The QMatrix4x4 class represents a 4x4 transformation matrix in 3D space. More...

` #include <QMatrix4x4>`

This class was introduced in Qt 4.6.

QMatrix4x4 () | |

QMatrix4x4 ( const qreal * values ) | |

QMatrix4x4 ( qreal m11, qreal m12, qreal m13, qreal m14, qreal m21, qreal m22, qreal m23, qreal m24, qreal m31, qreal m32, qreal m33, qreal m34, qreal m41, qreal m42, qreal m43, qreal m44 ) | |

QMatrix4x4 ( const QGenericMatrix<N, M, qreal> & matrix ) | |

QMatrix4x4 ( const QTransform & transform ) | |

QMatrix4x4 ( const QMatrix & matrix ) | |

QVector4D | column ( int index ) const |

const qreal * | constData () const |

void | copyDataTo ( qreal * values ) const |

qreal * | data () |

const qreal * | data () const |

qreal | determinant () const |

void | fill ( qreal value ) |

void | flipCoordinates () |

void | frustum ( qreal left, qreal right, qreal bottom, qreal top, qreal nearPlane, qreal farPlane ) |

QMatrix4x4 | inverted ( bool * invertible = 0 ) const |

bool | isIdentity () const |

void | lookAt ( const QVector3D & eye, const QVector3D & center, const QVector3D & up ) |

QPoint | map ( const QPoint & point ) const |

QPointF | map ( const QPointF & point ) const |

QVector3D | map ( const QVector3D & point ) const |

QVector4D | map ( const QVector4D & point ) const |

QRect | mapRect ( const QRect & rect ) const |

QRectF | mapRect ( const QRectF & rect ) const |

QVector3D | mapVector ( const QVector3D & vector ) const |

QMatrix3x3 | normalMatrix () const |

void | optimize () |

void | ortho ( qreal left, qreal right, qreal bottom, qreal top, qreal nearPlane, qreal farPlane ) |

void | ortho ( const QRect & rect ) |

void | ortho ( const QRectF & rect ) |

void | perspective ( qreal angle, qreal aspect, qreal nearPlane, qreal farPlane ) |

