qwmatrix.3qt

Linux下的基于X11的图形开发环境。

'\" t
.TH QWMatrix 3qt "9 December 2002" "Trolltech AS" \" -*- nroff -*-
.\" Copyright 1992-2001 Trolltech AS.  All rights reserved.  See the
.\" license file included in the distribution for a complete license
.\" statement.
.\"
.ad l
.nh
.SH NAME
QWMatrix \- 2D transformations of a coordinate system
.SH SYNOPSIS
\fC#include <qwmatrix.h>\fR
.PP
.SS "Public Members"
.in +1c
.ti -1c
.BI "\fBQWMatrix\fR ()"
.br
.ti -1c
.BI "\fBQWMatrix\fR ( double m11, double m12, double m21, double m22, double dx, double dy )"
.br
.ti -1c
.BI "void \fBsetMatrix\fR ( double m11, double m12, double m21, double m22, double dx, double dy )"
.br
.ti -1c
.BI "double \fBm11\fR () const"
.br
.ti -1c
.BI "double \fBm12\fR () const"
.br
.ti -1c
.BI "double \fBm21\fR () const"
.br
.ti -1c
.BI "double \fBm22\fR () const"
.br
.ti -1c
.BI "double \fBdx\fR () const"
.br
.ti -1c
.BI "double \fBdy\fR () const"
.br
.ti -1c
.BI "void \fBmap\fR ( int x, int y, int * tx, int * ty ) const"
.br
.ti -1c
.BI "void \fBmap\fR ( double x, double y, double * tx, double * ty ) const"
.br
.ti -1c
.BI "QRect \fBmapRect\fR ( const QRect & rect ) const"
.br
.ti -1c
.BI "QPoint \fBmap\fR ( const QPoint & p ) const"
.br
.ti -1c
.BI "QRect map ( const QRect & r ) const  \fI(obsolete)\fR"
.br
.ti -1c
.BI "QPointArray \fBmap\fR ( const QPointArray & a ) const"
.br
.ti -1c
.BI "QRegion \fBmap\fR ( const QRegion & r ) const"
.br
.ti -1c
.BI "QRegion \fBmapToRegion\fR ( const QRect & rect ) const"
.br
.ti -1c
.BI "QPointArray \fBmapToPolygon\fR ( const QRect & rect ) const"
.br
.ti -1c
.BI "void \fBreset\fR ()"
.br
.ti -1c
.BI "bool \fBisIdentity\fR () const"
.br
.ti -1c
.BI "QWMatrix & \fBtranslate\fR ( double dx, double dy )"
.br
.ti -1c
.BI "QWMatrix & \fBscale\fR ( double sx, double sy )"
.br
.ti -1c
.BI "QWMatrix & \fBshear\fR ( double sh, double sv )"
.br
.ti -1c
.BI "QWMatrix & \fBrotate\fR ( double a )"
.br
.ti -1c
.BI "bool \fBisInvertible\fR () const"
.br
.ti -1c
.BI "double \fBdet\fR () const"
.br
.ti -1c
.BI "QWMatrix \fBinvert\fR ( bool * invertible = 0 ) const"
.br
.ti -1c
.BI "bool \fBoperator==\fR ( const QWMatrix & m ) const"
.br
.ti -1c
.BI "bool \fBoperator!=\fR ( const QWMatrix & m ) const"
.br
.ti -1c
.BI "QWMatrix & \fBoperator*=\fR ( const QWMatrix & m )"
.br
.ti -1c
.BI "enum \fBTransformationMode\fR { Points, Areas }"
.br
.in -1c
.SS "Static Public Members"
.in +1c
.ti -1c
.BI "void \fBsetTransformationMode\fR ( QWMatrix::TransformationMode m )"
.br
.ti -1c
.BI "TransformationMode \fBtransformationMode\fR ()"
.br
.in -1c
.SH RELATED FUNCTION DOCUMENTATION
.in +1c
.ti -1c
.BI "QDataStream & \fBoperator<<\fR ( QDataStream & s, const QWMatrix & m )"
.br
.ti -1c
.BI "QDataStream & \fBoperator>>\fR ( QDataStream & s, QWMatrix & m )"
.br
.in -1c
.SH DESCRIPTION
The QWMatrix class specifies 2D transformations of a coordinate system.
.PP
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.
.PP
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.
.PP
Example:
.PP
.nf
.br
        MyWidget::paintEvent( QPaintEvent * )
.br
        {
.br
            QPainter p;                      // our painter
.br
            QWMatrix m;                      // our transformation matrix
.br
            m.rotate( 22.5 );                // rotated coordinate system
.br
            p.begin( this );                 // start painting
.br
            p.setWorldMatrix( m );           // use rotated coordinate system
.br
            p.drawText( 30,20, "detator" );  // draw rotated text at 30,20
.br
            p.end();                         // painting done
.br
        }
.br
.fi
.PP
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().
.PP
The QWMatrix class contains a 3x3 matrix of the form:
.nf
.TS
l
-
l.
m11	m12	0
m21	m22	0
dx	dy	1
.TE
.fi

.PP
A matrix transforms a point in the plane to another point:
.PP
.nf
.br
        x' = m11*x + m21*y + dx
.br
        y' = m22*y + m12*x + dy
.br
.fi
.PP
The point \fI(x, y)\fR is the original point, and \fI(x', y')\fR is the transformed point. \fI(x', y')\fR can be transformed back to \fI(x, y)\fR by performing the same operation on the inverted matrix.
.PP
The elements \fIdx\fR and \fIdy\fR specify horizontal and vertical translation. The elements \fIm11\fR and \fIm22\fR specify horizontal and vertical scaling. The elements \fIm12\fR and \fIm21\fR specify horizontal and vertical shearing.
.PP
The identity matrix has \fIm11\fR and \fIm22\fR set to 1; all others are set to 0. This matrix maps a point to itself.
.PP
Translation is the simplest transformation. Setting \fIdx\fR and \fIdy\fR will move the coordinate system \fIdx\fR units along the X axis and \fIdy\fR units along the Y axis.
.PP
Scaling can be done by setting \fIm11\fR and \fIm22\fR. For example, setting \fIm11\fR to 2 and \fIm22\fR to 1.5 will double the height and increase the width by 50%.
.PP
Shearing is controlled by \fIm12\fR and \fIm21\fR. Setting these elements to values different from zero will twist the coordinate system.
.PP
Rotation is achieved by carefully setting both the shearing factors and the scaling factors. The QWMatrix also has a function that sets rotation directly.
.PP
QWMatrix lets you combine transformations like this:
.PP
.nf
.br
        QWMatrix m;           // identity matrix
.br
        m.translate(10, -20); // first translate (10,-20)
.br
        m.rotate(25);         // then rotate 25 degrees
.br
        m.scale(1.2, 0.7);    // finally scale it
.br
.fi
.PP
Here's the same example using basic matrix operations:
.PP
.nf
.br
        double a    = pi/180 * 25;         // convert 25 to radians
.br
        double sina = sin(a);
.br
        double cosa = cos(a);
.br
        QWMatrix m1(0, 0, 0, 0, 10, -20);  // translation matrix
.br
        QWMatrix m2( cosa, sina,           // rotation matrix
.br
                    -sina, cosa, 0, 0 );
.br
        QWMatrix m3(1.2, 0, 0, 0.7, 0, 0); // scaling matrix
.br
        QWMatrix m;
.br
        m = m3 * m2 * m1;                  // combine all transformations
.br
.fi