# QMatrix4x4 Class

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

Header: | #include <QMatrix4x4> |

qmake: | QT += gui |

Since: | Qt 4.6 |

This class was introduced in Qt 4.6.

## Public Functions

QMatrix4x4(const QTransform &transform) | |

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

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

QMatrix4x4(const float *values) | |

QMatrix4x4() | |

QVector4D | column(int index) const |

const float * | constData() const |

void | copyDataTo(float *values) const |

float * | data() |

const float * | data() const |

double | determinant() const |

void | fill(float value) |

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

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

bool | isAffine() const |

bool | isIdentity() const |

void | lookAt(const QVector3D &eye, const QVector3D ¢er, 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(float left, float right, float bottom, float top, float nearPlane, float farPlane) |

void | ortho(const QRect &rect) |

void | ortho(const QRectF &rect) |

void | perspective(float verticalAngle, float aspectRatio, float nearPlane, float farPlane) |

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

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

void | rotate(const QQuaternion &quaternion) |

QVector4D | row(int index) const |

void | scale(const QVector3D &vector) |

void | scale(float x, float y) |

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

void | scale(float factor) |

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

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

void | setToIdentity() |

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

QTransform | toTransform() const |

QTransform | toTransform(float distanceToPlane) const |

void | translate(const QVector3D &vector) |

void | translate(float x, float y) |

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

QMatrix4x4 | transposed() const |

void | viewport(float left, float bottom, float width, float height, float nearPlane = 0.0f, float farPlane = 1.0f) |

void | viewport(const QRectF &rect) |

QVariant | operator QVariant() const |

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

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

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

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

QMatrix4x4 & | operator*=(float factor) |

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

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

QMatrix4x4 & | operator/=(float divisor) |

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

## Related Non-Members

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

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

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

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

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

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

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

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

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

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

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

QMatrix4x4 | operator*(const QMatrix4x4 &matrix, float 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, float divisor) |

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

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

## Detailed Description

The QMatrix4x4 class in general is treated as a row-major matrix, in that the constructors and operator() functions take data in row-major format, as is familiar in C-style usage.

Internally the data is stored as column-major format, so as to be optimal for passing to OpenGL functions, which expect column-major data.

When using these functions be aware that they return data in **column-major** format:

**See also **QVector3D and QGenericMatrix.

## Member Function Documentation

### QMatrix4x4::QMatrix4x4(const QTransform &*transform*)

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().

### template <int N, int M> QMatrix4x4::QMatrix4x4(const QGenericMatrix<N, M, float> &*matrix* = N)

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().

### QMatrix4x4::QMatrix4x4(float *m11*, float *m12*, float *m13*, float *m14*, float *m21*, float *m22*, float *m23*, float *m24*, float *m31*, float *m32*, float *m33*, float *m34*, float *m41*, float *m42*, float *m43*, float *m44*)

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().

### QMatrix4x4::QMatrix4x4(const float **values*)

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().

### QMatrix4x4::QMatrix4x4()

Constructs an identity matrix.

### QVector4D QMatrix4x4::column(int *index*) const

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

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

### const float *QMatrix4x4::constData() const

Returns a constant pointer to the raw data of this matrix. This raw data is stored in column-major format.

**See also **data().

### void QMatrix4x4::copyDataTo(float **values*) const

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

### float *QMatrix4x4::data()

Returns a pointer to the raw data of this matrix.

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

### const float *QMatrix4x4::data() const

Returns a constant pointer to the raw data of this matrix. This raw data is stored in column-major format.

**See also **constData().

### double QMatrix4x4::determinant() const

Returns the determinant of this matrix.

### void QMatrix4x4::fill(float *value*)

Fills all elements of this matrx with *value*.

### void QMatrix4x4::frustum(float *left*, float *right*, float *bottom*, float *top*, float *nearPlane*, float *farPlane*)

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().

### QMatrix4x4 QMatrix4x4::inverted(bool **invertible* = nullptr) const

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().

### bool QMatrix4x4::isAffine() const

Returns `true`

if this matrix is affine matrix; false otherwise.

An affine matrix is a 4x4 matrix with row 3 equal to (0, 0, 0, 1), e.g. no projective coefficients.

This function was introduced in Qt 5.5.

**See also **isIdentity().

### bool QMatrix4x4::isIdentity() const

Returns `true`

if this matrix is the identity; false otherwise.

**See also **setToIdentity().

### void QMatrix4x4::lookAt(const QVector3D &*eye*, const QVector3D &*center*, const QVector3D &*up*)

Multiplies this matrix by a viewing matrix derived from an eye point. 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*.

**Note: **The *up* vector must not be parallel to the line of sight from *eye* to *center*.

### QPoint QMatrix4x4::map(const QPoint &*point*) const

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

**See also **mapRect().

### QPointF QMatrix4x4::map(const QPointF &*point*) const

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

**See also **mapRect().

### QVector3D QMatrix4x4::map(const QVector3D &*point*) const

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

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

### QVector4D QMatrix4x4::map(const QVector4D &*point*) const

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

**See also **mapRect().

### QRect QMatrix4x4::mapRect(const QRect &*rect*) const

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().

### QRectF QMatrix4x4::mapRect(const QRectF &*rect*) const

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().

### QVector3D QMatrix4x4::mapVector(const QVector3D &*vector*) const

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().

### QMatrix3x3 QMatrix4x4::normalMatrix() const

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().

### void QMatrix4x4::optimize()

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().

