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#ifndef __Geom_MATRIX_H__
#define __Geom_MATRIX_H__
/** \file
* \brief Definition of Geom::Matrix types.
*
* Main authors:
* Lauris Kaplinski <lauris@kaplinski.com>:
* Original NRMatrix definition and related macros.
*
* Nathan Hurst <njh@mail.csse.monash.edu.au>:
* Geom::Matrix class version of the above.
*
* Michael G. Sloan <mgsloan@gmail.com>:
* Reorganization and additions.
*
* This code is in public domain.
*/
//#include <glib/gmessages.h>
#include <2geom/point.h>
namespace Geom {
/**
* The Matrix class.
*
* For purposes of multiplication, points should be thought of as row vectors
*
* \f$(p_X p_Y 1)\f$
*
* to be right-multiplied by transformation matrices of the form
* \f[
\left[
\begin{array}{ccc}
c_0&c_1&0 \\
c_2&c_3&0 \\
c_4&c_5&1
\end{array}
\right]
\f]
* (so the columns of the matrix correspond to the columns (elements) of the result,
* and the rows of the matrix correspond to columns (elements) of the "input").
*/
class Matrix {
private:
Coord _c[6];
public:
Matrix() {}
Matrix(Matrix const &m) {
for(int i = 0; i < 6; i++) {
_c[i] = m[i];
}
}
Matrix(Coord c0, Coord c1, Coord c2, Coord c3, Coord c4, Coord c5) {
_c[0] = c0; _c[1] = c1;
_c[2] = c2; _c[3] = c3;
_c[4] = c4; _c[5] = c5;
}
Matrix &operator=(Matrix const &m) {
for(int i = 0; i < 6; i++)
_c[i] = m._c[i];
return *this;
}
inline Coord operator[](unsigned const i) const { return _c[i]; }
inline Coord &operator[](unsigned const i) { return _c[i]; }
Point xAxis() const;
Point yAxis() const;
void setXAxis(Point const &vec);
void setYAxis(Point const &vec);
Point translation() const;
void setTranslation(Point const &loc);
double expansionX() const;
double expansionY() const;
inline Point expansion() const { return Point(expansionX(), expansionY()); }
void setExpansionX(double val);
void setExpansionY(double val);
void setIdentity();
bool isIdentity(Coord eps = EPSILON) const;
bool isTranslation(Coord eps = EPSILON) const;
bool isRotation(double eps = EPSILON) const;
bool isScale(double eps = EPSILON) const;
bool isUniformScale(double eps = EPSILON) const;
bool onlyScaleAndTranslation(double eps = EPSILON) const;
bool isSingular(double eps = EPSILON) const;
bool flips() const;
Matrix without_translation() const;
Matrix inverse() const;
Coord det() const;
Coord descrim2() const;
Coord descrim() const;
};
Matrix operator*(Matrix const &a, Matrix const &b);
inline Matrix &operator*=(Matrix &a, Matrix const &b) { a = a * b; return a; }
/** A function to print out the Matrix (for debugging) */
inline std::ostream &operator<< (std::ostream &out_file, const Geom::Matrix &m) {
out_file << "A: " << m[0] << " C: " << m[2] << " E: " << m[4] << "\n";
out_file << "B: " << m[1] << " D: " << m[3] << " F: " << m[5] << "\n";
return out_file;
}
/** Given a matrix m such that unit_circle = m*x, this returns the
* quadratic form x*A*x = 1. */
Matrix elliptic_quadratic_form(Matrix const &m);
/** Given a matrix (ignoring the translation) this returns the eigen
* values and vectors. */
class Eigen{
public:
Point vectors[2];
double values[2];
Eigen(Matrix const &m);
};
// Matrix factories
Matrix from_basis(const Point x_basis, const Point y_basis, const Point offset=Point(0,0));
/** Returns the Identity Matrix. */
inline Matrix identity() {
return Matrix(1.0, 0.0,
0.0, 1.0,
0.0, 0.0);
}
inline bool operator==(Matrix const &a, Matrix const &b) {
for(unsigned i = 0; i < 6; ++i) {
if ( a[i] != b[i] ) return false;
}
return true;
}
inline bool operator!=(Matrix const &a, Matrix const &b) { return !( a == b ); }
} /* namespace Geom */
#endif /* !__Geom_MATRIX_H__ */
/*
Local Variables:
mode:c++
c-file-style:"stroustrup"
c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +))
indent-tabs-mode:nil
fill-column:99
End:
*/
// vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:encoding=utf-8:textwidth=99 :
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