imathmatrix.h

image converter source code

    //----------------------
    // Scale the matrix by s
    //----------------------

    template <class S>
    const Matrix44 &	scale (const Vec3<S> &s);


    //------------------------------------------
    // Set matrix to translation by given vector
    //------------------------------------------

    template <class S>
    const Matrix44 &	setTranslation (const Vec3<S> &t);


    //-----------------------------
    // Return translation component
    //-----------------------------

    const Vec3<T>	translation () const;


    //--------------------------
    // Translate the matrix by t
    //--------------------------

    template <class S>
    const Matrix44 &	translate (const Vec3<S> &t);


    //-------------------------------------------------------------
    // Set matrix to shear by given vector h.  The resulting matrix
    //    will shear x for each y coord. by a factor of h[0] ;
    //    will shear x for each z coord. by a factor of h[1] ;
    //    will shear y for each z coord. by a factor of h[2] .
    //-------------------------------------------------------------

    template <class S>
    const Matrix44 &	setShear (const Vec3<S> &h);


    //------------------------------------------------------------
    // Set matrix to shear by given factors.  The resulting matrix
    //    will shear x for each y coord. by a factor of h.xy ;
    //    will shear x for each z coord. by a factor of h.xz ;
    //    will shear y for each z coord. by a factor of h.yz ; 
    //    will shear y for each x coord. by a factor of h.yx ;
    //    will shear z for each x coord. by a factor of h.zx ;
    //    will shear z for each y coord. by a factor of h.zy .
    //------------------------------------------------------------

    template <class S>
    const Matrix44 &	setShear (const Shear6<S> &h);


    //--------------------------------------------------------
    // Shear the matrix by given vector.  The composed matrix 
    // will be <shear> * <this>, where the shear matrix ...
    //    will shear x for each y coord. by a factor of h[0] ;
    //    will shear x for each z coord. by a factor of h[1] ;
    //    will shear y for each z coord. by a factor of h[2] .
    //--------------------------------------------------------

    template <class S>
    const Matrix44 &	shear (const Vec3<S> &h);


    //------------------------------------------------------------
    // Shear the matrix by the given factors.  The composed matrix 
    // will be <shear> * <this>, where the shear matrix ...
    //    will shear x for each y coord. by a factor of h.xy ;
    //    will shear x for each z coord. by a factor of h.xz ;
    //    will shear y for each z coord. by a factor of h.yz ;
    //    will shear y for each x coord. by a factor of h.yx ;
    //    will shear z for each x coord. by a factor of h.zx ;
    //    will shear z for each y coord. by a factor of h.zy .
    //------------------------------------------------------------

    template <class S>
    const Matrix44 &	shear (const Shear6<S> &h);


    //-------------------------------------------------
    // Limitations of type T (see also class limits<T>)
    //-------------------------------------------------

    static T		baseTypeMin()		{return limits<T>::min();}
    static T		baseTypeMax()		{return limits<T>::max();}
    static T		baseTypeSmallest()	{return limits<T>::smallest();}
    static T		baseTypeEpsilon()	{return limits<T>::epsilon();}
};


//--------------
// Stream output
//--------------

template <class T>
std::ostream &	operator << (std::ostream & s, const Matrix33<T> &m); 

template <class T>
std::ostream &	operator << (std::ostream & s, const Matrix44<T> &m); 


//---------------------------------------------
// Vector-times-matrix multiplication operators
//---------------------------------------------

template <class S, class T>
const Vec2<S> &		   operator *= (Vec2<S> &v, const Matrix33<T> &m);

template <class S, class T>
Vec2<S>			   operator * (const Vec2<S> &v, const Matrix33<T> &m);

template <class S, class T>
const Vec3<S> &		   operator *= (Vec3<S> &v, const Matrix33<T> &m);

template <class S, class T>
Vec3<S>			   operator * (const Vec3<S> &v, const Matrix33<T> &m);

template <class S, class T>
const Vec3<S> &		   operator *= (Vec3<S> &v, const Matrix44<T> &m);

template <class S, class T>
Vec3<S>			   operator * (const Vec3<S> &v, const Matrix44<T> &m);


//-------------------------
// Typedefs for convenience
//-------------------------

typedef Matrix33 <float>  M33f;
typedef Matrix33 <double> M33d;
typedef Matrix44 <float>  M44f;
typedef Matrix44 <double> M44d;


