--- /dev/null
+///////////////////////////////////////////////////////////////////////////
+//
+// Copyright (c) 2002, Industrial Light & Magic, a division of Lucas
+// Digital Ltd. LLC
+//
+// All rights reserved.
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are
+// met:
+// * Redistributions of source code must retain the above copyright
+// notice, this list of conditions and the following disclaimer.
+// * Redistributions in binary form must reproduce the above
+// copyright notice, this list of conditions and the following disclaimer
+// in the documentation and/or other materials provided with the
+// distribution.
+// * Neither the name of Industrial Light & Magic nor the names of
+// its contributors may be used to endorse or promote products derived
+// from this software without specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+//
+///////////////////////////////////////////////////////////////////////////
+
+
+
+#ifndef INCLUDED_IMATHMATRIX_H
+#define INCLUDED_IMATHMATRIX_H
+
+//----------------------------------------------------------------
+//
+// 2D (3x3) and 3D (4x4) transformation matrix templates.
+//
+//----------------------------------------------------------------
+
+#include "ImathPlatform.h"
+#include "ImathFun.h"
+#include "ImathExc.h"
+#include "ImathVec.h"
+#include "ImathShear.h"
+
+#include <iostream>
+#include <iomanip>
+
+
+namespace Imath {
+
+
+template <class T> class Matrix33
+{
+ public:
+
+ //-------------------
+ // Access to elements
+ //-------------------
+
+ T x[3][3];
+
+ T * operator [] (int i);
+ const T * operator [] (int i) const;
+
+
+ //-------------
+ // Constructors
+ //-------------
+
+ Matrix33 ();
+ // 1 0 0
+ // 0 1 0
+ // 0 0 1
+
+ Matrix33 (T a);
+ // a a a
+ // a a a
+ // a a a
+
+ Matrix33 (const T a[3][3]);
+ // a[0][0] a[0][1] a[0][2]
+ // a[1][0] a[1][1] a[1][2]
+ // a[2][0] a[2][1] a[2][2]
+
+ Matrix33 (T a, T b, T c, T d, T e, T f, T g, T h, T i);
+
+ // a b c
+ // d e f
+ // g h i
+
+
+ //--------------------------------
+ // Copy constructor and assignment
+ //--------------------------------
+
+ Matrix33 (const Matrix33 &v);
+
+ const Matrix33 & operator = (const Matrix33 &v);
+ const Matrix33 & operator = (T a);
+
+
+ //----------------------
+ // Compatibility with Sb
+ //----------------------
+
+ T * getValue ();
+ const T * getValue () const;
+
+ template <class S>
+ void getValue (Matrix33<S> &v) const;
+ template <class S>
+ Matrix33 & setValue (const Matrix33<S> &v);
+
+ template <class S>
+ Matrix33 & setTheMatrix (const Matrix33<S> &v);
+
+
+ //---------
+ // Identity
+ //---------
+
+ void makeIdentity();
+
+
+ //---------
+ // Equality
+ //---------
+
+ bool operator == (const Matrix33 &v) const;
+ bool operator != (const Matrix33 &v) const;
+
+ //-----------------------------------------------------------------------
+ // Compare two matrices and test if they are "approximately equal":
+ //
+ // equalWithAbsError (m, e)
+ //
+ // Returns true if the coefficients of this and m are the same with
+ // an absolute error of no more than e, i.e., for all i, j
+ //
+ // abs (this[i][j] - m[i][j]) <= e
+ //
+ // equalWithRelError (m, e)
+ //
+ // Returns true if the coefficients of this and m are the same with
+ // a relative error of no more than e, i.e., for all i, j
+ //
+ // abs (this[i] - v[i][j]) <= e * abs (this[i][j])
+ //-----------------------------------------------------------------------
+
+ bool equalWithAbsError (const Matrix33<T> &v, T e) const;
+ bool equalWithRelError (const Matrix33<T> &v, T e) const;
+
+
+ //------------------------
+ // Component-wise addition
+ //------------------------
+
+ const Matrix33 & operator += (const Matrix33 &v);
+ const Matrix33 & operator += (T a);
+ Matrix33 operator + (const Matrix33 &v) const;
+
+
+ //---------------------------
+ // Component-wise subtraction
+ //---------------------------
+
+ const Matrix33 & operator -= (const Matrix33 &v);
+ const Matrix33 & operator -= (T a);
+ Matrix33 operator - (const Matrix33 &v) const;
+
+
+ //------------------------------------
+ // Component-wise multiplication by -1
+ //------------------------------------
+
+ Matrix33 operator - () const;
+ const Matrix33 & negate ();
+
+
+ //------------------------------
+ // Component-wise multiplication
+ //------------------------------
+
+ const Matrix33 & operator *= (T a);
+ Matrix33 operator * (T a) const;
+
+
+ //-----------------------------------
+ // Matrix-times-matrix multiplication
+ //-----------------------------------
+
+ const Matrix33 & operator *= (const Matrix33 &v);
+ Matrix33 operator * (const Matrix33 &v) const;
+
+
+ //---------------------------------------------
+ // Vector-times-matrix multiplication; see also
+ // the "operator *" functions defined below.
+ //---------------------------------------------
+
+ template <class S>
+ void multVecMatrix(const Vec2<S> &src, Vec2<S> &dst) const;
+
+ template <class S>
+ void multDirMatrix(const Vec2<S> &src, Vec2<S> &dst) const;
+
+
+ //------------------------
+ // Component-wise division
+ //------------------------
+
+ const Matrix33 & operator /= (T a);
+ Matrix33 operator / (T a) const;
+
+
+ //------------------
+ // Transposed matrix
+ //------------------
+
+ const Matrix33 & transpose ();
+ Matrix33 transposed () const;
+
+
+ //------------------------------------------------------------
+ // Inverse matrix: If singExc is false, inverting a singular
+ // matrix produces an identity matrix. If singExc is true,
+ // inverting a singular matrix throws a SingMatrixExc.
+ //
+ // inverse() and invert() invert matrices using determinants;
+ // gjInverse() and gjInvert() use the Gauss-Jordan method.
+ //
+ // inverse() and invert() are significantly faster than
+ // gjInverse() and gjInvert(), but the results may be slightly
+ // less accurate.
+ //
+ //------------------------------------------------------------
+
+ const Matrix33 & invert (bool singExc = false)
+ throw (Iex::MathExc);
+
+ Matrix33<T> inverse (bool singExc = false) const
+ throw (Iex::MathExc);
+
+ const Matrix33 & gjInvert (bool singExc = false)
+ throw (Iex::MathExc);
+
+ Matrix33<T> gjInverse (bool singExc = false) const
+ throw (Iex::MathExc);
+
+
+ //-----------------------------------------
+ // Set matrix to rotation by r (in radians)
+ //-----------------------------------------
+
+ template <class S>
+ const Matrix33 & setRotation (S r);
+
+
+ //-----------------------------
+ // Rotate the given matrix by r
+ //-----------------------------
+
+ template <class S>
+ const Matrix33 & rotate (S r);
+
+
+ //--------------------------------------------
+ // Set matrix to scale by given uniform factor
+ //--------------------------------------------
+
+ const Matrix33 & setScale (T s);
+
+
+ //------------------------------------
+ // Set matrix to scale by given vector
+ //------------------------------------
+
+ template <class S>
+ const Matrix33 & setScale (const Vec2<S> &s);
+
+
+ //----------------------
+ // Scale the matrix by s
+ //----------------------
+
+ template <class S>
+ const Matrix33 & scale (const Vec2<S> &s);
+
+
+ //------------------------------------------
+ // Set matrix to translation by given vector
+ //------------------------------------------
+
+ template <class S>
+ const Matrix33 & setTranslation (const Vec2<S> &t);
