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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() and QPixmap::xForm().
If the matrix is singular (not invertible), the identity matrix is returned.
If *invertible is not null, the value of *invertible is set either to TRUE or FALSE to tell whether or not the matrix is invertible.
See also invertible().
Example: t14/cannon.cpp.
See also reset().
returns TRUE if the matrix is invertible, FALSE otherwise.
See also invert().
*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.
*tx = m11*x + m21*y + dx *ty = m22*y + m12*x + dy
The bounding rectangle is returned if rotation or shearing has been specified.
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: 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: 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: drawdemo/drawdemo.cpp, t14/cannon.cpp and xform/xform.cpp.
Remember that matrix multiplication is not commutative, thus a*b != b*a.
See also Format of the QDataStream operators.
See also Format of the QDataStream operators.
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