//---------------------------
// Implementation of Matrix33
//---------------------------

template <class T>
inline T *
Matrix33<T>::operator [] (int i)
{
    return x[i];
}

template <class T>
inline const T *
Matrix33<T>::operator [] (int i) const
{
    return x[i];
}

template <class T>
inline
Matrix33<T>::Matrix33 ()
{
    x[0][0] = 1;
    x[0][1] = 0;
    x[0][2] = 0;
    x[1][0] = 0;
    x[1][1] = 1;
    x[1][2] = 0;
    x[2][0] = 0;
    x[2][1] = 0;
    x[2][2] = 1;
}

template <class T>
inline
Matrix33<T>::Matrix33 (T a)
{
    x[0][0] = a;
    x[0][1] = a;
    x[0][2] = a;
    x[1][0] = a;
    x[1][1] = a;
    x[1][2] = a;
    x[2][0] = a;
    x[2][1] = a;
    x[2][2] = a;
}

template <class T>
inline
Matrix33<T>::Matrix33 (const T a[3][3]) 
{
    x[0][0] = a[0][0];
    x[0][1] = a[0][1];
    x[0][2] = a[0][2];
    x[1][0] = a[1][0];
    x[1][1] = a[1][1];
    x[1][2] = a[1][2];
    x[2][0] = a[2][0];
    x[2][1] = a[2][1];
    x[2][2] = a[2][2];
}

template <class T>
inline
Matrix33<T>::Matrix33 (T a, T b, T c, T d, T e, T f, T g, T h, T i)
{
    x[0][0] = a;
    x[0][1] = b;
    x[0][2] = c;
    x[1][0] = d;
    x[1][1] = e;
    x[1][2] = f;
    x[2][0] = g;
    x[2][1] = h;
    x[2][2] = i;
}

template <class T>
inline
Matrix33<T>::Matrix33 (const Matrix33 &v)
{
    x[0][0] = v.x[0][0];
    x[0][1] = v.x[0][1];
    x[0][2] = v.x[0][2];
    x[1][0] = v.x[1][0];
    x[1][1] = v.x[1][1];
    x[1][2] = v.x[1][2];
    x[2][0] = v.x[2][0];
    x[2][1] = v.x[2][1];
    x[2][2] = v.x[2][2];
}

template <class T>
inline const Matrix33<T> &
Matrix33<T>::operator = (const Matrix33 &v)
{
    x[0][0] = v.x[0][0];
    x[0][1] = v.x[0][1];
    x[0][2] = v.x[0][2];
    x[1][0] = v.x[1][0];
    x[1][1] = v.x[1][1];
    x[1][2] = v.x[1][2];
    x[2][0] = v.x[2][0];
    x[2][1] = v.x[2][1];
    x[2][2] = v.x[2][2];
    return *this;
}

template <class T>
inline const Matrix33<T> &
Matrix33<T>::operator = (T a)
{
    x[0][0] = a;
    x[0][1] = a;
    x[0][2] = a;
    x[1][0] = a;
    x[1][1] = a;
    x[1][2] = a;
    x[2][0] = a;
    x[2][1] = a;
    x[2][2] = a;
    return *this;
}

template <class T>
inline T *
Matrix33<T>::getValue ()
{
    return (T *) &x[0][0];
}

template <class T>
inline const T *
Matrix33<T>::getValue () const
{
    return (const T *) &x[0][0];
}

template <class T>
template <class S>
inline void
Matrix33<T>::getValue (Matrix33<S> &v) const
{
    v.x[0][0] = x[0][0];
    v.x[0][1] = x[0][1];
    v.x[0][2] = x[0][2];
    v.x[1][0] = x[1][0];
    v.x[1][1] = x[1][1];
    v.x[1][2] = x[1][2];
    v.x[2][0] = x[2][0];
    v.x[2][1] = x[2][1];
    v.x[2][2] = x[2][2];
}

template <class T>
template <class S>
inline Matrix33<T> &
Matrix33<T>::setValue (const Matrix33<S> &v)
{
    x[0][0] = v.x[0][0];
    x[0][1] = v.x[0][1];
    x[0][2] = v.x[0][2];
    x[1][0] = v.x[1][0];
    x[1][1] = v.x[1][1];
    x[1][2] = v.x[1][2];
    x[2][0] = v.x[2][0];
    x[2][1] = v.x[2][1];
    x[2][2] = v.x[2][2];
    return *this;
}