+
+
+ //-----------------------------
+ // Return translation component
+ //-----------------------------
+
+ Vec2<T> translation () const;
+
+
+ //--------------------------
+ // Translate the matrix by t
+ //--------------------------
+
+ template <class S>
+ const Matrix33 & translate (const Vec2<S> &t);
+
+
+ //-----------------------------------------------------------
+ // Set matrix to shear x for each y coord. by given factor xy
+ //-----------------------------------------------------------
+
+ template <class S>
+ const Matrix33 & setShear (const S &h);
+
+
+ //-------------------------------------------------------------
+ // Set matrix to shear x for each y coord. by given factor h[0]
+ // and to shear y for each x coord. by given factor h[1]
+ //-------------------------------------------------------------
+
+ template <class S>
+ const Matrix33 & setShear (const Vec2<S> &h);
+
+
+ //-----------------------------------------------------------
+ // Shear the matrix in x for each y coord. by given factor xy
+ //-----------------------------------------------------------
+
+ template <class S>
+ const Matrix33 & shear (const S &xy);
+
+
+ //-----------------------------------------------------------
+ // Shear the matrix in x for each y coord. by given factor xy
+ // and shear y for each x coord. by given factor yx
+ //-----------------------------------------------------------
+
+ template <class S>
+ const Matrix33 & shear (const Vec2<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();}
+};
+
+
+template <class T> class Matrix44
+{
+ public:
+
+ //-------------------
+ // Access to elements
+ //-------------------
+
+ T x[4][4];
+
+ T * operator [] (int i);
+ const T * operator [] (int i) const;
+
+
+ //-------------
+ // Constructors
+ //-------------
+
+ Matrix44 ();
+ // 1 0 0 0
+ // 0 1 0 0
+ // 0 0 1 0
+ // 0 0 0 1
+
+ Matrix44 (T a);
+ // a a a a
+ // a a a a
+ // a a a a
+ // a a a a
+
+ Matrix44 (const T a[4][4]) ;
+ // a[0][0] a[0][1] a[0][2] a[0][3]
+ // a[1][0] a[1][1] a[1][2] a[1][3]
+ // a[2][0] a[2][1] a[2][2] a[2][3]
+ // a[3][0] a[3][1] a[3][2] a[3][3]
+
+ Matrix44 (T a, T b, T c, T d, T e, T f, T g, T h,
+ T i, T j, T k, T l, T m, T n, T o, T p);
+
+ // a b c d
+ // e f g h
+ // i j k l
+ // m n o p
+
+ Matrix44 (Matrix33<T> r, Vec3<T> t);
+ // r r r 0
+ // r r r 0
+ // r r r 0
+ // t t t 1
+
+
+ //--------------------------------
+ // Copy constructor and assignment
+ //--------------------------------
+
+ Matrix44 (const Matrix44 &v);
+
+ const Matrix44 & operator = (const Matrix44 &v);
+ const Matrix44 & operator = (T a);
+
+
+ //----------------------
+ // Compatibility with Sb
+ //----------------------
+
+ T * getValue ();
+ const T * getValue () const;
+
+ template <class S>
+ void getValue (Matrix44<S> &v) const;
+ template <class S>
+ Matrix44 & setValue (const Matrix44<S> &v);
+
+ template <class S>
+ Matrix44 & setTheMatrix (const Matrix44<S> &v);
+
+ //---------
+ // Identity
+ //---------
+
+ void makeIdentity();
+
+
+ //---------
+ // Equality
+ //---------
+
+ bool operator == (const Matrix44 &v) const;
+ bool operator != (const Matrix44 &v) const;
+
+ //-----------------------------------------------------------------------
+ // Compare two matrices and test if they are "approximately equal":
+ //
+ // equalWithAbsError (m, e)
+ //
+ // Returns true if the coefficients of this and m are the same with
+ // an absolute error of no more than e, i.e., for all i, j
+ //
+ // abs (this[i][j] - m[i][j]) <= e
+ //
+ // equalWithRelError (m, e)
+ //
+ // Returns true if the coefficients of this and m are the same with
+ // a relative error of no more than e, i.e., for all i, j
+ //
+ // abs (this[i] - v[i][j]) <= e * abs (this[i][j])
+ //-----------------------------------------------------------------------
+
+ bool equalWithAbsError (const Matrix44<T> &v, T e) const;
+ bool equalWithRelError (const Matrix44<T> &v, T e) const;
+
+
+ //------------------------
+ // Component-wise addition
+ //------------------------
+
+ const Matrix44 & operator += (const Matrix44 &v);
+ const Matrix44 & operator += (T a);
+ Matrix44 operator + (const Matrix44 &v) const;
+
+
+ //---------------------------
+ // Component-wise subtraction
+ //---------------------------
+
+ const Matrix44 & operator -= (const Matrix44 &v);
+ const Matrix44 & operator -= (T a);
+ Matrix44 operator - (const Matrix44 &v) const;
+
+
+ //------------------------------------
+ // Component-wise multiplication by -1
+ //------------------------------------
+
+ Matrix44 operator - () const;
+ const Matrix44 & negate ();
+
+
+ //------------------------------
+ // Component-wise multiplication
+ //------------------------------
+
+ const Matrix44 & operator *= (T a);
+ Matrix44 operator * (T a) const;
+
+
+ //-----------------------------------
+ // Matrix-times-matrix multiplication
+ //-----------------------------------
+
+ const Matrix44 & operator *= (const Matrix44 &v);
+ Matrix44 operator * (const Matrix44 &v) const;
+
+ static void multiply (const Matrix44 &a, // assumes that
+ const Matrix44 &b, // &a != &c and
+ Matrix44 &c); // &b != &c.
+
+
+ //---------------------------------------------
+ // Vector-times-matrix multiplication; see also
+ // the "operator *" functions defined below.
+ //---------------------------------------------
+
+ template <class S>
+ void multVecMatrix(const Vec3<S> &src, Vec3<S> &dst) const;
+
+ template <class S>
+ void multDirMatrix(const Vec3<S> &src, Vec3<S> &dst) const;
+
+
+ //------------------------
+ // Component-wise division
+ //------------------------
+
+ const Matrix44 & operator /= (T a);
+ Matrix44 operator / (T a) const;
+
+
+ //------------------
+ // Transposed matrix
+ //------------------
+
+ const Matrix44 & transpose ();
+ Matrix44 transposed () const;
+
+
+ //------------------------------------------------------------
+ // Inverse matrix: If singExc is false, inverting a singular
+ // matrix produces an identity matrix. If singExc is true,
+ // inverting a singular matrix throws a SingMatrixExc.
+ //
+ // inverse() and invert() invert matrices using determinants;
+ // gjInverse() and gjInvert() use the Gauss-Jordan method.
+ //
+ // inverse() and invert() are significantly faster than
+ // gjInverse() and gjInvert(), but the results may be slightly
+ // less accurate.
+ //
+ //------------------------------------------------------------
+
+ const Matrix44 & invert (bool singExc = false)
+ throw (Iex::MathExc);
+
+ Matrix44<T> inverse (bool singExc = false) const
+ throw (Iex::MathExc);
+
+ const Matrix44 & gjInvert (bool singExc = false)
+ throw (Iex::MathExc);
+
+ Matrix44<T> gjInverse (bool singExc = false) const
+ throw (Iex::MathExc);
+
+
+ //--------------------------------------------------------
+ // Set matrix to rotation by XYZ euler angles (in radians)
+ //--------------------------------------------------------
+
+ template <class S>
+ const Matrix44 & setEulerAngles (const Vec3<S>& r);
+
+
+ //--------------------------------------------------------
+ // Set matrix to rotation around given axis by given angle
+ //--------------------------------------------------------
+
+ template <class S>
+ const Matrix44 & setAxisAngle (const Vec3<S>& ax, S ang);
+
+
+ //-------------------------------------------
