CopperSpice API  1.7.4
QMatrix4x4 Class Reference

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

## Public Methods

QMatrix4x4 ()

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

QMatrix4x4 (const QMatrix &matrix)

QMatrix4x4 (const qreal *values)

QMatrix4x4 (const QTransform &transform)

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)

QVector4D column (int index) const

const qrealconstData () const

void copyDataTo (qreal *values) const

qrealdata ()

const qrealdata () 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=nullptr) const

bool isAffine () 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

qrealoperator () (int row, int column)

const qrealoperator () (int row, int column) const

operator QVariant () const

bool operator!= (const QMatrix4x4 &other) const

QMatrix4x4 & operator*= (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

void optimize ()

void ortho (const QRect &rect)

void ortho (const QRectF &rect)

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

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

void rotate (const QQuaternion &quaternion)

void rotate (qreal angle, const QVector3D &vector)

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 factor)

void scale (qreal x, qreal y)

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

void setColumn (int index, const QVector4D &value)

void setRow (int index, const QVector4D &value)

void setToIdentity ()

QMatrix toAffine () const

template<int N, int M>
QGenericMatrix< N, M, qrealtoGenericMatrix () 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

void viewport (const QRectF &rect)

void viewport (qreal left, qreal bottom, qreal width, qreal height, qreal nearPlane=0.0, qreal farPlane=1.0)

## Friends

class QGraphicsRotation

## Detailed Description

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

QVector3D, QGenericMatrix

## Constructor & Destructor Documentation

 QMatrix4x4::QMatrix4x4 ( )
inline

Constructs an identity matrix.

 QMatrix4x4::QMatrix4x4 ( const qreal * values )
explicit

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.

copyDataTo(), optimize()
 QMatrix4x4::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 )
inline

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.

optimize()
template<int N, int M>
 QMatrix4x4::QMatrix4x4 ( const QGenericMatrix< N, M, qreal > & matrix )
inlineexplicit

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.

toGenericMatrix()
 QMatrix4x4::QMatrix4x4 ( const QTransform & transform )

Constructs a 4x4 matrix from the conventional 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.

toTransform(), optimize()
 QMatrix4x4::QMatrix4x4 ( const QMatrix & matrix )

Constructs a 4x4 matrix from a conventional 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.

toAffine(), optimize()

## Method Documentation

 QVector4D QMatrix4x4::column ( int index ) const
inline

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

setColumn(), row()
 const qreal * QMatrix4x4::constData ( ) const
inline

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

data()
 void QMatrix4x4::copyDataTo ( qreal * values ) const

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

 qreal * QMatrix4x4::data ( )
inline

Returns a pointer to the raw data of this matrix.

constData(), optimize()
 const qreal * QMatrix4x4::data ( ) const
inline

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

constData()
 qreal QMatrix4x4::determinant ( ) const

Returns the determinant of this matrix.

 void QMatrix4x4::fill ( qreal value )
inline

Fills all elements of this matrix with value.

 void QMatrix4x4::flipCoordinates ( )

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

ortho()
 void QMatrix4x4::frustum ( qreal left, qreal right, qreal bottom, qreal top, qreal nearPlane, qreal 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.

ortho(), perspective()
 QMatrix4x4 QMatrix4x4::inverted ( bool * invertible = nullptr ) const

Returns the inverse of this matrix. Returns the identity if this matrix can not 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.

determinant(), normalMatrix()
 bool QMatrix4x4::isAffine ( ) const
inline

Returns true if this matrix is an affine matrix, return false otherwise. An affine matrix is a 4x4 matrix with row 3 equal to (0, 0, 0, 1), e.g. no projective coefficients.

isIdentity()
 bool QMatrix4x4::isIdentity ( ) const
inline

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

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

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.

 QPoint QMatrix4x4::map ( const QPoint & point ) const
inline

Maps point by multiplying this matrix by point.

mapRect()
 QPointF QMatrix4x4::map ( const QPointF & point ) const
inline

Maps point by multiplying this matrix by point.

mapRect()
 QVector3D QMatrix4x4::map ( const QVector3D & point ) const
inline

Maps point by multiplying this matrix by point.

mapRect(), mapVector()
 QVector4D QMatrix4x4::map ( const QVector4D & point ) const
inline

Maps point by multiplying this matrix by point.

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.

