The QMatrix class specifies 2D transformations of a coordinate system. More…
Synopsis¶
Functions¶
def __eq__ (arg__1)
def __imul__ (arg__1)
def __mul__ (o)
def __ne__ (arg__1)
def __reduce__ ()
def __repr__ ()
def determinant ()
def dx ()
def dy ()
def inverted ()
def isIdentity ()
def isInvertible ()
def m11 ()
def m12 ()
def m21 ()
def m22 ()
def map (a)
def map (a)
def map (l)
def map (l)
def map (p)
def map (p)
def map (p)
def map (r)
def map (x, y)
def map (x, y)
def mapRect (arg__1)
def mapRect (arg__1)
def mapToPolygon (r)
def reset ()
def rotate (a)
def scale (sx, sy)
def setMatrix (m11, m12, m21, m22, dx, dy)
def shear (sh, sv)
def translate (dx, dy)
Detailed Description¶
A matrix specifies how to translate, scale, shear or rotate the coordinate system, and is typically used when rendering graphics. QMatrix , in contrast to QTransform , does not allow perspective transformations. QTransform is the recommended transformation class in Qt.
A QMatrix object can be built using the setMatrix() , scale() , rotate() , translate() and shear() functions. Alternatively, it can be built by applying
basic matrix operations. The matrix can also be defined when constructed, and it can be reset to the identity matrix (the default) using the reset() function.The QMatrix class supports mapping of graphic primitives: A given point, line, polygon, region, or painter path can be mapped to the coordinate system defined by this matrix using the map() function. In case of a rectangle, its coordinates can be transformed using the mapRect() function. A rectangle can also be transformed into a polygon (mapped to the coordinate system defined by this matrix), using the mapToPolygon() function.
QMatrix provides the isIdentity() function which returns
trueif the matrix is the identity matrix, and the isInvertible() function which returnstrueif the matrix is non-singular (i.e. AB = BA = I). The inverted() function returns an inverted copy of this matrix if it is invertible (otherwise it returns the identity matrix). In addition, QMatrix provides the determinant() function returning the matrix’s determinant.Finally, the QMatrix class supports matrix multiplication, and objects of the class can be streamed as well as compared.
Rendering Graphics¶
When rendering graphics, the matrix defines the transformations but the actual transformation is performed by the drawing routines in QPainter .
By default, QPainter operates on the associated device’s own coordinate system. The standard coordinate system of a QPaintDevice has its origin located at the top-left position. The x values increase to the right; y values increase downward. For a complete description, see the coordinate system documentation.
QPainter has functions to translate, scale, shear and rotate the coordinate system without using a QMatrix . For example:
Although these functions are very convenient, it can be more efficient to build a QMatrix and call setMatrix() if you want to perform more than a single transform operation. For example:
Basic Matrix Operations¶
A QMatrix object contains a 3 x 3 matrix. The
dxanddyelements specify horizontal and vertical translation. Them11andm22elements specify horizontal and vertical scaling. And finally, them21andm12elements specify horizontal and vertical shearing .QMatrix transforms a point in the plane to another point using the following formulas:
x' = m11*x + m21*y + dxy' = m22*y + m12*x + dyThe point (x, y) is the original point, and (x’, y’) is the transformed point. (x’, y’) can be transformed back to (x, y) by performing the same operation on the inverted() matrix.
The various matrix elements can be set when constructing the matrix, or by using the setMatrix() function later on. They can also be manipulated using the translate() , rotate() , scale() and shear() convenience functions, The currently set values can be retrieved using the m11() , m12() , m21() , m22() , dx() and dy() functions.
Translation is the simplest transformation. Setting
dxanddywill move the coordinate systemdxunits along the X axis anddyunits along the Y axis. Scaling can be done by settingm11andm22. For example, settingm11to 2 andm22to 1.5 will double the height and increase the width by 50%. The identity matrix hasm11andm22set to 1 (all others are set to 0) mapping a point to itself. Shearing is controlled bym12andm21. Setting these elements to values different from zero will twist the coordinate system. Rotation is achieved by carefully setting both the shearing factors and the scaling factors.Here’s the combined transformations example using basic matrix operations:
See also
QPainter QTransform Coordinate System Affine Transformations Example Transformations Example
- class PySide2.QtGui.QMatrix¶
PySide2.QtGui.QMatrix(other)
PySide2.QtGui.QMatrix(m11, m12, m21, m22, dx, dy)
- param m12:
float
- param dx:
float
- param dy:
float
- param other:
PySide2.QtGui.QMatrix
- param m21:
float
- param m22:
float
- param m11:
float
Constructs an identity matrix.
