///////////////////////////////////////////////////////////////////////////
//
// 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,
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// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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///////////////////////////////////////////////////////////////////////////
#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 <cstring>
#include <iostream>
#include <iomanip>
#include <string.h>
#if (defined _WIN32 || defined _WIN64) && defined _MSC_VER
// suppress exception specification warnings
#pragma warning(disable:4290)
#endif
namespace Imath {
enum Uninitialized {UNINITIALIZED};
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 (Uninitialized) {}
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);
template <class S> explicit Matrix33 (const Matrix33<S> &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.
//
// m.multVecMatrix(src,dst) implements a homogeneous transformation
// by computing Vec3 (src.x, src.y, 1) * m and dividing by the
// result's third element.
//
// m.multDirMatrix(src,dst) multiplies src by the upper left 2x2
// submatrix, ignoring the rest of matrix m.
//-----------------------------------------------------------------
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);
//------------------------------------------------
// Calculate the matrix minor of the (r,c) element
//------------------------------------------------
T minorOf (const int r, const int c) const;
//---------------------------------------------------
// Build a minor using the specified rows and columns
//---------------------------------------------------
T fastMinor (const int r0, const int r1,
const int c0, const int c1) const;
//------------
// Determinant
//------------
T determinant() const;
//-----------------------------------------
// 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);
//--------------------------------------------------------
// Number of the row and column dimensions, since
// Matrix33 is a square matrix.
//--------------------------------------------------------
static unsigned int dimensions() {return 3;}
//-------------------------------------------------
// 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();}
typedef T BaseType;
typedef Vec3<T> BaseVecType;
private:
template <typename R, typename S>
struct isSameType
{
enum {value = 0};
};
template <typename R>
struct isSameType<R, R>
{
enum {value = 1};
};
};
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 (Uninitialized) {}
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);
template <class S> explicit Matrix44 (const Matrix44<S> &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.
//
// m.multVecMatrix(src,dst) implements a homogeneous transformation
// by computing Vec4 (src.x, src.y, src.z, 1) * m and dividing by
// the result's third element.
//
// m.multDirMatrix(src,dst) multiplies src by the upper left 3x3
// submatrix, ignoring the rest of matrix m.
//-----------------------------------------------------------------
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);
//------------------------------------------------
// Calculate the matrix minor of the (r,c) element
//------------------------------------------------
T minorOf (const int r, const int c) const;
//---------------------------------------------------
// Build a minor using the specified rows and columns
//---------------------------------------------------
T fastMinor (const int r0, const int r1, const int r2,
const int c0, const int c1, const int c2) const;
//------------
// Determinant
//------------
T determinant() const;
//--------------------------------------------------------
// 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);
//--------------------------------------------------------
// Number of the row and column dimensions, since
// Matrix44 is a square matrix.
//--------------------------------------------------------
static unsigned int dimensions() {return 4;}
//------------------------------------------------------------
// 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();}
typedef T BaseType;
typedef Vec4<T> BaseVecType;
private:
template <typename R, typename S>
struct isSameType
{
enum {value = 0};
};
template <typename R>
struct isSameType<R, R>
{
enum {value = 1};
};
};
//--------------
// 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);
template <class S, class T>
const Vec4<S> & operator *= (Vec4<S> &v, const Matrix44<T> &m);
template <class S, class T>
Vec4<S> operator * (const Vec4<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 ()
{
memset (x, 0, sizeof (x));
x[0][0] = 1;
x[1][1] = 1;
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])
{
memcpy (x, a, sizeof (x));
}
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)
{
memcpy (x, v.x, sizeof (x));
}
template <class T>
template <class S>
inline
Matrix33<T>::Matrix33 (const Matrix33<S> &v)
{
x[0][0] = T (v.x[0][0]);
x[0][1] = T (v.x[0][1]);
x[0][2] = T (v.x[0][2]);
x[1][0] = T (v.x[1][0]);
x[1][1] = T (v.x[1][1]);
x[1][2] = T (v.x[1][2]);
x[2][0] = T (v.x[2][0]);
x[2][1] = T (v.x[2][1]);
x[2][2] = T (v.x[2][2]);
}
template <class T>
inline const Matrix33<T> &
