Detailed Description
The QWMatrix class specifies 2D transformations of a
coordinate system.
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 the 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 3x3 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 also 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(1, 0, 0, 1, 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.
Member Type Documentation
QWMatrix::TransformationMode
QWMatrix offers two transformation modes. Calculations can either
be done in terms of points (Points mode, the default), or in
terms of area (Area mode).
In Points mode the transformation is applied to the points that
mark out the shape's bounding line. In Areas mode the
transformation is applied in such a way that the area of the
contained region is correctly transformed under the matrix.
- QWMatrix::Points - transformations are applied to the shape's points.
- QWMatrix::Areas - transformations are applied (e.g. to the width and
height) so that the area is transformed.
Example:
Suppose we have a rectangle,
QRect( 10, 20, 30, 40 ) and a transformation matrix
QWMatrix( 2, 0, 0, 2, 0, 0 ) to double the rectangle's size.
In Points mode, the matrix will transform the top-left (10,20) and
the bottom-right (39,59) points producing a rectangle with its
top-left point at (20,40) and its bottom-right point at (78,118),
i.e. with a width of 59 and a height of 79.
In Areas mode, the matrix will transform the top-left point in
the same way as in Points mode to (20/40), and double the width
and height, so the bottom-right will become (69,99), i.e. a width
of 60 and a height of 80.
Because integer arithmetic is used (for speed), rounding
differences mean that the modes will produce slightly different
results given the same shape and the same transformation,
especially when scaling up. This also means that some operations
are not commutative.
Under Points mode, matrix * ( region1 | region2 ) is not equal to
matrix * region1 | matrix * region2. Under Area mode, matrix * (pointarray[i]) is not neccesarily equal to
(matrix * pointarry)[i].
Member Function Documentation
QWMatrix::QWMatrix ()
Constructs an identity matrix. All elements are set to zero except
m11 and m22 (scaling), which are set to 1.
QWMatrix::QWMatrix ( double m11, double m12, double m21, double m22, double dx, double dy )
Constructs a matrix with the elements, m11, m12, m21, m22, dx and dy.
double QWMatrix::det () const
Returns the matrix's determinant.
double QWMatrix::dx () const
Returns the horizontal translation.
double QWMatrix::dy () const
Returns the vertical translation.
QWMatrix QWMatrix::invert ( bool * invertible = 0 ) const
Returns the inverted matrix.
If the matrix is singular (not invertible), the identity matrix is
returned.
If invertible is not 0: the value of *invertible is set
to TRUE if the matrix is invertible; otherwise *invertible is
set to FALSE.
See also isInvertible().
Example: t14/cannon.cpp.
bool QWMatrix::isIdentity () const
Returns TRUE if the matrix is the identity matrix; otherwise returns FALSE.
See also reset().
bool QWMatrix::isInvertible () const
Returns TRUE if the matrix is invertible; otherwise returns FALSE.
See also invert().
double QWMatrix::m11 () const
Returns the X scaling factor.
double QWMatrix::m12 () const
Returns the vertical shearing factor.
double QWMatrix::m21 () const
Returns the horizontal shearing factor.
double QWMatrix::m22 () const
Returns the Y scaling factor.
void QWMatrix::map ( int x, int y, int * tx, int * ty ) const
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)
Examples: t14/cannon.cpp and xform/xform.cpp.
void QWMatrix::map ( double x, double y, double * tx, double * ty ) const
This is an overloaded member function, provided for convenience. It behaves essentially like the above function.
Transforms ( x, y ) to ( *tx, *ty ) using the
following formulae:
*tx = m11*x + m21*y + dx
*ty = m22*y + m12*x + dy
QPoint QWMatrix::map ( const QPoint & p ) const
This is an overloaded member function, provided for convenience. It behaves essentially like the above function.
Transforms p to using the formulae:
retx = m11*px + m21*py + dx (rounded to the nearest integer)
rety = m22*py + m12*px + dy (rounded to the nearest integer)
QRect QWMatrix::map ( const QRect & r ) const
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 is an overloaded member function, provided for convenience. It behaves essentially like the above function.
Returns the point array a transformed by calling map for each point.
QRegion QWMatrix::map ( const QRegion & r ) const
This is an overloaded member function, provided for convenience. It behaves essentially like the above function.
Transforms the region r.
Calling this method can be rather expensive, if rotations or
shearing are used.
QRect QWMatrix::mapRect ( const QRect & rect ) const
Returns the transformed rectangle rect.
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*().
Example: xform/xform.cpp.
QPointArray QWMatrix::mapToPolygon ( const QRect & rect ) const
Returns the transformed rectangle rect as a polygon.
Polygons and rectangles behave slightly differently
when transformed (due to integer rounding), so
matrix.map( QPointArray( rect ) ) is not always the same as
matrix.mapToPolygon( rect ).
QRegion QWMatrix::mapToRegion ( const QRect & rect ) const
Returns the transformed rectangle rect.
A rectangle which has been rotated or sheared may result in a
non-rectangular region being returned.
Calling this method can be 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().
bool QWMatrix::operator!= ( const QWMatrix & m ) const
Returns TRUE if this matrix is not equal to m; otherwise returns FALSE.
QWMatrix & QWMatrix::operator*= ( const QWMatrix & m )
Returns the result of multiplying this matrix by matrix m.
bool QWMatrix::operator== ( const QWMatrix & m ) const
Returns TRUE if this matrix is equal to m; otherwise returns FALSE.
void QWMatrix::reset ()
Resets the matrix to an identity matrix.
All elements are set to zero, except m11 and m22 (scaling)
which are set to 1.
See also isIdentity().
QWMatrix & QWMatrix::rotate ( double a )
Rotates the coordinate system a degrees counterclockwise.
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.
QWMatrix & QWMatrix::scale ( double sx, double sy )
Scales the coordinate system unit by sx horizontally and sy
vertically.
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, showimg/showimg.cpp, and xform/xform.cpp.
void QWMatrix::setMatrix ( double m11, double m12, double m21, double m22, double dx, double dy )
Sets the matrix elements to the specified values, m11, m12,
m21, m22, dx and dy.
Sets the transformation mode that QWMatrix and painter
transformations use to m.
See also QWMatrix::TransformationMode.
QWMatrix & QWMatrix::shear ( double sh, double sv )
Shears the coordinate system by sh horizontally and sv
vertically.
Returns a reference to the matrix.
See also translate(), scale(), and rotate().
Examples: drawdemo/drawdemo.cpp and xform/xform.cpp.
TransformationMode QWMatrix::transformationMode () [static]
Returns the current transformation mode.
See also QWMatrix::TransformationMode.
QWMatrix & QWMatrix::translate ( double dx, double dy )
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: canvas/canvas.cpp, drawdemo/drawdemo.cpp, t14/cannon.cpp, and xform/xform.cpp.
Related Functions
Writes the matrix m to the stream s and returns a reference
to the stream.
See also Format of the QDataStream operators.
Reads the matrix m from the stream s and returns a reference
to the stream.
See also Format of the QDataStream operators.
This file is part of the Qt toolkit.
Copyright © 1995-2005
Trolltech. All Rights Reserved.