+ // Rotate the matrix by XYZ euler angles in r
+ //-------------------------------------------
+
+ template <class S>
+ const Matrix44 & rotate (const Vec3<S> &r);
+
+
+ //--------------------------------------------
+ // Set matrix to scale by given uniform factor
+ //--------------------------------------------
+
+ const Matrix44 & setScale (T s);
+
+
+ //------------------------------------
+ // Set matrix to scale by given vector
+ //------------------------------------
+
+ template <class S>
+ const Matrix44 & setScale (const Vec3<S> &s);
+
+
+ //----------------------
+ // 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];
+ b = src[0] * x[0][1] + src[1] * x[1][1];
+
+ dst.x = a;
+ dst.y = b;
+}
+
+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>
+const Matrix33<T> &
+Matrix33<T>::transpose ()
+{
+ Matrix33 tmp (x[0][0],
+ x[1][0],
+ x[2][0],
+ x[0][1],
+ x[1][1],
+ x[2][1],
+ x[0][2],
+ x[1][2],
+ x[2][2]);
+ *this = tmp;
+ return *this;
+}
+
+template <class T>
+Matrix33<T>
+Matrix33<T>::transposed () const
+{
+ return Matrix33 (x[0][0],
+ x[1][0],
+ x[2][0],
+ x[0][1],
+ x[1][1],
+ x[2][1],
+ x[0][2],
+ x[1][2],
+ x[2][2]);
+}
+
+template <class T>
+const Matrix33<T> &
+Matrix33<T>::gjInvert (bool singExc) throw (Iex::MathExc)
+{
+ *this = gjInverse (singExc);
+ return *this;
+}
+
+template <class T>
+Matrix33<T>
+Matrix33<T>::gjInverse (bool singExc) const throw (Iex::MathExc)
+{
+ int i, j, k;
+ Matrix33 s;
+ Matrix33 t (*this);
+
+ // Forward elimination
+
+ for (i = 0; i < 2 ; i++)
+ {
+ int pivot = i;
+
+ T pivotsize = t[i][i];
+
+ if (pivotsize < 0)
+ pivotsize = -pivotsize;
+
+ for (j = i + 1; j < 3; j++)
+ {
+ T tmp = t[j][i];
+
+ if (tmp < 0)
+ tmp = -tmp;
+
+ if (tmp > pivotsize)
+ {
+ pivot = j;
+ pivotsize = tmp;
+ }
+ }
+
+ if (pivotsize == 0)
+ {
+ if (singExc)
+ throw ::Imath::SingMatrixExc ("Cannot invert singular matrix.");
+
+ return Matrix33();
+ }
+
+ if (pivot != i)
+ {
+ for (j = 0; j < 3; j++)
+ {
+ T tmp;
+
+ tmp = t[i][j];
+ t[i][j] = t[pivot][j];
+ t[pivot][j] = tmp;
+
+ tmp = s[i][j];
+ s[i][j] = s[pivot][j];
+ s[pivot][j] = tmp;
+ }
+ }
+
+ for (j = i + 1; j < 3; j++)
+ {
+ T f = t[j][i] / t[i][i];
+
+ for (k = 0; k < 3; k++)
+ {
+ t[j][k] -= f * t[i][k];
+ s[j][k] -= f * s[i][k];
+ }
+ }
+ }
+
+ // Backward substitution
+
+ for (i = 2; i >= 0; --i)
+ {
+ T f;
+
+ if ((f = t[i][i]) == 0)
+ {
+ if (singExc)
+ throw ::Imath::SingMatrixExc ("Cannot invert singular matrix.");
+
+ return Matrix33();
+ }
+
+ for (j = 0; j < 3; j++)
+ {
+ t[i][j] /= f;
+ s[i][j] /= f;
+ }
+
+ for (j = 0; j < i; j++)
+ {
+ f = t[j][i];
+
+ for (k = 0; k < 3; k++)
+ {
+ t[j][k] -= f * t[i][k];
+ s[j][k] -= f * s[i][k];
+ }
+ }
+ }
+
+ return s;
+}
+
+template <class T>
+const Matrix33<T> &
+Matrix33<T>::invert (bool singExc) throw (Iex::MathExc)
+{
+ *this = inverse (singExc);
+ return *this;
+}
+
+template <class T>
+Matrix33<T>
+Matrix33<T>::inverse (bool singExc) const throw (Iex::MathExc)
+{
+ if (x[0][2] != 0 || x[1][2] != 0 || x[2][2] != 1)
+ {
+ Matrix33 s (x[1][1] * x[2][2] - x[2][1] * x[1][2],
+ x[2][1] * x[0][2] - x[0][1] * x[2][2],
+ x[0][1] * x[1][2] - x[1][1] * x[0][2],
+
+ x[2][0] * x[1][2] - x[1][0] * x[2][2],
+ x[0][0] * x[2][2] - x[2][0] * x[0][2],
+ x[1][0] * x[0][2] - x[0][0] * x[1][2],
+
+ x[1][0] * x[2][1] - x[2][0] * x[1][1],
+ x[2][0] * x[0][1] - x[0][0] * x[2][1],
+ x[0][0] * x[1][1] - x[1][0] * x[0][1]);
+
+ T r = x[0][0] * s[0][0] + x[0][1] * s[1][0] + x[0][2] * s[2][0];
+
+ if (Imath::abs (r) >= 1)
+ {
+ for (int i = 0; i < 3; ++i)
+ {
+ for (int j = 0; j < 3; ++j)
+ {
+ s[i][j] /= r;
+ }
+ }
+ }
+ else
+ {
+ T mr = Imath::abs (r) / limits<T>::smallest();
+
+ for (int i = 0; i < 3; ++i)
+ {
+ for (int j = 0; j < 3; ++j)
+ {
+ if (mr > Imath::abs (s[i][j]))
+ {
+ s[i][j] /= r;
+ }
+ else
+ {
+ if (singExc)
+ throw SingMatrixExc ("Cannot invert "
+ "singular matrix.");
+ return Matrix33();
+ }
+ }
+ }
+ }
+
+ return s;
+ }
+ else
+ {
+ Matrix33 s ( x[1][1],
+ -x[0][1],
+ 0,
+
+ -x[1][0],
+ x[0][0],
+ 0,
+
+ 0,
+ 0,
+ 1);
+
+ T r = x[0][0] * x[1][1] - x[1][0] * x[0][1];
+
+ if (Imath::abs (r) >= 1)
+ {
+ for (int i = 0; i < 2; ++i)
+ {
+ for (int j = 0; j < 2; ++j)
+ {
+ s[i][j] /= r;
+ }
+ }
+ }
+ else
+ {
+ T mr = Imath::abs (r) / limits<T>::smallest();
+
+ for (int i = 0; i < 2; ++i)
+ {
+ for (int j = 0; j < 2; ++j)
+ {
+ if (mr > Imath::abs (s[i][j]))
+ {
+ s[i][j] /= r;
+ }
+ else
+ {
+ if (singExc)
+ throw SingMatrixExc ("Cannot invert "
+ "singular matrix.");
+ return Matrix33();
+ }
+ }
+ }
+ }
+
+ s[2][0] = -x[2][0] * s[0][0] - x[2][1] * s[1][0];
+ s[2][1] = -x[2][0] * s[0][1] - x[2][1] * s[1][1];
+
+ return s;
+ }
+}
+
+template <class T>
+template <class S>
+const Matrix33<T> &
+Matrix33<T>::setRotation (S r)
+{
+ S cos_r, sin_r;
+
+ cos_r = Math<T>::cos (r);
+ sin_r = Math<T>::sin (r);
+
+ x[0][0] = cos_r;
+ x[0][1] = sin_r;
+ x[0][2] = 0;
+
+ x[1][0] = -sin_r;
+ x[1][1] = cos_r;
+ x[1][2] = 0;
+
+ x[2][0] = 0;
+ x[2][1] = 0;
+ x[2][2] = 1;
+
+ return *this;
+}
+
+template <class T>
+template <class S>
+const Matrix33<T> &
+Matrix33<T>::rotate (S r)
+{
+ *this *= Matrix33<T>().setRotation (r);
+ return *this;
+}
+
+template <class T>
+const Matrix33<T> &
+Matrix33<T>::setScale (T s)
+{
+ x[0][0] = s;
+ x[0][1] = 0;
+ x[0][2] = 0;
+
+ x[1][0] = 0;
+ x[1][1] = s;
+ x[1][2] = 0;
+
+ x[2][0] = 0;
+ x[2][1] = 0;
+ x[2][2] = 1;
+
+ return *this;
+}
+
+template <class T>
+template <class S>
+const Matrix33<T> &
+Matrix33<T>::setScale (const Vec2<S> &s)
+{
+ x[0][0] = s[0];
+ x[0][1] = 0;
+ x[0][2] = 0;
+
+ x[1][0] = 0;
+ x[1][1] = s[1];
+ x[1][2] = 0;
+
+ x[2][0] = 0;
+ x[2][1] = 0;
+ x[2][2] = 1;
+
+ return *this;
+}
+
+template <class T>
+template <class S>
+const Matrix33<T> &
+Matrix33<T>::scale (const Vec2<S> &s)
+{
+ x[0][0] *= s[0];
+ x[0][1] *= s[0];
+ x[0][2] *= s[0];
+
+ x[1][0] *= s[1];
+ x[1][1] *= s[1];
+ x[1][2] *= s[1];
+
+ return *this;
+}
+
+template <class T>
+template <class S>
+const Matrix33<T> &
+Matrix33<T>::setTranslation (const Vec2<S> &t)
+{
+ 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] = t[0];
+ x[2][1] = t[1];
+ x[2][2] = 1;
+
+ return *this;
+}
+
+template <class T>
+inline Vec2<T>
+Matrix33<T>::translation () const
+{
+ return Vec2<T> (x[2][0], x[2][1]);
+}
+
+template <class T>
+template <class S>
+const Matrix33<T> &
+Matrix33<T>::translate (const Vec2<S> &t)
+{
+ x[2][0] += t[0] * x[0][0] + t[1] * x[1][0];
+ x[2][1] += t[0] * x[0][1] + t[1] * x[1][1];
+ x[2][2] += t[0] * x[0][2] + t[1] * x[1][2];
+
+ return *this;
+}
+
+template <class T>
+template <class S>
+const Matrix33<T> &
+Matrix33<T>::setShear (const S &xy)
+{
+ x[0][0] = 1;
+ x[0][1] = 0;
+ x[0][2] = 0;
+
+ x[1][0] = xy;
+ x[1][1] = 1;
+ x[1][2] = 0;
+
+ x[2][0] = 0;
+ x[2][1] = 0;
+ x[2][2] = 1;
+
+ return *this;
+}
+
+template <class T>
+template <class S>
+const Matrix33<T> &
+Matrix33<T>::setShear (const Vec2<S> &h)
+{
+ x[0][0] = 1;
+ x[0][1] = h[1];
+ x[0][2] = 0;
+
+ x[1][0] = h[0];
+ x[1][1] = 1;
+ x[1][2] = 0;
+
+ x[2][0] = 0;
+ x[2][1] = 0;
+ x[2][2] = 1;
+
+ return *this;
+}
+
+template <class T>
+template <class S>
+const Matrix33<T> &
+Matrix33<T>::shear (const S &xy)
+{
+ //
+ // In this case, we don't need a temp. copy of the matrix
+ // because we never use a value on the RHS after we've
+ // changed it on the LHS.
