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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: 5.0.2 (2014/07/09)
#include "Wm5MathematicsPCH.h"
#include "Wm5ApprEllipseFit2.h"
#include "Wm5ContBox2.h"
#include "Wm5DistPoint2Ellipse2.h"
#include "Wm5MinimizeN.h"
namespace Wm5
{
//----------------------------------------------------------------------------
template <typename Real>
EllipseFit2<Real>::EllipseFit2 (int numPoints, const Vector2<Real>* points,
Vector2<Real>& center, Matrix2<Real>& rotate, Real diag[2],
Real& error)
:
mNumPoints(numPoints),
mPoints(points)
{
// Energy function is E : R^5 -> R where
// V = (V0, V1, V2, V3, V4)
// = (D[0], D[1], U.x, U.y, atan2(R[0][1],R[0][0])).
mTemp = new1<Vector2<Real> >(numPoints);
MinimizeN<Real> minimizer(5, Energy, 8, 8, 32, this);
InitialGuess(numPoints, mPoints, center, rotate, diag);
Real angle = Math<Real>::ATan2(rotate[0][1], rotate[0][0]);
Real e0 = diag[0]*Math<Real>::FAbs(rotate[0][0]) +
diag[1]*Math<Real>::FAbs(rotate[1][0]);
Real e1 = diag[0]*Math<Real>::FAbs(rotate[0][1]) +
diag[1]*Math<Real>::FAbs(rotate[1][1]);
Real v0[5] =
{
((Real)0.5)*diag[0],
((Real)0.5)*diag[1],
center.X() - e0,
center.Y() - e1,
-Math<Real>::PI
};
Real v1[5] =
{
((Real)2)*diag[0],
((Real)2)*diag[1],
center.X() + e0,
center.Y() + e1,
Math<Real>::PI
};
Real vInitial[5] =
{
diag[0],
diag[1],
center.X(),
center.Y(),
angle
};
Real vMin[5];
minimizer.GetMinimum(v0, v1, vInitial, vMin, error);
diag[0] = vMin[0];
diag[1] = vMin[1];
center.X() = vMin[2];
center.Y() = vMin[3];
rotate.MakeRotation(-vMin[4]);
delete1(mTemp);
}
//----------------------------------------------------------------------------
template <typename Real>
void EllipseFit2<Real>::InitialGuess (int numPoints,
const Vector2<Real>* points, Vector2<Real>& center,
Matrix2<Real>& rotate, Real diag[2])
{
Box2<Real> box = ContOrientedBox(numPoints, points);
center = box.Center;
rotate[0][0] = box.Axis[0].X();
rotate[0][1] = box.Axis[0].Y();
rotate[1][0] = box.Axis[1].X();
rotate[1][1] = box.Axis[1].Y();
diag[0] = box.Extent[0];
diag[1] = box.Extent[1];
}
//----------------------------------------------------------------------------
template <typename Real>
Real EllipseFit2<Real>::Energy (const Real* input, void* userData)
{
EllipseFit2& self = *(EllipseFit2*)userData;
// Build rotation matrix.
Matrix2<Real> rotate(-input[4]);
Ellipse2<Real> ellipse(Vector2<Real>::ZERO, Vector2<Real>::UNIT_X,
Vector2<Real>::UNIT_Y, input[0], input[1]);
// 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)
{
Vector2<Real> diff(
self.mPoints[i].X() - input[2],
self.mPoints[i].Y() - input[3]);
self.mTemp[i] = rotate*diff;
Real dist = DistPoint2Ellipse2<Real>(self.mTemp[i], ellipse).Get();
energy += dist;
}
return energy;
}
//----------------------------------------------------------------------------
//----------------------------------------------------------------------------
// Explicit instantiation.
//----------------------------------------------------------------------------
template WM5_MATHEMATICS_ITEM
class EllipseFit2<float>;
template WM5_MATHEMATICS_ITEM
class EllipseFit2<double>;
//----------------------------------------------------------------------------
}
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