| /////////////////////////////////////////////////////////////////////////// |
| // |
| // Copyright (c) 2002, Industrial Light & Magic, a division of Lucas |
| // Digital Ltd. LLC |
| // |
| // All rights reserved. |
| // |
| // Redistribution and use in source and binary forms, with or without |
| // modification, are permitted provided that the following conditions are |
| // met: |
| // * Redistributions of source code must retain the above copyright |
| // notice, this list of conditions and the following disclaimer. |
| // * Redistributions in binary form must reproduce the above |
| // copyright notice, this list of conditions and the following disclaimer |
| // in the documentation and/or other materials provided with the |
| // distribution. |
| // * Neither the name of Industrial Light & Magic nor the names of |
| // its contributors may be used to endorse or promote products derived |
| // from this software without specific prior written permission. |
| // |
| // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS |
| // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT |
| // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR |
| // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT |
| // OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, |
| // SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT |
| // LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, |
| // DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY |
| // THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT |
| // (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE |
| // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. |
| // |
| /////////////////////////////////////////////////////////////////////////// |
| |
| |
| |
| #ifndef INCLUDED_IMATHMATRIX_H |
| #define INCLUDED_IMATHMATRIX_H |
| |
| //---------------------------------------------------------------- |
| // |
| // 2D (3x3) and 3D (4x4) transformation matrix templates. |
| // |
| //---------------------------------------------------------------- |
| |
| #include "ImathPlatform.h" |
| #include "ImathFun.h" |
| #include "ImathExc.h" |
| #include "ImathVec.h" |
| #include "ImathShear.h" |
| |
| #include <iostream> |
| #include <iomanip> |
| |
| #if (defined _WIN32 || defined _WIN64) && defined _MSC_VER |
| // suppress exception specification warnings |
| #pragma warning(disable:4290) |
| #endif |
| |
| |
| namespace Imath { |
| |
| |
| template <class T> class Matrix33 |
| { |
| public: |
| |
| //------------------- |
| // Access to elements |
| //------------------- |
| |
| T x[3][3]; |
| |
| T * operator [] (int i); |
| const T * operator [] (int i) const; |
| |
| |
| //------------- |
| // Constructors |
| //------------- |
| |
| Matrix33 (); |
| // 1 0 0 |
| // 0 1 0 |
| // 0 0 1 |
| |
| Matrix33 (T a); |
| // a a a |
| // a a a |
| // a a a |
| |
| Matrix33 (const T a[3][3]); |
| // a[0][0] a[0][1] a[0][2] |
| // a[1][0] a[1][1] a[1][2] |
| // a[2][0] a[2][1] a[2][2] |
| |
| Matrix33 (T a, T b, T c, T d, T e, T f, T g, T h, T i); |
| |
| // a b c |
| // d e f |
| // g h i |
| |
| |
| //-------------------------------- |
| // Copy constructor and assignment |
| //-------------------------------- |
| |
| Matrix33 (const Matrix33 &v); |
| |
| const Matrix33 & operator = (const Matrix33 &v); |
| const Matrix33 & operator = (T a); |
| |
| |
| //---------------------- |
| // Compatibility with Sb |
| //---------------------- |
| |
| T * getValue (); |
| const T * getValue () const; |
| |
| template <class S> |
| void getValue (Matrix33<S> &v) const; |
| template <class S> |
| Matrix33 & setValue (const Matrix33<S> &v); |
| |
| template <class S> |
| Matrix33 & setTheMatrix (const Matrix33<S> &v); |
| |
| |
| //--------- |
| // Identity |
| //--------- |
| |
| void makeIdentity(); |
| |
| |
| //--------- |
| // Equality |
| //--------- |
| |
| bool operator == (const Matrix33 &v) const; |
| bool operator != (const Matrix33 &v) const; |
| |
| //----------------------------------------------------------------------- |
| // Compare two matrices and test if they are "approximately equal": |
| // |
| // equalWithAbsError (m, e) |
| // |
| // Returns true if the coefficients of this and m are the same with |
| // an absolute error of no more than e, i.e., for all i, j |
| // |
| // abs (this[i][j] - m[i][j]) <= e |
| // |
| // equalWithRelError (m, e) |
| // |
| // Returns true if the coefficients of this and m are the same with |
| // a relative error of no more than e, i.e., for all i, j |
| // |
| // abs (this[i] - v[i][j]) <= e * abs (this[i][j]) |
| //----------------------------------------------------------------------- |
| |
| bool equalWithAbsError (const Matrix33<T> &v, T e) const; |
| bool equalWithRelError (const Matrix33<T> &v, T e) const; |
| |
| |
| //------------------------ |
| // Component-wise addition |
| //------------------------ |
| |
| const Matrix33 & operator += (const Matrix33 &v); |
| const Matrix33 & operator += (T a); |
| Matrix33 operator + (const Matrix33 &v) const; |
| |
| |
| //--------------------------- |
| // Component-wise subtraction |
| //--------------------------- |
| |
| const Matrix33 & operator -= (const Matrix33 &v); |
| const Matrix33 & operator -= (T a); |
| Matrix33 operator - (const Matrix33 &v) const; |
| |
| |
| //------------------------------------ |
| // Component-wise multiplication by -1 |
| //------------------------------------ |
| |
| Matrix33 operator - () const; |
| const Matrix33 & negate (); |
| |
| |
| //------------------------------ |
| // Component-wise multiplication |
| //------------------------------ |
| |
| const Matrix33 & operator *= (T a); |
| Matrix33 operator * (T a) const; |
| |
| |
| //----------------------------------- |
| // Matrix-times-matrix multiplication |
| //----------------------------------- |
| |
| const Matrix33 & operator *= (const Matrix33 &v); |
| Matrix33 operator * (const Matrix33 &v) const; |
| |
| |
| //--------------------------------------------- |
| // Vector-times-matrix multiplication; see also |
| // the "operator *" functions defined below. |
| //--------------------------------------------- |
| |
| template <class S> |
| void multVecMatrix(const Vec2<S> &src, Vec2<S> &dst) const; |
| |
| template <class S> |
| void multDirMatrix(const Vec2<S> &src, Vec2<S> &dst) const; |
| |
| |
| //------------------------ |
| // Component-wise division |
| //------------------------ |
| |
| const Matrix33 & operator /= (T a); |
| Matrix33 operator / (T a) const; |
| |
| |
| //------------------ |
| // Transposed matrix |
| //------------------ |
| |
| const Matrix33 & transpose (); |
| Matrix33 transposed () const; |
| |
| |
| //------------------------------------------------------------ |
| // Inverse matrix: If singExc is false, inverting a singular |
| // matrix produces an identity matrix. If singExc is true, |
| // inverting a singular matrix throws a SingMatrixExc. |
| // |
| // inverse() and invert() invert matrices using determinants; |
| // gjInverse() and gjInvert() use the Gauss-Jordan method. |
| // |
| // inverse() and invert() are significantly faster than |
| // gjInverse() and gjInvert(), but the results may be slightly |
| // less accurate. |
| // |
| //------------------------------------------------------------ |
| |
| const Matrix33 & invert (bool singExc = false) |
| throw (Iex::MathExc); |
| |
| Matrix33<T> inverse (bool singExc = false) const |
| throw (Iex::MathExc); |
| |
| const Matrix33 & gjInvert (bool singExc = false) |
| throw (Iex::MathExc); |
| |
| Matrix33<T> gjInverse (bool singExc = false) const |
| throw (Iex::MathExc); |
| |
| |
| //----------------------------------------- |
| // Set matrix to rotation by r (in radians) |
| //----------------------------------------- |
| |
| template <class S> |
| const Matrix33 & setRotation (S r); |
| |
| |
| //----------------------------- |
| // Rotate the given matrix by r |
| //----------------------------- |
| |
| template <class S> |
| const Matrix33 & rotate (S r); |
| |
| |
| //-------------------------------------------- |
| // Set matrix to scale by given uniform factor |
| //-------------------------------------------- |
| |
| const Matrix33 & setScale (T s); |
| |
| |
| //------------------------------------ |
| // Set matrix to scale by given vector |
| //------------------------------------ |
| |
| template <class S> |
| const Matrix33 & setScale (const Vec2<S> &s); |
| |
| |
| //---------------------- |
| // Scale the matrix by s |
| //---------------------- |
| |
| template <class S> |
| const Matrix33 & scale (const Vec2<S> &s); |
| |
| |
| //------------------------------------------ |
| // Set matrix to translation by given vector |
| //------------------------------------------ |
| |
| template <class S> |
| const Matrix33 & setTranslation (const Vec2<S> &t); |
| |
| |
| //----------------------------- |
| // Return translation component |
| //----------------------------- |
| |
| Vec2<T> translation () const; |
| |
| |
| //-------------------------- |
| // Translate the matrix by t |
| //-------------------------- |
| |
| template <class S> |
| const Matrix33 & translate (const Vec2<S> &t); |