void | rotate ( qreal angle, const QVector3D & vector ) |

void | rotate ( const QQuaternion & quaternion ) |

void | rotate ( qreal angle, qreal x, qreal y, qreal z = 0.0f ) |

QVector4D | row ( int index ) const |

void | scale ( const QVector3D & vector ) |

void | scale ( qreal x, qreal y ) |

void | scale ( qreal x, qreal y, qreal z ) |

void | scale ( qreal factor ) |

void | setColumn ( int index, const QVector4D & value ) |

void | setRow ( int index, const QVector4D & value ) |

void | setToIdentity () |

QMatrix | toAffine () const |

QGenericMatrix<N, M, qreal> | toGenericMatrix () const |

QTransform | toTransform () const |

QTransform | toTransform ( qreal distanceToPlane ) const |

void | translate ( const QVector3D & vector ) |

void | translate ( qreal x, qreal y ) |

void | translate ( qreal x, qreal y, qreal z ) |

QMatrix4x4 | transposed () const |

operator QVariant () const | |

bool | operator!= ( const QMatrix4x4 & other ) const |

const qreal & | operator() ( int row, int column ) const |

qreal & | operator() ( int row, int column ) |

QMatrix4x4 & | operator*= ( const QMatrix4x4 & other ) |

QMatrix4x4 & | operator*= ( qreal factor ) |

QMatrix4x4 & | operator+= ( const QMatrix4x4 & other ) |

QMatrix4x4 & | operator-= ( const QMatrix4x4 & other ) |

QMatrix4x4 & | operator/= ( qreal divisor ) |

bool | operator== ( const QMatrix4x4 & other ) const |

bool | qFuzzyCompare ( const QMatrix4x4 & m1, const QMatrix4x4 & m2 ) |

QMatrix4x4 | operator* ( const QMatrix4x4 & m1, const QMatrix4x4 & m2 ) |

QVector3D | operator* ( const QVector3D & vector, const QMatrix4x4 & matrix ) |

QVector3D | operator* ( const QMatrix4x4 & matrix, const QVector3D & vector ) |

QVector4D | operator* ( const QVector4D & vector, const QMatrix4x4 & matrix ) |

QVector4D | operator* ( const QMatrix4x4 & matrix, const QVector4D & vector ) |

QPoint | operator* ( const QPoint & point, const QMatrix4x4 & matrix ) |

QPointF | operator* ( const QPointF & point, const QMatrix4x4 & matrix ) |

QPoint | operator* ( const QMatrix4x4 & matrix, const QPoint & point ) |

QPointF | operator* ( const QMatrix4x4 & matrix, const QPointF & point ) |

QMatrix4x4 | operator* ( qreal factor, const QMatrix4x4 & matrix ) |

QMatrix4x4 | operator* ( const QMatrix4x4 & matrix, qreal factor ) |

QMatrix4x4 | operator+ ( const QMatrix4x4 & m1, const QMatrix4x4 & m2 ) |

QMatrix4x4 | operator- ( const QMatrix4x4 & m1, const QMatrix4x4 & m2 ) |

QMatrix4x4 | operator- ( const QMatrix4x4 & matrix ) |

QMatrix4x4 | operator/ ( const QMatrix4x4 & matrix, qreal divisor ) |

QDataStream & | operator<< ( QDataStream & stream, const QMatrix4x4 & matrix ) |

QDataStream & | operator>> ( QDataStream & stream, QMatrix4x4 & matrix ) |

The QMatrix4x4 class represents a 4x4 transformation matrix in 3D space.

**See also **QVector3D and QGenericMatrix.

Constructs an identity matrix.

Constructs a matrix from the given 16 floating-point *values*. The contents of the array *values* is assumed to be in row-major order.

If the matrix has a special type (identity, translate, scale, etc), the programmer should follow this constructor with a call to optimize() if they wish QMatrix4x4 to optimize further calls to translate(), scale(), etc.

**See also **copyDataTo() and optimize().

Constructs a matrix from the 16 elements *m11*, *m12*, *m13*, *m14*, *m21*, *m22*, *m23*, *m24*, *m31*, *m32*, *m33*, *m34*, *m41*, *m42*, *m43*, and *m44*. The elements are specified in row-major order.

If the matrix has a special type (identity, translate, scale, etc), the programmer should follow this constructor with a call to optimize() if they wish QMatrix4x4 to optimize further calls to translate(), scale(), etc.

**See also **optimize().

Constructs a 4x4 matrix from the left-most 4 columns and top-most 4 rows of *matrix*. If *matrix* has less than 4 columns or rows, the remaining elements are filled with elements from the identity matrix.

**See also **toGenericMatrix().

Constructs a 4x4 matrix from the conventional Qt 2D transformation matrix *transform*.

If *transform* has a special type (identity, translate, scale, etc), the programmer should follow this constructor with a call to optimize() if they wish QMatrix4x4 to optimize further calls to translate(), scale(), etc.

**See also **toTransform() and optimize().

Constructs a 4x4 matrix from a conventional Qt 2D affine transformation *matrix*.

If *matrix* has a special type (identity, translate, scale, etc), the programmer should follow this constructor with a call to optimize() if they wish QMatrix4x4 to optimize further calls to translate(), scale(), etc.

**See also **toAffine() and optimize().

Returns the elements of column *index* as a 4D vector.

**See also **setColumn() and row().

Returns a constant pointer to the raw data of this matrix.

**See also **data().

Retrieves the 16 items in this matrix and copies them to *values* in row-major order.

Returns a pointer to the raw data of this matrix.

**See also **constData() and optimize().

Returns a constant pointer to the raw data of this matrix.

**See also **constData().

Returns the determinant of this matrix.

Fills all elements of this matrx with *value*.

Flips between right-handed and left-handed coordinate systems by multiplying the y and z co-ordinates by -1. This is normally used to create a left-handed orthographic view without scaling the viewport as ortho() does.

**See also **ortho().

Multiplies this matrix by another that applies a perspective frustum projection for a window with lower-left corner (*left*, *bottom*), upper-right corner (*right*, *top*), and the specified *nearPlane* and *farPlane* clipping planes.

