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NAME

       SbMatrix — 4x4 matrix class

INHERITS FROM

       SbMatrix

SYNOPSIS

       #include <Inventor/SbLinear.h>

          Methods from class SbMatrix:

                         SbMatrix()
                         SbMatrix(float  a11,  float  a12, float a13, float a14, float a21, float
                              a22, float a23, float a24, float a31, float a32, float  a33,  float
                              a34, float a41, float a42, float a43, float a44)
                         SbMatrix(const SbMat &m)
     void                setValue(const SbMat &m)
     void                getValue(SbMat &m) const
     const SbMat &       getValue() const
     void                makeIdentity()
     static SbMatrix     identity()
     void                setRotate(const SbRotation &q)
     void                setScale(float s)
     void                setScale(const SbVec3f &s)
     void                setTranslate(const SbVec3f &t)
     void                setTransform(const SbVec3f &t, const SbRotation &r, const SbVec3f &s)
     void                setTransform(const  SbVec3f  &t,  const SbRotation &r, const SbVec3f &s,
                              const SbRotation &so)
     void                setTransform(const SbVec3f  &translation,  const  SbRotation  &rotation,
                              const  SbVec3f  &scaleFactor,  const  SbRotation &scaleOrientation,
                              const SbVec3f &center)
     void                getTransform(SbVec3f &t, SbRotation  &r,  SbVec3f  &s,  SbRotation  &so)
                              const
     void                getTransform(SbVec3f   &translation,   SbRotation   &rotation,   SbVec3f
                              &scaleFactor, SbRotation &scaleOrientation, const SbVec3f  &center)
                              const
     float               det3(int r1, int r2, int r3, int c1, int c2, int c3) const
     float               det3() const
     float               det4() const
     SbBool              factor(SbMatrix &r, SbVec3f &s, SbMatrix &u, SbVec3f &t, SbMatrix &proj)
                              const
     SbMatrix            inverse() const
     SbBool              LUDecomposition(int index[4], float &d)
     void                LUBackSubstitution(int index[4], float b[4]) const
     SbMatrix            transpose() const
     SbMatrix &          multRight(const SbMatrix &m)
     SbMatrix &          multLeft(const SbMatrix &m)
     void                multMatrixVec(const SbVec3f &src, SbVec3f &dst) const
     void                multVecMatrix(const SbVec3f &src, SbVec3f &dst) const
     void                multDirMatrix(const SbVec3f &src, SbVec3f &dst) const
     void                multLineMatrix(const SbLine &src, SbLine &dst) const
     void                print(FILE *fp) const
     float *             operator float*()
     SbMat               operator SbMat&()
     float *             operator [](int i)
     const float *       operator [](int i) const
     SbMatrix &          operator =(const SbMat &m)
     SbMatrix &          operator =(const SbMatrix &m)
     SbMatrix &          operator =(const SbRotation &q)
     SbMatrix &          operator *=(const SbMatrix &m)
     SbMatrix            operator *(const SbMatrix &m1, const SbMatrix &m2)
     int                 operator ==(const SbMatrix &m1, const SbMatrix &m2)
     int                 operator !=(const SbMatrix &m1, const SbMatrix &m2)
     SbBool              equals(const SbMatrix &m, float tolerance) const

DESCRIPTION

       4x4 matrix class/datatype used by many Inventor node and action classes. The matrices  are
       stored in row-major order.

METHODS

                         SbMatrix()
                         SbMatrix(float  a11,  float  a12, float a13, float a14, float a21, float
                              a22, float a23, float a24, float a31, float a32, float  a33,  float
                              a34, float a41, float a42, float a43, float a44)
                         SbMatrix(const SbMat &m)
          Constructors.

     void                setValue(const SbMat &m)
          Sets value from 4x4 array of elements.

     void                getValue(SbMat &m) const
     const SbMat &       getValue() const
          Returns 4x4 array of elements.

     void                makeIdentity()
          Sets matrix to be identity.

     static SbMatrix     identity()
          Returns an identity matrix.

     void                setRotate(const SbRotation &q)
          Sets matrix to rotate by given rotation.

     void                setScale(float s)
          Sets matrix to scale by given uniform factor.

     void                setScale(const SbVec3f &s)
          Sets matrix to scale by given vector.

     void                setTranslate(const SbVec3f &t)
          Sets matrix to translate by given vector.

     void                setTransform(const SbVec3f &t, const SbRotation &r, const SbVec3f &s)
     void                setTransform(const  SbVec3f  &t,  const SbRotation &r, const SbVec3f &s,
                              const SbRotation &so)
     void                setTransform(const SbVec3f  &translation,  const  SbRotation  &rotation,
                              const  SbVec3f  &scaleFactor,  const  SbRotation &scaleOrientation,
                              const SbVec3f &center)
          Composes the matrix based on a translation, rotation, scale, orientation for scale, and
          center.  The  center is the center point for scaling and rotation. The scaleOrientation
          chooses the primary axes for the scale.

