CopperSpice API  1.7.2
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.

See also
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.

See also
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.

See also
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.

See also
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.

See also
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.

See also
toAffine(), optimize()

Method Documentation

QVector4D QMatrix4x4::column ( int  index) const
inline

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

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

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

See also
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.

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

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

See also
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.

See also
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.

See also
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.

See also
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.

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

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 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.

See also
mapRect()
QPointF QMatrix4x4::map ( const QPointF point) const
inline

Maps point by multiplying this matrix by point.

See also
mapRect()
QVector3D QMatrix4x4::map ( const QVector3D point) const
inline

Maps point by multiplying this matrix by point.

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

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
inline

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()
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.

See also
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.

See also
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.

See also
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.

See also
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.

See also
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.

See also
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.

See also
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.

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

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

See also
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).

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

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

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

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

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

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

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

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

See also
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.

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

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

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

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

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

Sets this matrix to the identity.

See also
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.

See also
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.

See also
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.

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

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

See also
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.

See also
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)).