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#ifndef _mat2_h
#define _mat2_h
// #include <math.h>
#ifndef _real_h
# include "real.h"
#endif
#ifndef _vec2_h
# include "vec2.h"
#endif
//
// Member: r11 r12 tx
// r21 r22 ty
// 0 0 1
//
// Move: 1 0 tx Scale: sx 0 0 Rotate: cosa -sina 0
// 0 1 ty 0 sy 0 sina cosa 0
// 0 0 1 0 0 1 0 0 1
//
// ShearX: 1 a 0 ShearY: 1 0 0
// 0 1 0 b 1 0
// 0 0 1 0 0 1
//
// Multiplikation: C = A * B
// cr11 = ar11*br11 + ar12*br21;
// cr21 = ar21*br11 + ar22*br21;
// cr12 = ar11*br12 + ar12*br22;
// cr22 = ar21*br12 + ar22*br22;
// ctx = ar11*btx + ar12*bty + atx;
// cty = ar21*btx + ar22*bty + aty;
//
// inverse Matrix:
// detA = r11*r22 - r12*r21
//
// -1 r22/detA -r12/detA
// A = -r21/detA r11/detA
// tx = (r12*ty-r22*tx)/detA
// ty = (r21*tx-r11*ty)/detA
//
// Punktumrechnung:
// p2 = A * p1
// x2 = x1*r11 + y1*r12 + tx;
// y2 = x1*r21 + y1*r22 + ty;
//
// -1
// p1 = A * p2;
// x1 = ( x2*r22 - y2*r21)/detA - tx;
// y1 = (-x2*r12 + y2*r11)/detA - ty;
//
// -------------------------------------------------------------------------
class Mat2
{
public:
//
// Konstruktoren
//
Mat2()
{ r11=r22=1.0; r12=r21= tx=ty= 0.0; }
Mat2( const Mat2 &m )
{ r11=m.r11; r12=m.r12; r21=m.r21; r22=m.r22; tx=m.tx; ty=m.ty; }
Mat2(const Real &ir11, const Real &ir12, const Real &itx,
const Real &ir21, const Real &ir22, const Real &ity )
{ r11=ir11; r12=ir12; r21=ir21; r22=ir22; tx=itx; ty=ity; }
//
// Methoden zum Anwenden einer Transformation.
// Die der Transformation entsprechende Matrix wird von links!!
// in die aktuelle Matrix hineinmultipliziert.
//
Mat2 &Reset();
Mat2 &Move(const Real &dx, const Real &dy);
Mat2 &Move(const Vec2 &p);
Mat2 &MoveX(const Real &dx);
Mat2 &MoveY(const Real &dy);
Mat2 &Scale(const Real &sx, const Real &sy);
Mat2 &Scale(const Real &s);
Mat2 &ScaleX(const Real &sx);
Mat2 &ScaleY(const Real &sy);
Mat2 &ScaleAt(const Real &px, const Real &py,const Real &sx, const Real &sy);
Mat2 &ScaleAt(const Vec2 &p,const Real &sx, const Real &sy);
Mat2 &ScaleAt(const Real &px, const Real &py,const Real &s);
Mat2 &ScaleAt(const Vec2 &p,const Real &s);
Mat2 &Rotate(const Real &a);
Mat2 &RotateAt(const Real &px, const Real &py,const Real &a);
Mat2 &RotateAt(const Vec2 &p,const Real &a);
Mat2 &RotateDeg(const Real &a);
Mat2 &RotateDegAt(const Real &px, const Real &py,const Real &a);
Mat2 &RotateDegAt(const Vec2 &p,const Real &a);
Mat2 &ShearX(const Real& a);
Mat2 &ShearY(const Real& b);
Mat2 &Shear(const Real& a, const Real& b);
int IsRotated() const { return r12 || r21; }
//
// Zuweisungsoperator
//
const Mat2& operator=(const Mat2 &m)
{ r11=m.r11; r12=m.r12; r21=m.r21; r22=m.r22; tx=m.tx; ty=m.ty;
return *this; }
//
// Operatoren
//
const Mat2 &operator*=(const Mat2 &m);
