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 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
────
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(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].
<center>
[Image Omitted]
</center>
MEMBER FUNCTION DOCUMENTATIONQWMatrix::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*().
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:
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 X-axis and dy along the Y-
axis.
Returns a reference to the matrix.
See also scale(), shear(), and rotate().
Examples:
RELATED FUNCTION DOCUMENTATIONQDataStream & 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 1992-2007 Trolltech ASA, 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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(qwmatrix.3qt) and the Qt version (3.3.8).
Trolltech AS 2 February 2007 QWMatrix(3qt)
