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// Copyright (c) 2006 GeometryFactory (France). All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
//
// $URL: https://github.com/CGAL/cgal/blob/v6.1.1/Surface_mesh_simplification/include/CGAL/Cartesian/MatrixC33.h $
// $Id: include/CGAL/Cartesian/MatrixC33.h 08b27d3db14 $
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
//
// Author(s) : Fernando Cacciola <fernando.cacciola@geometryfactory.com>
//
#ifndef CGAL_CARTESIAN_MATRIXC33_H
#define CGAL_CARTESIAN_MATRIXC33_H
#include <CGAL/license/Surface_mesh_simplification.h>
#include <CGAL/determinant.h>
#include <CGAL/Null_matrix.h>
#include <CGAL/number_utils.h>
#include <CGAL/Vector_3.h>
#include <optional>
namespace CGAL {
template <class R_>
class MatrixC33
{
public:
typedef R_ R;
typedef typename R::FT RT;
typedef typename R::Vector_3 Vector_3;
MatrixC33(Null_matrix)
: mR0(NULL_VECTOR),
mR1(NULL_VECTOR),
mR2(NULL_VECTOR)
{}
MatrixC33(const RT& r0x, const RT& r0y, const RT& r0z,
const RT& r1x, const RT& r1y, const RT& r1z,
const RT& r2x, const RT& r2y, const RT& r2z)
: mR0(r0x,r0y,r0z),
mR1(r1x,r1y,r1z),
mR2(r2x,r2y,r2z)
{}
MatrixC33(const Vector_3& r0, const Vector_3& r1, const Vector_3& r2)
: mR0(r0),
mR1(r1),
mR2(r2)
{}
const Vector_3& r0() const { return mR0; }
const Vector_3& r1() const { return mR1; }
const Vector_3& r2() const { return mR2; }
Vector_3& r0() { return mR0; }
Vector_3& r1() { return mR1; }
Vector_3& r2() { return mR2; }
const Vector_3& operator[](int row) const { return row == 0 ? mR0 : (row == 1 ? mR1 : mR2); }
Vector_3& operator[](int row) { return row == 0 ? mR0 : (row == 1 ? mR1 : mR2); }
MatrixC33& operator+=(const MatrixC33& m)
{
mR0 = mR0 + m.r0();
mR1 = mR1 + m.r1();
mR2 = mR2 + m.r2();
return *this;
}
MatrixC33& operator-=(const MatrixC33& m)
{
mR0 = mR0 - m.r0();
mR1 = mR1 - m.r1();
mR2 = mR2 - m.r2();
return *this;
}
MatrixC33& operator*=(const RT& c)
{
mR0 = mR0 * c;
mR1 = mR1 * c;
mR2 = mR2 * c;
return *this;
}
MatrixC33& operator/=(const RT& c)
{
mR0 = mR0 / c;
mR1 = mR1 / c;
mR2 = mR2 / c;
return *this;
}
friend MatrixC33 operator+(const MatrixC33& a, const MatrixC33& b)
{
return MatrixC33(a.r0() + b.r0(),
a.r1() + b.r1(),
a.r2() + b.r2());
}
friend MatrixC33 operator-(const MatrixC33& a, const MatrixC33& b)
{
return MatrixC33(a.r0() - b.r0(),
a.r1() - b.r1(),
a.r2() - b.r2());
}
friend MatrixC33 operator*(const MatrixC33& m, const RT& c)
{
return MatrixC33(m.r0()*c, m.r1()*c, m.r2()*c);
}
friend MatrixC33 operator*(const RT& c, const MatrixC33& m)
{
return MatrixC33(m.r0()*c, m.r1()*c, m.r2()*c);
}
friend MatrixC33 operator/(const MatrixC33& m, const RT& c)
{
return MatrixC33(m.r0()/c, m.r1()/c, m.r2()/c);
}
friend Vector_3 operator*(const MatrixC33& m, const Vector_3& v)
{
return Vector_3(m.r0()*v, m.r1()*v, m.r2()*v);
}