template <class T>
template <class S>
inline Matrix33<T> &
Matrix33<T>::setTheMatrix (const Matrix33<S> &v)
{
    x[0][0] = v.x[0][0];
    x[0][1] = v.x[0][1];
    x[0][2] = v.x[0][2];
    x[1][0] = v.x[1][0];
    x[1][1] = v.x[1][1];
    x[1][2] = v.x[1][2];
    x[2][0] = v.x[2][0];
    x[2][1] = v.x[2][1];
    x[2][2] = v.x[2][2];
    return *this;
}

template <class T>
inline void
Matrix33<T>::makeIdentity()
{
    x[0][0] = 1;
    x[0][1] = 0;
    x[0][2] = 0;
    x[1][0] = 0;
    x[1][1] = 1;
    x[1][2] = 0;
    x[2][0] = 0;
    x[2][1] = 0;
    x[2][2] = 1;
}

template <class T>
bool
Matrix33<T>::operator == (const Matrix33 &v) const
{
    return x[0][0] == v.x[0][0] &&
	   x[0][1] == v.x[0][1] &&
	   x[0][2] == v.x[0][2] &&
	   x[1][0] == v.x[1][0] &&
	   x[1][1] == v.x[1][1] &&
	   x[1][2] == v.x[1][2] &&
	   x[2][0] == v.x[2][0] &&
	   x[2][1] == v.x[2][1] &&
	   x[2][2] == v.x[2][2];
}

template <class T>
bool
Matrix33<T>::operator != (const Matrix33 &v) const
{
    return x[0][0] != v.x[0][0] ||
	   x[0][1] != v.x[0][1] ||
	   x[0][2] != v.x[0][2] ||
	   x[1][0] != v.x[1][0] ||
	   x[1][1] != v.x[1][1] ||
	   x[1][2] != v.x[1][2] ||
	   x[2][0] != v.x[2][0] ||
	   x[2][1] != v.x[2][1] ||
	   x[2][2] != v.x[2][2];
}

template <class T>
bool
Matrix33<T>::equalWithAbsError (const Matrix33<T> &m, T e) const
{
    for (int i = 0; i < 3; i++)
	for (int j = 0; j < 3; j++)
	    if (!Imath::equalWithAbsError ((*this)[i][j], m[i][j], e))
		return false;

    return true;
}

template <class T>
bool
Matrix33<T>::equalWithRelError (const Matrix33<T> &m, T e) const
{
    for (int i = 0; i < 3; i++)
	for (int j = 0; j < 3; j++)
	    if (!Imath::equalWithRelError ((*this)[i][j], m[i][j], e))
		return false;

    return true;
}

template <class T>
const Matrix33<T> &
Matrix33<T>::operator += (const Matrix33<T> &v)
{
    x[0][0] += v.x[0][0];
    x[0][1] += v.x[0][1];
    x[0][2] += v.x[0][2];
    x[1][0] += v.x[1][0];
    x[1][1] += v.x[1][1];
    x[1][2] += v.x[1][2];
    x[2][0] += v.x[2][0];
    x[2][1] += v.x[2][1];
    x[2][2] += v.x[2][2];

    return *this;
}

template <class T>
const Matrix33<T> &
Matrix33<T>::operator += (T a)
{
    x[0][0] += a;
    x[0][1] += a;
    x[0][2] += a;
    x[1][0] += a;
    x[1][1] += a;
    x[1][2] += a;
    x[2][0] += a;
    x[2][1] += a;
    x[2][2] += a;
  
    return *this;
}

template <class T>
Matrix33<T>
Matrix33<T>::operator + (const Matrix33<T> &v) const
{
    return Matrix33 (x[0][0] + v.x[0][0],
		     x[0][1] + v.x[0][1],
		     x[0][2] + v.x[0][2],
		     x[1][0] + v.x[1][0],
		     x[1][1] + v.x[1][1],
		     x[1][2] + v.x[1][2],
		     x[2][0] + v.x[2][0],
		     x[2][1] + v.x[2][1],
		     x[2][2] + v.x[2][2]);
}

template <class T>
const Matrix33<T> &
Matrix33<T>::operator -= (const Matrix33<T> &v)
{
    x[0][0] -= v.x[0][0];
    x[0][1] -= v.x[0][1];
    x[0][2] -= v.x[0][2];
    x[1][0] -= v.x[1][0];
    x[1][1] -= v.x[1][1];
    x[1][2] -= v.x[1][2];
    x[2][0] -= v.x[2][0];
    x[2][1] -= v.x[2][1];
    x[2][2] -= v.x[2][2];
  
