# SbMatrix Class Reference
[Base classes]

`#include <Inventor/SbLinear.h>`

List of all members.

## Detailed Description

The SbMatrix class is a 4x4 dimensional representation of a matrix.

SbMatrix is used by many other classes in Coin. It provides storage for a 4x4 matrix in row-major mode. Many common geometrical operations which involves matrix calculations are implemented as methods on this class.

## Public Member Functions

| SbMatrix (void)
| SbMatrix (const float a11, const float a12, const float a13, const float a14, const float a21, const float a22, const float a23, const float a24, const float a31, const float a32, const float a33, const float a34, const float a41, const float a42, const float a43, const float a44)
| SbMatrix (const SbMat &matrix)
| SbMatrix (const SbMat *matrix)
| ~SbMatrix (void)
SbMatrix & | operator= (const SbMat &m)
| operator float * (void)
SbMatrix & | operator= (const SbMatrix &m)
void | setValue (const SbMat &m)
const SbMat & | getValue (void) const
void | makeIdentity (void)
void | setRotate (const SbRotation &q)
SbMatrix | inverse (void) const
float | det3 (int r1, int r2, int r3, int c1, int c2, int c3) const
float | det3 (void) const
float | det4 (void) const
SbBool | equals (const SbMatrix &m, float tolerance) const
| operator SbMat & (void)
float * | operator[] (int i)
const float * | operator[] (int i) const
SbMatrix & | operator= (const SbRotation &q)
SbMatrix & | operator *= (const SbMatrix &m)
void | getValue (SbMat &m) const
void | setScale (const 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
SbBool | factor (SbMatrix &r, SbVec3f &s, SbMatrix &u, SbVec3f &t, SbMatrix &proj)
SbBool | LUDecomposition (int index[4], float &d)
void | LUBackSubstitution (int index[4], float b[4]) const
SbMatrix | transpose (void) 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 | multVecMatrix (const SbVec4f &src, SbVec4f &dst) const
void | print (FILE *fp) const

## Static Public Member Functions

SbMatrix | identity (void)

## Friends

SbMatrix | operator * (const SbMatrix &m1, const SbMatrix &m2)
int | operator== (const SbMatrix &m1, const SbMatrix &m2)
int | operator!= (const SbMatrix &m1, const SbMatrix &m2)

## Constructor & Destructor Documentation

SbMatrix::SbMatrix | ( | void |  | ) |

| The default constructor does nothing. The matrix will be uninitialized.

SbMatrix::SbMatrix | ( | const float | a11,
|  | const float | a12,
|  | const float | a13,
|  | const float | a14,
|  | const float | a21,
|  | const float | a22,
|  | const float | a23,
|  | const float | a24,
|  | const float | a31,
|  | const float | a32,
|  | const float | a33,
|  | const float | a34,
|  | const float | a41,
|  | const float | a42,
|  | const float | a43,
|  | const float | a44
| ) |

| Constructs a matrix instance with the given initial elements.

SbMatrix::SbMatrix | ( | const SbMat & | matrix | ) |

| Constructs a matrix instance with the initial elements from the matrix argument.

SbMatrix::SbMatrix | ( | const SbMat * | matrix | ) |

| This constructor is courtesy of the Microsoft Visual C++ compiler.

SbMatrix::~SbMatrix | ( | void |  | ) |

| Default destructor does nothing.

## Member Function Documentation

SbMatrix & SbMatrix::operator= | ( | const SbMat & | m | ) |

| Assignment operator. Copies the elements from m to the matrix.

SbMatrix::operator float * | ( | void |  | ) |

| Return pointer to the matrix' 4x4 float array.

SbMatrix & SbMatrix::operator= | ( | const SbMatrix & | m | ) |

| Assignment operator. Copies the elements from m to the matrix.

void SbMatrix::setValue | ( | const SbMat & | m | ) |

Copies the elements from m into the matrix.

See also:
  getValue().

const SbMat & SbMatrix::getValue | ( | void |  | ) | const

Returns a pointer to the 2 dimensional float array with the matrix elements.

See also:
  setValue().

void SbMatrix::makeIdentity | ( | void |  | ) |

Set the matrix to be the identity matrix.

See also:
  identity().

void SbMatrix::setRotate | ( | const SbRotation & | q | ) |

Set matrix to be a rotation matrix with the given rotation.

See also:
  setTranslate(), setScale().

SbMatrix SbMatrix::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 SbMatrix::det4() is not equal to zero.

float SbMatrix::det3 | ( | int | r1,
|  | int | r2,
|  | int | r3,
|  | int | c1,
|  | int | c2,
|  | int | c3
| ) | const

| Returns the determinant of the 3x3 submatrix specified by the row and column indices.

float SbMatrix::det3 | ( | void |  | ) | const

| Returns the determinant of the upper left 3x3 submatrix.

float SbMatrix::det4 | ( | void |  | ) | const

| Returns the determinant of the matrix.

