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// 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 "Wm5ApprEllipsoidFit3.h"
#include "Wm5ContBox3.h"
#include "Wm5DistPoint3Ellipsoid3.h"
#include "Wm5MinimizeN.h"
namespace Wm5
{
//----------------------------------------------------------------------------
template <typename Real>
EllipsoidFit3<Real>::EllipsoidFit3 (int numPoints,
const Vector3<Real>* points, Vector3<Real>& center,
Matrix3<Real>& rotate, Real diag[3])
:
mNumPoints(numPoints),
mPoints(points)
{
// Energy function is E : R^9 -> R where
// V = (V0,V1,V2,V3,V4,V5,V6,V7,V8)
// = (D[0],D[1],D[2],U.X(),U,y,U.Z(),A0,A1,A2).
// For really scattered data, you might need a search function
mTemp = new1<Vector3<Real> >(numPoints);
MinimizeN<Real> minimizer(9, Energy, 8, 8, 32, this);
InitialGuess(numPoints, points, center, rotate, diag);
Real angle[3];
MatrixToAngles(rotate, angle);
Real extent[3] =
{
diag[0]*Math<Real>::FAbs(rotate[0][0]) +
diag[1]*Math<Real>::FAbs(rotate[0][1]) +
diag[2]*Math<Real>::FAbs(rotate[0][2]),
diag[0]*Math<Real>::FAbs(rotate[1][0]) +
diag[1]*Math<Real>::FAbs(rotate[1][1]) +
diag[2]*Math<Real>::FAbs(rotate[1][2]),
diag[0]*Math<Real>::FAbs(rotate[2][0]) +
diag[1]*Math<Real>::FAbs(rotate[2][1]) +
diag[2]*Math<Real>::FAbs(rotate[2][2])
};
Real v0[9] =
{
((Real)0.5)*diag[0],
((Real)0.5)*diag[1],
((Real)0.5)*diag[2],
center.X() - extent[0],
center.Y() - extent[1],
center.Z() - extent[2],
-Math<Real>::PI,
(Real)0,
(Real)0
};
Real v1[9] =
{
((Real)2)*diag[0],
((Real)2)*diag[1],
((Real)2)*diag[2],
center.X() + extent[0],
center.Y() + extent[1],
center.Z() + extent[2],
Math<Real>::PI,
Math<Real>::PI,
Math<Real>::PI
};
Real vInitial[9] =
{
diag[0],
diag[1],
diag[2],
center.X(),
center.Y(),
center.Z(),
angle[0],
angle[1],
angle[2]
};
Real vMin[9];
minimizer.GetMinimum(v0, v1, vInitial, vMin, mError);
diag[0] = vMin[0];
diag[1] = vMin[1];
diag[2] = vMin[2];
center.X() = vMin[3];
center.Y() = vMin[4];
center.Z() = vMin[5];
AnglesToMatrix(&vMin[6], rotate);
delete1(mTemp);
}
//----------------------------------------------------------------------------
template <typename Real>
EllipsoidFit3<Real>::operator Real ()
{
return mError;
}
//----------------------------------------------------------------------------
template <typename Real>
void EllipsoidFit3<Real>::InitialGuess (int numPoints,
const Vector3<Real>* points, Vector3<Real>& center,
Matrix3<Real>& rotate, Real diag[3])
{
Box3<Real> box = ContOrientedBox(numPoints, points);
center = box.Center;
rotate[0][0] = box.Axis[0].X();
rotate[0][1] = box.Axis[0].Y();
rotate[0][2] = box.Axis[0].Z();
rotate[1][0] = box.Axis[1].X();
rotate[1][1] = box.Axis[1].Y();
rotate[1][2] = box.Axis[1].Z();
rotate[2][0] = box.Axis[2].X();
rotate[2][1] = box.Axis[2].Y();
rotate[2][2] = box.Axis[2].Z();
diag[0] = box.Extent[0];
diag[1] = box.Extent[1];
diag[2] = box.Extent[2];
}
//----------------------------------------------------------------------------
template <typename Real>
Real EllipsoidFit3<Real>::Energy (const Real* input, void* userData)
{
EllipsoidFit3& self = *(EllipsoidFit3*)userData;
// Build rotation matrix.
Matrix3<Real> rotate;
AnglesToMatrix(&input[6], rotate);
// Uniformly scale the extents to keep reasonable floating point values
// in the distance calculations.
Real maxValue = input[0];
if (input[1] > maxValue)
{
maxValue = input[1];
}
if (input[2] > maxValue)
{
maxValue = input[2];
}
Real invMax = ((Real)1)/maxValue;
Ellipsoid3<Real> ellipsoid(Vector3<Real>::ZERO, Vector3<Real>::UNIT_X,
Vector3<Real>::UNIT_Y, Vector3<Real>::UNIT_Z, invMax*input[0],
invMax*input[1], invMax*input[2]);
// Transform the points to the coordinate system of center C and columns
// of rotation R.
Real energy = (Real)0;
for (int i = 0; i < self.mNumPoints; ++i)
{
Vector3<Real> diff(
self.mPoints[i].X() - input[3],
self.mPoints[i].Y() - input[4],
self.mPoints[i].Z() - input[5]);
self.mTemp[i] = invMax*(diff*rotate);
Real dist =
DistPoint3Ellipsoid3<Real>(self.mTemp[i], ellipsoid).Get();
energy += maxValue*dist;
}
return energy;
}
//----------------------------------------------------------------------------
template <typename Real>
void EllipsoidFit3<Real>::MatrixToAngles (const Matrix3<Real>& rotate,
Real* angle)
{
// rotation axis = (cos(a0)sin(a1),sin(a0)sin(a1),cos(a1))
// a0 in [-pi,pi], a1 in [0,pi], a2 in [0,pi]
Vector3<Real> axis;
rotate.ExtractAxisAngle(axis, angle[2]);
if (-(Real)1 < axis.Z())
{
if (axis.Z() < (Real)1)
{
angle[0] = Math<Real>::ATan2(axis.Y(), axis.X());
angle[1] = Math<Real>::ACos(axis.Z());
}
else
{
angle[0] = (Real)0;
angle[1] = (Real)0;
}
}
else
{
angle[0] = (Real)0;
angle[1] = Math<Real>::PI;
}
}
//----------------------------------------------------------------------------
template <typename Real>
void EllipsoidFit3<Real>::AnglesToMatrix (const Real* angle,
Matrix3<Real>& rotate)
{
// rotation axis = (cos(a0)sin(a1),sin(a0)sin(a1),cos(a1))
// a0 in [-pi,pi], a1 in [0,pi], a2 in [0,pi]
Real cs0 = Math<Real>::Cos(angle[0]);
Real sn0 = Math<Real>::Sin(angle[0]);
Real cs1 = Math<Real>::Cos(angle[1]);
Real sn1 = Math<Real>::Sin(angle[1]);
Vector3<Real> axis(cs0*sn1, sn0*sn1, cs1);
rotate.MakeRotation(axis, angle[2]);
}
//----------------------------------------------------------------------------
//----------------------------------------------------------------------------
// Explicit instantiation.
//----------------------------------------------------------------------------
template WM5_MATHEMATICS_ITEM
class EllipsoidFit3<float>;
template WM5_MATHEMATICS_ITEM
class EllipsoidFit3<double>;
//----------------------------------------------------------------------------
}
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