### void QMatrix4x4::ortho(float *left*, float *right*, float *bottom*, float *top*, float *nearPlane*, float *farPlane*)

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().

### void QMatrix4x4::ortho(const QRect &*rect*)

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().

### void QMatrix4x4::ortho(const QRectF &*rect*)

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().

### void QMatrix4x4::perspective(float *verticalAngle*, float *aspectRatio*, float *nearPlane*, float *farPlane*)

Multiplies this matrix by another that applies a perspective projection. The vertical field of view will be *verticalAngle* degrees within a window with a given *aspectRatio* that determines the horizontal field of view. The projection will have the specified *nearPlane* and *farPlane* clipping planes which are the distances from the viewer to the corresponding planes.

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

### void QMatrix4x4::rotate(float *angle*, const QVector3D &*vector*)

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

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

### void QMatrix4x4::rotate(float *angle*, float *x*, float *y*, float *z* = 0.0f)

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().

### void QMatrix4x4::rotate(const QQuaternion &*quaternion*)

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.

### QVector4D QMatrix4x4::row(int *index*) const

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

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

### void QMatrix4x4::scale(const QVector3D &*vector*)

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

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

### void QMatrix4x4::scale(float *x*, float *y*)

This is an overloaded function.

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

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

### void QMatrix4x4::scale(float *x*, float *y*, float *z*)

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().

### void QMatrix4x4::scale(float *factor*)

This is an overloaded function.

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

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

### void QMatrix4x4::setColumn(int *index*, const QVector4D &*value*)

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

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

### void QMatrix4x4::setRow(int *index*, const QVector4D &*value*)

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

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

### void QMatrix4x4::setToIdentity()

Sets this matrix to the identity.

**See also **isIdentity().

### template <int N, int M> QGenericMatrix<N, M, float> QMatrix4x4::toGenericMatrix() const

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.

### QTransform QMatrix4x4::toTransform() const

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().

### QTransform QMatrix4x4::toTransform(float *distanceToPlane*) const

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().

### void QMatrix4x4::translate(const QVector3D &*vector*)

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

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

### void QMatrix4x4::translate(float *x*, float *y*)

This is an overloaded function.

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

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

### void QMatrix4x4::translate(float *x*, float *y*, float *z*)

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().

### QMatrix4x4 QMatrix4x4::transposed() const

Returns this matrix, transposed about its diagonal.

### void QMatrix4x4::viewport(float *left*, float *bottom*, float *width*, float *height*, float *nearPlane* = 0.0f, float *farPlane* = 1.0f)

Multiplies this matrix by another that performs the scale and bias transformation used by OpenGL to transform from normalized device coordinates (NDC) to viewport (window) coordinates. That is it maps points from the cube ranging over [-1, 1] in each dimension to the viewport with it's near-lower-left corner at (*left*, *bottom*, *nearPlane*) and with size (*width*, *height*, *farPlane* - *nearPlane*).

This matches the transform used by the fixed function OpenGL viewport transform controlled by the functions glViewport() and glDepthRange().

### void QMatrix4x4::viewport(const QRectF &*rect*)

This is an overloaded function.

Sets up viewport transform for viewport bounded by *rect* and with near and far set to 0 and 1 respectively.

### QVariant QMatrix4x4::operator QVariant() const

Returns the matrix as a QVariant.

### bool QMatrix4x4::operator!=(const QMatrix4x4 &*other*) const

Returns `true`

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

### const float &QMatrix4x4::operator()(int *row*, int *column*) const

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

### float &QMatrix4x4::operator()(int *row*, int *column*)

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().

### QMatrix4x4 &QMatrix4x4::operator*=(const QMatrix4x4 &*other*)

Multiplies the contents of *other* by this matrix.

### QMatrix4x4 &QMatrix4x4::operator*=(float *factor*)

This is an overloaded function.

Multiplies all elements of this matrix by *factor*.

### QMatrix4x4 &QMatrix4x4::operator+=(const QMatrix4x4 &*other*)

Adds the contents of *other* to this matrix.

### QMatrix4x4 &QMatrix4x4::operator-=(const QMatrix4x4 &*other*)

Subtracts the contents of *other* from this matrix.

### QMatrix4x4 &QMatrix4x4::operator/=(float *divisor*)

This is an overloaded function.

Divides all elements of this matrix by *divisor*.

### bool QMatrix4x4::operator==(const QMatrix4x4 &*other*) const

Returns `true`

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

## Related Non-Members

### bool qFuzzyCompare(const QMatrix4x4 &*m1*, const QMatrix4x4 &*m2*)

Returns `true`

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

### QMatrix4x4 operator*(float *factor*, const QMatrix4x4 &*matrix*)

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

### QMatrix4x4 operator*(const QMatrix4x4 &*matrix*, float *factor*)

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

### QMatrix4x4 operator+(const QMatrix4x4 &*m1*, const QMatrix4x4 &*m2*)

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

### QMatrix4x4 operator-(const QMatrix4x4 &*m1*, const QMatrix4x4 &*m2*)

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

### QMatrix4x4 operator-(const QMatrix4x4 &*matrix*)

This is an overloaded function.

Returns the negation of *matrix*.

### QMatrix4x4 operator/(const QMatrix4x4 &*matrix*, float *divisor*)

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

### QDataStream &operator<<(QDataStream &*stream*, const QMatrix4x4 &*matrix*)

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

**See also **Serializing Qt Data Types.

### QDataStream &operator>>(QDataStream &*stream*, QMatrix4x4 &*matrix*)

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.

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