+ //
+
+ x[1][0] += xy * x[0][0];
+ x[1][1] += xy * x[0][1];
+ x[1][2] += xy * x[0][2];
+
+ return *this;
+}
+
+template <class T>
+template <class S>
+const Matrix33<T> &
+Matrix33<T>::shear (const Vec2<S> &h)
+{
+ Matrix33<T> P (*this);
+
+ x[0][0] = P[0][0] + h[1] * P[1][0];
+ x[0][1] = P[0][1] + h[1] * P[1][1];
+ x[0][2] = P[0][2] + h[1] * P[1][2];
+
+ x[1][0] = P[1][0] + h[0] * P[0][0];
+ x[1][1] = P[1][1] + h[0] * P[0][1];
+ x[1][2] = P[1][2] + h[0] * P[0][2];
+
+ return *this;
+}
+
+
+//---------------------------
+// Implementation of Matrix44
+//---------------------------
+
+template <class T>
+inline T *
+Matrix44<T>::operator [] (int i)
+{
+ return x[i];
+}
+
+template <class T>
+inline const T *
+Matrix44<T>::operator [] (int i) const
+{
+ return x[i];
+}
+
+template <class T>
+inline
+Matrix44<T>::Matrix44 ()
+{
+ x[0][0] = 1;
+ x[0][1] = 0;
+ x[0][2] = 0;
+ x[0][3] = 0;
+ x[1][0] = 0;
+ x[1][1] = 1;
+ x[1][2] = 0;
+ x[1][3] = 0;
+ x[2][0] = 0;
+ x[2][1] = 0;
+ x[2][2] = 1;
+ x[2][3] = 0;
+ x[3][0] = 0;
+ x[3][1] = 0;
+ x[3][2] = 0;
+ x[3][3] = 1;
+}
+
+template <class T>
+inline
+Matrix44<T>::Matrix44 (T a)
+{
+ x[0][0] = a;
+ x[0][1] = a;
+ x[0][2] = a;
+ x[0][3] = a;
+ x[1][0] = a;
+ x[1][1] = a;
+ x[1][2] = a;
+ x[1][3] = a;
+ x[2][0] = a;
+ x[2][1] = a;
+ x[2][2] = a;
+ x[2][3] = a;
+ x[3][0] = a;
+ x[3][1] = a;
+ x[3][2] = a;
+ x[3][3] = a;
+}
+
+template <class T>
+inline
+Matrix44<T>::Matrix44 (const T a[4][4])
+{
+ x[0][0] = a[0][0];
+ x[0][1] = a[0][1];
+ x[0][2] = a[0][2];
+ x[0][3] = a[0][3];
+ x[1][0] = a[1][0];
+ x[1][1] = a[1][1];
+ x[1][2] = a[1][2];
+ x[1][3] = a[1][3];
+ x[2][0] = a[2][0];
+ x[2][1] = a[2][1];
+ x[2][2] = a[2][2];
+ x[2][3] = a[2][3];
+ x[3][0] = a[3][0];
+ x[3][1] = a[3][1];
+ x[3][2] = a[3][2];
+ x[3][3] = a[3][3];
+}
+
+template <class T>
+inline
+Matrix44<T>::Matrix44 (T a, T b, T c, T d, T e, T f, T g, T h,
+ T i, T j, T k, T l, T m, T n, T o, T p)
+{
+ x[0][0] = a;
+ x[0][1] = b;
+ x[0][2] = c;
+ x[0][3] = d;
+ x[1][0] = e;
+ x[1][1] = f;
+ x[1][2] = g;
+ x[1][3] = h;
+ x[2][0] = i;
+ x[2][1] = j;
+ x[2][2] = k;
+ x[2][3] = l;
+ x[3][0] = m;
+ x[3][1] = n;
+ x[3][2] = o;
+ x[3][3] = p;
+}
+
+
+template <class T>
+inline
+Matrix44<T>::Matrix44 (Matrix33<T> r, Vec3<T> t)
+{
+ x[0][0] = r[0][0];
+ x[0][1] = r[0][1];
+ x[0][2] = r[0][2];
+ x[0][3] = 0;
+ x[1][0] = r[1][0];
+ x[1][1] = r[1][1];
+ x[1][2] = r[1][2];
+ x[1][3] = 0;
+ x[2][0] = r[2][0];
+ x[2][1] = r[2][1];
+ x[2][2] = r[2][2];
+ x[2][3] = 0;
+ x[3][0] = t[0];
+ x[3][1] = t[1];
+ x[3][2] = t[2];
+ x[3][3] = 1;
+}
+
+template <class T>
+inline
+Matrix44<T>::Matrix44 (const Matrix44 &v)
+{
+ x[0][0] = v.x[0][0];
+ x[0][1] = v.x[0][1];
+ x[0][2] = v.x[0][2];
+ x[0][3] = v.x[0][3];
+ x[1][0] = v.x[1][0];
+ x[1][1] = v.x[1][1];
+ x[1][2] = v.x[1][2];
+ x[1][3] = v.x[1][3];
+ x[2][0] = v.x[2][0];
+ x[2][1] = v.x[2][1];
+ x[2][2] = v.x[2][2];
+ x[2][3] = v.x[2][3];
+ x[3][0] = v.x[3][0];
+ x[3][1] = v.x[3][1];
+ x[3][2] = v.x[3][2];
+ x[3][3] = v.x[3][3];
+}
+
+template <class T>
+inline const Matrix44<T> &
+Matrix44<T>::operator = (const Matrix44 &v)
+{
+ x[0][0] = v.x[0][0];
+ x[0][1] = v.x[0][1];
+ x[0][2] = v.x[0][2];
+ x[0][3] = v.x[0][3];
+ x[1][0] = v.x[1][0];
+ x[1][1] = v.x[1][1];
+ x[1][2] = v.x[1][2];
+ x[1][3] = v.x[1][3];
+ x[2][0] = v.x[2][0];
+ x[2][1] = v.x[2][1];
+ x[2][2] = v.x[2][2];
+ x[2][3] = v.x[2][3];
+ x[3][0] = v.x[3][0];
+ x[3][1] = v.x[3][1];
+ x[3][2] = v.x[3][2];
+ x[3][3] = v.x[3][3];
+ return *this;
+}
+
+template <class T>
+inline const Matrix44<T> &
+Matrix44<T>::operator = (T a)
+{
+ x[0][0] = a;
+ x[0][1] = a;
+ x[0][2] = a;
+ x[0][3] = a;
+ x[1][0] = a;
+ x[1][1] = a;
+ x[1][2] = a;
+ x[1][3] = a;
+ x[2][0] = a;
+ x[2][1] = a;
+ x[2][2] = a;
+ x[2][3] = a;
+ x[3][0] = a;
+ x[3][1] = a;
+ x[3][2] = a;
+ x[3][3] = a;
+ return *this;
+}
+
+template <class T>
+inline T *
+Matrix44<T>::getValue ()
+{
+ return (T *) &x[0][0];
+}
+
+template <class T>
+inline const T *
+Matrix44<T>::getValue () const
+{
+ return (const T *) &x[0][0];
+}
+
+template <class T>
+template <class S>
+inline void
+Matrix44<T>::getValue (Matrix44<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[0][3] = x[0][3];
+ v.x[1][0] = x[1][0];
+ v.x[1][1] = x[1][1];
+ v.x[1][2] = x[1][2];
+ v.x[1][3] = x[1][3];
+ v.x[2][0] = x[2][0];
+ v.x[2][1] = x[2][1];
+ v.x[2][2] = x[2][2];
+ v.x[2][3] = x[2][3];
+ v.x[3][0] = x[3][0];
+ v.x[3][1] = x[3][1];
+ v.x[3][2] = x[3][2];
+ v.x[3][3] = x[3][3];
+}
+
+template <class T>
+template <class S>
+inline Matrix44<T> &
+Matrix44<T>::setValue (const Matrix44<S> &v)
+{
+ x[0][0] = v.x[0][0];
+ x[0][1] = v.x[0][1];
+ x[0][2] = v.x[0][2];
+ x[0][3] = v.x[0][3];
+ x[1][0] = v.x[1][0];
+ x[1][1] = v.x[1][1];
+ x[1][2] = v.x[1][2];
+ x[1][3] = v.x[1][3];
+ x[2][0] = v.x[2][0];
+ x[2][1] = v.x[2][1];
+ x[2][2] = v.x[2][2];
+ x[2][3] = v.x[2][3];
+ x[3][0] = v.x[3][0];
+ x[3][1] = v.x[3][1];
+ x[3][2] = v.x[3][2];
+ x[3][3] = v.x[3][3];
+ return *this;
+}
+
+template <class T>
+template <class S>
+inline Matrix44<T> &
+Matrix44<T>::setTheMatrix (const Matrix44<S> &v)
+{
+ x[0][0] = v.x[0][0];
+ x[0][1] = v.x[0][1];
+ x[0][2] = v.x[0][2];
+ x[0][3] = v.x[0][3];
+ x[1][0] = v.x[1][0];
+ x[1][1] = v.x[1][1];
+ x[1][2] = v.x[1][2];
+ x[1][3] = v.x[1][3];
+ x[2][0] = v.x[2][0];
+ x[2][1] = v.x[2][1];
+ x[2][2] = v.x[2][2];
+ x[2][3] = v.x[2][3];
+ x[3][0] = v.x[3][0];
+ x[3][1] = v.x[3][1];
+ x[3][2] = v.x[3][2];
+ x[3][3] = v.x[3][3];
+ return *this;
+}
+
+template <class T>
+inline void
+Matrix44<T>::makeIdentity()
+{
+ x[0][0] = 1;
+ x[0][1] = 0;
+ x[0][2] = 0;
+ x[0][3] = 0;
+ x[1][0] = 0;
+ x[1][1] = 1;
+ x[1][2] = 0;
+ x[1][3] = 0;
+ x[2][0] = 0;
+ x[2][1] = 0;
+ x[2][2] = 1;
+ x[2][3] = 0;
+ x[3][0] = 0;
+ x[3][1] = 0;
+ x[3][2] = 0;
+ x[3][3] = 1;
+}
+
+template <class T>
+bool
+Matrix44<T>::operator == (const Matrix44 &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[0][3] == v.x[0][3] &&
+ x[1][0] == v.x[1][0] &&
+ x[1][1] == v.x[1][1] &&
+ x[1][2] == v.x[1][2] &&
+ x[1][3] == v.x[1][3] &&
+ x[2][0] == v.x[2][0] &&
+ x[2][1] == v.x[2][1] &&
+ x[2][2] == v.x[2][2] &&
+ x[2][3] == v.x[2][3] &&
+ x[3][0] == v.x[3][0] &&
+ x[3][1] == v.x[3][1] &&
