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NAME

       SbDPMatrix -

       The SbDPMatrix class is a 4x4 dimensional representation of a double-precision matrix.

       This class is like the SbMatrix class, but uses double-precision floating point values for
       its elements. For more class documentation, see SbMatrix.

SYNOPSIS

       #include <Inventor/SbDPMatrix.h>

   Public Member Functions
       SbDPMatrix (void)
       SbDPMatrix (const double a11, const double a12, const double a13, const double a14, const
           double a21, const double a22, const double a23, const double a24, const double a31,
           const double a32, const double a33, const double a34, const double a41, const double
           a42, const double a43, const double a44)
       SbDPMatrix (const SbDPMat &matrix)
       SbDPMatrix (const SbDPMat *matrix)
       SbDPMatrix (const SbMatrix &matrix)
       ~SbDPMatrix (void)
       SbDPMatrix & operator= (const SbDPMat &m)
       operator double * (void)
       SbDPMatrix & operator= (const SbDPMatrix &m)
       void setValue (const SbDPMat &m)
       const SbDPMat & getValue (void) const
       void makeIdentity (void)
       void setRotate (const SbDPRotation &q)
       SbDPMatrix inverse (void) const
       double det3 (int r1, int r2, int r3, int c1, int c2, int c3) const
       double det3 (void) const
       double det4 (void) const
       SbBool equals (const SbDPMatrix &m, double tolerance) const
       operator SbDPMat & (void)
       double * operator[] (int i)
       const double * operator[] (int i) const
       SbDPMatrix & operator= (const SbDPRotation &q)
       SbDPMatrix & operator*= (const SbDPMatrix &m)
       void getValue (SbDPMat &m) const
       void setScale (const double s)
       void setScale (const SbVec3d &s)
       void setTranslate (const SbVec3d &t)
       void setTransform (const SbVec3d &t, const SbDPRotation &r, const SbVec3d &s)
       void setTransform (const SbVec3d &t, const SbDPRotation &r, const SbVec3d &s, const
           SbDPRotation &so)
       void setTransform (const SbVec3d &translation, const SbDPRotation &rotation, const SbVec3d
           &scaleFactor, const SbDPRotation &scaleOrientation, const SbVec3d &center)
       void getTransform (SbVec3d &t, SbDPRotation &r, SbVec3d &s, SbDPRotation &so) const
       void getTransform (SbVec3d &translation, SbDPRotation &rotation, SbVec3d &scaleFactor,
           SbDPRotation &scaleOrientation, const SbVec3d &center) const
       SbBool factor (SbDPMatrix &r, SbVec3d &s, SbDPMatrix &u, SbVec3d &t, SbDPMatrix &proj)
       SbBool LUDecomposition (int index[4], double &d)
       void LUBackSubstitution (int index[4], double b[4]) const
       SbDPMatrix transpose (void) const
       SbDPMatrix & multRight (const SbDPMatrix &m)
       SbDPMatrix & multLeft (const SbDPMatrix &m)
       void multMatrixVec (const SbVec3d &src, SbVec3d &dst) const
       void multVecMatrix (const SbVec3d &src, SbVec3d &dst) const
       void multDirMatrix (const SbVec3d &src, SbVec3d &dst) const
       void multLineMatrix (const SbDPLine &src, SbDPLine &dst) const
       void multVecMatrix (const SbVec4d &src, SbVec4d &dst) const
       void print (FILE *fp) const

   Static Public Member Functions
       static SbDPMatrix identity (void)

   Friends
       SbDPMatrix operator* (const SbDPMatrix &m1, const SbDPMatrix &m2)
       int operator== (const SbDPMatrix &m1, const SbDPMatrix &m2)
       int operator!= (const SbDPMatrix &m1, const SbDPMatrix &m2)

Detailed Description

       The SbDPMatrix class is a 4x4 dimensional representation of a double-precision matrix.

       This class is like the SbMatrix class, but uses double-precision floating point values for
       its elements. For more class documentation, see SbMatrix.

       Since:
           Coin 2.0.

Constructor & Destructor Documentation

   SbDPMatrix::SbDPMatrix (void) The default constructor does nothing. The matrix will be
       uninitialized.
   SbDPMatrix::SbDPMatrix (const doublea11, const doublea12, const doublea13, const doublea14,
       const doublea21, const doublea22, const doublea23, const doublea24, const doublea31, const
       doublea32, const doublea33, const doublea34, const doublea41, const doublea42, const
       doublea43, const doublea44) Constructs a matrix instance with the given initial elements.
   SbDPMatrix::SbDPMatrix (const SbDPMat &matrixref) Constructs a matrix instance with the
       initial elements from the matrix argument.
   SbDPMatrix::SbDPMatrix (const SbDPMat *matrixptr) This constructor is courtesy of the
       Microsoft Visual C++ compiler.
   SbDPMatrix::SbDPMatrix (const SbMatrix &matrixref) This constructor converts a single-
       precision matrix to a double-precision matrix.
   SbDPMatrix::~SbDPMatrix (void) Default destructor does nothing.