**See also **ortho() and perspective().

Returns the inverse of this matrix. Returns the identity if this matrix cannot be inverted; i.e. determinant() is zero. If *invertible* is not null, then true will be written to that location if the matrix can be inverted; false otherwise.

If the matrix is recognized as the identity or an orthonormal matrix, then this function will quickly invert the matrix using optimized routines.

**See also **determinant() and normalMatrix().

Returns true if this matrix is the identity; false otherwise.

**See also **setToIdentity().

Multiplies this matrix by another that applies an *eye* position transformation. The *center* value indicates the center of the view that the *eye* is looking at. The *up* value indicates which direction should be considered up with respect to the *eye*.

Maps *point* by multiplying this matrix by *point*.

**See also **mapRect().

Maps *point* by multiplying this matrix by *point*.

**See also **mapRect().

Maps *point* by multiplying this matrix by *point*.

**See also **mapRect() and mapVector().

Maps *point* by multiplying this matrix by *point*.

**See also **mapRect().

Maps *rect* by multiplying this matrix by the corners of *rect* and then forming a new rectangle from the results. The returned rectangle will be an ordinary 2D rectangle with sides parallel to the horizontal and vertical axes.

**See also **map().

Maps *rect* by multiplying this matrix by the corners of *rect* and then forming a new rectangle from the results. The returned rectangle will be an ordinary 2D rectangle with sides parallel to the horizontal and vertical axes.

**See also **map().

Maps *vector* by multiplying the top 3x3 portion of this matrix by *vector*. The translation and projection components of this matrix are ignored.

**See also **map().

Returns the normal matrix corresponding to this 4x4 transformation. The normal matrix is the transpose of the inverse of the top-left 3x3 part of this 4x4 matrix. If the 3x3 sub-matrix is not invertible, this function returns the identity.

**See also **inverted().

Optimize the usage of this matrix from its current elements.

Some operations such as translate(), scale(), and rotate() can be performed more efficiently if the matrix being modified is already known to be the identity, a previous translate(), a previous scale(), etc.

Normally the QMatrix4x4 class keeps track of this special type internally as operations are performed. However, if the matrix is modified directly with operator()() or data(), then QMatrix4x4 will lose track of the special type and will revert to the safest but least efficient operations thereafter.

By calling optimize() after directly modifying the matrix, the programmer can force QMatrix4x4 to recover the special type if the elements appear to conform to one of the known optimized types.

**See also **operator()(), data(), and translate().

Multiplies this matrix by another that applies an orthographic projection for a window with lower-left corner (*left*, *bottom*), upper-right corner (*right*, *top*), and the specified *nearPlane* and *farPlane* clipping planes.

**See also **frustum() and perspective().

This is an overloaded function.

Multiplies this matrix by another that applies an orthographic projection for a window with boundaries specified by *rect*. The near and far clipping planes will be -1 and 1 respectively.

**See also **frustum() and perspective().

This is an overloaded function.

Multiplies this matrix by another that applies an orthographic projection for a window with boundaries specified by *rect*. The near and far clipping planes will be -1 and 1 respectively.

**See also **frustum() and perspective().

Multiplies this matrix by another that applies a perspective projection. The field of view will be *angle* degrees within a window with a given *aspect* ratio. The projection will have the specified *nearPlane* and *farPlane* clipping planes.

**See also **ortho() and frustum().

Multiples this matrix by another that rotates coordinates through *angle* degrees about *vector*.

**See also **scale() and translate().

Multiples this matrix by another that rotates coordinates according to a specified *quaternion*. The *quaternion* is assumed to have been normalized.

**See also **scale(), translate(), and QQuaternion.

This is an overloaded function.

Multiplies this matrix by another that rotates coordinates through *angle* degrees about the vector (*x*, *y*, *z*).

**See also **scale() and translate().

Returns the elements of row *index* as a 4D vector.

**See also **setRow() and column().

Multiplies this matrix by another that scales coordinates by the components of *vector*.

**See also **translate() and rotate().

This is an overloaded function.

Multiplies this matrix by another that scales coordinates by the components *x*, and *y*.

**See also **translate() and rotate().

This is an overloaded function.

Multiplies this matrix by another that scales coordinates by the components *x*, *y*, and *z*.