+ x[3][2] == v.x[3][2] &&
+ x[3][3] == v.x[3][3];
+}
+
+template <class T>
+bool
+Matrix44<T>::operator != (const Matrix44 &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[0][3] != v.x[0][3] ||
+ x[1][0] != v.x[1][0] ||
+ x[1][1] != v.x[1][1] ||
+ x[1][2] != v.x[1][2] ||
+ x[1][3] != v.x[1][3] ||
+ x[2][0] != v.x[2][0] ||
+ x[2][1] != v.x[2][1] ||
+ x[2][2] != v.x[2][2] ||
+ x[2][3] != v.x[2][3] ||
+ x[3][0] != v.x[3][0] ||
+ x[3][1] != v.x[3][1] ||
+ x[3][2] != v.x[3][2] ||
+ x[3][3] != v.x[3][3];
+}
+
+template <class T>
+bool
+Matrix44<T>::equalWithAbsError (const Matrix44<T> &m, T e) const
+{
+ for (int i = 0; i < 4; i++)
+ for (int j = 0; j < 4; j++)
+ if (!Imath::equalWithAbsError ((*this)[i][j], m[i][j], e))
+ return false;
+
+ return true;
+}
+
+template <class T>
+bool
+Matrix44<T>::equalWithRelError (const Matrix44<T> &m, T e) const
+{
+ for (int i = 0; i < 4; i++)
+ for (int j = 0; j < 4; j++)
+ if (!Imath::equalWithRelError ((*this)[i][j], m[i][j], e))
+ return false;
+
+ return true;
+}
+
+template <class T>
+const Matrix44<T> &
+Matrix44<T>::operator += (const Matrix44<T> &v)
+{
+ x[0][0] += v.x[0][0];
+ x[0][1] += v.x[0][1];
+ x[0][2] += v.x[0][2];
+ x[0][3] += v.x[0][3];
+ x[1][0] += v.x[1][0];
+ x[1][1] += v.x[1][1];
+ x[1][2] += v.x[1][2];
+ x[1][3] += v.x[1][3];
+ x[2][0] += v.x[2][0];
+ x[2][1] += v.x[2][1];
+ x[2][2] += v.x[2][2];
+ x[2][3] += v.x[2][3];
+ x[3][0] += v.x[3][0];
+ x[3][1] += v.x[3][1];
+ x[3][2] += v.x[3][2];
+ x[3][3] += v.x[3][3];
+
+ return *this;
+}
+
+template <class T>
+const Matrix44<T> &
+Matrix44<T>::operator += (T a)
+{
+ x[0][0] += a;
+ x[0][1] += a;
+ x[0][2] += a;
+ x[0][3] += a;
+ x[1][0] += a;
+ x[1][1] += a;
+ x[1][2] += a;
+ x[1][3] += a;
+ x[2][0] += a;
+ x[2][1] += a;
+ x[2][2] += a;
+ x[2][3] += a;
+ x[3][0] += a;
+ x[3][1] += a;
+ x[3][2] += a;
+ x[3][3] += a;
+
+ return *this;
+}
+
+template <class T>
+Matrix44<T>
+Matrix44<T>::operator + (const Matrix44<T> &v) const
+{
+ return Matrix44 (x[0][0] + v.x[0][0],
+ x[0][1] + v.x[0][1],
+ x[0][2] + v.x[0][2],
+ x[0][3] + v.x[0][3],
+ x[1][0] + v.x[1][0],
+ x[1][1] + v.x[1][1],
+ x[1][2] + v.x[1][2],
+ x[1][3] + v.x[1][3],
+ x[2][0] + v.x[2][0],
+ x[2][1] + v.x[2][1],
+ x[2][2] + v.x[2][2],
+ x[2][3] + v.x[2][3],
+ x[3][0] + v.x[3][0],
+ x[3][1] + v.x[3][1],
+ x[3][2] + v.x[3][2],
+ x[3][3] + v.x[3][3]);
+}
+
+template <class T>
+const Matrix44<T> &
+Matrix44<T>::operator -= (const Matrix44<T> &v)
+{
+ x[0][0] -= v.x[0][0];
+ x[0][1] -= v.x[0][1];
+ x[0][2] -= v.x[0][2];
+ x[0][3] -= v.x[0][3];
+ x[1][0] -= v.x[1][0];
+ x[1][1] -= v.x[1][1];
+ x[1][2] -= v.x[1][2];
+ x[1][3] -= v.x[1][3];
+ x[2][0] -= v.x[2][0];
+ x[2][1] -= v.x[2][1];
+ x[2][2] -= v.x[2][2];
+ x[2][3] -= v.x[2][3];
+ x[3][0] -= v.x[3][0];
+ x[3][1] -= v.x[3][1];
+ x[3][2] -= v.x[3][2];
+ x[3][3] -= v.x[3][3];
+
+ return *this;
+}
+
+template <class T>
+const Matrix44<T> &
+Matrix44<T>::operator -= (T a)
+{
+ x[0][0] -= a;
+ x[0][1] -= a;
+ x[0][2] -= a;
+ x[0][3] -= a;
+ x[1][0] -= a;
+ x[1][1] -= a;
+ x[1][2] -= a;
+ x[1][3] -= a;
+ x[2][0] -= a;
+ x[2][1] -= a;
+ x[2][2] -= a;
+ x[2][3] -= a;
+ x[3][0] -= a;
+ x[3][1] -= a;
+ x[3][2] -= a;
+ x[3][3] -= a;
+
+ return *this;
+}
+
+template <class T>
+Matrix44<T>
+Matrix44<T>::operator - (const Matrix44<T> &v) const
+{
+ return Matrix44 (x[0][0] - v.x[0][0],
+ x[0][1] - v.x[0][1],
+ x[0][2] - v.x[0][2],
+ x[0][3] - v.x[0][3],
+ x[1][0] - v.x[1][0],
+ x[1][1] - v.x[1][1],
+ x[1][2] - v.x[1][2],
+ x[1][3] - v.x[1][3],
+ x[2][0] - v.x[2][0],
+ x[2][1] - v.x[2][1],
+ x[2][2] - v.x[2][2],
+ x[2][3] - v.x[2][3],
+ x[3][0] - v.x[3][0],
+ x[3][1] - v.x[3][1],
+ x[3][2] - v.x[3][2],
+ x[3][3] - v.x[3][3]);
+}
+
+template <class T>
+Matrix44<T>
+Matrix44<T>::operator - () const
+{
+ return Matrix44 (-x[0][0],
+ -x[0][1],
+ -x[0][2],
+ -x[0][3],
+ -x[1][0],
+ -x[1][1],
+ -x[1][2],
+ -x[1][3],
+ -x[2][0],
+ -x[2][1],
+ -x[2][2],
+ -x[2][3],
+ -x[3][0],
+ -x[3][1],
+ -x[3][2],
+ -x[3][3]);
+}
+
+template <class T>
+const Matrix44<T> &
+Matrix44<T>::negate ()
+{
+ x[0][0] = -x[0][0];
+ x[0][1] = -x[0][1];
+ x[0][2] = -x[0][2];
+ x[0][3] = -x[0][3];
+ x[1][0] = -x[1][0];
+ x[1][1] = -x[1][1];
+ x[1][2] = -x[1][2];
+ x[1][3] = -x[1][3];
+ x[2][0] = -x[2][0];
+ x[2][1] = -x[2][1];
+ x[2][2] = -x[2][2];
+ x[2][3] = -x[2][3];
+ x[3][0] = -x[3][0];
+ x[3][1] = -x[3][1];
+ x[3][2] = -x[3][2];
+ x[3][3] = -x[3][3];
+
+ return *this;
+}
+
+template <class T>
+const Matrix44<T> &
+Matrix44<T>::operator *= (T a)
+{
+ x[0][0] *= a;
+ x[0][1] *= a;
+ x[0][2] *= a;
+ x[0][3] *= a;
+ x[1][0] *= a;
+ x[1][1] *= a;
+ x[1][2] *= a;
+ x[1][3] *= a;
+ x[2][0] *= a;
+ x[2][1] *= a;
+ x[2][2] *= a;
+ x[2][3] *= a;
+ x[3][0] *= a;
+ x[3][1] *= a;
+ x[3][2] *= a;
+ x[3][3] *= a;
+
+ return *this;
+}
+
+template <class T>
+Matrix44<T>
+Matrix44<T>::operator * (T a) const
+{
+ return Matrix44 (x[0][0] * a,
+ x[0][1] * a,
+ x[0][2] * a,
+ x[0][3] * a,
+ x[1][0] * a,
+ x[1][1] * a,
+ x[1][2] * a,
+ x[1][3] * a,
+ x[2][0] * a,
+ x[2][1] * a,
+ x[2][2] * a,
+ x[2][3] * a,
+ x[3][0] * a,
+ x[3][1] * a,
+ x[3][2] * a,
+ x[3][3] * a);
+}
+
+template <class T>
+inline Matrix44<T>
+operator * (T a, const Matrix44<T> &v)
+{
+ return v * a;
+}
+
+template <class T>
+inline const Matrix44<T> &
+Matrix44<T>::operator *= (const Matrix44<T> &v)
+{
+ Matrix44 tmp (T (0));
+
+ multiply (*this, v, tmp);
+ *this = tmp;
+ return *this;
+}
+
+template <class T>
+inline Matrix44<T>
+Matrix44<T>::operator * (const Matrix44<T> &v) const
+{
+ Matrix44 tmp (T (0));
+
+ multiply (*this, v, tmp);
+ return tmp;
+}
+
+template <class T>
+void
+Matrix44<T>::multiply (const Matrix44<T> &a,
+ const Matrix44<T> &b,
+ Matrix44<T> &c)
+{
+ register const T * restrict ap = &a.x[0][0];
+ register const T * restrict bp = &b.x[0][0];
+ register T * restrict cp = &c.x[0][0];
+
+ register T a0, a1, a2, a3;
+
+ a0 = ap[0];
+ a1 = ap[1];
+ a2 = ap[2];
+ a3 = ap[3];
+
+ cp[0] = a0 * bp[0] + a1 * bp[4] + a2 * bp[8] + a3 * bp[12];
+ cp[1] = a0 * bp[1] + a1 * bp[5] + a2 * bp[9] + a3 * bp[13];
+ cp[2] = a0 * bp[2] + a1 * bp[6] + a2 * bp[10] + a3 * bp[14];
+ cp[3] = a0 * bp[3] + a1 * bp[7] + a2 * bp[11] + a3 * bp[15];
+
+ a0 = ap[4];