     void                getTransform(SbVec3f &t, SbRotation  &r,  SbVec3f  &s,  SbRotation  &so)
                              const
          Return translation, rotation, scale, and scale orientation components of the matrix.

     void                getTransform(SbVec3f   &translation,   SbRotation   &rotation,   SbVec3f
                              &scaleFactor, SbRotation &scaleOrientation, const SbVec3f  &center)
                              const
          Decomposes  the  matrix into a translation, rotation, scale, and scale orientation. Any
          projection information is discarded. The decomposition depends upon  choice  of  center
          point  for  rotation and scaling, which is optional as the last parameter. Note that if
          the center is 0, decompose() is the same as factor()  where  t  is  translation,  u  is
          rotation, s is scaleFactor, and r is ScaleOrientation.

     float               det3(int r1, int r2, int r3, int c1, int c2, int c3) const
          Returns  determinant of 3x3 submatrix composed of given row and column indices (0-3 for
          each).

     float               det3() const
          Returns determinant of upper-left 3x3 submatrix.

     float               det4() const
          Returns determinant of entire matrix.

     SbBool              factor(SbMatrix &r, SbVec3f &s, SbMatrix &u, SbVec3f &t, SbMatrix &proj)
                              const
          Factors  a matrix m into 5 pieces: m = r s r^ u t, where r^ means transpose of r, and r
          and u are rotations, s is a scale, and t is a translation. Any  projection  information
          is returned in proj. NOTE: the projection matrix is always set to identity.

     SbMatrix            inverse() const
          Returns  inverse  of  matrix.  Results  are  undefined  for  singular matrices. Uses LU
          decomposition.

     SbBool              LUDecomposition(int index[4], float &d)
          Perform in-place LU decomposition of matrix. index is index of rows in matrix. d is the
          parity of row swaps. Returns FALSE if singular.

     void                LUBackSubstitution(int index[4], float b[4]) const
          Perform  back-substitution  on  LU-decomposed matrix. Index is permutation of rows from
          original matrix.

     SbMatrix            transpose() const
          Returns transpose of matrix.

     SbMatrix &          multRight(const SbMatrix &m)
     SbMatrix &          multLeft(const SbMatrix &m)
          Multiplies matrix by given matrix on right or left.

     void                multMatrixVec(const SbVec3f &src, SbVec3f &dst) const
          Multiplies matrix by given column vector, giving vector result.

     void                multVecMatrix(const SbVec3f &src, SbVec3f &dst) const
          Multiplies given row vector by matrix, giving vector result.

     void                multDirMatrix(const SbVec3f &src, SbVec3f &dst) const
          Multiplies given row vector by matrix, giving vector result. src is  assumed  to  be  a
          direction  vector,  so  translation  part  of  matrix  is ignored. Note: if you wish to
          transform surface points and normals by a matrix, call multVecMatrix()  for the  points
          and call multDirMatrix()  on the inverse transpose of the matrix for the normals.

     void                multLineMatrix(const SbLine &src, SbLine &dst) const
          Multiplies  the  given  line's  origin  by  the matrix, and the line's direction by the
          rotation portion of the matrix.

     void                print(FILE *fp) const
          Prints a formatted version of the matrix to the given file pointer.

     float *             operator float*()
          Cast: returns pointer to storage of first element.

     SbMat               operator SbMat&()
          Cast: returns reference to 4x4 array.

     float *             operator [](int i)
     const float *       operator [](int i) const
          Make it look like a usual matrix (so you can do m[3][2]).

     SbMatrix &          operator =(const SbMat &m)
          Sets value from 4x4 array of elements.

     SbMatrix &          operator =(const SbMatrix &m)
          Set the matrix from another SbMatrix.

     SbMatrix &          operator =(const SbRotation &q)
          Set the matrix from an SbRotation.

     SbMatrix &          operator *=(const SbMatrix &m)
          Performs right multiplication with another matrix.

     SbMatrix            operator *(const SbMatrix &m1, const SbMatrix &m2)
          Binary multiplication of matrices.

     int                 operator ==(const SbMatrix &m1, const SbMatrix &m2)
     int                 operator !=(const SbMatrix &m1, const SbMatrix &m2)
          Equality comparison operators.

     SbBool              equals(const SbMatrix &m, float tolerance) const
          Equality comparison within given tolerance, for each component.

SEE ALSO

       SbVec3f, SbRotation

                                                                                  SbMatrix(3IV)()