| |
| |
| //----------------------------------------------------------- |
| // Set matrix to shear x for each y coord. by given factor xy |
| //----------------------------------------------------------- |
| |
| template <class S> |
| const Matrix33 & setShear (const S &h); |
| |
| |
| //------------------------------------------------------------- |
| // Set matrix to shear x for each y coord. by given factor h[0] |
| // and to shear y for each x coord. by given factor h[1] |
| //------------------------------------------------------------- |
| |
| template <class S> |
| const Matrix33 & setShear (const Vec2<S> &h); |
| |
| |
| //----------------------------------------------------------- |
| // Shear the matrix in x for each y coord. by given factor xy |
| //----------------------------------------------------------- |
| |
| template <class S> |
| const Matrix33 & shear (const S &xy); |
| |
| |
| //----------------------------------------------------------- |
| // Shear the matrix in x for each y coord. by given factor xy |
| // and shear y for each x coord. by given factor yx |
| //----------------------------------------------------------- |
| |
| template <class S> |
| const Matrix33 & shear (const Vec2<S> &h); |
| |
| |
| //------------------------------------------------- |
| // Limitations of type T (see also class limits<T>) |
| //------------------------------------------------- |
| |
| static T baseTypeMin() {return limits<T>::min();} |
| static T baseTypeMax() {return limits<T>::max();} |
| static T baseTypeSmallest() {return limits<T>::smallest();} |
| static T baseTypeEpsilon() {return limits<T>::epsilon();} |
| }; |
| |
| |
| template <class T> class Matrix44 |
| { |
| public: |
| |
| //------------------- |
| // Access to elements |
| //------------------- |
| |
| T x[4][4]; |
| |
| T * operator [] (int i); |
| const T * operator [] (int i) const; |
| |
| |
| //------------- |
| // Constructors |
| //------------- |
| |
| Matrix44 (); |
| // 1 0 0 0 |
| // 0 1 0 0 |
| // 0 0 1 0 |
| // 0 0 0 1 |
| |
| Matrix44 (T a); |
| // a a a a |
| // a a a a |
| // a a a a |
| // a a a a |
| |
| Matrix44 (const T a[4][4]) ; |
| // a[0][0] a[0][1] a[0][2] a[0][3] |
| // a[1][0] a[1][1] a[1][2] a[1][3] |
| // a[2][0] a[2][1] a[2][2] a[2][3] |
| // a[3][0] a[3][1] a[3][2] a[3][3] |
| |
| Matrix44 (T a, T b, T c, T d, T e, T f, T g, T h, |
| T i, T j, T k, T l, T m, T n, T o, T p); |
| |
| // a b c d |
| // e f g h |
| // i j k l |
| // m n o p |
| |
| Matrix44 (Matrix33<T> r, Vec3<T> t); |
| // r r r 0 |
| // r r r 0 |
| // r r r 0 |
| // t t t 1 |
| |
| |
| //-------------------------------- |
| // Copy constructor and assignment |
| //-------------------------------- |
| |
| Matrix44 (const Matrix44 &v); |
| |
| const Matrix44 & operator = (const Matrix44 &v); |
| const Matrix44 & operator = (T a); |
| |
| |
| //---------------------- |
| // Compatibility with Sb |
| //---------------------- |
| |
| T * getValue (); |
| const T * getValue () const; |
| |
| template <class S> |
| void getValue (Matrix44<S> &v) const; |
| template <class S> |
| Matrix44 & setValue (const Matrix44<S> &v); |
| |
| template <class S> |
| Matrix44 & setTheMatrix (const Matrix44<S> &v); |
| |
| //--------- |
| // Identity |
| //--------- |
| |
| void makeIdentity(); |
| |
| |
| //--------- |
| // Equality |
| //--------- |
| |
| bool operator == (const Matrix44 &v) const; |
| bool operator != (const Matrix44 &v) const; |
| |
| //----------------------------------------------------------------------- |
| // Compare two matrices and test if they are "approximately equal": |
| // |
| // equalWithAbsError (m, e) |
| // |
| // Returns true if the coefficients of this and m are the same with |
| // an absolute error of no more than e, i.e., for all i, j |
| // |
| // abs (this[i][j] - m[i][j]) <= e |
| // |
| // equalWithRelError (m, e) |
| // |
| // Returns true if the coefficients of this and m are the same with |
| // a relative error of no more than e, i.e., for all i, j |
| // |
| // abs (this[i] - v[i][j]) <= e * abs (this[i][j]) |
| //----------------------------------------------------------------------- |
| |
| bool equalWithAbsError (const Matrix44<T> &v, T e) const; |
| bool equalWithRelError (const Matrix44<T> &v, T e) const; |
| |
| |
| //------------------------ |
| // Component-wise addition |
| //------------------------ |
| |
| const Matrix44 & operator += (const Matrix44 &v); |
| const Matrix44 & operator += (T a); |
| Matrix44 operator + (const Matrix44 &v) const; |
| |
| |
| //--------------------------- |
| // Component-wise subtraction |
| //--------------------------- |
| |
| const Matrix44 & operator -= (const Matrix44 &v); |
| const Matrix44 & operator -= (T a); |
| Matrix44 operator - (const Matrix44 &v) const; |
| |
| |
| //------------------------------------ |
| // Component-wise multiplication by -1 |
| //------------------------------------ |
| |
| Matrix44 operator - () const; |
| const Matrix44 & negate (); |
| |
| |
| //------------------------------ |
| // Component-wise multiplication |
| //------------------------------ |
| |
| const Matrix44 & operator *= (T a); |
| Matrix44 operator * (T a) const; |
| |
| |
| //----------------------------------- |
| // Matrix-times-matrix multiplication |
| //----------------------------------- |
| |
| const Matrix44 & operator *= (const Matrix44 &v); |
| Matrix44 operator * (const Matrix44 &v) const; |
| |
| static void multiply (const Matrix44 &a, // assumes that |
| const Matrix44 &b, // &a != &c and |
| Matrix44 &c); // &b != &c. |
| |
| |
| //--------------------------------------------- |
| // Vector-times-matrix multiplication; see also |
| // the "operator *" functions defined below. |
| //--------------------------------------------- |
| |
| template <class S> |
| void multVecMatrix(const Vec3<S> &src, Vec3<S> &dst) const; |
| |
| template <class S> |
| void multDirMatrix(const Vec3<S> &src, Vec3<S> &dst) const; |
| |
| |
| //------------------------ |
| // Component-wise division |
| //------------------------ |
| |
| const Matrix44 & operator /= (T a); |
| Matrix44 operator / (T a) const; |
| |
| |
| //------------------ |
| // Transposed matrix |
| //------------------ |
| |
| const Matrix44 & transpose (); |
| Matrix44 transposed () const; |
| |
| |
| //------------------------------------------------------------ |
| // Inverse matrix: If singExc is false, inverting a singular |
| // matrix produces an identity matrix. If singExc is true, |
| // inverting a singular matrix throws a SingMatrixExc. |
| // |
| // inverse() and invert() invert matrices using determinants; |
| // gjInverse() and gjInvert() use the Gauss-Jordan method. |
| // |
| // inverse() and invert() are significantly faster than |
| // gjInverse() and gjInvert(), but the results may be slightly |
| // less accurate. |
| // |
| //------------------------------------------------------------ |
| |
| const Matrix44 & invert (bool singExc = false) |
| throw (Iex::MathExc); |
| |
| Matrix44<T> inverse (bool singExc = false) const |
| throw (Iex::MathExc); |
| |
| const Matrix44 & gjInvert (bool singExc = false) |
| throw (Iex::MathExc); |
| |
| Matrix44<T> gjInverse (bool singExc = false) const |
| throw (Iex::MathExc); |
| |
| |
| //-------------------------------------------------------- |
| // Set matrix to rotation by XYZ euler angles (in radians) |
| //-------------------------------------------------------- |
| |
| template <class S> |
| const Matrix44 & setEulerAngles (const Vec3<S>& r); |
| |
| |
| //-------------------------------------------------------- |
| // Set matrix to rotation around given axis by given angle |
| //-------------------------------------------------------- |
| |
| template <class S> |
| const Matrix44 & setAxisAngle (const Vec3<S>& ax, S ang); |
| |
| |
| //------------------------------------------- |
| // Rotate the matrix by XYZ euler angles in r |
| //------------------------------------------- |
| |
| template <class S> |
| const Matrix44 & rotate (const Vec3<S> &r); |
| |
| |
| //-------------------------------------------- |
| // Set matrix to scale by given uniform factor |
| //-------------------------------------------- |
| |
| const Matrix44 & setScale (T s); |
| |
| |
| //------------------------------------ |
| // Set matrix to scale by given vector |
| //------------------------------------ |
| |
| template <class S> |
| const Matrix44 & setScale (const Vec3<S> &s); |
| |
| |
| //---------------------- |
| // Scale the matrix by s |
| //---------------------- |
| |
| template <class S> |
| const Matrix44 & scale (const Vec3<S> &s); |
| |
| |
| //------------------------------------------ |
| // Set matrix to translation by given vector |
| //------------------------------------------ |
| |
| template <class S> |
| const Matrix44 & setTranslation (const Vec3<S> &t); |
| |
| |
| //----------------------------- |
| // Return translation component |
| //----------------------------- |
| |
| const Vec3<T> translation () const; |
| |
| |
| //-------------------------- |
| // Translate the matrix by t |
| //-------------------------- |
| |
| template <class S> |
