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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 | // 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)
#ifndef WM5CONTELLIPSOID3MINCR_H
#define WM5CONTELLIPSOID3MINCR_H
#include "Wm5MathematicsLIB.h"
#include "Wm5Matrix3.h"
namespace Wm5
{
// Compute the minimum-volume ellipsoid, (X-C)^T R D R^T (X-C) = 1, given the
// center C and orientation matrix R. The columns of R are the axes of the
// ellipsoid. The algorithm computes the diagonal matrix D. The minimum
// volume is (4*pi/3)/sqrt(D[0]*D[1]*D[2]), where D = diag(D[0],D[1],D[2]).
// The problem is equivalent to maximizing the product D[0]*D[1]*D[2] for a
// given C and R, and subject to the constraints
// (P[i]-C)^T R D R^T (P[i]-C) <= 1
// for all input points P[i] with 0 <= i < N. Each constraint has the form
// A[0]*D[0] + A[1]*D[1] + A[2]*D[2] <= 1
// where A[0] >= 0, A[1] >= 0, and A[2] >= 0.
template <typename Real>
class WM5_MATHEMATICS_ITEM ContEllipsoid3MinCR
{
public:
ContEllipsoid3MinCR (int numPoints, const Vector3<Real>* points,
const Vector3<Real>& C, const Matrix3<Real>& R, Real D[3]);
private:
void FindEdgeMax (std::vector<Vector3<Real> >& A, int& plane0,
int& plane1, Real D[3]);
void FindFacetMax (std::vector<Vector3<Real> >& A, int& plane0,
Real D[3]);
void MaxProduct (std::vector<Vector3<Real> >& A, Real D[3]);
};
typedef ContEllipsoid3MinCR<float> ContEllipsoid3MinCRf;
typedef ContEllipsoid3MinCR<double> ContEllipsoid3MinCRd;
}
#endif
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