+ a1 = ap[5];
+ a2 = ap[6];
+ a3 = ap[7];
+
+ cp[4] = a0 * bp[0] + a1 * bp[4] + a2 * bp[8] + a3 * bp[12];
+ cp[5] = a0 * bp[1] + a1 * bp[5] + a2 * bp[9] + a3 * bp[13];
+ cp[6] = a0 * bp[2] + a1 * bp[6] + a2 * bp[10] + a3 * bp[14];
+ cp[7] = a0 * bp[3] + a1 * bp[7] + a2 * bp[11] + a3 * bp[15];
+
+ a0 = ap[8];
+ a1 = ap[9];
+ a2 = ap[10];
+ a3 = ap[11];
+
+ cp[8] = a0 * bp[0] + a1 * bp[4] + a2 * bp[8] + a3 * bp[12];
+ cp[9] = a0 * bp[1] + a1 * bp[5] + a2 * bp[9] + a3 * bp[13];
+ cp[10] = a0 * bp[2] + a1 * bp[6] + a2 * bp[10] + a3 * bp[14];
+ cp[11] = a0 * bp[3] + a1 * bp[7] + a2 * bp[11] + a3 * bp[15];
+
+ a0 = ap[12];
+ a1 = ap[13];
+ a2 = ap[14];
+ a3 = ap[15];
+
+ cp[12] = a0 * bp[0] + a1 * bp[4] + a2 * bp[8] + a3 * bp[12];
+ cp[13] = a0 * bp[1] + a1 * bp[5] + a2 * bp[9] + a3 * bp[13];
+ cp[14] = a0 * bp[2] + a1 * bp[6] + a2 * bp[10] + a3 * bp[14];
+ cp[15] = a0 * bp[3] + a1 * bp[7] + a2 * bp[11] + a3 * bp[15];
+}
+
+template <class T> template <class S>
+void
+Matrix44<T>::multVecMatrix(const Vec3<S> &src, Vec3<S> &dst) const
+{
+ S a, b, c, w;
+
+ a = src[0] * x[0][0] + src[1] * x[1][0] + src[2] * x[2][0] + x[3][0];
+ b = src[0] * x[0][1] + src[1] * x[1][1] + src[2] * x[2][1] + x[3][1];
+ c = src[0] * x[0][2] + src[1] * x[1][2] + src[2] * x[2][2] + x[3][2];
+ w = src[0] * x[0][3] + src[1] * x[1][3] + src[2] * x[2][3] + x[3][3];
+
+ dst.x = a / w;
+ dst.y = b / w;
+ dst.z = c / w;
+}
+
+template <class T> template <class S>
+void
+Matrix44<T>::multDirMatrix(const Vec3<S> &src, Vec3<S> &dst) const
+{
+ S a, b, c;
+
+ a = src[0] * x[0][0] + src[1] * x[1][0] + src[2] * x[2][0];
+ b = src[0] * x[0][1] + src[1] * x[1][1] + src[2] * x[2][1];
+ c = src[0] * x[0][2] + src[1] * x[1][2] + src[2] * x[2][2];
+
+ dst.x = a;
+ dst.y = b;
+ dst.z = c;
+}
+
+template <class T>
+const Matrix44<T> &
+Matrix44<T>::operator /= (T a)
+{
+ x[0][0] /= a;
+ x[0][1] /= a;
+ x[0][2] /= a;
+ x[0][3] /= a;
+ x[1][0] /= a;
+ x[1][1] /= a;
+ x[1][2] /= a;
+ x[1][3] /= a;
+ x[2][0] /= a;
+ x[2][1] /= a;
+ x[2][2] /= a;
+ x[2][3] /= a;
+ x[3][0] /= a;
+ x[3][1] /= a;
+ x[3][2] /= a;
+ x[3][3] /= a;
+
+ return *this;
+}
+
+template <class T>
+Matrix44<T>
+Matrix44<T>::operator / (T a) const
+{
+ return Matrix44 (x[0][0] / a,
+ x[0][1] / a,
+ x[0][2] / a,
+ x[0][3] / a,
+ x[1][0] / a,
+ x[1][1] / a,
+ x[1][2] / a,
+ x[1][3] / a,
+ x[2][0] / a,
+ x[2][1] / a,
+ x[2][2] / a,
+ x[2][3] / a,
+ x[3][0] / a,
+ x[3][1] / a,
+ x[3][2] / a,
+ x[3][3] / a);
+}
+
+template <class T>
+const Matrix44<T> &
+Matrix44<T>::transpose ()
+{
+ Matrix44 tmp (x[0][0],
+ x[1][0],
+ x[2][0],
+ x[3][0],
+ x[0][1],
+ x[1][1],
+ x[2][1],
+ x[3][1],
+ x[0][2],
+ x[1][2],
+ x[2][2],
+ x[3][2],
+ x[0][3],
+ x[1][3],
+ x[2][3],
+ x[3][3]);
+ *this = tmp;
+ return *this;
+}
+
+template <class T>
+Matrix44<T>
+Matrix44<T>::transposed () const
+{
+ return Matrix44 (x[0][0],
+ x[1][0],
+ x[2][0],
+ x[3][0],
+ x[0][1],
+ x[1][1],
+ x[2][1],
+ x[3][1],
+ x[0][2],
+ x[1][2],
+ x[2][2],
+ x[3][2],
+ x[0][3],
+ x[1][3],
+ x[2][3],
+ x[3][3]);
+}
+
+template <class T>
+const Matrix44<T> &
+Matrix44<T>::gjInvert (bool singExc) throw (Iex::MathExc)
+{
+ *this = gjInverse (singExc);
+ return *this;
+}
+
+template <class T>
+Matrix44<T>
+Matrix44<T>::gjInverse (bool singExc) const throw (Iex::MathExc)
+{
+ int i, j, k;
+ Matrix44 s;
+ Matrix44 t (*this);
+
+ // Forward elimination
+
+ for (i = 0; i < 3 ; i++)
+ {
+ int pivot = i;
+
+ T pivotsize = t[i][i];
+
+ if (pivotsize < 0)
+ pivotsize = -pivotsize;
+
+ for (j = i + 1; j < 4; j++)
+ {
+ T tmp = t[j][i];
+
+ if (tmp < 0)
+ tmp = -tmp;
+
+ if (tmp > pivotsize)
+ {
+ pivot = j;
+ pivotsize = tmp;
+ }
+ }
+
+ if (pivotsize == 0)
+ {
+ if (singExc)
+ throw ::Imath::SingMatrixExc ("Cannot invert singular matrix.");
+
+ return Matrix44();
+ }
+
+ if (pivot != i)
+ {
+ for (j = 0; j < 4; j++)
+ {
+ T tmp;
+
+ tmp = t[i][j];
+ t[i][j] = t[pivot][j];
+ t[pivot][j] = tmp;
+
+ tmp = s[i][j];
+ s[i][j] = s[pivot][j];
+ s[pivot][j] = tmp;
+ }
+ }
+
+ for (j = i + 1; j < 4; j++)
+ {
+ T f = t[j][i] / t[i][i];
+
+ for (k = 0; k < 4; k++)
+ {
+ t[j][k] -= f * t[i][k];
+ s[j][k] -= f * s[i][k];
+ }
+ }
+ }
+
+ // Backward substitution
+
+ for (i = 3; i >= 0; --i)
+ {
+ T f;
+
+ if ((f = t[i][i]) == 0)
+ {
+ if (singExc)
+ throw ::Imath::SingMatrixExc ("Cannot invert singular matrix.");
+
+ return Matrix44();
+ }
+
+ for (j = 0; j < 4; j++)
+ {
+ t[i][j] /= f;
+ s[i][j] /= f;
+ }
+
+ for (j = 0; j < i; j++)
+ {
+ f = t[j][i];
+
+ for (k = 0; k < 4; k++)
+ {
+ t[j][k] -= f * t[i][k];
+ s[j][k] -= f * s[i][k];
+ }
+ }
+ }
+
+ return s;
+}
+
+template <class T>
+const Matrix44<T> &
+Matrix44<T>::invert (bool singExc) throw (Iex::MathExc)
+{
+ *this = inverse (singExc);
+ return *this;
+}
+
+template <class T>
+Matrix44<T>
+Matrix44<T>::inverse (bool singExc) const throw (Iex::MathExc)
+{
+ if (x[0][3] != 0 || x[1][3] != 0 || x[2][3] != 0 || x[3][3] != 1)
+ return gjInverse(singExc);
+
+ Matrix44 s (x[1][1] * x[2][2] - x[2][1] * x[1][2],
+ x[2][1] * x[0][2] - x[0][1] * x[2][2],
+ x[0][1] * x[1][2] - x[1][1] * x[0][2],
+ 0,
+
+ x[2][0] * x[1][2] - x[1][0] * x[2][2],
+ x[0][0] * x[2][2] - x[2][0] * x[0][2],
+ x[1][0] * x[0][2] - x[0][0] * x[1][2],
+ 0,
+
+ x[1][0] * x[2][1] - x[2][0] * x[1][1],
+ x[2][0] * x[0][1] - x[0][0] * x[2][1],
+ x[0][0] * x[1][1] - x[1][0] * x[0][1],
+ 0,
+
+ 0,
+ 0,
+ 0,
+ 1);
+
+ T r = x[0][0] * s[0][0] + x[0][1] * s[1][0] + x[0][2] * s[2][0];
+
+ if (Imath::abs (r) >= 1)
+ {
+ for (int i = 0; i < 3; ++i)
+ {
+ for (int j = 0; j < 3; ++j)
+ {
+ s[i][j] /= r;
+ }
+ }
+ }
+ else
+ {
+ T mr = Imath::abs (r) / limits<T>::smallest();
+
+ for (int i = 0; i < 3; ++i)
+ {
+ for (int j = 0; j < 3; ++j)
+ {
+ if (mr > Imath::abs (s[i][j]))
+ {
+ s[i][j] /= r;
+ }
+ else
+ {
+ if (singExc)
+ throw SingMatrixExc ("Cannot invert singular matrix.");
+
+ return Matrix44();
+ }
+ }
+ }
+ }
+
+ s[3][0] = -x[3][0] * s[0][0] - x[3][1] * s[1][0] - x[3][2] * s[2][0];
+ s[3][1] = -x[3][0] * s[0][1] - x[3][1] * s[1][1] - x[3][2] * s[2][1];
+ s[3][2] = -x[3][0] * s[0][2] - x[3][1] * s[1][2] - x[3][2] * s[2][2];
+
+ return s;
+}
+
+template <class T>
+template <class S>
+const Matrix44<T> &
+Matrix44<T>::setEulerAngles (const Vec3<S>& r)