| const Matrix44 & translate (const Vec3<S> &t); |
| |
| |
| //------------------------------------------------------------- |
| // Set matrix to shear by given vector h. The resulting matrix |
| // will shear x for each y coord. by a factor of h[0] ; |
| // will shear x for each z coord. by a factor of h[1] ; |
| // will shear y for each z coord. by a factor of h[2] . |
| //------------------------------------------------------------- |
| |
| template <class S> |
| const Matrix44 & setShear (const Vec3<S> &h); |
| |
| |
| //------------------------------------------------------------ |
| // Set matrix to shear by given factors. The resulting matrix |
| // will shear x for each y coord. by a factor of h.xy ; |
| // will shear x for each z coord. by a factor of h.xz ; |
| // will shear y for each z coord. by a factor of h.yz ; |
| // will shear y for each x coord. by a factor of h.yx ; |
| // will shear z for each x coord. by a factor of h.zx ; |
| // will shear z for each y coord. by a factor of h.zy . |
| //------------------------------------------------------------ |
| |
| template <class S> |
| const Matrix44 & setShear (const Shear6<S> &h); |
| |
| |
| //-------------------------------------------------------- |
| // Shear the matrix by given vector. The composed matrix |
| // will be <shear> * <this>, where the shear matrix ... |
| // will shear x for each y coord. by a factor of h[0] ; |
| // will shear x for each z coord. by a factor of h[1] ; |
| // will shear y for each z coord. by a factor of h[2] . |
| //-------------------------------------------------------- |
| |
| template <class S> |
| const Matrix44 & shear (const Vec3<S> &h); |
| |
| |
| //------------------------------------------------------------ |
| // Shear the matrix by the given factors. The composed matrix |
| // will be <shear> * <this>, where the shear matrix ... |
| // will shear x for each y coord. by a factor of h.xy ; |
| // will shear x for each z coord. by a factor of h.xz ; |
| // will shear y for each z coord. by a factor of h.yz ; |
| // will shear y for each x coord. by a factor of h.yx ; |
| // will shear z for each x coord. by a factor of h.zx ; |
| // will shear z for each y coord. by a factor of h.zy . |
| //------------------------------------------------------------ |
| |
| template <class S> |
| const Matrix44 & shear (const Shear6<S> &h); |
| |
| |
| //------------------------------------------------- |
| // Limitations of type T (see also class limits<T>) |
| //------------------------------------------------- |
| |
| static T baseTypeMin() {return limits<T>::min();} |
| static T baseTypeMax() {return limits<T>::max();} |
| static T baseTypeSmallest() {return limits<T>::smallest();} |
| static T baseTypeEpsilon() {return limits<T>::epsilon();} |
| }; |
| |
| |
| //-------------- |
| // Stream output |
| //-------------- |
| |
| template <class T> |
| std::ostream & operator << (std::ostream & s, const Matrix33<T> &m); |
| |
| template <class T> |
| std::ostream & operator << (std::ostream & s, const Matrix44<T> &m); |
| |
| |
| //--------------------------------------------- |
| // Vector-times-matrix multiplication operators |
| //--------------------------------------------- |
| |
| template <class S, class T> |
| const Vec2<S> & operator *= (Vec2<S> &v, const Matrix33<T> &m); |
| |
| template <class S, class T> |
| Vec2<S> operator * (const Vec2<S> &v, const Matrix33<T> &m); |
| |
| template <class S, class T> |
| const Vec3<S> & operator *= (Vec3<S> &v, const Matrix33<T> &m); |
| |
| template <class S, class T> |
| Vec3<S> operator * (const Vec3<S> &v, const Matrix33<T> &m); |
| |
| template <class S, class T> |
| const Vec3<S> & operator *= (Vec3<S> &v, const Matrix44<T> &m); |
| |
| template <class S, class T> |
| Vec3<S> operator * (const Vec3<S> &v, const Matrix44<T> &m); |
| |
| |
| //------------------------- |
| // Typedefs for convenience |
| //------------------------- |
| |
| typedef Matrix33 <float> M33f; |
| typedef Matrix33 <double> M33d; |
| typedef Matrix44 <float> M44f; |
| typedef Matrix44 <double> M44d; |
| |
| |
| //--------------------------- |
| // Implementation of Matrix33 |
| //--------------------------- |
| |
| template <class T> |
| inline T * |
| Matrix33<T>::operator [] (int i) |
| { |
| return x[i]; |
| } |
| |
| template <class T> |
| inline const T * |
| Matrix33<T>::operator [] (int i) const |
| { |
| return x[i]; |
| } |
| |
| template <class T> |
| inline |
| Matrix33<T>::Matrix33 () |
| { |
| x[0][0] = 1; |
| x[0][1] = 0; |
| x[0][2] = 0; |
| x[1][0] = 0; |
| x[1][1] = 1; |
| x[1][2] = 0; |
| x[2][0] = 0; |
| x[2][1] = 0; |
| x[2][2] = 1; |
| } |
| |
| template <class T> |
| inline |
| Matrix33<T>::Matrix33 (T a) |
| { |
| x[0][0] = a; |
| x[0][1] = a; |
| x[0][2] = a; |
| x[1][0] = a; |
| x[1][1] = a; |
| x[1][2] = a; |
| x[2][0] = a; |
| x[2][1] = a; |
| x[2][2] = a; |
| } |
| |
| template <class T> |
| inline |
| Matrix33<T>::Matrix33 (const T a[3][3]) |
| { |
| x[0][0] = a[0][0]; |
| x[0][1] = a[0][1]; |
| x[0][2] = a[0][2]; |
| x[1][0] = a[1][0]; |
| x[1][1] = a[1][1]; |
| x[1][2] = a[1][2]; |
| x[2][0] = a[2][0]; |
| x[2][1] = a[2][1]; |
| x[2][2] = a[2][2]; |
| } |
| |
| template <class T> |
| inline |
| Matrix33<T>::Matrix33 (T a, T b, T c, T d, T e, T f, T g, T h, T i) |
| { |
| x[0][0] = a; |
| x[0][1] = b; |
| x[0][2] = c; |
| x[1][0] = d; |
| x[1][1] = e; |
| x[1][2] = f; |
| x[2][0] = g; |
| x[2][1] = h; |
| x[2][2] = i; |
| } |
| |
| template <class T> |
| inline |
| Matrix33<T>::Matrix33 (const Matrix33 &v) |
| { |
| x[0][0] = v.x[0][0]; |
| x[0][1] = v.x[0][1]; |
| x[0][2] = v.x[0][2]; |
| x[1][0] = v.x[1][0]; |
| x[1][1] = v.x[1][1]; |
| x[1][2] = v.x[1][2]; |
| x[2][0] = v.x[2][0]; |
| x[2][1] = v.x[2][1]; |
| x[2][2] = v.x[2][2]; |
| } |
| |
| template <class T> |
| inline const Matrix33<T> & |
| Matrix33<T>::operator = (const Matrix33 &v) |
| { |
| x[0][0] = v.x[0][0]; |
| x[0][1] = v.x[0][1]; |
| x[0][2] = v.x[0][2]; |
| x[1][0] = v.x[1][0]; |
| x[1][1] = v.x[1][1]; |
| x[1][2] = v.x[1][2]; |
| x[2][0] = v.x[2][0]; |
| x[2][1] = v.x[2][1]; |
| x[2][2] = v.x[2][2]; |
| return *this; |
| } |
| |
| template <class T> |
| inline const Matrix33<T> & |
| Matrix33<T>::operator = (T a) |
| { |
| x[0][0] = a; |
| x[0][1] = a; |
| x[0][2] = a; |
| x[1][0] = a; |
| x[1][1] = a; |
| x[1][2] = a; |
| x[2][0] = a; |
| x[2][1] = a; |
| x[2][2] = a; |
| return *this; |
| } |
| |
| template <class T> |
| inline T * |
| Matrix33<T>::getValue () |
| { |
| return (T *) &x[0][0]; |
| } |
| |
| template <class T> |
| inline const T * |
| Matrix33<T>::getValue () const |
| { |
| return (const T *) &x[0][0]; |
| } |
| |
| template <class T> |
| template <class S> |
| inline void |
| Matrix33<T>::getValue (Matrix33<S> &v) const |
| { |
| v.x[0][0] = x[0][0]; |
| v.x[0][1] = x[0][1]; |
| v.x[0][2] = x[0][2]; |
| v.x[1][0] = x[1][0]; |
| v.x[1][1] = x[1][1]; |
| v.x[1][2] = x[1][2]; |
| v.x[2][0] = x[2][0]; |
| v.x[2][1] = x[2][1]; |
| v.x[2][2] = x[2][2]; |
| } |
| |
| template <class T> |
| template <class S> |
| inline Matrix33<T> & |
| Matrix33<T>::setValue (const Matrix33<S> &v) |
| { |
| x[0][0] = v.x[0][0]; |
| x[0][1] = v.x[0][1]; |
| x[0][2] = v.x[0][2]; |
| x[1][0] = v.x[1][0]; |
| x[1][1] = v.x[1][1]; |
| x[1][2] = v.x[1][2]; |
| x[2][0] = v.x[2][0]; |
| x[2][1] = v.x[2][1]; |
| x[2][2] = v.x[2][2]; |
| return *this; |
| } |
| |
| template <class T> |
| template <class S> |
| inline Matrix33<T> & |
| Matrix33<T>::setTheMatrix (const Matrix33<S> &v) |
| { |
| x[0][0] = v.x[0][0]; |
| x[0][1] = v.x[0][1]; |
| x[0][2] = v.x[0][2]; |
| x[1][0] = v.x[1][0]; |
| x[1][1] = v.x[1][1]; |
| x[1][2] = v.x[1][2]; |
| x[2][0] = v.x[2][0]; |
| x[2][1] = v.x[2][1]; |
| x[2][2] = v.x[2][2]; |
| return *this; |
| } |
| |
| template <class T> |
| inline void |
| Matrix33<T>::makeIdentity() |
| { |
| x[0][0] = 1; |
| x[0][1] = 0; |
| x[0][2] = 0; |
| x[1][0] = 0; |
| x[1][1] = 1; |
| x[1][2] = 0; |
| x[2][0] = 0; |
| x[2][1] = 0; |
| x[2][2] = 1; |
| } |
| |
| template <class T> |
| bool |
| Matrix33<T>::operator == (const Matrix33 &v) const |
| { |
| return x[0][0] == v.x[0][0] && |
| x[0][1] == v.x[0][1] && |
| x[0][2] == v.x[0][2] && |
| x[1][0] == v.x[1][0] && |
| x[1][1] == v.x[1][1] && |
| x[1][2] == v.x[1][2] && |
| x[2][0] == v.x[2][0] && |
| x[2][1] == v.x[2][1] && |
| x[2][2] == v.x[2][2]; |
| } |
| |
| template <class T> |
| bool |
| Matrix33<T>::operator != (const Matrix33 &v) const |
| { |
| return x[0][0] != v.x[0][0] || |
| x[0][1] != v.x[0][1] || |
| x[0][2] != v.x[0][2] || |
| x[1][0] != v.x[1][0] || |
| x[1][1] != v.x[1][1] || |
| x[1][2] != v.x[1][2] || |
| x[2][0] != v.x[2][0] || |
| x[2][1] != v.x[2][1] || |
| x[2][2] != v.x[2][2]; |
| } |
| |
| template <class T> |
| bool |
| Matrix33<T>::equalWithAbsError (const Matrix33<T> &m, T e) const |
| { |
| for (int i = 0; i < 3; i++) |
| for (int j = 0; j < 3; j++) |
| if (!Imath::equalWithAbsError ((*this)[i][j], m[i][j], e)) |
| return false; |
| |
| return true; |
| } |
| |
| template <class T> |
| bool |
| Matrix33<T>::equalWithRelError (const Matrix33<T> &m, T e) const |
| { |
| for (int i = 0; i < 3; i++) |
| for (int j = 0; j < 3; j++) |
