class QMatrix4x4

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

Added in version 4.6.

Synopsis

Methods

Note

This documentation may contain snippets that were automatically translated from C++ to Python. We always welcome contributions to the snippet translation. If you see an issue with the translation, you can also let us know by creating a ticket on https:/bugreports.qt.io/projects/PYSIDE

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:

  • data()

  • constData()

See also

QVector3D QGenericMatrix

class Flag
__init__()

Constructs an identity matrix.

__init__(transform)
Parameters:

transform – QTransform

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.

__init__(values)
Parameters:

values – float

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.

__init__(m11, m12, m13, m14, m21, m22, m23, m24, m31, m32, m33, m34, m41, m42, m43, m44)
Parameters:

  • 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 – float

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()

__dummy(arg__1)
Parameters:

arg__1 – .list of float

__mgetitem__()
Return type:

object

__reduce__()
Return type:

str

__repr__()
Return type:

str

column(index)
Parameters:

index – int

Return type:

QVector4D

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

See also

setColumn() row()

copyDataTo()
Return type:

Tuple

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

determinant()
Return type:

float

Returns the determinant of this matrix.

fill(value)
Parameters:

value – float

Fills all elements of this matrx with value.

flags()
Return type:

Combination of Flag

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()

frustum(left, right, bottom, top, nearPlane, farPlane)
Parameters:

  • left – float

  • right – float

  • bottom – float

  • top – float

  • nearPlane – float

  • farPlane – float

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.

inverted()
Return type:

PyTuple

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.

isAffine()
Return type:

bool

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.

See also

isIdentity()

isIdentity()
Return type:

bool

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

See also

setToIdentity()

lookAt(eye, center, up)
Parameters:

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.

map(point)
Parameters:

point – QPoint

Return type:

QPoint

Maps point by multiplying this matrix by point. The matrix is applied pre-point.

See also

mapRect()

map(point)
Parameters:

point – QPointF

Return type:

QPointF

Maps point by post-multiplying this matrix by point. The matrix is applied pre-point.

See also

mapRect()

map(point)
Parameters:

point – QVector3D

Return type:

QVector3D

Maps point by multiplying this matrix by point extended to a 4D vector by assuming 1.0 for the w coordinate. The matrix is applied pre-point.

Note

This function is not the same as mapVector() . For points, always use map() . mapVector() is suitable for vectors (directions) only.

See also

mapRect() mapVector()

map(point)
Parameters:

point – QVector4D

Return type:

QVector4D

Maps point by multiplying this matrix by point. The matrix is applied pre-point.

See also

mapRect()

mapRect(rect)
Parameters:

rect – QRect

Return type:

QRect

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()

mapRect(rect)
Parameters:

rect – QRectF

Return type:

QRectF

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()

mapVector(vector)
Parameters:

vector – QVector3D

Return type:

QVector3D

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

See also

map()

normalMatrix()
Return type:

QMatrix3x3

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()

__ne__(other)
Parameters:

other – QMatrix4x4

Return type:

bool

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

__mul__(m2)
Parameters:

m2 – QMatrix4x4

Return type:

QMatrix4x4

Returns the product of m1 and m2.

__mul__(factor)
Parameters:

factor – float

Return type:

QMatrix4x4

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

__mul__(factor)
Parameters:

factor – float

Return type:

QMatrix4x4

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

__imul__(other)
Parameters:

other – QMatrix4x4

Return type:

QMatrix4x4

Multiplies the contents of other by this matrix.

__imul__(factor)
Parameters:

factor – float

Return type:

QMatrix4x4

This is an overloaded function.

Multiplies all elements of this matrix by factor.

__add__(m2)
Parameters:

m2 – QMatrix4x4

Return type:

QMatrix4x4

Returns the sum of m1 and m2.

__iadd__(other)
Parameters:

other – QMatrix4x4

Return type:

QMatrix4x4

Adds the contents of other to this matrix.

__sub__()
Return type:

QMatrix4x4

This is an overloaded function.

Returns the negation of matrix.

__sub__(m2)
Parameters:

m2 – QMatrix4x4

Return type:

QMatrix4x4

Returns the difference of m1 and m2.

__isub__(other)
Parameters:

other – QMatrix4x4

Return type:

QMatrix4x4

Subtracts the contents of other from this matrix.

__div__(divisor)
Parameters:

divisor – float

Return type:

QMatrix4x4

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

operator/=(divisor)
Parameters:

divisor – float

Return type:

QMatrix4x4

This is an overloaded function.

Divides all elements of this matrix by divisor.

__eq__(other)
Parameters:

other – QMatrix4x4

Return type:

bool

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

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() (int, int) 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()(int, int) data() translate()

ortho(rect)
Parameters:

rect – QRect

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.

ortho(rect)
Parameters:

rect – QRectF

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.

ortho(left, right, bottom, top, nearPlane, farPlane)
Parameters:

  • left – float

  • right – float

  • bottom – float

  • top – float

  • nearPlane – float

  • farPlane – float

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.

perspective(verticalAngle, aspectRatio, nearPlane, farPlane)
Parameters:

  • verticalAngle – float

  • aspectRatio – float

  • nearPlane – float

  • farPlane – float

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() frustum()

projectedRotate(angle, x, y, z)
Parameters:

  • angle – float

  • x – float

  • y – float

  • z – float

projectedRotate(angle, x, y, z, distanceToPlane)
Parameters:

  • angle – float

  • x – float

  • y – float

  • z – float

  • distanceToPlane – float

rotate(quaternion)
Parameters:

quaternion – QQuaternion

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

rotate(angle, vector)
Parameters:

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

See also

scale() translate()

rotate(angle, x, y[, z=0.0f])
Parameters:

  • angle – float

  • x – float

  • y – float

  • z – float

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() translate()

row(index)
Parameters:

index – int

Return type:

QVector4D

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

See also

setRow() column()

scale(vector)
Parameters:

vector – QVector3D

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

scale(factor)
Parameters:

factor – float

This is an overloaded function.

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

scale(x, y)
Parameters:

  • x – float

  • y – float

This is an overloaded function.

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

scale(x, y, z)
Parameters:

  • x – float

  • y – float

  • z – float

This is an overloaded function.

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

setColumn(index, value)
Parameters:

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

See also

column() setRow()

setRow(index, value)
Parameters:

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

See also

row() setColumn()

setToIdentity()

Sets this matrix to the identity.

See also

isIdentity()

toTransform()
Return type:

QTransform

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 coordinate should be dropped rather than projected.

toTransform(distanceToPlane)
Parameters:

distanceToPlane – float

Return type:

QTransform

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 coordinate. The value of 1024 corresponds to the projection factor used by 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.

translate(vector)
Parameters:

vector – QVector3D

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

See also

scale() rotate()

translate(x, y)
Parameters:

  • x – float

  • y – float

This is an overloaded function.

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

See also

scale() rotate()

translate(x, y, z)
Parameters:

  • x – float

  • y – float

  • z – float

This is an overloaded function.

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

See also

scale() rotate()

transposed()
Return type:

QMatrix4x4

Returns this matrix, transposed about its diagonal.

viewport(rect)
Parameters:

rect – QRectF

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.

viewport(left, bottom, width, height[, nearPlane=0.0f[, farPlane=1.0f]])
Parameters:

  • left – float

  • bottom – float

  • width – float

  • height – float

  • nearPlane – float

  • farPlane – float

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().