+{
+ S cos_rz, sin_rz, cos_ry, sin_ry, cos_rx, sin_rx;
+
+ cos_rz = Math<T>::cos (r[2]);
+ cos_ry = Math<T>::cos (r[1]);
+ cos_rx = Math<T>::cos (r[0]);
+
+ sin_rz = Math<T>::sin (r[2]);
+ sin_ry = Math<T>::sin (r[1]);
+ sin_rx = Math<T>::sin (r[0]);
+
+ x[0][0] = cos_rz * cos_ry;
+ x[0][1] = sin_rz * cos_ry;
+ x[0][2] = -sin_ry;
+ x[0][3] = 0;
+
+ x[1][0] = -sin_rz * cos_rx + cos_rz * sin_ry * sin_rx;
+ x[1][1] = cos_rz * cos_rx + sin_rz * sin_ry * sin_rx;
+ x[1][2] = cos_ry * sin_rx;
+ x[1][3] = 0;
+
+ x[2][0] = sin_rz * sin_rx + cos_rz * sin_ry * cos_rx;
+ x[2][1] = -cos_rz * sin_rx + sin_rz * sin_ry * cos_rx;
+ x[2][2] = cos_ry * cos_rx;
+ x[2][3] = 0;
+
+ x[3][0] = 0;
+ x[3][1] = 0;
+ x[3][2] = 0;
+ x[3][3] = 1;
+
+ return *this;
+}
+
+template <class T>
+template <class S>
+const Matrix44<T> &
+Matrix44<T>::setAxisAngle (const Vec3<S>& axis, S angle)
+{
+ Vec3<S> unit (axis.normalized());
+ S sine = Math<T>::sin (angle);
+ S cosine = Math<T>::cos (angle);
+
+ x[0][0] = unit[0] * unit[0] * (1 - cosine) + cosine;
+ x[0][1] = unit[0] * unit[1] * (1 - cosine) + unit[2] * sine;
+ x[0][2] = unit[0] * unit[2] * (1 - cosine) - unit[1] * sine;
+ x[0][3] = 0;
+
+ x[1][0] = unit[0] * unit[1] * (1 - cosine) - unit[2] * sine;
+ x[1][1] = unit[1] * unit[1] * (1 - cosine) + cosine;
+ x[1][2] = unit[1] * unit[2] * (1 - cosine) + unit[0] * sine;
+ x[1][3] = 0;
+
+ x[2][0] = unit[0] * unit[2] * (1 - cosine) + unit[1] * sine;
+ x[2][1] = unit[1] * unit[2] * (1 - cosine) - unit[0] * sine;
+ x[2][2] = unit[2] * unit[2] * (1 - cosine) + cosine;
+ x[2][3] = 0;
+
+ x[3][0] = 0;
+ x[3][1] = 0;
+ x[3][2] = 0;
+ x[3][3] = 1;
+
+ return *this;
+}
+
+template <class T>
+template <class S>
+const Matrix44<T> &
+Matrix44<T>::rotate (const Vec3<S> &r)
+{
+ S cos_rz, sin_rz, cos_ry, sin_ry, cos_rx, sin_rx;
+ S m00, m01, m02;
+ S m10, m11, m12;
+ S m20, m21, m22;
+
+ cos_rz = Math<S>::cos (r[2]);
+ cos_ry = Math<S>::cos (r[1]);
+ cos_rx = Math<S>::cos (r[0]);
+
+ sin_rz = Math<S>::sin (r[2]);
+ sin_ry = Math<S>::sin (r[1]);
+ sin_rx = Math<S>::sin (r[0]);
+
+ m00 = cos_rz * cos_ry;
+ m01 = sin_rz * cos_ry;
+ m02 = -sin_ry;
+ m10 = -sin_rz * cos_rx + cos_rz * sin_ry * sin_rx;
+ m11 = cos_rz * cos_rx + sin_rz * sin_ry * sin_rx;
+ m12 = cos_ry * sin_rx;
+ m20 = -sin_rz * -sin_rx + cos_rz * sin_ry * cos_rx;
+ m21 = cos_rz * -sin_rx + sin_rz * sin_ry * cos_rx;
+ m22 = cos_ry * cos_rx;
+
+ Matrix44<T> P (*this);
+
+ x[0][0] = P[0][0] * m00 + P[1][0] * m01 + P[2][0] * m02;
+ x[0][1] = P[0][1] * m00 + P[1][1] * m01 + P[2][1] * m02;
+ x[0][2] = P[0][2] * m00 + P[1][2] * m01 + P[2][2] * m02;
+ x[0][3] = P[0][3] * m00 + P[1][3] * m01 + P[2][3] * m02;
+
+ x[1][0] = P[0][0] * m10 + P[1][0] * m11 + P[2][0] * m12;
+ x[1][1] = P[0][1] * m10 + P[1][1] * m11 + P[2][1] * m12;
+ x[1][2] = P[0][2] * m10 + P[1][2] * m11 + P[2][2] * m12;
+ x[1][3] = P[0][3] * m10 + P[1][3] * m11 + P[2][3] * m12;
+
+ x[2][0] = P[0][0] * m20 + P[1][0] * m21 + P[2][0] * m22;
+ x[2][1] = P[0][1] * m20 + P[1][1] * m21 + P[2][1] * m22;
+ x[2][2] = P[0][2] * m20 + P[1][2] * m21 + P[2][2] * m22;
+ x[2][3] = P[0][3] * m20 + P[1][3] * m21 + P[2][3] * m22;
+
+ return *this;
+}
+
+template <class T>
+const Matrix44<T> &
+Matrix44<T>::setScale (T s)
+{
+ x[0][0] = s;
+ x[0][1] = 0;
+ x[0][2] = 0;
+ x[0][3] = 0;
+
+ x[1][0] = 0;
+ x[1][1] = s;
+ x[1][2] = 0;
+ x[1][3] = 0;
+
+ x[2][0] = 0;
+ x[2][1] = 0;
+ x[2][2] = s;
+ x[2][3] = 0;
+
+ x[3][0] = 0;
+ x[3][1] = 0;
+ x[3][2] = 0;
+ x[3][3] = 1;
+
+ return *this;
+}
+
+template <class T>
+template <class S>
+const Matrix44<T> &
+Matrix44<T>::setScale (const Vec3<S> &s)
+{
+ x[0][0] = s[0];
+ x[0][1] = 0;
+ x[0][2] = 0;
+ x[0][3] = 0;
+
+ x[1][0] = 0;
+ x[1][1] = s[1];
+ x[1][2] = 0;
+ x[1][3] = 0;
+
+ x[2][0] = 0;
+ x[2][1] = 0;
+ x[2][2] = s[2];
+ x[2][3] = 0;
+
+ x[3][0] = 0;
+ x[3][1] = 0;
+ x[3][2] = 0;
+ x[3][3] = 1;
+
+ return *this;
+}
+
+template <class T>
+template <class S>
+const Matrix44<T> &
+Matrix44<T>::scale (const Vec3<S> &s)
+{
+ x[0][0] *= s[0];
+ x[0][1] *= s[0];
+ x[0][2] *= s[0];
+ x[0][3] *= s[0];
+
+ x[1][0] *= s[1];
+ x[1][1] *= s[1];
+ x[1][2] *= s[1];
+ x[1][3] *= s[1];
+
+ x[2][0] *= s[2];
+ x[2][1] *= s[2];
+ x[2][2] *= s[2];
+ x[2][3] *= s[2];
+
+ return *this;
+}
+
+template <class T>
+template <class S>
+const Matrix44<T> &
+Matrix44<T>::setTranslation (const Vec3<S> &t)
+{
+ x[0][0] = 1;
+ x[0][1] = 0;
+ x[0][2] = 0;
+ x[0][3] = 0;
+
+ x[1][0] = 0;
+ x[1][1] = 1;
+ x[1][2] = 0;
+ x[1][3] = 0;
+
+ x[2][0] = 0;
+ x[2][1] = 0;
+ x[2][2] = 1;
+ x[2][3] = 0;
+
+ x[3][0] = t[0];
+ x[3][1] = t[1];
+ x[3][2] = t[2];
+ x[3][3] = 1;
+
+ return *this;
+}
+
+template <class T>
+inline const Vec3<T>
+Matrix44<T>::translation () const
+{
+ return Vec3<T> (x[3][0], x[3][1], x[3][2]);
+}
+
+template <class T>
+template <class S>
+const Matrix44<T> &
+Matrix44<T>::translate (const Vec3<S> &t)
+{
+ x[3][0] += t[0] * x[0][0] + t[1] * x[1][0] + t[2] * x[2][0];
+ x[3][1] += t[0] * x[0][1] + t[1] * x[1][1] + t[2] * x[2][1];
+ x[3][2] += t[0] * x[0][2] + t[1] * x[1][2] + t[2] * x[2][2];
+ x[3][3] += t[0] * x[0][3] + t[1] * x[1][3] + t[2] * x[2][3];
+
+ return *this;
+}
+
+template <class T>
+template <class S>
+const Matrix44<T> &
+Matrix44<T>::setShear (const Vec3<S> &h)
+{
+ x[0][0] = 1;
+ x[0][1] = 0;
+ x[0][2] = 0;
+ x[0][3] = 0;
+
+ x[1][0] = h[0];
+ x[1][1] = 1;
+ x[1][2] = 0;
+ x[1][3] = 0;
+
+ x[2][0] = h[1];
+ x[2][1] = h[2];
+ x[2][2] = 1;
+ x[2][3] = 0;
+
+ x[3][0] = 0;
+ x[3][1] = 0;
+ x[3][2] = 0;
+ x[3][3] = 1;
+
+ return *this;
+}
+
+template <class T>
+template <class S>
+const Matrix44<T> &
+Matrix44<T>::setShear (const Shear6<S> &h)
+{
+ x[0][0] = 1;
+ x[0][1] = h.yx;
+ x[0][2] = h.zx;
+ x[0][3] = 0;
+
+ x[1][0] = h.xy;
+ x[1][1] = 1;
+ x[1][2] = h.zy;
+ x[1][3] = 0;
+
+ x[2][0] = h.xz;
+ x[2][1] = h.yz;
+ x[2][2] = 1;
+ x[2][3] = 0;
+
+ x[3][0] = 0;
+ x[3][1] = 0;
+ x[3][2] = 0;
+ x[3][3] = 1;
+
+ return *this;
+}
+
+template <class T>
+template <class S>
+const Matrix44<T> &
+Matrix44<T>::shear (const Vec3<S> &h)
+{
+ //
+ // In this case, we don't need a temp. copy of the matrix
+ // because we never use a value on the RHS after we've
+ // changed it on the LHS.