friend Vector_3 operator*(const Vector_3& v, const MatrixC33& m)
{
return Vector_3(v*m.r0(), v*m.r1(), v*m.r2());
}
friend std::ostream& operator<<(std::ostream & os, const MatrixC33& m)
{
return os << m.r0() << std::endl
<< m.r1() << std::endl
<< m.r2() << std::endl;
}
RT determinant() const
{
return CGAL::determinant(r0().x(), r0().y(), r0().z(),
r1().x(), r1().y(), r1().z(),
r2().x(), r2().y(), r2().z());
}
MatrixC33& transpose()
{
mR0 = Vector_3(r0().x(),r1().x(),r2().x());
mR1 = Vector_3(r0().y(),r1().y(),r2().y());
mR2 = Vector_3(r0().z(),r1().z(),r2().z());
return *this;
}
private:
Vector_3 mR0;
Vector_3 mR1;
Vector_3 mR2;
};
template<class R>
inline
MatrixC33<R> direct_product(const Vector_3<R>& u,
const Vector_3<R>& v)
{
return MatrixC33<R>(v * u.x(),
v * u.y(),
v * u.z());
}
template<class R>
MatrixC33<R> transposed_matrix(const MatrixC33<R>& m)
{
MatrixC33<R> copy = m;
copy.Transpose();
return copy;
}
template<class R>
MatrixC33<R> cofactors_matrix(const MatrixC33<R>& m)
{
typedef typename R::RT RT;
RT c00 = determinant(m.r1().y(),m.r1().z(),m.r2().y(),m.r2().z());
RT c01 = -determinant(m.r1().x(),m.r1().z(),m.r2().x(),m.r2().z());
RT c02 = determinant(m.r1().x(),m.r1().y(),m.r2().x(),m.r2().y());
RT c10 = -determinant(m.r0().y(),m.r0().z(),m.r2().y(),m.r2().z());
RT c11 = determinant(m.r0().x(),m.r0().z(),m.r2().x(),m.r2().z());
RT c12 = -determinant(m.r0().x(),m.r0().y(),m.r2().x(),m.r2().y());
RT c20 = determinant(m.r0().y(),m.r0().z(),m.r1().y(),m.r1().z());
RT c21 = -determinant(m.r0().x(),m.r0().z(),m.r1().x(),m.r1().z());
RT c22 = determinant(m.r0().x(),m.r0().y(),m.r1().x(),m.r1().y());
return MatrixC33<R>(c00,c01,c02,
c10,c11,c12,
c20,c21,c22);
}
template<class R>
MatrixC33<R> adjoint_matrix(const MatrixC33<R>& m)
{
return cofactors_matrix(m).transpose();
}
template<class R>
std::optional< MatrixC33<R> > inverse_matrix(const MatrixC33<R>& m)
{
typedef typename R::RT RT;
typedef MatrixC33<R> Matrix;
typedef std::optional<Matrix> result_type;
result_type rInverse;
RT det = m.determinant();
if(! CGAL_NTS is_zero(det))
{
RT c00 = (m.r1().y()*m.r2().z() - m.r1().z()*m.r2().y()) / det;
RT c01 = (m.r2().y()*m.r0().z() - m.r0().y()*m.r2().z()) / det;
RT c02 = (m.r0().y()*m.r1().z() - m.r1().y()*m.r0().z()) / det;
RT c10 = (m.r1().z()*m.r2().x() - m.r1().x()*m.r2().z()) / det;
RT c11 = (m.r0().x()*m.r2().z() - m.r2().x()*m.r0().z()) / det;
RT c12 = (m.r1().x()*m.r0().z() - m.r0().x()*m.r1().z()) / det;
RT c20 = (m.r1().x()*m.r2().y() - m.r2().x()*m.r1().y()) / det;
RT c21 = (m.r2().x()*m.r0().y() - m.r0().x()*m.r2().y()) / det;
RT c22 = (m.r0().x()*m.r1().y() - m.r0().y()*m.r1().x()) / det;
rInverse = result_type(Matrix(c00,c01,c02,
c10,c11,c12,
c20,c21,c22));
}
return rInverse;
}
} // namespace CGAL
#endif // CGAL_CARTESIAN_MATRIXC33_H //
// EOF //
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