Matrix33<T>::operator = (const Matrix33 &v)
{
memcpy (x, v.x, sizeof (x));
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
{
if (isSameType<S,T>::value)
{
memcpy (v.x, x, sizeof (x));
}
else
{
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)
{
if (isSameType<S,T>::value)
{
memcpy (x, v.x, sizeof (x));
}
else
{
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)
{
if (isSameType<S,T>::value)
{
memcpy (x, v.x, sizeof (x));
}
else
{
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()
{
memset (x, 0, sizeof (x));
x[0][0] = 1;
x[1][1] = 1;
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>
inline T
Matrix33<T>::minorOf (const int r, const int c) const
{
int r0 = 0 + (r < 1 ? 1 : 0);
int r1 = 1 + (r < 2 ? 1 : 0);
int c0 = 0 + (c < 1 ? 1 : 0);
int c1 = 1 + (c < 2 ? 1 : 0);
return x[r0][c0]*x[r1][c1] - x[r1][c0]*x[r0][c1];
}
template <class T>
inline T
Matrix33<T>::fastMinor( const int r0, const int r1,
const int c0, const int c1) const
{
return x[r0][c0]*x[r1][c1] - x[r0][c1]*x[r1][c0];
}
template <class T>
inline T
Matrix33<T>::determinant () const
{
return x[0][0]*(x[1][1]*x[2][2] - x[1][2]*x[2][1]) +
x[0][1]*(x[1][2]*x[2][0] - x[1][0]*x[2][2]) +
x[0][2]*(x[1][0]*x[2][1] - x[1][1]*x[2][0]);
}
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)
{
memset (x, 0, sizeof (x));
x[0][0] = s;
x[1][1] = s;
x[2][2] = 1;
return *this;
}
template <class T>
template <class S>
const Matrix33<T> &
Matrix33<T>::setScale (const Vec2<S> &s)
{
memset (x, 0, sizeof (x));
x[0][0] = s[0];
x[1][1] = s[1];
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 ()
{
memset (x, 0, sizeof (x));
x[0][0] = 1;
x[1][1] = 1;
x[2][2] = 1;
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])
{
memcpy (x, a, sizeof (x));
}
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>
template <class S>
inline
Matrix44<T>::Matrix44 (const Matrix44<S> &v)
{
x[0][0] = T (v.x[0][0]);
x[0][1] = T (v.x[0][1]);
x[0][2] = T (v.x[0][2]);
x[0][3] = T (v.x[0][3]);
x[1][0] = T (v.x[1][0]);
x[1][1] = T (v.x[1][1]);
x[1][2] = T (v.x[1][2]);
x[1][3] = T (v.x[1][3]);
x[2][0] = T (v.x[2][0]);
x[2][1] = T (v.x[2][1]);
x[2][2] = T (v.x[2][2]);
x[2][3] = T (v.x[2][3]);
x[3][0] = T (v.x[3][0]);
x[3][1] = T (v.x[3][1]);
x[3][2] = T (v.x[3][2]);
x[3][3] = T (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
{
if (isSameType<S,T>::value)
{
memcpy (v.x, x, sizeof (x));
}
else
{
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)
{
if (isSameType<S,T>::value)
{
memcpy (x, v.x, sizeof (x));
}
else
{
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)
{
if (isSameType<S,T>::value)
{
memcpy (x, v.x, sizeof (x));
}
else
{
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()
{
memset (x, 0, sizeof (x));
x[0][0] = 1;
x[1][1] = 1;
x[2][2] = 1;
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 * IMATH_RESTRICT ap = &a.x[0][0];
register const T * IMATH_RESTRICT bp = &b.x[0][0];
register T * IMATH_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>
inline T
Matrix44<T>::fastMinor( const int r0, const int r1, const int r2,
const int c0, const int c1, const int c2) const
{
return x[r0][c0] * (x[r1][c1]*x[r2][c2] - x[r1][c2]*x[r2][c1])
+ x[r0][c1] * (x[r1][c2]*x[r2][c0] - x[r1][c0]*x[r2][c2])
+ x[r0][c2] * (x[r1][c0]*x[r2][c1] - x[r1][c1]*x[r2][c0]);
}
template <class T>
inline T
Matrix44<T>::minorOf (const int r, const int c) const
{
int r0 = 0 + (r < 1 ? 1 : 0);
int r1 = 1 + (r < 2 ? 1 : 0);
int r2 = 2 + (r < 3 ? 1 : 0);
int c0 = 0 + (c < 1 ? 1 : 0);
int c1 = 1 + (c < 2 ? 1 : 0);
int c2 = 2 + (c < 3 ? 1 : 0);
Matrix33<T> working (x[r0][c0],x[r1][c0],x[r2][c0],
x[r0][c1],x[r1][c1],x[r2][c1],
x[r0][c2],x[r1][c2],x[r2][c2]);
return working.determinant();
}
template <class T>
inline T
Matrix44<T>::determinant () const
{
T sum = (T)0;
if (x[0][3] != 0.) sum -= x[0][3] * fastMinor(1,2,3,0,1,2);
if (x[1][3] != 0.) sum += x[1][3] * fastMinor(0,2,3,0,1,2);
if (x[2][3] != 0.) sum -= x[2][3] * fastMinor(0,1,3,0,1,2);
if (x[3][3] != 0.) sum += x[3][3] * fastMinor(0,1,2,0,1,2);
return sum;
}
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)
{
memset (x, 0, sizeof (x));
x[0][0] = s;
x[1][1] = s;
x[2][2] = s;
x[3][3] = 1;
return *this;
}
template <class T>
template <class S>
const Matrix44<T> &
Matrix44<T>::setScale (const Vec3<S> &s)
{
memset (x, 0, sizeof (x));
x[0][0] = s[0];
x[1][1] = s[1];
x[2][2] = s[2];
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);
}
template <class S, class T>
inline const Vec4<S> &
operator *= (Vec4<S> &v, const Matrix44<T> &m)
{
S x = S(v.x * m[0][0] + v.y * m[1][0] + v.z * m[2][0] + v.w * m[3][0]);
S y = S(v.x * m[0][1] + v.y * m[1][1] + v.z * m[2][1] + v.w * m[3][1]);
S z = S(v.x * m[0][2] + v.y * m[1][2] + v.z * m[2][2] + v.w * m[3][2]);
S w = S(v.x * m[0][3] + v.y * m[1][3] + v.z * m[2][3] + v.w * m[3][3]);
v.x = x;
v.y = y;
v.z = z;
v.w = w;
return v;
}
template <class S, class T>
inline Vec4<S>
operator * (const Vec4<S> &v, const Matrix44<T> &m)
{
S x = S(v.x * m[0][0] + v.y * m[1][0] + v.z * m[2][0] + v.w * m[3][0]);
S y = S(v.x * m[0][1] + v.y * m[1][1] + v.z * m[2][1] + v.w * m[3][1]);
S z = S(v.x * m[0][2] + v.y * m[1][2] + v.z * m[2][2] + v.w * m[3][2]);
S w = S(v.x * m[0][3] + v.y * m[1][3] + v.z * m[2][3] + v.w * m[3][3]);
return Vec4<S> (x, y, z, w);
}
} // namespace Imath
#endif