| if (!Imath::equalWithRelError ((*this)[i][j], m[i][j], e)) |
| return false; |
| |
| return true; |
| } |
| |
| template <class T> |
| const Matrix33<T> & |
| Matrix33<T>::operator += (const Matrix33<T> &v) |
| { |
| x[0][0] += v.x[0][0]; |
| x[0][1] += v.x[0][1]; |
| x[0][2] += v.x[0][2]; |
| x[1][0] += v.x[1][0]; |
| x[1][1] += v.x[1][1]; |
| x[1][2] += v.x[1][2]; |
| x[2][0] += v.x[2][0]; |
| x[2][1] += v.x[2][1]; |
| x[2][2] += v.x[2][2]; |
| |
| return *this; |
| } |
| |
| template <class T> |
| const Matrix33<T> & |
| Matrix33<T>::operator += (T a) |
| { |
| x[0][0] += a; |
| x[0][1] += a; |
| x[0][2] += a; |
| x[1][0] += a; |
| x[1][1] += a; |
| x[1][2] += a; |
| x[2][0] += a; |
| x[2][1] += a; |
| x[2][2] += a; |
| |
| return *this; |
| } |
| |
| template <class T> |
| Matrix33<T> |
| Matrix33<T>::operator + (const Matrix33<T> &v) const |
| { |
| return Matrix33 (x[0][0] + v.x[0][0], |
| x[0][1] + v.x[0][1], |
| x[0][2] + v.x[0][2], |
| x[1][0] + v.x[1][0], |
| x[1][1] + v.x[1][1], |
| x[1][2] + v.x[1][2], |
| x[2][0] + v.x[2][0], |
| x[2][1] + v.x[2][1], |
| x[2][2] + v.x[2][2]); |
| } |
| |
| template <class T> |
| const Matrix33<T> & |
| Matrix33<T>::operator -= (const Matrix33<T> &v) |
| { |
| x[0][0] -= v.x[0][0]; |
| x[0][1] -= v.x[0][1]; |
| x[0][2] -= v.x[0][2]; |
| x[1][0] -= v.x[1][0]; |
| x[1][1] -= v.x[1][1]; |
| x[1][2] -= v.x[1][2]; |
| x[2][0] -= v.x[2][0]; |
| x[2][1] -= v.x[2][1]; |
| x[2][2] -= v.x[2][2]; |
| |
| return *this; |
| } |
| |
| template <class T> |
| const Matrix33<T> & |
| Matrix33<T>::operator -= (T a) |
| { |
| x[0][0] -= a; |
| x[0][1] -= a; |
| x[0][2] -= a; |
| x[1][0] -= a; |
| x[1][1] -= a; |
| x[1][2] -= a; |
| x[2][0] -= a; |
| x[2][1] -= a; |
| x[2][2] -= a; |
| |
| return *this; |
| } |
| |
| template <class T> |
| Matrix33<T> |
| Matrix33<T>::operator - (const Matrix33<T> &v) const |
| { |
| return Matrix33 (x[0][0] - v.x[0][0], |
| x[0][1] - v.x[0][1], |
| x[0][2] - v.x[0][2], |
| x[1][0] - v.x[1][0], |
| x[1][1] - v.x[1][1], |
| x[1][2] - v.x[1][2], |
| x[2][0] - v.x[2][0], |
| x[2][1] - v.x[2][1], |
| x[2][2] - v.x[2][2]); |
| } |
| |
| template <class T> |
| Matrix33<T> |
| Matrix33<T>::operator - () const |
| { |
| return Matrix33 (-x[0][0], |
| -x[0][1], |
| -x[0][2], |
| -x[1][0], |
| -x[1][1], |
| -x[1][2], |
| -x[2][0], |
| -x[2][1], |
| -x[2][2]); |
| } |
| |
| template <class T> |
| const Matrix33<T> & |
| Matrix33<T>::negate () |
| { |
| x[0][0] = -x[0][0]; |
| x[0][1] = -x[0][1]; |
| x[0][2] = -x[0][2]; |
| x[1][0] = -x[1][0]; |
| x[1][1] = -x[1][1]; |
| x[1][2] = -x[1][2]; |
| x[2][0] = -x[2][0]; |
| x[2][1] = -x[2][1]; |
| x[2][2] = -x[2][2]; |
| |
| return *this; |
| } |
| |
| template <class T> |
| const Matrix33<T> & |
| Matrix33<T>::operator *= (T a) |
| { |
| x[0][0] *= a; |
| x[0][1] *= a; |
| x[0][2] *= a; |
| x[1][0] *= a; |
| x[1][1] *= a; |
| x[1][2] *= a; |
| x[2][0] *= a; |
| x[2][1] *= a; |
| x[2][2] *= a; |
| |
| return *this; |
| } |
| |
| template <class T> |
| Matrix33<T> |
| Matrix33<T>::operator * (T a) const |
| { |
| return Matrix33 (x[0][0] * a, |
| x[0][1] * a, |
| x[0][2] * a, |
| x[1][0] * a, |
| x[1][1] * a, |
| x[1][2] * a, |
| x[2][0] * a, |
| x[2][1] * a, |
| x[2][2] * a); |
| } |
| |
| template <class T> |
| inline Matrix33<T> |
| operator * (T a, const Matrix33<T> &v) |
| { |
| return v * a; |
| } |
| |
| template <class T> |
| const Matrix33<T> & |
| Matrix33<T>::operator *= (const Matrix33<T> &v) |
| { |
| Matrix33 tmp (T (0)); |
| |
| for (int i = 0; i < 3; i++) |
| for (int j = 0; j < 3; j++) |
| for (int k = 0; k < 3; k++) |
| tmp.x[i][j] += x[i][k] * v.x[k][j]; |
| |
| *this = tmp; |
| return *this; |
| } |
| |
| template <class T> |
| Matrix33<T> |
| Matrix33<T>::operator * (const Matrix33<T> &v) const |
| { |
| Matrix33 tmp (T (0)); |
| |
| for (int i = 0; i < 3; i++) |
| for (int j = 0; j < 3; j++) |
| for (int k = 0; k < 3; k++) |
| tmp.x[i][j] += x[i][k] * v.x[k][j]; |
| |
| return tmp; |
| } |
| |
| template <class T> |
| template <class S> |
| void |
| Matrix33<T>::multVecMatrix(const Vec2<S> &src, Vec2<S> &dst) const |
| { |
| S a, b, w; |
| |
| a = src[0] * x[0][0] + src[1] * x[1][0] + x[2][0]; |
| b = src[0] * x[0][1] + src[1] * x[1][1] + x[2][1]; |
| w = src[0] * x[0][2] + src[1] * x[1][2] + x[2][2]; |
| |
| dst.x = a / w; |
| dst.y = b / w; |
| } |
| |
| template <class T> |
| template <class S> |
| void |
| Matrix33<T>::multDirMatrix(const Vec2<S> &src, Vec2<S> &dst) const |
| { |
| S a, b; |
| |
| a = src[0] * x[0][0] + src[1] * x[1][0]; |
| b = src[0] * x[0][1] + src[1] * x[1][1]; |
| |
| dst.x = a; |
| dst.y = b; |
| } |
| |
| template <class T> |
| const Matrix33<T> & |
| Matrix33<T>::operator /= (T a) |
| { |
| x[0][0] /= a; |
| x[0][1] /= a; |
| x[0][2] /= a; |
| x[1][0] /= a; |
| x[1][1] /= a; |
| x[1][2] /= a; |
| x[2][0] /= a; |
| x[2][1] /= a; |
| x[2][2] /= a; |
| |
| return *this; |
| } |
| |
| template <class T> |
| Matrix33<T> |
| Matrix33<T>::operator / (T a) const |
| { |
| return Matrix33 (x[0][0] / a, |
| x[0][1] / a, |
| x[0][2] / a, |
| x[1][0] / a, |
| x[1][1] / a, |
| x[1][2] / a, |
| x[2][0] / a, |
| x[2][1] / a, |
| x[2][2] / a); |
| } |
| |
| template <class T> |
| const Matrix33<T> & |
| Matrix33<T>::transpose () |
| { |
| Matrix33 tmp (x[0][0], |
| x[1][0], |
| x[2][0], |
| x[0][1], |
| x[1][1], |
| x[2][1], |
| x[0][2], |
| x[1][2], |
| x[2][2]); |
| *this = tmp; |
| return *this; |
| } |
| |
| template <class T> |
| Matrix33<T> |
| Matrix33<T>::transposed () const |
| { |
| return Matrix33 (x[0][0], |
| x[1][0], |
| x[2][0], |
| x[0][1], |
| x[1][1], |
| x[2][1], |
| x[0][2], |
| x[1][2], |
| x[2][2]); |
| } |
| |
| template <class T> |
| const Matrix33<T> & |
| Matrix33<T>::gjInvert (bool singExc) throw (Iex::MathExc) |
| { |
| *this = gjInverse (singExc); |
| return *this; |
| } |
| |
| template <class T> |
| Matrix33<T> |
| Matrix33<T>::gjInverse (bool singExc) const throw (Iex::MathExc) |
| { |
| int i, j, k; |
| Matrix33 s; |
| Matrix33 t (*this); |
| |
| // Forward elimination |
| |
| for (i = 0; i < 2 ; i++) |
| { |
| int pivot = i; |
| |
| T pivotsize = t[i][i]; |
| |
| if (pivotsize < 0) |
| pivotsize = -pivotsize; |
| |
| for (j = i + 1; j < 3; j++) |
| { |
| T tmp = t[j][i]; |
| |
| if (tmp < 0) |
| tmp = -tmp; |
| |
| if (tmp > pivotsize) |
| { |
| pivot = j; |
| pivotsize = tmp; |
| } |
| } |
| |
| if (pivotsize == 0) |
| { |
| if (singExc) |
| throw ::Imath::SingMatrixExc ("Cannot invert singular matrix."); |
| |
| return Matrix33(); |
| } |
| |
| if (pivot != i) |
| { |
| for (j = 0; j < 3; j++) |
| { |
| T tmp; |
| |
| tmp = t[i][j]; |
| t[i][j] = t[pivot][j]; |
| t[pivot][j] = tmp; |
| |
| tmp = s[i][j]; |
| s[i][j] = s[pivot][j]; |
| s[pivot][j] = tmp; |
| } |
| } |
| |
| for (j = i + 1; j < 3; j++) |
| { |
| T f = t[j][i] / t[i][i]; |
| |
| for (k = 0; k < 3; k++) |
| { |
| t[j][k] -= f * t[i][k]; |
| s[j][k] -= f * s[i][k]; |
| } |
| } |
| } |
| |
| // Backward substitution |
| |
| for (i = 2; i >= 0; --i) |
| { |
| T f; |
| |
| if ((f = t[i][i]) == 0) |
| { |
| if (singExc) |
| throw ::Imath::SingMatrixExc ("Cannot invert singular matrix."); |
| |
| return Matrix33(); |
| } |
| |
| for (j = 0; j < 3; j++) |
| { |
| t[i][j] /= f; |
| s[i][j] /= f; |
| } |
| |
| for (j = 0; j < i; j++) |
| { |
| f = t[j][i]; |
| |
| for (k = 0; k < 3; k++) |
| { |
| t[j][k] -= f * t[i][k]; |
| s[j][k] -= f * s[i][k]; |
| } |
| } |
| } |
| |
| return s; |
| } |
| |
| template <class T> |
| const Matrix33<T> & |
| Matrix33<T>::invert (bool singExc) throw (Iex::MathExc) |
| { |
| *this = inverse (singExc); |
| return *this; |
| } |
| |
| template <class T> |
| Matrix33<T> |
| Matrix33<T>::inverse (bool singExc) const throw (Iex::MathExc) |
| { |
| if (x[0][2] != 0 || x[1][2] != 0 || x[2][2] != 1) |
| { |
| Matrix33 s (x[1][1] * x[2][2] - x[2][1] * x[1][2], |
| x[2][1] * x[0][2] - x[0][1] * x[2][2], |
| x[0][1] * x[1][2] - x[1][1] * x[0][2], |
| |
| x[2][0] * x[1][2] - x[1][0] * x[2][2], |
| x[0][0] * x[2][2] - x[2][0] * x[0][2], |
| x[1][0] * x[0][2] - x[0][0] * x[1][2], |
| |
| x[1][0] * x[2][1] - x[2][0] * x[1][1], |
| x[2][0] * x[0][1] - x[0][0] * x[2][1], |
| x[0][0] * x[1][1] - x[1][0] * x[0][1]); |
| |
| T r = x[0][0] * s[0][0] + x[0][1] * s[1][0] + x[0][2] * s[2][0]; |
| |
| if (Imath::abs (r) >= 1) |
| { |
| for (int i = 0; i < 3; ++i) |
| { |
| for (int j = 0; j < 3; ++j) |
| { |
| s[i][j] /= r; |
| } |
| } |
| } |
| else |
| { |
| T mr = Imath::abs (r) / limits<T>::smallest(); |
| |
| for (int i = 0; i < 3; ++i) |
| { |
| for (int j = 0; j < 3; ++j) |
| { |
| if (mr > Imath::abs (s[i][j])) |
| { |
| s[i][j] /= r; |
| } |
| else |
| { |
| if (singExc) |
| throw SingMatrixExc ("Cannot invert " |
| "singular matrix."); |
| return Matrix33(); |
| } |
| } |
| } |
| } |
| |
| return s; |
| } |
| else |
| { |
| Matrix33 s ( x[1][1], |
| -x[0][1], |
| 0, |
| |
| -x[1][0], |
| x[0][0], |
| 0, |
| |
| 0, |
| 0, |
| 1); |
| |
| T r = x[0][0] * x[1][1] - x[1][0] * x[0][1]; |
| |
| if (Imath::abs (r) >= 1) |
| { |
| for (int i = 0; i < 2; ++i) |
| { |
| for (int j = 0; j < 2; ++j) |
| { |
| s[i][j] /= r; |
| } |
| } |
| } |
| else |
| { |
| T mr = Imath::abs (r) / limits<T>::smallest(); |
| |