+ //
+
+ for (int i=0; i < 4; i++)
+ {
+ x[2][i] += h[1] * x[0][i] + h[2] * x[1][i];
+ x[1][i] += h[0] * x[0][i];
+ }
+
+ return *this;
+}
+
+template <class T>
+template <class S>
+const Matrix44<T> &
+Matrix44<T>::shear (const Shear6<S> &h)
+{
+ Matrix44<T> P (*this);
+
+ for (int i=0; i < 4; i++)
+ {
+ x[0][i] = P[0][i] + h.yx * P[1][i] + h.zx * P[2][i];
+ x[1][i] = h.xy * P[0][i] + P[1][i] + h.zy * P[2][i];
+ x[2][i] = h.xz * P[0][i] + h.yz * P[1][i] + P[2][i];
+ }
+
+ return *this;
+}
+
+
+//--------------------------------
+// Implementation of stream output
+//--------------------------------
+
+template <class T>
+std::ostream &
+operator << (std::ostream &s, const Matrix33<T> &m)
+{
+ std::ios_base::fmtflags oldFlags = s.flags();
+ int width;
+
+ if (s.flags() & std::ios_base::fixed)
+ {
+ s.setf (std::ios_base::showpoint);
+ width = s.precision() + 5;
+ }
+ else
+ {
+ s.setf (std::ios_base::scientific);
+ s.setf (std::ios_base::showpoint);
+ width = s.precision() + 8;
+ }
+
+ s << "(" << std::setw (width) << m[0][0] <<
+ " " << std::setw (width) << m[0][1] <<
+ " " << std::setw (width) << m[0][2] << "\n" <<
+
+ " " << std::setw (width) << m[1][0] <<
+ " " << std::setw (width) << m[1][1] <<
+ " " << std::setw (width) << m[1][2] << "\n" <<
+
+ " " << std::setw (width) << m[2][0] <<
+ " " << std::setw (width) << m[2][1] <<
+ " " << std::setw (width) << m[2][2] << ")\n";
+
+ s.flags (oldFlags);
+ return s;
+}
+
+template <class T>
+std::ostream &
+operator << (std::ostream &s, const Matrix44<T> &m)
+{
+ std::ios_base::fmtflags oldFlags = s.flags();
+ int width;
+
+ if (s.flags() & std::ios_base::fixed)
+ {
+ s.setf (std::ios_base::showpoint);
+ width = s.precision() + 5;
+ }
+ else
+ {
+ s.setf (std::ios_base::scientific);
+ s.setf (std::ios_base::showpoint);
+ width = s.precision() + 8;
+ }
+
+ s << "(" << std::setw (width) << m[0][0] <<
+ " " << std::setw (width) << m[0][1] <<
+ " " << std::setw (width) << m[0][2] <<
+ " " << std::setw (width) << m[0][3] << "\n" <<
+
+ " " << std::setw (width) << m[1][0] <<
+ " " << std::setw (width) << m[1][1] <<
+ " " << std::setw (width) << m[1][2] <<
+ " " << std::setw (width) << m[1][3] << "\n" <<
+
+ " " << std::setw (width) << m[2][0] <<
+ " " << std::setw (width) << m[2][1] <<
+ " " << std::setw (width) << m[2][2] <<
+ " " << std::setw (width) << m[2][3] << "\n" <<
+
+ " " << std::setw (width) << m[3][0] <<
+ " " << std::setw (width) << m[3][1] <<
+ " " << std::setw (width) << m[3][2] <<
+ " " << std::setw (width) << m[3][3] << ")\n";
+
+ s.flags (oldFlags);
+ return s;
+}
+
+
+//---------------------------------------------------------------
+// Implementation of vector-times-matrix multiplication operators
+//---------------------------------------------------------------
+
+template <class S, class T>
+inline const Vec2<S> &
+operator *= (Vec2<S> &v, const Matrix33<T> &m)
+{
+ S x = S(v.x * m[0][0] + v.y * m[1][0] + m[2][0]);
+ S y = S(v.x * m[0][1] + v.y * m[1][1] + m[2][1]);
+ S w = S(v.x * m[0][2] + v.y * m[1][2] + m[2][2]);
+
+ v.x = x / w;
+ v.y = y / w;
+
+ return v;
+}
+
+template <class S, class T>
+inline Vec2<S>
+operator * (const Vec2<S> &v, const Matrix33<T> &m)
+{
+ S x = S(v.x * m[0][0] + v.y * m[1][0] + m[2][0]);
+ S y = S(v.x * m[0][1] + v.y * m[1][1] + m[2][1]);
+ S w = S(v.x * m[0][2] + v.y * m[1][2] + m[2][2]);
+
+ return Vec2<S> (x / w, y / w);
+}
+
+
+template <class S, class T>
+inline const Vec3<S> &
+operator *= (Vec3<S> &v, const Matrix33<T> &m)
+{
+ S x = S(v.x * m[0][0] + v.y * m[1][0] + v.z * m[2][0]);
+ S y = S(v.x * m[0][1] + v.y * m[1][1] + v.z * m[2][1]);
+ S z = S(v.x * m[0][2] + v.y * m[1][2] + v.z * m[2][2]);
+
+ v.x = x;
+ v.y = y;
+ v.z = z;
+
+ return v;
+}
+
+
+template <class S, class T>
+inline Vec3<S>
+operator * (const Vec3<S> &v, const Matrix33<T> &m)
+{
+ S x = S(v.x * m[0][0] + v.y * m[1][0] + v.z * m[2][0]);
+ S y = S(v.x * m[0][1] + v.y * m[1][1] + v.z * m[2][1]);
+ S z = S(v.x * m[0][2] + v.y * m[1][2] + v.z * m[2][2]);
+
+ return Vec3<S> (x, y, z);
+}
+
+
+template <class S, class T>
+inline const Vec3<S> &
+operator *= (Vec3<S> &v, const Matrix44<T> &m)
+{
+ S x = S(v.x * m[0][0] + v.y * m[1][0] + v.z * m[2][0] + m[3][0]);
+ S y = S(v.x * m[0][1] + v.y * m[1][1] + v.z * m[2][1] + m[3][1]);
+ S z = S(v.x * m[0][2] + v.y * m[1][2] + v.z * m[2][2] + m[3][2]);
+ S w = S(v.x * m[0][3] + v.y * m[1][3] + v.z * m[2][3] + m[3][3]);
+
+ v.x = x / w;
+ v.y = y / w;
+ v.z = z / w;
+
+ return v;
+}
+
+template <class S, class T>
+inline Vec3<S>
+operator * (const Vec3<S> &v, const Matrix44<T> &m)
+{
+ S x = S(v.x * m[0][0] + v.y * m[1][0] + v.z * m[2][0] + m[3][0]);
+ S y = S(v.x * m[0][1] + v.y * m[1][1] + v.z * m[2][1] + m[3][1]);
+ S z = S(v.x * m[0][2] + v.y * m[1][2] + v.z * m[2][2] + m[3][2]);
+ S w = S(v.x * m[0][3] + v.y * m[1][3] + v.z * m[2][3] + m[3][3]);
+
+ return Vec3<S> (x / w, y / w, z / w);
+}
+
+} // namespace Imath
+
+
+
+#endif
projects / opencv / blobdiff