
QWMatrix(3qt) QWMatrix(3qt)
NAME
QWMatrix  2D transformations of a coordinate system
SYNOPSIS
#include <qwmatrix.h>
Public Members
QWMatrix ()
QWMatrix ( double m11, double m12, double m21, double m22, double dx, double dy )
void setMatrix ( double m11, double m12, double m21, double m22, double dx, double dy )
double m11 () const
double m12 () const
double m21 () const
double m22 () const
double dx () const
double dy () const
void map ( int x, int y, int * tx, int * ty ) const
void map ( double x, double y, double * tx, double * ty ) const
QRect mapRect ( const QRect & rect ) const
QPoint map ( const QPoint & p ) const
QRect map ( const QRect & r ) const (obsolete)
QPointArray map ( const QPointArray & a ) const
QRegion map ( const QRegion & r ) const
QRegion mapToRegion ( const QRect & rect ) const
QPointArray mapToPolygon ( const QRect & rect ) const
void reset ()
bool isIdentity () const
QWMatrix & translate ( double dx, double dy )
QWMatrix & scale ( double sx, double sy )
QWMatrix & shear ( double sh, double sv )
QWMatrix & rotate ( double a )
bool isInvertible () const
double det () const
QWMatrix invert ( bool * invertible = 0 ) const
bool operator== ( const QWMatrix & m ) const
bool operator!= ( const QWMatrix & m ) const
QWMatrix & operator*= ( const QWMatrix & m )
enum TransformationMode { Points, Areas }
Static Public Members
void setTransformationMode ( QWMatrix::TransformationMode m )
TransformationMode transformationMode ()
RELATED FUNCTION DOCUMENTATION
QDataStream & operator<< ( QDataStream & s, const QWMatrix & m )
QDataStream & operator>> ( QDataStream & s, QWMatrix & m )
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 topleft
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 userdefined 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

m21
dx
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(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.
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 topleft (10,20) and the bottomright
(39,59) points producing a rectangle with its topleft 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 topleft point in the same way as in Points
mode to (20/40), and double the width and height, so the bottomright 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].
<center>
[Image Omitted]
</center>
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:
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.
QPointArray QWMatrix::map ( const QPointArray & a ) const
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*().
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 nonrectangular 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:
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:
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.
void QWMatrix::setTransformationMode ( QWMatrix::TransformationMode m ) [static]
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:
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 Xaxis and dy along the Yaxis.
Returns a reference to the matrix.
See also scale(), shear(), and rotate().
Examples:
RELATED FUNCTION DOCUMENTATION
QDataStream &; operator<< ( QDataStream & s, const QWMatrix & m )
Writes the matrix m to the stream s and returns a reference to the stream.
See also Format of the QDataStream operators.
QDataStream &; operator>> ( QDataStream & s, QWMatrix & m )
Reads the matrix m from the stream s and returns a reference to the stream.
See also Format of the QDataStream operators.
SEE ALSO
http://doc.trolltech.com/qwmatrix.html http://www.trolltech.com/faq/tech.html
COPYRIGHT
Copyright 19922001 Trolltech AS, http://www.trolltech.com. See the license file included
in the distribution for a complete license statement.
AUTHOR
Generated automatically from the source code.
BUGS
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If you find errors in this manual page, please report them to qtbugs@trolltech.com.
Please include the name of the manual page (qwmatrix.3qt) and the Qt version (3.1.1).
Trolltech AS 9 December 2002 QWMatrix(3qt) 