    return *this;
}

template <class T>
const Matrix33<T> &
Matrix33<T>::operator -= (T a)
{
    x[0][0] -= a;
    x[0][1] -= a;
    x[0][2] -= a;
    x[1][0] -= a;
    x[1][1] -= a;
    x[1][2] -= a;
    x[2][0] -= a;
    x[2][1] -= a;
    x[2][2] -= a;
  
    return *this;
}

template <class T>
Matrix33<T>
Matrix33<T>::operator - (const Matrix33<T> &v) const
{
    return Matrix33 (x[0][0] - v.x[0][0],
		     x[0][1] - v.x[0][1],
		     x[0][2] - v.x[0][2],
		     x[1][0] - v.x[1][0],
		     x[1][1] - v.x[1][1],
		     x[1][2] - v.x[1][2],
		     x[2][0] - v.x[2][0],
		     x[2][1] - v.x[2][1],
		     x[2][2] - v.x[2][2]);
}

template <class T>
Matrix33<T>
Matrix33<T>::operator - () const
{
    return Matrix33 (-x[0][0],
		     -x[0][1],
		     -x[0][2],
		     -x[1][0],
		     -x[1][1],
		     -x[1][2],
		     -x[2][0],
		     -x[2][1],
		     -x[2][2]);
}

template <class T>
const Matrix33<T> &
Matrix33<T>::negate ()
{
    x[0][0] = -x[0][0];
    x[0][1] = -x[0][1];
    x[0][2] = -x[0][2];
    x[1][0] = -x[1][0];
    x[1][1] = -x[1][1];
    x[1][2] = -x[1][2];
    x[2][0] = -x[2][0];
    x[2][1] = -x[2][1];
    x[2][2] = -x[2][2];

    return *this;
}

template <class T>
const Matrix33<T> &
Matrix33<T>::operator *= (T a)
{
    x[0][0] *= a;
    x[0][1] *= a;
    x[0][2] *= a;
    x[1][0] *= a;
    x[1][1] *= a;
    x[1][2] *= a;
    x[2][0] *= a;
    x[2][1] *= a;
    x[2][2] *= a;
  
    return *this;
}

template <class T>
Matrix33<T>
Matrix33<T>::operator * (T a) const
{
    return Matrix33 (x[0][0] * a,
		     x[0][1] * a,
		     x[0][2] * a,
		     x[1][0] * a,
		     x[1][1] * a,
		     x[1][2] * a,
		     x[2][0] * a,
		     x[2][1] * a,
		     x[2][2] * a);
}

template <class T>
inline Matrix33<T>
operator * (T a, const Matrix33<T> &v)
{
    return v * a;
}

template <class T>
const Matrix33<T> &
Matrix33<T>::operator *= (const Matrix33<T> &v)
{
    Matrix33 tmp (T (0));

    for (int i = 0; i < 3; i++)
	for (int j = 0; j < 3; j++)
	    for (int k = 0; k < 3; k++)
		tmp.x[i][j] += x[i][k] * v.x[k][j];

    *this = tmp;
    return *this;
}

template <class T>
Matrix33<T>
Matrix33<T>::operator * (const Matrix33<T> &v) const
{
    Matrix33 tmp (T (0));

    for (int i = 0; i < 3; i++)
	for (int j = 0; j < 3; j++)
	    for (int k = 0; k < 3; k++)
		tmp.x[i][j] += x[i][k] * v.x[k][j];

    return tmp;
}

template <class T>
template <class S>
void
Matrix33<T>::multVecMatrix(const Vec2<S> &src, Vec2<S> &dst) const
{
    S a, b, w;

    a = src[0] * x[0][0] + src[1] * x[1][0] + x[2][0];
    b = src[0] * x[0][1] + src[1] * x[1][1] + x[2][1];
    w = src[0] * x[0][2] + src[1] * x[1][2] + x[2][2];

    dst.x = a / w;
    dst.y = b / w;
}

template <class T>
template <class S>
void
Matrix33<T>::multDirMatrix(const Vec2<S> &src, Vec2<S> &dst) const
{
    S a, b;

    a = src[0] * x[0][0] + src[1] * x[1][0];