Member Function Documentation

   SbDPMatrix & SbDPMatrix::operator= (const SbDPMat &m) Assignment operator. Copies the elements
       from m to the matrix.
   SbDPMatrix::operator double * (void) Return pointer to the matrix' 4x4 double array.
   SbDPMatrix & SbDPMatrix::operator= (const SbDPMatrix &m) Assignment operator. Copies the
       elements from m to the matrix.
   void SbDPMatrix::setValue (const SbDPMat &m) Copies the elements from m into the matrix.
       See also:
           getValue().

   const SbDPMat & SbDPMatrix::getValue (void) const Returns a pointer to the 2 dimensional
       double array with the matrix elements.
       See also:
           setValue().

   void SbDPMatrix::makeIdentity (void) Set the matrix to be the identity matrix.
       See also:
           identity().

   void SbDPMatrix::setRotate (const SbDPRotation &q) Set matrix to be a rotation matrix with the
       given rotation.
       See also:
           setTranslate(), setScale().

   SbDPMatrix SbDPMatrix::inverse (void) const Return a new matrix which is the inverse matrix of
       this.
       The user is responsible for checking that this is a valid operation to execute, by first
       making sure that the result of SbDPMatrix::det4() is not equal to zero.

   double SbDPMatrix::det3 (intr1, intr2, intr3, intc1, intc2, intc3) const Returns the
       determinant of the 3x3 submatrix specified by the row and column indices.
   double SbDPMatrix::det3 (void) const Returns the determinant of the upper left 3x3 submatrix.
   double SbDPMatrix::det4 (void) const Returns the determinant of the matrix.
   SbBool SbDPMatrix::equals (const SbDPMatrix &m, doubletolerance) const Check if the m matrix
       is equal to this one, within the given tolerance value. The tolerance value is applied in
       the comparison on a component by component basis.
   SbDPMatrix::operator SbDPMat & (void) Return pointer to the matrix' 4x4 double array.
   double * SbDPMatrix::operator[] (inti) Returns pointer to the 4 element array representing a
       matrix row. i should be within [0, 3].
       See also:
           getValue(), setValue().

   const double * SbDPMatrix::operator[] (inti) const Returns pointer to the 4 element array
       representing a matrix row. i should be within [0, 3].
       See also:
           getValue(), setValue().

   SbDPMatrix & SbDPMatrix::operator= (const SbDPRotation &q) Set matrix to be a rotation matrix
       with the given rotation.
       See also:
           setRotate().

   SbDPMatrix & SbDPMatrix::operator*= (const SbDPMatrix &m) Right-multiply with the m matrix.
       See also:
           multRight().

   void SbDPMatrix::getValue (SbDPMat &m) const Return matrix components in the SbDPMat
       structure.
       See also:
           setValue().

   SbDPMatrix SbDPMatrix::identity (void) [static] Return the identity matrix.
       See also:
           makeIdentity().

   void SbDPMatrix::setScale (const doubles) Set matrix to be a pure scaling matrix. Scale
       factors are specified by s.
       See also:
           setRotate(), setTranslate().

   void SbDPMatrix::setScale (const SbVec3d &s) Set matrix to be a pure scaling matrix. Scale
       factors in x, y and z is specified by the s vector.
       See also:
           setRotate(), setTranslate().

   void SbDPMatrix::setTranslate (const SbVec3d &t) Make this matrix into a pure translation
       matrix (no scale or rotation components) with the given vector as the translation.
       See also:
           setRotate(), setScale().

   void SbDPMatrix::setTransform (const SbVec3d &t, const SbDPRotation &r, const SbVec3d &s) Set
       translation, rotation and scaling all at once. The resulting matrix gets calculated like
       this:
         M = S * R * T

       where S, R and T is scaling, rotation and translation matrices.

       See also:
           setTranslate(), setRotate(), setScale() and getTransform().

   void SbDPMatrix::setTransform (const SbVec3d &t, const SbDPRotation &r, const SbVec3d &s,
       const SbDPRotation &so) Set translation, rotation and scaling all at once with a specified
       scale orientation. The resulting matrix gets calculated like this:
         M = Ro-¹ * S * Ro * R * T

       where Ro is the scale orientation, and S, R and T is scaling, rotation and translation.

       See also:
           setTranslate(), setRotate(), setScale() and getTransform().

   void SbDPMatrix::setTransform (const SbVec3d &translation, const SbDPRotation &rotation, const
       SbVec3d &scaleFactor, const SbDPRotation &scaleOrientation, const SbVec3d &center) Set
       translation, rotation and scaling all at once with a specified scale orientation and
       center point. The resulting matrix gets calculated like this:
         M = -Tc * Ro-¹ * S * Ro * R * T * Tc

       where Tc is the center point, Ro the scale orientation, S, R and T is scaling, rotation
       and translation.