Mat2 operator*(const Mat2 &m) const
{
Mat2 help(*this);
return help*=m;
}
void Invert(Mat2 *m) const;
Mat2 operator!() const
{ Mat2 m;
Invert( &m );
return m;
}
Vec2 operator*(const Vec2 &p) const {
return Vec2( r11*p.X() + r12*p.Y() + tx, r21*p.X() + r22*p.Y() + ty );
}
//
// Zugriff auf Koeffizienten
//
void Split( Real *sh, Real *sx, Real *sy, Real *angle, Real *mx, Real *my ) const;
protected:
Real r11, r12, tx;
Real r21, r22, ty;
};
inline Mat2 &Mat2::Reset()
{ r11=r22=1.0; r12=r21= tx=ty= 0.0; return *this; }
inline Mat2 &Mat2::Move(const Real &dx, const Real &dy)
{ tx+=dx; ty+=dy; return *this; }
inline Mat2 &Mat2::Move(const Vec2 &p)
{ tx+=p.X(); ty+=p.Y(); return *this; }
inline Mat2 &Mat2::MoveX(const Real &dx)
{ tx+=dx; return *this; }
inline Mat2 &Mat2::MoveY(const Real &dy)
{ ty+=dy; return *this; }
inline Mat2 &Mat2::Scale(const Real &sx, const Real &sy)
{ r11*=sx; r21*=sy; r12*=sx; r22*=sy; tx*=sx; ty*=sy; return *this; }
inline Mat2 &Mat2::Scale(const Real &s)
{ return Scale(s,s); }
inline Mat2 &Mat2::ScaleX(const Real &sx)
{ r11*=sx; r12*=sx; tx*=sx; return *this; }
inline Mat2 &Mat2::ScaleY(const Real &sy)
{ r21*=sy; r22*=sy; ty*=sy; return *this; }
inline Mat2 &Mat2::ScaleAt(const Real &px, const Real &py,const Real &sx, const Real &sy)
{ return Move(-px,-py).Scale(sx,sy).Move(px,py); }
inline Mat2 &Mat2::ScaleAt(const Vec2 &p,const Real &sx, const Real &sy)
{ return Move(-p).Scale(sx,sy).Move(p); }
inline Mat2 &Mat2::ScaleAt(const Real &px, const Real &py,const Real &s)
{ return Move(-px,-py).Scale(s).Move(px,py); }
inline Mat2 &Mat2::ScaleAt(const Vec2 &p,const Real &s)
{ return Move(-p).Scale(s).Move(p); }
inline Mat2 &Mat2::Rotate(const Real &a)
{ Mat2 help(*this);
r11 = r22 = cos(a);
r12 = -( r21 = sin(a) );
tx = ty = 0.0;
operator*=(help);
return *this;
}
inline Mat2 &Mat2::RotateDeg(const Real &a)
{ return Rotate(a/Real(180/M_PI)); }
inline Mat2 &Mat2::RotateAt(const Real &px, const Real &py,const Real &a)
{ return Move(-px,-py).Rotate(a).Move(px,py); }
inline Mat2 &Mat2::RotateDegAt(const Real &px, const Real &py,const Real &a)
{ return Move(-px,-py).Rotate(a/Real(180/M_PI)).Move(px,py); }
inline Mat2 &Mat2::RotateAt(const Vec2 &p,const Real &a)
{ return Move(-p).Rotate(a).Move(p); }
inline Mat2 &Mat2::RotateDegAt(const Vec2 &p,const Real &a)
{ return Move(-p).Rotate(a/Real(180/M_PI)).Move(p); }
inline Mat2 &Mat2::ShearX(const Real& a)
{ r11+=a*r21; r12+=a*r22; tx+=a*ty; return *this; }
inline Mat2 &Mat2::ShearY(const Real& b)
{ r21+=b*r11; r22+=b*r12; ty+=b*tx; return *this; }
inline Mat2 &Mat2::Shear(const Real& a, const Real& b)
{ return ShearX(a).ShearY(b); }
#endif /* __Mat2_H */
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