All elements are set to zero except
m11andm22(specifying the scale), which are set to 1.See also
reset()
Constructs a matrix with the elements,
m11,m12,m21,m22,dxanddy.See also
setMatrix()
- PySide2.QtGui.QMatrix.__reduce__()¶
- Return type:
object
- PySide2.QtGui.QMatrix.__repr__()¶
- Return type:
object
- PySide2.QtGui.QMatrix.determinant()¶
- Return type:
float
Returns the matrix’s determinant.
- PySide2.QtGui.QMatrix.dx()¶
- Return type:
float
Returns the horizontal translation factor.
See also
translate()
Basic Matrix Operations
- PySide2.QtGui.QMatrix.dy()¶
- Return type:
float
Returns the vertical translation factor.
See also
translate()
Basic Matrix Operations
- PySide2.QtGui.QMatrix.inverted()¶
- Return type:
PyTuple
Returns an inverted copy of this matrix.
If the matrix is singular (not invertible), the returned matrix is the identity matrix. If
invertibleis valid (i.e. not 0), its value is set to true if the matrix is invertible, otherwise it is set to false.See also
isInvertible()
- PySide2.QtGui.QMatrix.isIdentity()¶
- Return type:
bool
Returns
trueif the matrix is the identity matrix, otherwise returnsfalse.See also
reset()
- PySide2.QtGui.QMatrix.isInvertible()¶
- Return type:
bool
Returns
trueif the matrix is invertible, otherwise returnsfalse.See also
inverted()
- PySide2.QtGui.QMatrix.m11()¶
- Return type:
float
Returns the horizontal scaling factor.
See also
scale()
Basic Matrix Operations
- PySide2.QtGui.QMatrix.m12()¶
- Return type:
float
Returns the vertical shearing factor.
See also
shear()
Basic Matrix Operations
- PySide2.QtGui.QMatrix.m21()¶
- Return type:
float
Returns the horizontal shearing factor.
See also
shear()
Basic Matrix Operations
- PySide2.QtGui.QMatrix.m22()¶
- Return type:
float
Returns the vertical scaling factor.
See also
scale()
Basic Matrix Operations
- PySide2.QtGui.QMatrix.map(x, y)¶
- Parameters:
x – float
y – float
Maps the given coordinates
xandyinto the coordinate system defined by this matrix. The resulting values are put in *``tx`` and *``ty`` , respectively.The coordinates are transformed using the following formulas:
x' = m11*x + m21*y + dxy' = m22*y + m12*x + dy
The point (x, y) is the original point, and (x’, y’) is the transformed point.
See also
Basic Matrix Operations
- PySide2.QtGui.QMatrix.map(x, y)
- Parameters:
x – int
y – int
This is an overloaded function.
Maps the given coordinates
xandyinto the coordinate system defined by this matrix. The resulting values are put in *``tx`` and *``ty`` , respectively. Note that the transformed coordinates are rounded to the nearest integer.