**See also **translate() and rotate().

This is an overloaded function.

Multiplies this matrix by another that scales coordinates by the given *factor*.

**See also **translate() and rotate().

Sets the elements of column *index* to the components of *value*.

**See also **column() and setRow().

Sets the elements of row *index* to the components of *value*.

**See also **row() and setColumn().

Sets this matrix to the identity.

**See also **isIdentity().

Returns the conventional Qt 2D affine transformation matrix that corresponds to this matrix. It is assumed that this matrix only contains 2D affine transformation elements.

**See also **toTransform().

Constructs a NxM generic matrix from the left-most N columns and top-most M rows of this 4x4 matrix. If N or M is greater than 4, then the remaining elements are filled with elements from the identity matrix.

Returns the conventional Qt 2D transformation matrix that corresponds to this matrix.

The returned QTransform is formed by simply dropping the third row and third column of the QMatrix4x4. This is suitable for implementing orthographic projections where the z co-ordinate should be dropped rather than projected.

**See also **toAffine().

Returns the conventional Qt 2D transformation matrix that corresponds to this matrix.

If *distanceToPlane* is non-zero, it indicates a projection factor to use to adjust for the z co-ordinate. The value of 1024 corresponds to the projection factor used by QTransform::rotate() for the x and y axes.

If *distanceToPlane* is zero, then the returned QTransform is formed by simply dropping the third row and third column of the QMatrix4x4. This is suitable for implementing orthographic projections where the z co-ordinate should be dropped rather than projected.

**See also **toAffine().

Multiplies this matrix by another that translates coordinates by the components of *vector*.

**See also **scale() and rotate().

This is an overloaded function.

Multiplies this matrix by another that translates coordinates by the components *x*, and *y*.

**See also **scale() and rotate().

This is an overloaded function.

Multiplies this matrix by another that translates coordinates by the components *x*, *y*, and *z*.

**See also **scale() and rotate().

Returns this matrix, transposed about its diagonal.

Returns the matrix as a QVariant.

Returns true if this matrix is not identical to *other*; false otherwise. This operator uses an exact floating-point comparison.

Returns a constant reference to the element at position (*row*, *column*) in this matrix.

Returns a reference to the element at position (*row*, *column*) in this matrix so that the element can be assigned to.

**See also **optimize(), setColumn(), and setRow().

Multiplies the contents of *other* by this matrix.

This is an overloaded function.

Multiplies all elements of this matrix by *factor*.

Adds the contents of *other* to this matrix.

Subtracts the contents of *other* from this matrix.

This is an overloaded function.

Divides all elements of this matrix by *divisor*.

Returns true if this matrix is identical to *other*; false otherwise. This operator uses an exact floating-point comparison.

Returns true if *m1* and *m2* are equal, allowing for a small fuzziness factor for floating-point comparisons; false otherwise.

Returns the product of *m1* and *m2*.

Returns the result of transforming *vector* according to *matrix*, with the matrix applied post-vector.

Returns the result of transforming *vector* according to *matrix*, with the matrix applied pre-vector.

Returns the result of transforming *vector* according to *matrix*, with the matrix applied post-vector.

Returns the result of transforming *vector* according to *matrix*, with the matrix applied pre-vector.

Returns the result of transforming *point* according to *matrix*, with the matrix applied post-point.

Returns the result of transforming *point* according to *matrix*, with the matrix applied post-point.

Returns the result of transforming *point* according to *matrix*, with the matrix applied pre-point.

Returns the result of transforming *point* according to *matrix*, with the matrix applied pre-point.

Returns the result of multiplying all elements of *matrix* by *factor*.

Returns the result of multiplying all elements of *matrix* by *factor*.

Returns the sum of *m1* and *m2*.

Returns the difference of *m1* and *m2*.

This is an overloaded function.

Returns the negation of *matrix*.

Returns the result of dividing all elements of *matrix* by *divisor*.

Writes the given *matrix* to the given *stream* and returns a reference to the stream.

**See also **Serializing Qt Data Types.

Reads a 4x4 matrix from the given *stream* into the given *matrix* and returns a reference to the stream.

**See also **Serializing Qt Data Types.