D(edge.End.Position.X * _scale + offset.X, 0, edge.End.Position.Y * _scale + offset.Y));
Vector3D axis_x = path[1] - path[0];
axis_x.Normalize();
axes.Add(axis_x);
axes.Add(new Vector3D(0, 0, 1));
Vector3D axis_z = Vector3D.CrossProduct(axes[0], axes[1]);
axis_z.Normalize();
axes.Add(axis_z);
}
ucs = GeometricTransforms.PackUCS(pivot, axes[0], axes[1], axes[2]);
}