SbBool SbMatrix::equals | ( | const SbMatrix & | m,
|  | float | tolerance
| ) | 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.

SbMatrix::operator SbMat & | ( | void |  | ) |

| Return pointer to the matrix' 4x4 float array.

float * SbMatrix::operator[] | ( | int | i | ) |

Returns pointer to the 4 element array representing a matrix row. i should be within [0, 3].

See also:
  getValue(), setValue().

const float * SbMatrix::operator[] | ( | int | i | ) | const

Returns pointer to the 4 element array representing a matrix row. i should be within [0, 3].

See also:
  getValue(), setValue().

SbMatrix & SbMatrix::operator= | ( | const SbRotation & | q | ) |

Set matrix to be a rotation matrix with the given rotation.

See also:
  setRotate().

SbMatrix & SbMatrix::operator *= | ( | const SbMatrix & | m | ) |

Right-multiply with the m matrix.

See also:
  multRight().

void SbMatrix::getValue | ( | SbMat & | m | ) | const

Return matrix components in the SbMat structure.

See also:
  setValue().

SbMatrix SbMatrix::identity | ( | void |  | ) | `[static]`

Return the identity matrix.

See also:
  makeIdentity().

void SbMatrix::setScale | ( | const float | s | ) |

Set matrix to be a pure scaling matrix. Scale factors are specified by s.

See also:
  setRotate(), setTranslate().

void SbMatrix::setScale | ( | const SbVec3f & | 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 SbMatrix::setTranslate | ( | const SbVec3f & | 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 SbMatrix::setTransform | ( | const SbVec3f & | t,
|  | const SbRotation & | r,
|  | const SbVec3f & | 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 SbMatrix::setTransform | ( | const SbVec3f & | t,
|  | const SbRotation & | r,
|  | const SbVec3f & | s,
|  | const SbRotation & | 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 SbMatrix::setTransform | ( | const SbVec3f & | translation,
|  | const SbRotation & | rotation,
|  | const SbVec3f & | scaleFactor,
|  | const SbRotation & | scaleOrientation,
|  | const SbVec3f & | 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 SbMatrix::getTransform | ( | SbVec3f & | t,
|  | SbRotation & | r,
|  | SbVec3f & | s,
|  | SbRotation & | so
| ) | const

Factor the matrix back into its translation, rotation, scale and scaleorientation components.

See also:
  factor()

void SbMatrix::getTransform | ( | SbVec3f & | translation,
|  | SbRotation & | rotation,
|  | SbVec3f & | scaleFactor,
|  | SbRotation & | scaleOrientation,
|  | const SbVec3f & | 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 SbMatrix::factor | ( | SbMatrix & | r,
|  | SbVec3f & | s,
|  | SbMatrix & | u,
|  | SbVec3f & | t,
|  | SbMatrix & | proj
| ) |

This function is not implemented in Coin.

See also:
  getTransform()

SbBool SbMatrix::LUDecomposition | ( | int | index[4],
|  | float & | 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:
  SbMatrix::LUBackSubstitution

void SbMatrix::LUBackSubstitution | ( | int | index[4],
|  | float | b[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 SbMatrix::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.

SbMatrix SbMatrix::transpose | ( | void |  | ) | const

| Returns the transpose of this matrix.

SbMatrix & SbMatrix::multRight | ( | const SbMatrix & | m | ) |

Let this matrix be right-multiplied by m. Returns reference to self.

See also:
  multLeft()

SbMatrix & SbMatrix::multLeft | ( | const SbMatrix & | m | ) |

Let this matrix be left-multiplied by m. Returns reference to self.

See also:
  multRight()

void SbMatrix::multMatrixVec | ( | const SbVec3f & | src,
|  | SbVec3f & | 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 SbMatrix::multVecMatrix | ( | const SbVec3f & | src,
|  | SbVec3f & | 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 dst be the same SbVec3f instance.

This method can be used (using the current model matrix) to transform a point from an object coordinate systems to the world coordinate system.

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

void SbMatrix::multDirMatrix | ( | const SbVec3f & | src,
|  | SbVec3f & | 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 SbMatrix::multLineMatrix | ( | const SbLine & | src,
|  | SbLine & | 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 SbMatrix::multVecMatrix | ( | const SbVec4f & | src,
|  | SbVec4f & | 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 SbMatrix::print | ( | FILE * | fp | ) | const

| Write out the matrix contents to the given file.

## Friends And Related Function Documentation

SbMatrix operator * | ( | const SbMatrix & | m1,
|  | const SbMatrix & | m2
| ) | `[friend]`

| Multiplies matrix m1 with matrix m2 and returns the resultant matrix.

int operator== | ( | const SbMatrix & | m1,
|  | const SbMatrix & | 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 SbMatrix & | m1,
|  | const SbMatrix & | 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().

The documentation for this class was generated from the following files:

- SbMatrix.h
- SbMatrix.cpp