| for (int i = 0; i < 2; ++i) |
| { |
| for (int j = 0; j < 2; ++j) |
| { |
| if (mr > Imath::abs (s[i][j])) |
| { |
| s[i][j] /= r; |
| } |
| else |
| { |
| if (singExc) |
| throw SingMatrixExc ("Cannot invert " |
| "singular matrix."); |
| return Matrix33(); |
| } |
| } |
| } |
| } |
| |
| s[2][0] = -x[2][0] * s[0][0] - x[2][1] * s[1][0]; |
| s[2][1] = -x[2][0] * s[0][1] - x[2][1] * s[1][1]; |
| |
| return s; |
| } |
| } |
| |
| template <class T> |
| template <class S> |
| const Matrix33<T> & |
| Matrix33<T>::setRotation (S r) |
| { |
| S cos_r, sin_r; |
| |
| cos_r = Math<T>::cos (r); |
| sin_r = Math<T>::sin (r); |
| |
| x[0][0] = cos_r; |
| x[0][1] = sin_r; |
| x[0][2] = 0; |
| |
| x[1][0] = -sin_r; |
| x[1][1] = cos_r; |
| x[1][2] = 0; |
| |
| x[2][0] = 0; |
| x[2][1] = 0; |
| x[2][2] = 1; |
| |
| return *this; |
| } |
| |
| template <class T> |
| template <class S> |
| const Matrix33<T> & |
| Matrix33<T>::rotate (S r) |
| { |
| *this *= Matrix33<T>().setRotation (r); |
| return *this; |
| } |
| |
| template <class T> |
| const Matrix33<T> & |
| Matrix33<T>::setScale (T s) |
| { |
| x[0][0] = s; |
| x[0][1] = 0; |
| x[0][2] = 0; |
| |
| x[1][0] = 0; |
| x[1][1] = s; |
| x[1][2] = 0; |
| |
| x[2][0] = 0; |
| x[2][1] = 0; |
| x[2][2] = 1; |
| |
| return *this; |
| } |
| |
| template <class T> |
| template <class S> |
| const Matrix33<T> & |
| Matrix33<T>::setScale (const Vec2<S> &s) |
| { |
| x[0][0] = s[0]; |
| x[0][1] = 0; |
| x[0][2] = 0; |
| |
| x[1][0] = 0; |
| x[1][1] = s[1]; |
| x[1][2] = 0; |
| |
| x[2][0] = 0; |
| x[2][1] = 0; |
| x[2][2] = 1; |
| |
| return *this; |
| } |
| |
| template <class T> |
| template <class S> |
| const Matrix33<T> & |
| Matrix33<T>::scale (const Vec2<S> &s) |
| { |
| x[0][0] *= s[0]; |
| x[0][1] *= s[0]; |
| x[0][2] *= s[0]; |
| |
| x[1][0] *= s[1]; |
| x[1][1] *= s[1]; |
| x[1][2] *= s[1]; |
| |
| return *this; |
| } |
| |
| template <class T> |
| template <class S> |
| const Matrix33<T> & |
| Matrix33<T>::setTranslation (const Vec2<S> &t) |
| { |
| x[0][0] = 1; |
| x[0][1] = 0; |
| x[0][2] = 0; |
| |
| x[1][0] = 0; |
| x[1][1] = 1; |
| x[1][2] = 0; |
| |
| x[2][0] = t[0]; |
| x[2][1] = t[1]; |
| x[2][2] = 1; |
| |
| return *this; |
| } |
| |
| template <class T> |
| inline Vec2<T> |
| Matrix33<T>::translation () const |
| { |
| return Vec2<T> (x[2][0], x[2][1]); |
| } |
| |
| template <class T> |
| template <class S> |
| const Matrix33<T> & |
| Matrix33<T>::translate (const Vec2<S> &t) |
| { |
| x[2][0] += t[0] * x[0][0] + t[1] * x[1][0]; |
| x[2][1] += t[0] * x[0][1] + t[1] * x[1][1]; |
| x[2][2] += t[0] * x[0][2] + t[1] * x[1][2]; |
| |
| return *this; |
| } |
| |
| template <class T> |
| template <class S> |
| const Matrix33<T> & |
| Matrix33<T>::setShear (const S &xy) |
| { |
| x[0][0] = 1; |
| x[0][1] = 0; |
| x[0][2] = 0; |
| |
| x[1][0] = xy; |
| x[1][1] = 1; |
| x[1][2] = 0; |
| |
| x[2][0] = 0; |
| x[2][1] = 0; |
| x[2][2] = 1; |
| |
| return *this; |
| } |
| |
| template <class T> |
| template <class S> |
| const Matrix33<T> & |
| Matrix33<T>::setShear (const Vec2<S> &h) |
| { |
| x[0][0] = 1; |
| x[0][1] = h[1]; |
| x[0][2] = 0; |
| |
| x[1][0] = h[0]; |
| x[1][1] = 1; |
| x[1][2] = 0; |
| |
| x[2][0] = 0; |
| x[2][1] = 0; |
| x[2][2] = 1; |
| |
| return *this; |
| } |
| |
| template <class T> |
| template <class S> |
| const Matrix33<T> & |
| Matrix33<T>::shear (const S &xy) |
| { |
| // |
| // In this case, we don't need a temp. copy of the matrix |
| // because we never use a value on the RHS after we've |
| // changed it on the LHS. |
| // |
| |
| x[1][0] += xy * x[0][0]; |
| x[1][1] += xy * x[0][1]; |
| x[1][2] += xy * x[0][2]; |
| |
| return *this; |
| } |
| |
| template <class T> |
| template <class S> |
| const Matrix33<T> & |
| Matrix33<T>::shear (const Vec2<S> &h) |
| { |
| Matrix33<T> P (*this); |
| |
| x[0][0] = P[0][0] + h[1] * P[1][0]; |
| x[0][1] = P[0][1] + h[1] * P[1][1]; |
| x[0][2] = P[0][2] + h[1] * P[1][2]; |
| |
| x[1][0] = P[1][0] + h[0] * P[0][0]; |
| x[1][1] = P[1][1] + h[0] * P[0][1]; |
| x[1][2] = P[1][2] + h[0] * P[0][2]; |
| |
| return *this; |
| } |
| |
| |
| //--------------------------- |
| // Implementation of Matrix44 |
| //--------------------------- |
| |
| template <class T> |
| inline T * |
| Matrix44<T>::operator [] (int i) |
| { |
| return x[i]; |
| } |
| |
| template <class T> |
| inline const T * |
| Matrix44<T>::operator [] (int i) const |
| { |
| return x[i]; |
| } |
| |
| template <class T> |
| inline |
| Matrix44<T>::Matrix44 () |
| { |
| x[0][0] = 1; |
| x[0][1] = 0; |
| x[0][2] = 0; |
| x[0][3] = 0; |
| x[1][0] = 0; |
| x[1][1] = 1; |
| x[1][2] = 0; |
| x[1][3] = 0; |
| x[2][0] = 0; |
| x[2][1] = 0; |
| x[2][2] = 1; |
| x[2][3] = 0; |
| x[3][0] = 0; |
| x[3][1] = 0; |
| x[3][2] = 0; |
| x[3][3] = 1; |
| } |
| |
| template <class T> |
| inline |
| Matrix44<T>::Matrix44 (T a) |
| { |
| x[0][0] = a; |
| x[0][1] = a; |
| x[0][2] = a; |
| x[0][3] = a; |
| x[1][0] = a; |
| x[1][1] = a; |
| x[1][2] = a; |
| x[1][3] = a; |
| x[2][0] = a; |
| x[2][1] = a; |
| x[2][2] = a; |
| x[2][3] = a; |
| x[3][0] = a; |
| x[3][1] = a; |
| x[3][2] = a; |
| x[3][3] = a; |
| } |
| |
| template <class T> |
| inline |
| Matrix44<T>::Matrix44 (const T a[4][4]) |
| { |
| x[0][0] = a[0][0]; |
| x[0][1] = a[0][1]; |
| x[0][2] = a[0][2]; |
| x[0][3] = a[0][3]; |
| x[1][0] = a[1][0]; |
| x[1][1] = a[1][1]; |
| x[1][2] = a[1][2]; |
| x[1][3] = a[1][3]; |
| x[2][0] = a[2][0]; |
| x[2][1] = a[2][1]; |
| x[2][2] = a[2][2]; |
| x[2][3] = a[2][3]; |
| x[3][0] = a[3][0]; |
| x[3][1] = a[3][1]; |
| x[3][2] = a[3][2]; |
| x[3][3] = a[3][3]; |
| } |
| |
| template <class T> |
| inline |
| Matrix44<T>::Matrix44 (T a, T b, T c, T d, T e, T f, T g, T h, |
| T i, T j, T k, T l, T m, T n, T o, T p) |
| { |
| x[0][0] = a; |
| x[0][1] = b; |
| x[0][2] = c; |
| x[0][3] = d; |
| x[1][0] = e; |
| x[1][1] = f; |
| x[1][2] = g; |
| x[1][3] = h; |
| x[2][0] = i; |
| x[2][1] = j; |
| x[2][2] = k; |
| x[2][3] = l; |
| x[3][0] = m; |
| x[3][1] = n; |
| x[3][2] = o; |
| x[3][3] = p; |
| } |
| |
| |
| template <class T> |
| inline |
| Matrix44<T>::Matrix44 (Matrix33<T> r, Vec3<T> t) |
| { |
| x[0][0] = r[0][0]; |
| x[0][1] = r[0][1]; |
| x[0][2] = r[0][2]; |
| x[0][3] = 0; |
| x[1][0] = r[1][0]; |
| x[1][1] = r[1][1]; |
| x[1][2] = r[1][2]; |
| x[1][3] = 0; |
| x[2][0] = r[2][0]; |
| x[2][1] = r[2][1]; |
| x[2][2] = r[2][2]; |
| x[2][3] = 0; |
| x[3][0] = t[0]; |
| x[3][1] = t[1]; |
| x[3][2] = t[2]; |
| x[3][3] = 1; |
| } |
| |
| template <class T> |
| inline |
| Matrix44<T>::Matrix44 (const Matrix44 &v) |
| { |
| x[0][0] = v.x[0][0]; |
| x[0][1] = v.x[0][1]; |
| x[0][2] = v.x[0][2]; |
| x[0][3] = v.x[0][3]; |
| x[1][0] = v.x[1][0]; |
| x[1][1] = v.x[1][1]; |
| x[1][2] = v.x[1][2]; |
| x[1][3] = v.x[1][3]; |
| x[2][0] = v.x[2][0]; |
| x[2][1] = v.x[2][1]; |
| x[2][2] = v.x[2][2]; |
| x[2][3] = v.x[2][3]; |
| x[3][0] = v.x[3][0]; |
| x[3][1] = v.x[3][1]; |
| x[3][2] = v.x[3][2]; |
| x[3][3] = v.x[3][3]; |
| } |
| |
| template <class T> |
| inline const Matrix44<T> & |
| Matrix44<T>::operator = (const Matrix44 &v) |
| { |
| x[0][0] = v.x[0][0]; |
| x[0][1] = v.x[0][1]; |
| x[0][2] = v.x[0][2]; |
| x[0][3] = v.x[0][3]; |
| x[1][0] = v.x[1][0]; |
| x[1][1] = v.x[1][1]; |
| x[1][2] = v.x[1][2]; |
| x[1][3] = v.x[1][3]; |
| x[2][0] = v.x[2][0]; |
| x[2][1] = v.x[2][1]; |
| x[2][2] = v.x[2][2]; |
| x[2][3] = v.x[2][3]; |
| x[3][0] = v.x[3][0]; |
| x[3][1] = v.x[3][1]; |
| x[3][2] = v.x[3][2]; |
| x[3][3] = v.x[3][3]; |
| return *this; |
| } |
| |
| template <class T> |
| inline const Matrix44<T> & |
| Matrix44<T>::operator = (T a) |
| { |
| x[0][0] = a; |
| x[0][1] = a; |
| x[0][2] = a; |
| x[0][3] = a; |
| x[1][0] = a; |
| x[1][1] = a; |
| x[1][2] = a; |
| x[1][3] = a; |
| x[2][0] = a; |
| x[2][1] = a; |
| x[2][2] = a; |
| x[2][3] = a; |
| x[3][0] = a; |
| x[3][1] = a; |
| x[3][2] = a; |
| x[3][3] = a; |
| return *this; |
| } |
| |
| template <class T> |
| inline T * |
| Matrix44<T>::getValue () |
| { |
| return (T *) &x[0][0]; |
| } |
| |
| template <class T> |
| inline const T * |
| Matrix44<T>::getValue () const |
| { |
| return (const T *) &x[0][0]; |
| } |
| |
| template <class T> |
| template <class S> |
| inline void |
| Matrix44<T>::getValue (Matrix44<S> &v) const |
| { |
| v.x[0][0] = x[0][0]; |
| v.x[0][1] = x[0][1]; |
| v.x[0][2] = x[0][2]; |
| v.x[0][3] = x[0][3]; |
| v.x[1][0] = x[1][0]; |
| v.x[1][1] = x[1][1]; |
| v.x[1][2] = x[1][2]; |
| v.x[1][3] = x[1][3]; |
| v.x[2][0] = x[2][0]; |
| v.x[2][1] = x[2][1]; |
| v.x[2][2] = x[2][2]; |
| v.x[2][3] = x[2][3]; |
| v.x[3][0] = x[3][0]; |
| v.x[3][1] = x[3][1]; |
| v.x[3][2] = x[3][2]; |
| v.x[3][3] = x[3][3]; |
| } |
| |
| template <class T> |
| template <class S> |
| inline Matrix44<T> & |
| Matrix44<T>::setValue (const Matrix44<S> &v) |
| { |
| x[0][0] = v.x[0][0]; |
| x[0][1] = v.x[0][1]; |
| x[0][2] = v.x[0][2]; |
| x[0][3] = v.x[0][3]; |
| x[1][0] = v.x[1][0]; |
| x[1][1] = v.x[1][1]; |
| x[1][2] = v.x[1][2]; |
| x[1][3] = v.x[1][3]; |
| x[2][0] = v.x[2][0]; |
| x[2][1] = v.x[2][1]; |
| x[2][2] = v.x[2][2]; |
| x[2][3] = v.x[2][3]; |
| x[3][0] = v.x[3][0]; |
| x[3][1] = v.x[3][1]; |
| x[3][2] = v.x[3][2]; |
| x[3][3] = v.x[3][3]; |
