X-Git-Url: https://vcs.maemo.org/git/?a=blobdiff_plain;f=otherlibs%2F_graphics%2Finclude%2FOpenEXR%2FImathMatrix.h;fp=otherlibs%2F_graphics%2Finclude%2FOpenEXR%2FImathMatrix.h;h=0000000000000000000000000000000000000000;hb=e4c14cdbdf2fe805e79cd96ded236f57e7b89060;hp=6192d3c435b1403b6b6f7c3ade9f70930e047b22;hpb=454138ff8a20f6edb9b65a910101403d8b520643;p=opencv diff --git a/otherlibs/_graphics/include/OpenEXR/ImathMatrix.h b/otherlibs/_graphics/include/OpenEXR/ImathMatrix.h deleted file mode 100644 index 6192d3c..0000000 --- a/otherlibs/_graphics/include/OpenEXR/ImathMatrix.h +++ /dev/null @@ -1,3249 +0,0 @@ -/////////////////////////////////////////////////////////////////////////// -// -// 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 -#include - - -namespace Imath { - - -template 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 - void getValue (Matrix33 &v) const; - template - Matrix33 & setValue (const Matrix33 &v); - - template - Matrix33 & setTheMatrix (const Matrix33 &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 &v, T e) const; - bool equalWithRelError (const Matrix33 &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 - void multVecMatrix(const Vec2 &src, Vec2 &dst) const; - - template - void multDirMatrix(const Vec2 &src, Vec2 &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 inverse (bool singExc = false) const - throw (Iex::MathExc); - - const Matrix33 & gjInvert (bool singExc = false) - throw (Iex::MathExc); - - Matrix33 gjInverse (bool singExc = false) const - throw (Iex::MathExc); - - - //----------------------------------------- - // Set matrix to rotation by r (in radians) - //----------------------------------------- - - template - const Matrix33 & setRotation (S r); - - - //----------------------------- - // Rotate the given matrix by r - //----------------------------- - - template - 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 - const Matrix33 & setScale (const Vec2 &s); - - - //---------------------- - // Scale the matrix by s - //---------------------- - - template - const Matrix33 & scale (const Vec2 &s); - - - //------------------------------------------ - // Set matrix to translation by given vector - //------------------------------------------ - - template - const Matrix33 & setTranslation (const Vec2 &t); - - - //----------------------------- - // Return translation component - //----------------------------- - - Vec2 translation () const; - - - //-------------------------- - // Translate the matrix by t - //-------------------------- - - template - const Matrix33 & translate (const Vec2 &t); - - - //----------------------------------------------------------- - // Set matrix to shear x for each y coord. by given factor xy - //----------------------------------------------------------- - - template - 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 - const Matrix33 & setShear (const Vec2 &h); - - - //----------------------------------------------------------- - // Shear the matrix in x for each y coord. by given factor xy - //----------------------------------------------------------- - - template - 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 - const Matrix33 & shear (const Vec2 &h); - - - //------------------------------------------------- - // Limitations of type T (see also class limits) - //------------------------------------------------- - - static T baseTypeMin() {return limits::min();} - static T baseTypeMax() {return limits::max();} - static T baseTypeSmallest() {return limits::smallest();} - static T baseTypeEpsilon() {return limits::epsilon();} -}; - - -template 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 r, Vec3 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 - void getValue (Matrix44 &v) const; - template - Matrix44 & setValue (const Matrix44 &v); - - template - Matrix44 & setTheMatrix (const Matrix44 &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 &v, T e) const; - bool equalWithRelError (const Matrix44 &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 - void multVecMatrix(const Vec3 &src, Vec3 &dst) const; - - template - void multDirMatrix(const Vec3 &src, Vec3 &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 inverse (bool singExc = false) const - throw (Iex::MathExc); - - const Matrix44 & gjInvert (bool singExc = false) - throw (Iex::MathExc); - - Matrix44 gjInverse (bool singExc = false) const - throw (Iex::MathExc); - - - //-------------------------------------------------------- - // Set matrix to rotation by XYZ euler angles (in radians) - //-------------------------------------------------------- - - template - const Matrix44 & setEulerAngles (const Vec3& r); - - - //-------------------------------------------------------- - // Set matrix to rotation around given axis by given angle - //-------------------------------------------------------- - - template - const Matrix44 & setAxisAngle (const Vec3& ax, S ang); - - - //------------------------------------------- - // Rotate the matrix by XYZ euler angles in r - //------------------------------------------- - - template - const Matrix44 & rotate (const Vec3 &r); - - - //-------------------------------------------- - // Set