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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, and Y values increase downwards.
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, and 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 horisontal and vertical translation. The elements m11 and m22 specify horisontal and vertical scaling. The elements m12 and m21 specify horisontal and vertical shearing.
The identity matrix has m11 and m22 set to 1, all others 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
The same example, but 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 that translate, scale, shear and rotate the coordinate system without using a QWMatrix. These functions are very convenient, however, if you want to perform more than a single transform operation, it is more efficient to build a QWMatrix and call QPainter::setWorldMatrix().
See also QPainter::setWorldMatrix() and QPixmap::xForm().
Examples: qtimage/qtimage.cpp xform/xform.cpp drawdemo/drawdemo.cpp qmag/qmag.cpp desktop/desktop.cpp movies/main.cpp
Constructs an identity matrix. All elements are set to zero, except m11 and m22 (scaling) which are set to 1.
Constructs a matrix with the specified elements.
Returns the horizontal translation.
Returns the vertical translation.
Returns the inverted matrix.
If the matrix is singular (not invertible), then the identity matrix is returned.
If *invertible is not null, then the value of *invertible will be set to TRUE or FALSE to tell if the matrix is invertible or not.
Returns the X scaling factor.
Returns the vertical shearing factor.
Returns the horizontal shearing factor.
Returns the Y scaling factor.
Returns the transformed p.
Returns the point array a transformed by calling map for each point.
Examples: xform/xform.cpp
Returns the transformed rectangle r.
If rotation or shearing has been specified, then the bounding rectangle will be returned.
Transforms (x,y) to (*tx,*ty), using the formulae:
*tx = m11*x + m21*y + dx
*ty = m22*y + m12*x + dy
Transforms (x,y) to (*tx,*ty), using the formulae:
*tx = m11*x + m21*y + dx -- (rounded to the nearest integer)
*ty = m22*y + m12*x + dy -- (rounded to the nearest integer)
Returns TRUE if this matrix is not equal to m.
Returns the result of multiplying this matrix with m.
Returns TRUE if this matrix is equal to m.
Resets the matrix to an identity matrix.
All elements are set to zero, except m11 and m22 (scaling) that are set to 1.
Rotates the coordinate system a degrees counterclockwise.
Returns a reference to the matrix.
See also translate(), scale() and shear().
Examples: xform/xform.cpp drawdemo/drawdemo.cpp desktop/desktop.cpp
Scales the coordinate system unit by sx horizontally and sy vertically.
Returns a reference to the matrix.
See also translate(), shear() and rotate().
Examples: qtimage/qtimage.cpp xform/xform.cpp movies/main.cpp
Sets the matrix elements to the specified values.
Shears the coordinate system by sh horizontally and sv vertically.
Returns a reference to the matrix.
See also translate(), scale() and rotate().
Examples: xform/xform.cpp drawdemo/drawdemo.cpp
Moves the coordinate system dx along the X-axis and dy along the Y-axis.
Returns a reference to the matrix.
See also scale(), shear() and rotate().
Examples: xform/xform.cpp drawdemo/drawdemo.cpp
Returns the product m1 * m2.
Remember that matrix multiplication is not commutative, thus a*b != b*a.
Writes a matrix to the stream and returns a reference to the stream.
See also Format of the QDataStream operators
Reads a matrix from the stream and returns a reference to the stream.
See also Format of the QDataStream operators
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