| return *this; |
| } |
| |
| template <class T> |
| template <class S> |
| inline Matrix44<T> & |
| Matrix44<T>::setTheMatrix (const Matrix44<S> &v) |
| { |
| x[0][0] = v.x[0][0]; |
| x[0][1] = v.x[0][1]; |
| x[0][2] = v.x[0][2]; |
| x[0][3] = v.x[0][3]; |
| x[1][0] = v.x[1][0]; |
| x[1][1] = v.x[1][1]; |
| x[1][2] = v.x[1][2]; |
| x[1][3] = v.x[1][3]; |
| x[2][0] = v.x[2][0]; |
| x[2][1] = v.x[2][1]; |
| x[2][2] = v.x[2][2]; |
| x[2][3] = v.x[2][3]; |
| x[3][0] = v.x[3][0]; |
| x[3][1] = v.x[3][1]; |
| x[3][2] = v.x[3][2]; |
| x[3][3] = v.x[3][3]; |
| return *this; |
| } |
| |
| template <class T> |
| inline void |
| Matrix44<T>::makeIdentity() |
| { |
| x[0][0] = 1; |
| x[0][1] = 0; |
| x[0][2] = 0; |
| x[0][3] = 0; |
| x[1][0] = 0; |
| x[1][1] = 1; |
| x[1][2] = 0; |
| x[1][3] = 0; |
| x[2][0] = 0; |
| x[2][1] = 0; |
| x[2][2] = 1; |
| x[2][3] = 0; |
| x[3][0] = 0; |
| x[3][1] = 0; |
| x[3][2] = 0; |
| x[3][3] = 1; |
| } |
| |
| template <class T> |
| bool |
| Matrix44<T>::operator == (const Matrix44 &v) const |
| { |
| return x[0][0] == v.x[0][0] && |
| x[0][1] == v.x[0][1] && |
| x[0][2] == v.x[0][2] && |
| x[0][3] == v.x[0][3] && |
| x[1][0] == v.x[1][0] && |
| x[1][1] == v.x[1][1] && |
| x[1][2] == v.x[1][2] && |
| x[1][3] == v.x[1][3] && |
| x[2][0] == v.x[2][0] && |
| x[2][1] == v.x[2][1] && |
| x[2][2] == v.x[2][2] && |
| x[2][3] == v.x[2][3] && |
| x[3][0] == v.x[3][0] && |
| x[3][1] == v.x[3][1] && |
| x[3][2] == v.x[3][2] && |
| x[3][3] == v.x[3][3]; |
| } |
| |
| template <class T> |
| bool |
| Matrix44<T>::operator != (const Matrix44 &v) const |
| { |
| return x[0][0] != v.x[0][0] || |
| x[0][1] != v.x[0][1] || |
| x[0][2] != v.x[0][2] || |
| x[0][3] != v.x[0][3] || |
| x[1][0] != v.x[1][0] || |
| x[1][1] != v.x[1][1] || |
| x[1][2] != v.x[1][2] || |
| x[1][3] != v.x[1][3] || |
| x[2][0] != v.x[2][0] || |
| x[2][1] != v.x[2][1] || |
| x[2][2] != v.x[2][2] || |
| x[2][3] != v.x[2][3] || |
| x[3][0] != v.x[3][0] || |
| x[3][1] != v.x[3][1] || |
| x[3][2] != v.x[3][2] || |
| x[3][3] != v.x[3][3]; |
| } |
| |
| template <class T> |
| bool |
| Matrix44<T>::equalWithAbsError (const Matrix44<T> &m, T e) const |
| { |
| for (int i = 0; i < 4; i++) |
| for (int j = 0; j < 4; j++) |
| if (!Imath::equalWithAbsError ((*this)[i][j], m[i][j], e)) |
| return false; |
| |
| return true; |
| } |
| |
| template <class T> |
| bool |
| Matrix44<T>::equalWithRelError (const Matrix44<T> &m, T e) const |
| { |
| for (int i = 0; i < 4; i++) |
| for (int j = 0; j < 4; j++) |
| if (!Imath::equalWithRelError ((*this)[i][j], m[i][j], e)) |
| return false; |
| |
| return true; |
| } |
| |
| template <class T> |
| const Matrix44<T> & |
| Matrix44<T>::operator += (const Matrix44<T> &v) |
| { |
| x[0][0] += v.x[0][0]; |
| x[0][1] += v.x[0][1]; |
| x[0][2] += v.x[0][2]; |
| x[0][3] += v.x[0][3]; |
| x[1][0] += v.x[1][0]; |
| x[1][1] += v.x[1][1]; |
| x[1][2] += v.x[1][2]; |
| x[1][3] += v.x[1][3]; |
| x[2][0] += v.x[2][0]; |
| x[2][1] += v.x[2][1]; |
| x[2][2] += v.x[2][2]; |
| x[2][3] += v.x[2][3]; |
| x[3][0] += v.x[3][0]; |
| x[3][1] += v.x[3][1]; |
| x[3][2] += v.x[3][2]; |
| x[3][3] += v.x[3][3]; |
| |
| return *this; |
| } |
| |
| template <class T> |
| const Matrix44<T> & |
| Matrix44<T>::operator += (T a) |
| { |
| x[0][0] += a; |
| x[0][1] += a; |
| x[0][2] += a; |
| x[0][3] += a; |
| x[1][0] += a; |
| x[1][1] += a; |
| x[1][2] += a; |
| x[1][3] += a; |
| x[2][0] += a; |
| x[2][1] += a; |
| x[2][2] += a; |
| x[2][3] += a; |
| x[3][0] += a; |
| x[3][1] += a; |
| x[3][2] += a; |
| x[3][3] += a; |
| |
| return *this; |
| } |
| |
| template <class T> |
| Matrix44<T> |
| Matrix44<T>::operator + (const Matrix44<T> &v) const |
| { |
| return Matrix44 (x[0][0] + v.x[0][0], |
| x[0][1] + v.x[0][1], |
| x[0][2] + v.x[0][2], |
| x[0][3] + v.x[0][3], |
| x[1][0] + v.x[1][0], |
| x[1][1] + v.x[1][1], |
| x[1][2] + v.x[1][2], |
| x[1][3] + v.x[1][3], |
| x[2][0] + v.x[2][0], |
| x[2][1] + v.x[2][1], |
| x[2][2] + v.x[2][2], |
| x[2][3] + v.x[2][3], |
| x[3][0] + v.x[3][0], |
| x[3][1] + v.x[3][1], |
| x[3][2] + v.x[3][2], |
| x[3][3] + v.x[3][3]); |
| } |
| |
| template <class T> |
| const Matrix44<T> & |
| Matrix44<T>::operator -= (const Matrix44<T> &v) |
| { |
| x[0][0] -= v.x[0][0]; |
| x[0][1] -= v.x[0][1]; |
| x[0][2] -= v.x[0][2]; |
| x[0][3] -= v.x[0][3]; |
| x[1][0] -= v.x[1][0]; |
| x[1][1] -= v.x[1][1]; |
| x[1][2] -= v.x[1][2]; |
| x[1][3] -= v.x[1][3]; |
| x[2][0] -= v.x[2][0]; |
| x[2][1] -= v.x[2][1]; |
| x[2][2] -= v.x[2][2]; |
| x[2][3] -= v.x[2][3]; |
| x[3][0] -= v.x[3][0]; |
| x[3][1] -= v.x[3][1]; |
| x[3][2] -= v.x[3][2]; |
| x[3][3] -= v.x[3][3]; |
| |
| return *this; |
| } |
| |
| template <class T> |
| const Matrix44<T> & |
| Matrix44<T>::operator -= (T a) |
| { |
| x[0][0] -= a; |
| x[0][1] -= a; |
| x[0][2] -= a; |
| x[0][3] -= a; |
| x[1][0] -= a; |
| x[1][1] -= a; |
| x[1][2] -= a; |
| x[1][3] -= a; |
| x[2][0] -= a; |
| x[2][1] -= a; |
| x[2][2] -= a; |
| x[2][3] -= a; |
| x[3][0] -= a; |
| x[3][1] -= a; |
| x[3][2] -= a; |
| x[3][3] -= a; |
| |
| return *this; |
| } |
| |
| template <class T> |
| Matrix44<T> |
| Matrix44<T>::operator - (const Matrix44<T> &v) const |
| { |
| return Matrix44 (x[0][0] - v.x[0][0], |
| x[0][1] - v.x[0][1], |
| x[0][2] - v.x[0][2], |
| x[0][3] - v.x[0][3], |
| x[1][0] - v.x[1][0], |
| x[1][1] - v.x[1][1], |
| x[1][2] - v.x[1][2], |
| x[1][3] - v.x[1][3], |
| x[2][0] - v.x[2][0], |
| x[2][1] - v.x[2][1], |
| x[2][2] - v.x[2][2], |
| x[2][3] - v.x[2][3], |
| x[3][0] - v.x[3][0], |
| x[3][1] - v.x[3][1], |
| x[3][2] - v.x[3][2], |
| x[3][3] - v.x[3][3]); |
| } |
| |
| template <class T> |
| Matrix44<T> |
| Matrix44<T>::operator - () const |
| { |
| return Matrix44 (-x[0][0], |
| -x[0][1], |
| -x[0][2], |
| -x[0][3], |
| -x[1][0], |
| -x[1][1], |
| -x[1][2], |
| -x[1][3], |
| -x[2][0], |
| -x[2][1], |
| -x[2][2], |
| -x[2][3], |
| -x[3][0], |
| -x[3][1], |
| -x[3][2], |
| -x[3][3]); |
| } |
| |
| template <class T> |
| const Matrix44<T> & |
| Matrix44<T>::negate () |
| { |
| x[0][0] = -x[0][0]; |
| x[0][1] = -x[0][1]; |
| x[0][2] = -x[0][2]; |
| x[0][3] = -x[0][3]; |
| x[1][0] = -x[1][0]; |
| x[1][1] = -x[1][1]; |
| x[1][2] = -x[1][2]; |
| x[1][3] = -x[1][3]; |
| x[2][0] = -x[2][0]; |
| x[2][1] = -x[2][1]; |
| x[2][2] = -x[2][2]; |
| x[2][3] = -x[2][3]; |
| x[3][0] = -x[3][0]; |
| x[3][1] = -x[3][1]; |
| x[3][2] = -x[3][2]; |
| x[3][3] = -x[3][3]; |
| |
| return *this; |
| } |
| |
| template <class T> |
| const Matrix44<T> & |
| Matrix44<T>::operator *= (T a) |
| { |
| x[0][0] *= a; |
| x[0][1] *= a; |
| x[0][2] *= a; |
| x[0][3] *= a; |
| x[1][0] *= a; |
| x[1][1] *= a; |
| x[1][2] *= a; |
| x[1][3] *= a; |
| x[2][0] *= a; |
| x[2][1] *= a; |
| x[2][2] *= a; |
| x[2][3] *= a; |
| x[3][0] *= a; |
| x[3][1] *= a; |
| x[3][2] *= a; |
| x[3][3] *= a; |
| |
| return *this; |
| } |
| |
| template <class T> |
| Matrix44<T> |
| Matrix44<T>::operator * (T a) const |
| { |
| return Matrix44 (x[0][0] * a, |
| x[0][1] * a, |
| x[0][2] * a, |
| x[0][3] * a, |
| x[1][0] * a, |
| x[1][1] * a, |
| x[1][2] * a, |
| x[1][3] * a, |
| x[2][0] * a, |
| x[2][1] * a, |
| x[2][2] * a, |
| x[2][3] * a, |
| x[3][0] * a, |
| x[3][1] * a, |
| x[3][2] * a, |
| x[3][3] * a); |
| } |
| |
| template <class T> |
| inline Matrix44<T> |
| operator * (T a, const Matrix44<T> &v) |
| { |
| return v * a; |
| } |
| |
| template <class T> |
| inline const Matrix44<T> & |
| Matrix44<T>::operator *= (const Matrix44<T> &v) |
| { |
| Matrix44 tmp (T (0)); |
| |
| multiply (*this, v, tmp); |
| *this = tmp; |
| return *this; |
| } |
| |
| template <class T> |
| inline Matrix44<T> |
| Matrix44<T>::operator * (const Matrix44<T> &v) const |
| { |
| Matrix44 tmp (T (0)); |
| |
| multiply (*this, v, tmp); |
| return tmp; |
| } |
| |
| template <class T> |
| void |
| Matrix44<T>::multiply (const Matrix44<T> &a, |
| const Matrix44<T> &b, |
| Matrix44<T> &c) |
| { |
| register const T * restrict ap = &a.x[0][0]; |
| register const T * restrict bp = &b.x[0][0]; |
| register T * restrict cp = &c.x[0][0]; |
| |
| register T a0, a1, a2, a3; |
| |
| a0 = ap[0]; |
| a1 = ap[1]; |
| a2 = ap[2]; |
| a3 = ap[3]; |
| |
| cp[0] = a0 * bp[0] + a1 * bp[4] + a2 * bp[8] + a3 * bp[12]; |
| cp[1] = a0 * bp[1] + a1 * bp[5] + a2 * bp[9] + a3 * bp[13]; |
| cp[2] = a0 * bp[2] + a1 * bp[6] + a2 * bp[10] + a3 * bp[14]; |
| cp[3] = a0 * bp[3] + a1 * bp[7] + a2 * bp[11] + a3 * bp[15]; |
| |
| a0 = ap[4]; |
| a1 = ap[5]; |
| a2 = ap[6]; |
| a3 = ap[7]; |
| |
| cp[4] = a0 * bp[0] + a1 * bp[4] + a2 * bp[8] + a3 * bp[12]; |
| cp[5] = a0 * bp[1] + a1 * bp[5] + a2 * bp[9] + a3 * bp[13]; |
| cp[6] = a0 * bp[2] + a1 * bp[6] + a2 * bp[10] + a3 * bp[14]; |
| cp[7] = a0 * bp[3] + a1 * bp[7] + a2 * bp[11] + a3 * bp[15]; |
| |
| a0 = ap[8]; |
| a1 = ap[9]; |
| a2 = ap[10]; |
| a3 = ap[11]; |
| |
| cp[8] = a0 * bp[0] + a1 * bp[4] + a2 * bp[8] + a3 * bp[12]; |
| cp[9] = a0 * bp[1] + a1 * bp[5] + a2 * bp[9] + a3 * bp[13]; |
| cp[10] = a0 * bp[2] + a1 * bp[6] + a2 * bp[10] + a3 * bp[14]; |
| cp[11] = a0 * bp[3] + a1 * bp[7] + a2 * bp[11] + a3 * bp[15]; |
| |
| a0 = ap[12]; |
| a1 = ap[13]; |
| a2 = ap[14]; |
| a3 = ap[15]; |
| |
| cp[12] = a0 * bp[0] + a1 * bp[4] + a2 * bp[8] + a3 * bp[12]; |