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.

map()
 QVector3D QMatrix4x4::mapVector ( const QVector3D & vector ) const
inline

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

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.

inverted()
 qreal & QMatrix4x4::operator () ( int row, int column )
inline

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

optimize(), setColumn(), setRow()
 const qreal & QMatrix4x4::operator () ( int row, int column ) const
inline

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

column(), row()
 QMatrix4x4::operator QVariant ( ) const

Returns the matrix as a QVariant.

 bool QMatrix4x4::operator!= ( const QMatrix4x4 & other ) const
inline

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

 QMatrix4x4 & QMatrix4x4::operator*= ( QMatrix4x4 other )
inline

Multiplies the contents of other by this matrix.

 QMatrix4x4 & QMatrix4x4::operator*= ( qreal factor )
inline

Multiplies all elements of this matrix by factor.

 QMatrix4x4 & QMatrix4x4::operator+= ( const QMatrix4x4 & other )
inline

Adds the contents of other to this matrix.

 QMatrix4x4 & QMatrix4x4::operator-= ( const QMatrix4x4 & other )
inline

Subtracts the contents of other from this matrix.

 QMatrix4x4 & QMatrix4x4::operator/= ( qreal divisor )

Divides all elements of this matrix by divisor.

 bool QMatrix4x4::operator== ( const QMatrix4x4 & other ) const
inline

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

 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.

operator()(), data(), translate()
 void QMatrix4x4::ortho ( const QRect & rect )

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.

frustum(), perspective()
 void QMatrix4x4::ortho ( const QRectF & rect )

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.

frustum(), perspective()
 void QMatrix4x4::ortho ( qreal left, qreal right, qreal bottom, qreal top, qreal nearPlane, qreal 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.

frustum(), perspective()
 void QMatrix4x4::perspective ( qreal angle, qreal aspect, qreal nearPlane, qreal farPlane )

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.

ortho(), frustum()
 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.

scale(), translate(), QQuaternion
 void QMatrix4x4::rotate ( qreal angle, const QVector3D & vector )

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

scale(), translate()
 void QMatrix4x4::rotate ( qreal angle, qreal x, qreal y, qreal z = 0.0f )

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

scale(), translate()
 QVector4D QMatrix4x4::row ( int index ) const
inline

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

setRow(), column()
 void QMatrix4x4::scale ( const QVector3D & vector )

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

translate(), rotate()
 void QMatrix4x4::scale ( qreal factor )

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

translate(), rotate()
 void QMatrix4x4::scale ( qreal x, qreal y )

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

translate(), rotate()
 void QMatrix4x4::scale ( qreal x, qreal y, qreal z )

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

translate(), rotate()
 void QMatrix4x4::setColumn ( int index, const QVector4D & value )
inline

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

column(), setRow()
 void QMatrix4x4::setRow ( int index, const QVector4D & value )
inline

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

row(), setColumn()
 void QMatrix4x4::setToIdentity ( )
inline

Sets this matrix to the identity.

isIdentity()
 QMatrix QMatrix4x4::toAffine ( ) const

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

toTransform()
template<int N, int M>
 QGenericMatrix< N, M, qreal > 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 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 coordinate should be dropped rather than projected.

toAffine()
 QTransform QMatrix4x4::toTransform ( qreal distanceToPlane ) const

Returns the conventional 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 coordinate. 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 coordinate should be dropped rather than projected.

toAffine()
 void QMatrix4x4::translate ( const QVector3D & vector )

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

scale(), rotate()
 void QMatrix4x4::translate ( qreal x, qreal y )

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

scale(), rotate()
 void QMatrix4x4::translate ( qreal x, qreal y, qreal z )

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

scale(), rotate()
 QMatrix4x4 QMatrix4x4::transposed ( ) const

Returns this matrix, transposed about its diagonal.

 void QMatrix4x4::viewport ( const QRectF & rect )
inline

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

 void QMatrix4x4::viewport ( qreal left, qreal bottom, qreal width, qreal height, qreal nearPlane = 0.0, qreal farPlane = 1.0 )

Multiplies this matrix by a viewport matrix. The result can be used to transform from normalized device coordinates (NDC) to viewport (window) coordinates.

Points are mapped from the cube ranging over [-1, 1] in each dimension to the viewport with the near-lower-left corner at (left, bottom, nearPlane) and with size (width, height, (farPlane - nearPlane)).