       See also:
           setTranslate(), setRotate(), setScale() and getTransform().

   void SbDPMatrix::getTransform (SbVec3d &t, SbDPRotation &r, SbVec3d &s, SbDPRotation &so)
       const Factor the matrix back into its translation, rotation, scale and scaleorientation
       components.
       See also:
           factor()

   void SbDPMatrix::getTransform (SbVec3d &translation, SbDPRotation &rotation, SbVec3d
       &scaleFactor, SbDPRotation &scaleOrientation, const SbVec3d &center) const Factor the
       matrix back into its translation, rotation, scaleFactor and scaleorientation components.
       Will eliminate the center variable from the matrix.
       See also:
           factor()

   SbBool SbDPMatrix::LUDecomposition (intindex[4], double &d) This function produces a permuted
       LU decomposition of the matrix. It uses the common single-row-pivoting strategy.
       FALSE is returned if the matrix is singular, which it never is, because of small
       adjustment values inserted if a singularity is found (as Open Inventor does too).

       The parity argument is always set to 1.0 or -1.0. Don't really know what it's for, so it's
       not checked for correctness.

       The index[] argument returns the permutation that was done on the matrix to LU-decompose
       it. index[i] is the row that row i was swapped with at step i in the decomposition, so
       index[] is not the actual permutation of the row indexes!

       BUGS: The function does not produce results that are numerically identical with those
       produced by Open Inventor for the same matrices, because the pivoting strategy in OI was
       never fully understood.

       See also:
           SbDPMatrix::LUBackSubstitution

   void SbDPMatrix::LUBackSubstitution (intindex[4], doubleb[4]) const This function does a solve
       on the 'Ax = b' system, given that the matrix is LU-decomposed in advance. First, a
       forward substitution is done on the lower system (Ly = b), and then a backwards
       substitution is done on the upper triangular system (Ux = y).
       The index[] argument is the one returned from SbDPMatrix::LUDecomposition(), so see that
       function for an explanation.

       The b[] argument must contain the b vector in 'Ax = b' when calling the function. After
       the function has solved the system, the b[] vector contains the x vector.

       BUGS: As is done by Open Inventor, unsolvable x values will not return NaN but 0.

   SbDPMatrix SbDPMatrix::transpose (void) const Returns the transpose of this matrix.
   SbDPMatrix & SbDPMatrix::multRight (const SbDPMatrix &m) Let this matrix be right-multiplied
       by m. Returns reference to self.
       See also:
           multLeft()

   SbDPMatrix & SbDPMatrix::multLeft (const SbDPMatrix &m) Let this matrix be left-multiplied by
       m. Returns reference to self.
       See also:
           multRight()

   void SbDPMatrix::multMatrixVec (const SbVec3d &src, SbVec3d &dst) const Multiply src vector
       with this matrix and return the result in dst. Multiplication is done with the vector on
       the right side of the expression, i.e. dst = M * src.
       See also:
           multVecMatrix(), multDirMatrix() and multLineMatrix().

   void SbDPMatrix::multVecMatrix (const SbVec3d &src, SbVec3d &dst) const Multiply src vector
       with this matrix and return the result in dst. Multiplication is done with the vector on
       the left side of the expression, i.e. dst = src * M.
       It is safe to let src and  be the same SbVec3d instance.

       See also:
           multMatrixVec(), multDirMatrix() and multLineMatrix().

   void SbDPMatrix::multDirMatrix (const SbVec3d &src, SbVec3d &dst) const Multiplies src by the
       matrix. src is assumed to be a direction vector, and the translation components of the
       matrix are therefore ignored.
       Multiplication is done with the vector on the left side of the expression, i.e. dst = src
       * M.

       See also:
           multVecMatrix(), multMatrixVec() and multLineMatrix().

   void SbDPMatrix::multLineMatrix (const SbDPLine &src, SbDPLine &dst) const Multiplies line
       point with the full matrix and multiplies the line direction with the matrix without the
       translation components.
       See also:
           multVecMatrix(), multMatrixVec() and multDirMatrix().

   void SbDPMatrix::multVecMatrix (const SbVec4d &src, SbVec4d &dst) const This is an overloaded
       member function, provided for convenience. It differs from the above function only in what
       argument(s) it accepts.
   void SbDPMatrix::print (FILE *fp) const Write out the matrix contents to the given file.

Friends And Related Function Documentation

   SbDPMatrix operator* (const SbDPMatrix &m1, const SbDPMatrix &m2) [friend] Multiplies matrix
       m1 with matrix m2 and returns the resultant matrix.
   int operator== (const SbDPMatrix &m1, const SbDPMatrix &m2) [friend] Compare matrices to see
       if they are equal. For two matrices to be equal, all their individual elements must be
       equal.
       See also:
           equals().

   int operator!= (const SbDPMatrix &m1, const SbDPMatrix &m2) [friend] Compare matrices to see
       if they are not equal. For two matrices to not be equal, it is enough that at least one of
       their elements are unequal.
       See also:
           equals().

Author

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