| cp[13] = a0 * bp[1] + a1 * bp[5] + a2 * bp[9] + a3 * bp[13]; |
| cp[14] = a0 * bp[2] + a1 * bp[6] + a2 * bp[10] + a3 * bp[14]; |
| cp[15] = a0 * bp[3] + a1 * bp[7] + a2 * bp[11] + a3 * bp[15]; |
| } |
| |
| template <class T> template <class S> |
| void |
| Matrix44<T>::multVecMatrix(const Vec3<S> &src, Vec3<S> &dst) const |
| { |
| S a, b, c, w; |
| |
| a = src[0] * x[0][0] + src[1] * x[1][0] + src[2] * x[2][0] + x[3][0]; |
| b = src[0] * x[0][1] + src[1] * x[1][1] + src[2] * x[2][1] + x[3][1]; |
| c = src[0] * x[0][2] + src[1] * x[1][2] + src[2] * x[2][2] + x[3][2]; |
| w = src[0] * x[0][3] + src[1] * x[1][3] + src[2] * x[2][3] + x[3][3]; |
| |
| dst.x = a / w; |
| dst.y = b / w; |
| dst.z = c / w; |
| } |
| |
| template <class T> template <class S> |
| void |
| Matrix44<T>::multDirMatrix(const Vec3<S> &src, Vec3<S> &dst) const |
| { |
| S a, b, c; |
| |
| a = src[0] * x[0][0] + src[1] * x[1][0] + src[2] * x[2][0]; |
| b = src[0] * x[0][1] + src[1] * x[1][1] + src[2] * x[2][1]; |
| c = src[0] * x[0][2] + src[1] * x[1][2] + src[2] * x[2][2]; |
| |
| dst.x = a; |
| dst.y = b; |
| dst.z = c; |
| } |
| |
| template <class T> |
| const Matrix44<T> & |
| Matrix44<T>::operator /= (T a) |
| { |
| x[0][0] /= a; |
| x[0][1] /= a; |
| x[0][2] /= a; |
| x[0][3] /= a; |
| x[1][0] /= a; |
| x[1][1] /= a; |
| x[1][2] /= a; |
| x[1][3] /= a; |
| x[2][0] /= a; |
| x[2][1] /= a; |
| x[2][2] /= a; |
| x[2][3] /= a; |
| x[3][0] /= a; |
| x[3][1] /= a; |
| x[3][2] /= a; |
| x[3][3] /= a; |
| |
| return *this; |
| } |
| |
| template <class T> |
| Matrix44<T> |
| Matrix44<T>::operator / (T a) const |
| { |
| return Matrix44 (x[0][0] / a, |
| x[0][1] / a, |
| x[0][2] / a, |
| x[0][3] / a, |
| x[1][0] / a, |
| x[1][1] / a, |
| x[1][2] / a, |
| x[1][3] / a, |
| x[2][0] / a, |
| x[2][1] / a, |
| x[2][2] / a, |
| x[2][3] / a, |
| x[3][0] / a, |
| x[3][1] / a, |
| x[3][2] / a, |
| x[3][3] / a); |
| } |
| |
| template <class T> |
| const Matrix44<T> & |
| Matrix44<T>::transpose () |
| { |
| Matrix44 tmp (x[0][0], |
| x[1][0], |
| x[2][0], |
| x[3][0], |
| x[0][1], |
| x[1][1], |
| x[2][1], |
| x[3][1], |
| x[0][2], |
| x[1][2], |
| x[2][2], |
| x[3][2], |
| x[0][3], |
| x[1][3], |
| x[2][3], |
| x[3][3]); |
| *this = tmp; |
| return *this; |
| } |
| |
| template <class T> |
| Matrix44<T> |
| Matrix44<T>::transposed () const |
| { |
| return Matrix44 (x[0][0], |
| x[1][0], |
| x[2][0], |
| x[3][0], |
| x[0][1], |
| x[1][1], |
| x[2][1], |
| x[3][1], |
| x[0][2], |
| x[1][2], |
| x[2][2], |
| x[3][2], |
| x[0][3], |
| x[1][3], |
| x[2][3], |
| x[3][3]); |
| } |
| |
| template <class T> |
| const Matrix44<T> & |
| Matrix44<T>::gjInvert (bool singExc) throw (Iex::MathExc) |
| { |
| *this = gjInverse (singExc); |
| return *this; |
| } |
| |
| template <class T> |
| Matrix44<T> |
| Matrix44<T>::gjInverse (bool singExc) const throw (Iex::MathExc) |
| { |
| int i, j, k; |
| Matrix44 s; |
| Matrix44 t (*this); |
| |
| // Forward elimination |
| |
| for (i = 0; i < 3 ; i++) |
| { |
| int pivot = i; |
| |
| T pivotsize = t[i][i]; |
| |
| if (pivotsize < 0) |
| pivotsize = -pivotsize; |
| |
| for (j = i + 1; j < 4; j++) |
| { |
| T tmp = t[j][i]; |
| |
| if (tmp < 0) |
| tmp = -tmp; |
| |
| if (tmp > pivotsize) |
| { |
| pivot = j; |
| pivotsize = tmp; |
| } |
| } |
| |
| if (pivotsize == 0) |
| { |
| if (singExc) |
| throw ::Imath::SingMatrixExc ("Cannot invert singular matrix."); |
| |
| return Matrix44(); |
| } |
| |
| if (pivot != i) |
| { |
| for (j = 0; j < 4; j++) |
| { |
| T tmp; |
| |
| tmp = t[i][j]; |
| t[i][j] = t[pivot][j]; |
| t[pivot][j] = tmp; |
| |
| tmp = s[i][j]; |
| s[i][j] = s[pivot][j]; |
| s[pivot][j] = tmp; |
| } |
| } |
| |
| for (j = i + 1; j < 4; j++) |
| { |
| T f = t[j][i] / t[i][i]; |
| |
| for (k = 0; k < 4; k++) |
| { |
| t[j][k] -= f * t[i][k]; |
| s[j][k] -= f * s[i][k]; |
| } |
| } |
| } |
| |
| // Backward substitution |
| |
| for (i = 3; i >= 0; --i) |
| { |
| T f; |
| |
| if ((f = t[i][i]) == 0) |
| { |
| if (singExc) |
| throw ::Imath::SingMatrixExc ("Cannot invert singular matrix."); |
| |
| return Matrix44(); |
| } |
| |
| for (j = 0; j < 4; j++) |
| { |
| t[i][j] /= f; |
| s[i][j] /= f; |
| } |
| |
| for (j = 0; j < i; j++) |
| { |
| f = t[j][i]; |
| |
| for (k = 0; k < 4; k++) |
| { |
| t[j][k] -= f * t[i][k]; |
| s[j][k] -= f * s[i][k]; |
| } |
| } |
| } |
| |
| return s; |
| } |
| |
| template <class T> |
| const Matrix44<T> & |
| Matrix44<T>::invert (bool singExc) throw (Iex::MathExc) |
| { |
| *this = inverse (singExc); |
| return *this; |
| } |
| |
| template <class T> |
| Matrix44<T> |
| Matrix44<T>::inverse (bool singExc) const throw (Iex::MathExc) |
| { |
| if (x[0][3] != 0 || x[1][3] != 0 || x[2][3] != 0 || x[3][3] != 1) |
| return gjInverse(singExc); |
| |
| Matrix44 s (x[1][1] * x[2][2] - x[2][1] * x[1][2], |
| x[2][1] * x[0][2] - x[0][1] * x[2][2], |
| x[0][1] * x[1][2] - x[1][1] * x[0][2], |
| 0, |
| |
| x[2][0] * x[1][2] - x[1][0] * x[2][2], |
| x[0][0] * x[2][2] - x[2][0] * x[0][2], |
| x[1][0] * x[0][2] - x[0][0] * x[1][2], |
| 0, |
| |
| x[1][0] * x[2][1] - x[2][0] * x[1][1], |
| x[2][0] * x[0][1] - x[0][0] * x[2][1], |
| x[0][0] * x[1][1] - x[1][0] * x[0][1], |
| 0, |
| |
| 0, |
| 0, |
| 0, |
| 1); |
| |
| T r = x[0][0] * s[0][0] + x[0][1] * s[1][0] + x[0][2] * s[2][0]; |
| |
| if (Imath::abs (r) >= 1) |
| { |
| for (int i = 0; i < 3; ++i) |
| { |
| for (int j = 0; j < 3; ++j) |
| { |
| s[i][j] /= r; |
| } |
| } |
| } |
| else |
| { |
| T mr = Imath::abs (r) / limits<T>::smallest(); |
| |
| for (int i = 0; i < 3; ++i) |
| { |
| for (int j = 0; j < 3; ++j) |
| { |
| if (mr > Imath::abs (s[i][j])) |
| { |
| s[i][j] /= r; |
| } |
| else |
| { |
| if (singExc) |
| throw SingMatrixExc ("Cannot invert singular matrix."); |
| |
| return Matrix44(); |
| } |
| } |
| } |
| } |
| |
| s[3][0] = -x[3][0] * s[0][0] - x[3][1] * s[1][0] - x[3][2] * s[2][0]; |
| s[3][1] = -x[3][0] * s[0][1] - x[3][1] * s[1][1] - x[3][2] * s[2][1]; |
| s[3][2] = -x[3][0] * s[0][2] - x[3][1] * s[1][2] - x[3][2] * s[2][2]; |
| |
| return s; |
| } |
| |
| template <class T> |
| template <class S> |
| const Matrix44<T> & |
| Matrix44<T>::setEulerAngles (const Vec3<S>& r) |
| { |
| S cos_rz, sin_rz, cos_ry, sin_ry, cos_rx, sin_rx; |
| |
| cos_rz = Math<T>::cos (r[2]); |
| cos_ry = Math<T>::cos (r[1]); |
| cos_rx = Math<T>::cos (r[0]); |
| |
| sin_rz = Math<T>::sin (r[2]); |
| sin_ry = Math<T>::sin (r[1]); |
| sin_rx = Math<T>::sin (r[0]); |
| |
| x[0][0] = cos_rz * cos_ry; |
| x[0][1] = sin_rz * cos_ry; |
| x[0][2] = -sin_ry; |
| x[0][3] = 0; |
| |
| x[1][0] = -sin_rz * cos_rx + cos_rz * sin_ry * sin_rx; |
| x[1][1] = cos_rz * cos_rx + sin_rz * sin_ry * sin_rx; |
| x[1][2] = cos_ry * sin_rx; |
| x[1][3] = 0; |
| |
| x[2][0] = sin_rz * sin_rx + cos_rz * sin_ry * cos_rx; |
| x[2][1] = -cos_rz * sin_rx + sin_rz * sin_ry * cos_rx; |
| x[2][2] = cos_ry * cos_rx; |
| x[2][3] = 0; |
| |
| x[3][0] = 0; |
| x[3][1] = 0; |
| x[3][2] = 0; |
| x[3][3] = 1; |
| |
| return *this; |
| } |
| |
| template <class T> |
| template <class S> |
| const Matrix44<T> & |
| Matrix44<T>::setAxisAngle (const Vec3<S>& axis, S angle) |
| { |
| Vec3<S> unit (axis.normalized()); |
| S sine = Math<T>::sin (angle); |
| S cosine = Math<T>::cos (angle); |
| |
| x[0][0] = unit[0] * unit[0] * (1 - cosine) + cosine; |
| x[0][1] = unit[0] * unit[1] * (1 - cosine) + unit[2] * sine; |
| x[0][2] = unit[0] * unit[2] * (1 - cosine) - unit[1] * sine; |
| x[0][3] = 0; |
| |
| x[1][0] = unit[0] * unit[1] * (1 - cosine) - unit[2] * sine; |
| x[1][1] = unit[1] * unit[1] * (1 - cosine) + cosine; |
| x[1][2] = unit[1] * unit[2] * (1 - cosine) + unit[0] * sine; |
| x[1][3] = 0; |
| |
| x[2][0] = unit[0] * unit[2] * (1 - cosine) + unit[1] * sine; |
| x[2][1] = unit[1] * unit[2] * (1 - cosine) - unit[0] * sine; |
| x[2][2] = unit[2] * unit[2] * (1 - cosine) + cosine; |
| x[2][3] = 0; |
| |
| x[3][0] = 0; |
| x[3][1] = 0; |
| x[3][2] = 0; |
| x[3][3] = 1; |
| |
| return *this; |
| } |
| |
| template <class T> |
| template <class S> |
| const Matrix44<T> & |
| Matrix44<T>::rotate (const Vec3<S> &r) |
| { |
| S cos_rz, sin_rz, cos_ry, sin_ry, cos_rx, sin_rx; |
| S m00, m01, m02; |
| S m10, m11, m12; |
| S m20, m21, m22; |
| |
| cos_rz = Math<S>::cos (r[2]); |
| cos_ry = Math<S>::cos (r[1]); |
| cos_rx = Math<S>::cos (r[0]); |
| |
| sin_rz = Math<S>::sin (r[2]); |
| sin_ry = Math<S>::sin (r[1]); |
| sin_rx = Math<S>::sin (r[0]); |
| |
| m00 = cos_rz * cos_ry; |
| m01 = sin_rz * cos_ry; |
| m02 = -sin_ry; |
| m10 = -sin_rz * cos_rx + cos_rz * sin_ry * sin_rx; |
| m11 = cos_rz * cos_rx + sin_rz * sin_ry * sin_rx; |
| m12 = cos_ry * sin_rx; |
| m20 = -sin_rz * -sin_rx + cos_rz * sin_ry * cos_rx; |
| m21 = cos_rz * -sin_rx + sin_rz * sin_ry * cos_rx; |
| m22 = cos_ry * cos_rx; |
| |
| Matrix44<T> P (*this); |
| |
| x[0][0] = P[0][0] * m00 + P[1][0] * m01 + P[2][0] * m02; |
| x[0][1] = P[0][1] * m00 + P[1][1] * m01 + P[2][1] * m02; |
| x[0][2] = P[0][2] * m00 + P[1][2] * m01 + P[2][2] * m02; |
| x[0][3] = P[0][3] * m00 + P[1][3] * m01 + P[2][3] * m02; |
| |
| x[1][0] = P[0][0] * m10 + P[1][0] * m11 + P[2][0] * m12; |
| x[1][1] = P[0][1] * m10 + P[1][1] * m11 + P[2][1] * m12; |
| x[1][2] = P[0][2] * m10 + P[1][2] * m11 + P[2][2] * m12; |