- PySide2.QtGui.QMatrix.map(r)
- Parameters:
r – PySide2.QtGui.QRegion
- Return type:
PySide2.QtGui.QRegion
- PySide2.QtGui.QMatrix.map(a)
- Parameters:
a – PySide2.QtGui.QPolygonF
- Return type:
PySide2.QtGui.QPolygonF
- PySide2.QtGui.QMatrix.map(a)
- Parameters:
a – PySide2.QtGui.QPolygon
- Return type:
PySide2.QtGui.QPolygon
- PySide2.QtGui.QMatrix.map(p)
- Parameters:
p – PySide2.QtCore.QPoint
- Return type:
QPoint
- PySide2.QtGui.QMatrix.map(p)
- Parameters:
p – PySide2.QtGui.QPainterPath
- Return type:
PySide2.QtGui.QPainterPath
- PySide2.QtGui.QMatrix.map(l)
- Parameters:
l – PySide2.QtCore.QLineF
- Return type:
PySide2.QtCore.QLineF
- PySide2.QtGui.QMatrix.map(l)
- Parameters:
l – PySide2.QtCore.QLine
- Return type:
PySide2.QtCore.QLine
- PySide2.QtGui.QMatrix.map(p)
- Parameters:
p – PySide2.QtCore.QPointF
- Return type:
PySide2.QtCore.QPointF
- PySide2.QtGui.QMatrix.mapRect(arg__1)¶
- Parameters:
arg__1 – PySide2.QtCore.QRect
- Return type:
PySide2.QtCore.QRect
- PySide2.QtGui.QMatrix.mapRect(arg__1)
- Parameters:
arg__1 – PySide2.QtCore.QRectF
- Return type:
PySide2.QtCore.QRectF
- PySide2.QtGui.QMatrix.mapToPolygon(r)¶
- Parameters:
r – PySide2.QtCore.QRect
- Return type:
PySide2.QtGui.QPolygon
Creates and returns a QPolygon representation of the given
rectangle, mapped into the coordinate system defined by this matrix.The rectangle’s coordinates are transformed using the following formulas:
x' = m11*x + m21*y + dxy' = m22*y + m12*x + dy
Polygons and rectangles behave slightly differently when transformed (due to integer rounding), so
matrix.map(QPolygon(rectangle))is not always the same asmatrix.mapToPolygon(rectangle).See also
mapRect()
Basic Matrix Operations
- PySide2.QtGui.QMatrix.__ne__(arg__1)¶
- Parameters:
arg__1 – PySide2.QtGui.QMatrix
- Return type:
bool
Returns
trueif this matrix is not equal to the givenmatrix, otherwise returnsfalse.
- PySide2.QtGui.QMatrix.__mul__(o)¶
- Parameters:
o – PySide2.QtGui.QMatrix
- Return type:
PySide2.QtGui.QMatrix
Returns the result of multiplying this matrix by the given
matrix.Note that matrix multiplication is not commutative, i.e. a*b != b*a.
- PySide2.QtGui.QMatrix.__imul__(arg__1)¶
- Parameters:
arg__1 – PySide2.QtGui.QMatrix
- Return type:
PySide2.QtGui.QMatrix
This is an overloaded function.
Returns the result of multiplying this matrix by the given
matrix.
- PySide2.QtGui.QMatrix.__eq__(arg__1)¶
- Parameters:
arg__1 – PySide2.QtGui.QMatrix
- Return type:
bool
Returns
trueif this matrix is equal to the givenmatrix, otherwise returnsfalse.
- PySide2.QtGui.QMatrix.reset()¶
Resets the matrix to an identity matrix, i.e. all elements are set to zero, except
m11andm22(specifying the scale) which are set to 1.See also
QMatrix()isIdentity()Basic Matrix Operations
- PySide2.QtGui.QMatrix.rotate(a)¶
- Parameters:
a – float
- Return type:
PySide2.QtGui.QMatrix
Rotates the coordinate system the given
degreescounterclockwise.Note that if you apply a QMatrix to a point defined in widget coordinates, the direction of the rotation will be clockwise because the y-axis points downwards.
Returns a reference to the matrix.
See also
setMatrix()
- PySide2.QtGui.QMatrix.scale(sx, sy)¶
- Parameters:
sx – float
sy – float
- Return type:
PySide2.QtGui.QMatrix
Scales the coordinate system by
sxhorizontally andsyvertically, and returns a reference to the matrix.See also
setMatrix()
- PySide2.QtGui.QMatrix.setMatrix(m11, m12, m21, m22, dx, dy)¶
- Parameters:
m11 – float
m12 – float
m21 – float
m22 – float
dx – float
dy – float
Sets the matrix elements to the specified values,
m11,m12,m21,m22,dxanddy.Note that this function replaces the previous values. QMatrix provide the translate() , rotate() , scale() and shear() convenience functions to manipulate the various matrix elements based on the currently defined coordinate system.
See also
QMatrix()
- PySide2.QtGui.QMatrix.shear(sh, sv)¶
- Parameters:
sh – float
sv – float
- Return type:
PySide2.QtGui.QMatrix
Shears the coordinate system by
shhorizontally andsvvertically, and returns a reference to the matrix.See also
setMatrix()
- PySide2.QtGui.QMatrix.translate(dx, dy)¶
- Parameters:
dx – float
dy – float
- Return type:
PySide2.QtGui.QMatrix
Moves the coordinate system
dxalong the x axis anddyalong the y axis, and returns a reference to the matrix.See also
setMatrix()
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