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The QWMatrix class specifies 2D transformations of a coordinate system. More...
#include <qwmatrix.h>
The standard coordinate system of a paint device has the origin located at the top-left position. X values increase to the right; Y values increase downward.
This coordinate system is default for the QPainter, which renders graphics in a paint device. A user-defined coordinate system can be specified by setting a QWMatrix for the painter.
Example:
MyWidget::paintEvent( QPaintEvent * )
{
QPainter p; // our painter
QWMatrix m; // our transformation matrix
m.rotate( 22.5 ); // rotated coordinate system
p.begin( this ); // start painting
p.setWorldMatrix( m ); // use rotated coordinate system
p.drawText( 30,20, "detator" ); // draw rotated text at 30,20
p.end(); // painting done
}
A matrix specifies how to translate, scale, shear or rotate the graphics; the actual transformation is performed by the drawing routines in QPainter and by QPixmap::xForm().
The QWMatrix class contains a 3*3 matrix of the form:
m11 m12 0
m21 m22 0
dx dy 1
A matrix transforms a point in the plane to another point:
x' = m11*x + m21*y + dx
y' = m22*y + m12*x + dy
The 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 elements dx and dy specify horizontal and vertical translation. The elements m11 and m22 specify horizontal and vertical scaling. The elements m12 and m21 specify horizontal and vertical shearing.
The identity matrix has m11 and m22 set to 1; all others are set to 0. This matrix maps a point to itself.
Translation is the simplest transformation. Setting dx and dy will move the coordinate system dx units along the X axis and dy units along the Y axis.
Scaling can be done by setting m11 and m22. For example, setting m11 to 2 and m22 to 1.5 will double the height and increase the width by 50%.
Shearing is controlled by m12 and m21. 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. The QWMatrix has a function that sets rotation directly.
QWMatrix lets you combine transformations like this:
QWMatrix m; // identity matrix
m.translate(10, -20); // first translate (10,-20)
m.rotate(25); // then rotate 25 degrees
m.scale(1.2, 0.7); // finally scale it
Here's the same example using basic matrix operations:
double a = pi/180 * 25; // convert 25 to radians
double sina = sin(a);
double cosa = cos(a);
QWMatrix m1(0, 0, 0, 0, 10, -20); // translation matrix
QWMatrix m2( cosa, sina, // rotation matrix
-sina, cosa, 0, 0 );
QWMatrix m3(1.2, 0, 0, 0.7, 0, 0); // scaling matrix
QWMatrix m;
m = m3 * m2 * m1; // combine all transformations
QPainter has functions to translate, scale, shear and rotate the coordinate system without using a QWMatrix. Although these functions are very convenient, it can be more efficient to build a QWMatrix and call QPainter::setWorldMatrix() if you want to perform more than a single transform operation.
See also QPainter::setWorldMatrix(), QPixmap::xForm(), Graphics Classes and Image Processing Classes.
Returns the horizontal translation.
Returns the vertical translation.
If the matrix is singular (not invertible), the identity matrix is returned.
If invertible is not null, the value of *invertible is set to TRUE if the matrix is invertible or to FALSE if the matrix is not invertible.
See also isInvertible().
Example: t14/cannon.cpp.
See also reset().
Returns TRUE if the matrix is invertible; otherwise returns FALSE.
See also invert().
Returns the X scaling factor.
Returns the vertical shearing factor.
Returns the horizontal shearing factor.
Returns the Y scaling factor.
*tx = m11*x + m21*y + dx (rounded to the nearest integer)
*ty = m22*y + m12*x + dy (rounded to the nearest integer)
Examples: t14/cannon.cpp and xform/xform.cpp.
Transforms ( x, y ) to ( *tx, *ty ) using the following formulae:
*tx = m11*x + m21*y + dx
*ty = m22*y + m12*x + dy
This function is obsolete. It is provided to keep old source working. We strongly advise against using it in new code.
Does the same as operator *( const QPoint &)
This function is obsolete. It is provided to keep old source working. We strongly advise against using it in new code.
Please use QWMatrix::mapRect() instead.
Note that this method does return the bounding rectangle of the r, when shearing or rotations are used.
This function is obsolete. It is provided to keep old source working. We strongly advise against using it in new code.
Does the same as operator *( const QPointArray &)
The bounding rectangle is returned if rotation or shearing has been specified.
If you need to know the exact region rect maps to use operator*().
See also operator*().
retx = m11*px + m21*py + dx (rounded to the nearest integer)
rety = m22*py + m12*px + dy (rounded to the nearest integer)
Transforms the rectangle r.
Rotation and shearing a rectangle results in a more general region, which is returned here.
Calling this method can be rather expensive, if rotations or shearing are used. If you just need to know the bounding rectangle of the returned region, use mapRect() which is a lot faster than this function.
See also QWMatrix::mapRect().
Transforms the region r.
Calling this method can be rather expensive, if rotations or shearing are used.
Returns the point array a transformed by calling map for each point.
All elements are set to zero, except m11 and m22 (scaling) that are set to 1.
See also isIdentity().
Returns a reference to the matrix.
See also translate(), scale() and shear().
Examples: canvas/canvas.cpp, desktop/desktop.cpp, drawdemo/drawdemo.cpp, t14/cannon.cpp and xform/xform.cpp.
Returns a reference to the matrix.
See also translate(), shear() and rotate().
Examples: canvas/canvas.cpp, fileiconview/qfileiconview.cpp, movies/main.cpp, qmag/qmag.cpp, qtimage/qtimage.cpp, showimg/showimg.cpp and xform/xform.cpp.
Returns a reference to the matrix.
See also translate(), scale() and rotate().
Examples: drawdemo/drawdemo.cpp and xform/xform.cpp.
Returns a reference to the matrix.
See also scale(), shear() and rotate().
Examples: canvas/canvas.cpp, drawdemo/drawdemo.cpp, t14/cannon.cpp and xform/xform.cpp.
Returns the product of m1 * m2.
Note that matrix multiplication is not commutative, i.e. a*b != b*a.
See also Format of the QDataStream operators.
See also Format of the QDataStream operators.
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