| x[1][3] = P[0][3] * m10 + P[1][3] * m11 + P[2][3] * m12; |
| |
| x[2][0] = P[0][0] * m20 + P[1][0] * m21 + P[2][0] * m22; |
| x[2][1] = P[0][1] * m20 + P[1][1] * m21 + P[2][1] * m22; |
| x[2][2] = P[0][2] * m20 + P[1][2] * m21 + P[2][2] * m22; |
| x[2][3] = P[0][3] * m20 + P[1][3] * m21 + P[2][3] * m22; |
| |
| return *this; |
| } |
| |
| template <class T> |
| const Matrix44<T> & |
| Matrix44<T>::setScale (T s) |
| { |
| x[0][0] = s; |
| x[0][1] = 0; |
| x[0][2] = 0; |
| x[0][3] = 0; |
| |
| x[1][0] = 0; |
| x[1][1] = s; |
| x[1][2] = 0; |
| x[1][3] = 0; |
| |
| x[2][0] = 0; |
| x[2][1] = 0; |
| x[2][2] = s; |
| x[2][3] = 0; |
| |
| x[3][0] = 0; |
| x[3][1] = 0; |
| x[3][2] = 0; |
| x[3][3] = 1; |
| |
| return *this; |
| } |
| |
| template <class T> |
| template <class S> |
| const Matrix44<T> & |
| Matrix44<T>::setScale (const Vec3<S> &s) |
| { |
| x[0][0] = s[0]; |
| x[0][1] = 0; |
| x[0][2] = 0; |
| x[0][3] = 0; |
| |
| x[1][0] = 0; |
| x[1][1] = s[1]; |
| x[1][2] = 0; |
| x[1][3] = 0; |
| |
| x[2][0] = 0; |
| x[2][1] = 0; |
| x[2][2] = s[2]; |
| x[2][3] = 0; |
| |
| x[3][0] = 0; |
| x[3][1] = 0; |
| x[3][2] = 0; |
| x[3][3] = 1; |
| |
| return *this; |
| } |
| |
| template <class T> |
| template <class S> |
| const Matrix44<T> & |
| Matrix44<T>::scale (const Vec3<S> &s) |
| { |
| x[0][0] *= s[0]; |
| x[0][1] *= s[0]; |
| x[0][2] *= s[0]; |
| x[0][3] *= s[0]; |
| |
| x[1][0] *= s[1]; |
| x[1][1] *= s[1]; |
| x[1][2] *= s[1]; |
| x[1][3] *= s[1]; |
| |
| x[2][0] *= s[2]; |
| x[2][1] *= s[2]; |
| x[2][2] *= s[2]; |
| x[2][3] *= s[2]; |
| |
| return *this; |
| } |
| |
| template <class T> |
| template <class S> |
| const Matrix44<T> & |
| Matrix44<T>::setTranslation (const Vec3<S> &t) |
| { |
| x[0][0] = 1; |
| x[0][1] = 0; |
| x[0][2] = 0; |
| x[0][3] = 0; |
| |
| x[1][0] = 0; |
| x[1][1] = 1; |
| x[1][2] = 0; |
| x[1][3] = 0; |
| |
| x[2][0] = 0; |
| x[2][1] = 0; |
| x[2][2] = 1; |
| x[2][3] = 0; |
| |
| x[3][0] = t[0]; |
| x[3][1] = t[1]; |
| x[3][2] = t[2]; |
| x[3][3] = 1; |
| |
| return *this; |
| } |
| |
| template <class T> |
| inline const Vec3<T> |
| Matrix44<T>::translation () const |
| { |
| return Vec3<T> (x[3][0], x[3][1], x[3][2]); |
| } |
| |
| template <class T> |
| template <class S> |
| const Matrix44<T> & |
| Matrix44<T>::translate (const Vec3<S> &t) |
| { |
| x[3][0] += t[0] * x[0][0] + t[1] * x[1][0] + t[2] * x[2][0]; |
| x[3][1] += t[0] * x[0][1] + t[1] * x[1][1] + t[2] * x[2][1]; |
| x[3][2] += t[0] * x[0][2] + t[1] * x[1][2] + t[2] * x[2][2]; |
| x[3][3] += t[0] * x[0][3] + t[1] * x[1][3] + t[2] * x[2][3]; |
| |
| return *this; |
| } |
| |
| template <class T> |
| template <class S> |
| const Matrix44<T> & |
| Matrix44<T>::setShear (const Vec3<S> &h) |
| { |
| x[0][0] = 1; |
| x[0][1] = 0; |
| x[0][2] = 0; |
| x[0][3] = 0; |
| |
| x[1][0] = h[0]; |
| x[1][1] = 1; |
| x[1][2] = 0; |
| x[1][3] = 0; |
| |
| x[2][0] = h[1]; |
| x[2][1] = h[2]; |
| x[2][2] = 1; |
| x[2][3] = 0; |
| |
| x[3][0] = 0; |
| x[3][1] = 0; |
| x[3][2] = 0; |
| x[3][3] = 1; |
| |
| return *this; |
| } |
| |
| template <class T> |
| template <class S> |
| const Matrix44<T> & |
| Matrix44<T>::setShear (const Shear6<S> &h) |
| { |
| x[0][0] = 1; |
| x[0][1] = h.yx; |
| x[0][2] = h.zx; |
| x[0][3] = 0; |
| |
| x[1][0] = h.xy; |
| x[1][1] = 1; |
| x[1][2] = h.zy; |
| x[1][3] = 0; |
| |
| x[2][0] = h.xz; |
| x[2][1] = h.yz; |
| x[2][2] = 1; |
| x[2][3] = 0; |
| |
| x[3][0] = 0; |
| x[3][1] = 0; |
| x[3][2] = 0; |
| x[3][3] = 1; |
| |
| return *this; |
| } |
| |
| template <class T> |
| template <class S> |
| const Matrix44<T> & |
| Matrix44<T>::shear (const Vec3<S> &h) |
| { |
| // |
| // In this case, we don't need a temp. copy of the matrix |
| // because we never use a value on the RHS after we've |
| // changed it on the LHS. |
| // |
| |
| for (int i=0; i < 4; i++) |
| { |
| x[2][i] += h[1] * x[0][i] + h[2] * x[1][i]; |
| x[1][i] += h[0] * x[0][i]; |
| } |
| |
| return *this; |
| } |
| |
| template <class T> |
| template <class S> |
| const Matrix44<T> & |
| Matrix44<T>::shear (const Shear6<S> &h) |
| { |
| Matrix44<T> P (*this); |
| |
| for (int i=0; i < 4; i++) |
| { |
| x[0][i] = P[0][i] + h.yx * P[1][i] + h.zx * P[2][i]; |
| x[1][i] = h.xy * P[0][i] + P[1][i] + h.zy * P[2][i]; |
| x[2][i] = h.xz * P[0][i] + h.yz * P[1][i] + P[2][i]; |
| } |
| |
| return *this; |
| } |
| |
| |
| //-------------------------------- |
| // Implementation of stream output |
| //-------------------------------- |
| |
| template <class T> |
| std::ostream & |
| operator << (std::ostream &s, const Matrix33<T> &m) |
| { |
| std::ios_base::fmtflags oldFlags = s.flags(); |
| int width; |
| |
| if (s.flags() & std::ios_base::fixed) |
| { |
| s.setf (std::ios_base::showpoint); |
| width = s.precision() + 5; |
| } |
| else |
| { |
| s.setf (std::ios_base::scientific); |
| s.setf (std::ios_base::showpoint); |
| width = s.precision() + 8; |
| } |
| |
| s << "(" << std::setw (width) << m[0][0] << |
| " " << std::setw (width) << m[0][1] << |
| " " << std::setw (width) << m[0][2] << "\n" << |
| |
| " " << std::setw (width) << m[1][0] << |
| " " << std::setw (width) << m[1][1] << |
| " " << std::setw (width) << m[1][2] << "\n" << |
| |
| " " << std::setw (width) << m[2][0] << |
| " " << std::setw (width) << m[2][1] << |
| " " << std::setw (width) << m[2][2] << ")\n"; |
| |
| s.flags (oldFlags); |
| return s; |
| } |
| |
| template <class T> |
| std::ostream & |
| operator << (std::ostream &s, const Matrix44<T> &m) |
| { |
| std::ios_base::fmtflags oldFlags = s.flags(); |
| int width; |
| |
| if (s.flags() & std::ios_base::fixed) |
| { |
| s.setf (std::ios_base::showpoint); |
| width = s.precision() + 5; |
| } |
| else |
| { |
| s.setf (std::ios_base::scientific); |
| s.setf (std::ios_base::showpoint); |
| width = s.precision() + 8; |
| } |
| |
| s << "(" << std::setw (width) << m[0][0] << |
| " " << std::setw (width) << m[0][1] << |
| " " << std::setw (width) << m[0][2] << |
| " " << std::setw (width) << m[0][3] << "\n" << |
| |
| " " << std::setw (width) << m[1][0] << |
| " " << std::setw (width) << m[1][1] << |
| " " << std::setw (width) << m[1][2] << |
| " " << std::setw (width) << m[1][3] << "\n" << |
| |
| " " << std::setw (width) << m[2][0] << |
| " " << std::setw (width) << m[2][1] << |
| " " << std::setw (width) << m[2][2] << |
| " " << std::setw (width) << m[2][3] << "\n" << |
| |
| " " << std::setw (width) << m[3][0] << |
| " " << std::setw (width) << m[3][1] << |
| " " << std::setw (width) << m[3][2] << |
| " " << std::setw (width) << m[3][3] << ")\n"; |
| |
| s.flags (oldFlags); |
| return s; |
| } |
| |
| |
| //--------------------------------------------------------------- |
| // Implementation of vector-times-matrix multiplication operators |
| //--------------------------------------------------------------- |
| |
| template <class S, class T> |
| inline const Vec2<S> & |
| operator *= (Vec2<S> &v, const Matrix33<T> &m) |
| { |
| S x = S(v.x * m[0][0] + v.y * m[1][0] + m[2][0]); |
| S y = S(v.x * m[0][1] + v.y * m[1][1] + m[2][1]); |
| S w = S(v.x * m[0][2] + v.y * m[1][2] + m[2][2]); |
| |
| v.x = x / w; |
| v.y = y / w; |
| |
| return v; |
| } |
| |
| template <class S, class T> |
| inline Vec2<S> |
| operator * (const Vec2<S> &v, const Matrix33<T> &m) |
| { |
| S x = S(v.x * m[0][0] + v.y * m[1][0] + m[2][0]); |
| S y = S(v.x * m[0][1] + v.y * m[1][1] + m[2][1]); |
| S w = S(v.x * m[0][2] + v.y * m[1][2] + m[2][2]); |
| |
| return Vec2<S> (x / w, y / w); |
| } |
| |
| |
| template <class S, class T> |
| inline const Vec3<S> & |
| operator *= (Vec3<S> &v, const Matrix33<T> &m) |
| { |
| S x = S(v.x * m[0][0] + v.y * m[1][0] + v.z * m[2][0]); |
| S y = S(v.x * m[0][1] + v.y * m[1][1] + v.z * m[2][1]); |
| S z = S(v.x * m[0][2] + v.y * m[1][2] + v.z * m[2][2]); |
| |
| v.x = x; |
| v.y = y; |
| v.z = z; |
| |
| return v; |
| } |
| |
| |
| template <class S, class T> |
| inline Vec3<S> |
| operator * (const Vec3<S> &v, const Matrix33<T> &m) |
| { |
| S x = S(v.x * m[0][0] + v.y * m[1][0] + v.z * m[2][0]); |
| S y = S(v.x * m[0][1] + v.y * m[1][1] + v.z * m[2][1]); |
| S z = S(v.x * m[0][2] + v.y * m[1][2] + v.z * m[2][2]); |
| |
| return Vec3<S> (x, y, z); |
| } |
| |
| |
| template <class S, class T> |
| inline const Vec3<S> & |
| operator *= (Vec3<S> &v, const Matrix44<T> &m) |
| { |
| S x = S(v.x * m[0][0] + v.y * m[1][0] + v.z * m[2][0] + m[3][0]); |
| S y = S(v.x * m[0][1] + v.y * m[1][1] + v.z * m[2][1] + m[3][1]); |
| S z = S(v.x * m[0][2] + v.y * m[1][2] + v.z * m[2][2] + m[3][2]); |
| S w = S(v.x * m[0][3] + v.y * m[1][3] + v.z * m[2][3] + m[3][3]); |
| |
| v.x = x / w; |
| v.y = y / w; |
| v.z = z / w; |
| |
| return v; |
| } |
| |
| template <class S, class T> |
| inline Vec3<S> |
| operator * (const Vec3<S> &v, const Matrix44<T> &m) |
| { |
| S x = S(v.x * m[0][0] + v.y * m[1][0] + v.z * m[2][0] + m[3][0]); |
| S y = S(v.x * m[0][1] + v.y * m[1][1] + v.z * m[2][1] + m[3][1]); |
| S z = S(v.x * m[0][2] + v.y * m[1][2] + v.z * m[2][2] + m[3][2]); |
| S w = S(v.x * m[0][3] + v.y * m[1][3] + v.z * m[2][3] + m[3][3]); |
| |
| return Vec3<S> (x / w, y / w, z / w); |
| } |
| |
| } // namespace Imath |
| |
| |
| |
| #endif |