1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
|
// Geometric Tools, LLC
// Copyright (c) 1998-2014
// Distributed under the Boost Software License, Version 1.0.
// http://www.boost.org/LICENSE_1_0.txt
// http://www.geometrictools.com/License/Boost/LICENSE_1_0.txt
//
// File Version: 5.0.1 (2010/10/01)
#include "Wm5MathematicsPCH.h"
#include "Wm5ApprLineFit3.h"
#include "Wm5EigenDecomposition.h"
namespace Wm5
{
//----------------------------------------------------------------------------
template <typename Real>
Line3<Real> OrthogonalLineFit3 (int numPoints, const Vector3<Real>* points)
{
Line3<Real> line(Vector3<Real>::ZERO, Vector3<Real>::ZERO);
// Compute the mean of the points.
line.Origin = points[0];
int i;
for (i = 1; i < numPoints; i++)
{
line.Origin += points[i];
}
Real invNumPoints = ((Real)1)/numPoints;
line.Origin *= invNumPoints;
// Compute the covariance matrix of the points.
Real sumXX = (Real)0, sumXY = (Real)0, sumXZ = (Real)0;
Real sumYY = (Real)0, sumYZ = (Real)0, sumZZ = (Real)0;
for (i = 0; i < numPoints; i++)
{
Vector3<Real> diff = points[i] - line.Origin;
sumXX += diff[0]*diff[0];
sumXY += diff[0]*diff[1];
sumXZ += diff[0]*diff[2];
sumYY += diff[1]*diff[1];
sumYZ += diff[1]*diff[2];
sumZZ += diff[2]*diff[2];
}
sumXX *= invNumPoints;
sumXY *= invNumPoints;
sumXZ *= invNumPoints;
sumYY *= invNumPoints;
sumYZ *= invNumPoints;
sumZZ *= invNumPoints;
// Set up the eigensolver.
EigenDecomposition<Real> esystem(3);
esystem(0,0) = sumYY+sumZZ;
esystem(0,1) = -sumXY;
esystem(0,2) = -sumXZ;
esystem(1,0) = esystem(0,1);
esystem(1,1) = sumXX+sumZZ;
esystem(1,2) = -sumYZ;
esystem(2,0) = esystem(0,2);
esystem(2,1) = esystem(1,2);
esystem(2,2) = sumXX+sumYY;
// Compute eigenstuff, smallest eigenvalue is in last position.
esystem.Solve(false);
// Unit-length direction for best-fit line.
line.Direction = esystem.GetEigenvector3(2);
return line;
}
//----------------------------------------------------------------------------
//----------------------------------------------------------------------------
// Explicit instantiation.
//----------------------------------------------------------------------------
template WM5_MATHEMATICS_ITEM
Line3<float> OrthogonalLineFit3<float> (int, const Vector3<float>*);
template WM5_MATHEMATICS_ITEM
Line3<double> OrthogonalLineFit3<double> (int, const Vector3<double>*);
//----------------------------------------------------------------------------
}
|