matrix to scale by given uniform factor - //-------------------------------------------- - - const Matrix44 & setScale (T s); - - - //------------------------------------ - // Set matrix to scale by given vector - //------------------------------------ - - template - const Matrix44 & setScale (const Vec3 &s); - - - //---------------------- - // Scale the matrix by s - //---------------------- - - template - const Matrix44 & scale (const Vec3 &s); - - - //------------------------------------------ - // Set matrix to translation by given vector - //------------------------------------------ - - template - const Matrix44 & setTranslation (const Vec3 &t); - - - //----------------------------- - // Return translation component - //----------------------------- - - const Vec3 translation () const; - - - //-------------------------- - // Translate the matrix by t - //-------------------------- - - template - const Matrix44 & translate (const Vec3 &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 - const Matrix44 & setShear (const Vec3 &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 - const Matrix44 & setShear (const Shear6 &h); - - - //-------------------------------------------------------- - // Shear the matrix by given vector. The composed matrix - // will be * , 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 - const Matrix44 & shear (const Vec3 &h); - - - //------------------------------------------------------------ - // Shear the matrix by the given factors. The composed matrix - // will be * , 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 - const Matrix44 & shear (const Shear6 &h); - - - //------------------------------------------------- - // Limitations of type T (see also class limits) - //------------------------------------------------- - - static T baseTypeMin() {return limits::min();} - static T baseTypeMax() {return limits::max();} - static T baseTypeSmallest() {return limits::smallest();} - static T baseTypeEpsilon() {return limits::epsilon();} -}; - - -//-------------- -// Stream output -//-------------- - -template -std::ostream & operator << (std::ostream & s, const Matrix33 &m); - -template -std::ostream & operator << (std::ostream & s, const Matrix44 &m); - - -//--------------------------------------------- -// Vector-times-matrix multiplication operators -//--------------------------------------------- - -template -const Vec2 & operator *= (Vec2 &v, const Matrix33 &m); - -template -Vec2 operator * (const Vec2 &v, const Matrix33 &m); - -template -const Vec3 & operator *= (Vec3 &v, const Matrix33 &m); - -template -Vec3 operator * (const Vec3 &v, const Matrix33 &m); - -template -const Vec3 & operator *= (Vec3 &v, const Matrix44 &m); - -template -Vec3 operator * (const Vec3 &v, const Matrix44 &m); - - -//------------------------- -// Typedefs for convenience -//------------------------- - -typedef Matrix33 M33f; -typedef Matrix33 M33d; -typedef Matrix44 M44f; -typedef Matrix44 M44d; - - -//--------------------------- -// Implementation of Matrix33 -//--------------------------- - -template -inline T * -Matrix33::operator [] (int i) -{ - return x[i]; -} - -template -inline const T * -Matrix33::operator [] (int i) const -{ - return x[i]; -} - -template -inline -Matrix33::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 -inline -Matrix33::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 -inline -Matrix33::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 -inline -Matrix33::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 -inline -Matrix33::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 -inline const Matrix33 & -Matrix33::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 -inline const Matrix33 & -Matrix33::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 -inline T * -Matrix33::getValue () -{ - return (T *) &x[0][0]; -} - -template -inline const T * -Matrix33::getValue () const -{ - return (const T *) &x[0][0]; -} - -template -template -inline void -Matrix33::getValue (Matrix33 &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 -template -inline Matrix33 & -Matrix33::setValue (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 -template -inline Matrix33 & -Matrix33::setTheMatrix (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 -inline void -Matrix33::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 -bool -Matrix33::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 -bool -Matrix33::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 -bool -Matrix33::equalWithAbsError (const Matrix33 &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 -bool -Matrix33::equalWithRelError (const Matrix33 &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 -const Matrix33 & -Matrix33::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 -const Matrix33 & -Matrix33::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 -Matrix33 -Matrix33::operator + (const Matrix33 &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 -const Matrix33 & -Matrix33::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 -const Matrix33 & -Matrix33::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 -Matrix33 -Matrix33::operator - (const Matrix33 &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 -Matrix33 -Matrix33::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 -const Matrix33 & -Matrix33::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 -const Matrix33 & -Matrix33::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 -Matrix33 -Matrix33::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 -inline Matrix33 -operator * (T a, const Matrix33 &v) -{ - return v * a; -} - -template -const Matrix33 & -Matrix33::operator *= (const Matrix33 &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 -Matrix33 -Matrix33::operator * (const Matrix33 &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 -template -void -Matrix33::multVecMatrix(const Vec2 &src, Vec2 &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 -template -void -Matrix33::multDirMatrix(const Vec2 &src, Vec2 &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 -const Matrix33 & -Matrix33::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 -Matrix33 -Matrix33::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 -const Matrix33 & -Matrix33::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 -Matrix33 -Matrix33::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 -const Matrix33 & -Matrix33::gjInvert (bool singExc) throw (Iex::MathExc) -{ - *this = gjInverse (singExc); - return *this; -} - -template -Matrix33 -Matrix33::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 -const Matrix33 & -Matrix33::invert (bool singExc) throw (Iex::MathExc) -{ - *this = inverse (singExc); - return *this; -} - -template -Matrix33 -Matrix33::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::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::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 -template -const Matrix33 & -Matrix33::setRotation (S r) -{ - S cos_r, sin_r; - - cos_r = Math::cos (r); - sin_r = Math::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 -template -const Matrix33 & -Matrix33::rotate (S r) -{ - *this *= Matrix33().setRotation (r); - return *this; -} - -template -const Matrix33 & -Matrix33::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 -template -const Matrix33 & -Matrix33::setScale (const Vec2 &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 -template -const Matrix33 & -Matrix33::scale (const Vec2 &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 -template -const Matrix33 & -Matrix33::setTranslation (const Vec2 &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 -inline Vec2 -Matrix33::translation () const -{ - return Vec2 (x[2][0], x[2][1]); -} - -template -template -const Matrix33 & -Matrix33::translate (const Vec2 &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 -template -const Matrix33 & -Matrix33::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 -template -const Matrix33 & -Matrix33::setShear (const Vec2 &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 -template -const Matrix33 & -Matrix33::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 -template -const Matrix33 & -Matrix33::shear (const Vec2 &h) -{ - Matrix33 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 -inline T * -Matrix44::operator [] (int i) -{ - return x[i]; -} - -template -inline const T * -Matrix44::operator [] (int i) const -{ - return x[i]; -} - -template -inline -Matrix44::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 -inline -Matrix44::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 -inline -Matrix44::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 -inline -Matrix44::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 -inline -Matrix44::Matrix44 (Matrix33 r, Vec3 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 -inline -Matrix44::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 -inline const Matrix44 & -Matrix44::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 -inline const Matrix44 & -Matrix44::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 -inline T * -Matrix44::getValue () -{ - return (T *) &x[0][0]; -} - -template -inline const T * -Matrix44::getValue () const -{ - return (const T *) &x[0][0]; -} - -template -template -inline void -Matrix44::getValue (Matrix44 &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 -template -inline Matrix44 & -Matrix44::setValue (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 -template -inline Matrix44 & -Matrix44::setTheMatrix (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 -inline void -Matrix44::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 -bool -Matrix44::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 -bool -Matrix44::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 -bool -Matrix44::equalWithAbsError (const Matrix44 &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 -bool -Matrix44::equalWithRelError (const Matrix44 &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 -const Matrix44 & -Matrix44::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 -const Matrix44 & -Matrix44::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 -Matrix44 -Matrix44::operator + (const Matrix44 &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 -const Matrix44 & -Matrix44::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 -const Matrix44 & -Matrix44::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 -Matrix44 -Matrix44::operator - (const Matrix44 &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 -Matrix44 -Matrix44::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 -const Matrix44 & -Matrix44::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 -const Matrix44 & -Matrix44::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 -Matrix44 -Matrix44::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 -inline Matrix44 -operator * (T a, const Matrix44 &v) -{ - return v * a; -} - -template -inline const Matrix44 & -Matrix44::operator *= (const Matrix44 &v) -{ - Matrix44 tmp (T (0)); - - multiply (*this, v, tmp); - *this = tmp; - return *this; -} - -template -inline Matrix44 -Matrix44::operator * (const Matrix44 &v) const -{ - Matrix44 tmp (T (0)); - - multiply (*this, v, tmp); - return tmp; -} - -template -void -Matrix44::multiply (const Matrix44 &a, - const Matrix44 &b, - Matrix44 &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 template -void -Matrix44::multVecMatrix(const Vec3 &src, Vec3 &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 template -void -Matrix44::multDirMatrix(const Vec3 &src, Vec3 &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 -const Matrix44 & -Matrix44::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 -Matrix44 -Matrix44::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 -const Matrix44 & -Matrix44::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 -Matrix44 -Matrix44::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 -const Matrix44 & -Matrix44::gjInvert (bool singExc) throw (Iex::MathExc) -{ - *this = gjInverse (singExc); - return *this; -} - -template -Matrix44 -Matrix44::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 -const Matrix44 & -Matrix44::invert (bool singExc) throw (Iex::MathExc) -{ - *this = inverse (singExc); - return *this; -} - -template -Matrix44 -Matrix44::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::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 -template -const Matrix44 & -Matrix44::setEulerAngles (const Vec3& r) -{ - S cos_rz, sin_rz, cos_ry, sin_ry, cos_rx, sin_rx; - - cos_rz = Math::cos (r[2]); - cos_ry = Math::cos (r[1]); - cos_rx = Math::cos (r[0]); - - sin_rz = Math::sin (r[2]); - sin_ry = Math::sin (r[1]); - sin_rx = Math::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 -template -const Matrix44 & -Matrix44::setAxisAngle (const Vec3& axis, S angle) -{ - Vec3 unit (axis.normalized()); - S sine = Math::sin (angle); - S cosine = Math::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 -template -const Matrix44 & -Matrix44::rotate (const Vec3 &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::cos (r[2]); - cos_ry = Math::cos (r[1]); - cos_rx = Math::cos (r[0]); - - sin_rz = Math::sin (r[2]); - sin_ry = Math::sin (r[1]); - sin_rx = Math::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 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 -const Matrix44 & -Matrix44::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 -template -const Matrix44 & -Matrix44::setScale (const Vec3 &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 -template -const Matrix44 & -Matrix44::scale (const Vec3 &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 -template -const Matrix44 & -Matrix44::setTranslation (const Vec3 &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 -inline const Vec3 -Matrix44::translation () const -{ - return Vec3 (x[3][0], x[3][1], x[3][2]); -} - -template -template -const Matrix44 & -Matrix44::translate (const Vec3 &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 -template -const Matrix44 & -Matrix44::setShear (const Vec3 &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 -template -const Matrix44 & -Matrix44::setShear (const Shear6 &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 -template -const Matrix44 & -Matrix44::shear (const Vec3 &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 -template -const Matrix44 & -Matrix44::shear (const Shear6 &h) -{ - Matrix44 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 -std::ostream & -operator << (std::ostream &s, const Matrix33 &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 -std::ostream & -operator << (std::ostream &s, const Matrix44 &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 -inline const Vec2 & -operator *= (Vec2 &v, const Matrix33 &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 -inline Vec2 -operator * (const Vec2 &v, const Matrix33 &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 (x / w, y / w); -} - - -template -inline const Vec3 & -operator *= (Vec3 &v, const Matrix33 &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 -inline Vec3 -operator * (const Vec3 &v, const Matrix33 &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 (x, y, z); -} - - -template -inline const Vec3 & -operator *= (Vec3 &v, const Matrix44 &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 -inline Vec3 -operator * (const Vec3 &v, const Matrix44 &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 (x / w, y / w, z / w); -} - -} // namespace Imath - - - -#endif