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+/****************************************************************************
+**
+** Copyright (C) 2009 Nokia Corporation and/or its subsidiary(-ies).
+** Contact: Qt Software Information (qt-info@nokia.com)
+**
+** This file is part of the QtGui module of the Qt Toolkit.
+**
+** $QT_BEGIN_LICENSE:LGPL$
+** No Commercial Usage
+** This file contains pre-release code and may not be distributed.
+** You may use this file in accordance with the terms and conditions
+** contained in the either Technology Preview License Agreement or the
+** Beta Release License Agreement.
+**
+** GNU Lesser General Public License Usage
+** Alternatively, this file may be used under the terms of the GNU Lesser
+** General Public License version 2.1 as published by the Free Software
+** Foundation and appearing in the file LICENSE.LGPL included in the
+** packaging of this file. Please review the following information to
+** ensure the GNU Lesser General Public License version 2.1 requirements
+** will be met: http://www.gnu.org/licenses/old-licenses/lgpl-2.1.html.
+**
+** In addition, as a special exception, Nokia gives you certain
+** additional rights. These rights are described in the Nokia Qt LGPL
+** Exception version 1.0, included in the file LGPL_EXCEPTION.txt in this
+** package.
+**
+** GNU General Public License Usage
+** Alternatively, this file may be used under the terms of the GNU
+** General Public License version 3.0 as published by the Free Software
+** Foundation and appearing in the file LICENSE.GPL included in the
+** packaging of this file. Please review the following information to
+** ensure the GNU General Public License version 3.0 requirements will be
+** met: http://www.gnu.org/copyleft/gpl.html.
+**
+** If you are unsure which license is appropriate for your use, please
+** contact the sales department at qt-sales@nokia.com.
+** $QT_END_LICENSE$
+**
+****************************************************************************/
+#include "qtransform.h"
+
+#include "qdatastream.h"
+#include "qdebug.h"
+#include "qmatrix.h"
+#include "qregion.h"
+#include "qpainterpath.h"
+#include "qvariant.h"
+#include <qmath.h>
+
+QT_BEGIN_NAMESPACE
+
+#define Q_NEAR_CLIP 0.000001
+
+
+#define MAP(x, y, nx, ny) \
+ do { \
+ qreal FX_ = x; \
+ qreal FY_ = y; \
+ switch(t) { \
+ case TxNone: \
+ nx = FX_; \
+ ny = FY_; \
+ break; \
+ case TxTranslate: \
+ nx = FX_ + affine._dx; \
+ ny = FY_ + affine._dy; \
+ break; \
+ case TxScale: \
+ nx = affine._m11 * FX_ + affine._dx; \
+ ny = affine._m22 * FY_ + affine._dy; \
+ break; \
+ case TxRotate: \
+ case TxShear: \
+ case TxProject: \
+ nx = affine._m11 * FX_ + affine._m21 * FY_ + affine._dx; \
+ ny = affine._m12 * FX_ + affine._m22 * FY_ + affine._dy; \
+ if (t == TxProject) { \
+ qreal w = 1./(m_13 * FX_ + m_23 * FY_ + m_33); \
+ nx *= w; \
+ ny *= w; \
+ } \
+ } \
+ } while (0)
+
+/*!
+ \class QTransform
+ \brief The QTransform class specifies 2D transformations of a coordinate system.
+ \since 4.3
+ \ingroup multimedia
+
+ A transformation specifies how to translate, scale, shear, rotate
+ or project the coordinate system, and is typically used when
+ rendering graphics.
+
+ QTransform differs from QMatrix in that it is a true 3x3 matrix,
+ allowing perspective transformations. QTransform's toAffine()
+ method allows casting QTransform to QMatrix. If a perspective
+ transformation has been specified on the matrix, then the
+ conversion to an affine QMatrix will cause loss of data.
+
+ QTransform is the recommended transformation class in Qt.
+
+ A QTransform object can be built using the setMatrix(), scale(),
+ rotate(), translate() and shear() functions. Alternatively, it
+ can be built by applying \l {QTransform#Basic Matrix
+ Operations}{basic matrix operations}. The matrix can also be
+ defined when constructed, and it can be reset to the identity
+ matrix (the default) using the reset() function.
+
+ The QTransform class supports mapping of graphic primitives: A given
+ point, line, polygon, region, or painter path can be mapped to the
+ coordinate system defined by \e this matrix using the map()
+ function. In case of a rectangle, its coordinates can be
+ transformed using the mapRect() function. A rectangle can also be
+ transformed into a \e polygon (mapped to the coordinate system
+ defined by \e this matrix), using the mapToPolygon() function.
+
+ QTransform provides the isIdentity() function which returns true if
+ the matrix is the identity matrix, and the isInvertible() function
+ which returns true if the matrix is non-singular (i.e. AB = BA =
+ I). The inverted() function returns an inverted copy of \e this
+ matrix if it is invertible (otherwise it returns the identity
+ matrix). In addition, QTransform provides the det() function
+ returning the matrix's determinant.
+
+ Finally, the QTransform class supports matrix multiplication, and
+ objects of the class can be streamed as well as compared.
+
+ \tableofcontents
+
+ \section1 Rendering Graphics
+
+ When rendering graphics, the matrix defines the transformations
+ but the actual transformation is performed by the drawing routines
+ in QPainter.
+
+ By default, QPainter operates on the associated device's own
+ coordinate system. The standard coordinate system of a
+ QPaintDevice has its origin located at the top-left position. The
+ \e x values increase to the right; \e y values increase
+ downward. For a complete description, see the \l {The Coordinate
+ System}{coordinate system} documentation.
+
+ QPainter has functions to translate, scale, shear and rotate the
+ coordinate system without using a QTransform. For example:
+
+ \table 100%
+ \row
+ \o \inlineimage qtransform-simpletransformation.png
+ \o
+ \snippet doc/src/snippets/transform/main.cpp 0
+ \endtable
+
+ Although these functions are very convenient, it can be more
+ efficient to build a QTransform and call QPainter::setTransform() if you
+ want to perform more than a single transform operation. For
+ example:
+
+ \table 100%
+ \row
+ \o \inlineimage qtransform-combinedtransformation.png
+ \o
+ \snippet doc/src/snippets/transform/main.cpp 1
+ \endtable
+
+ \section1 Basic Matrix Operations
+
+ \image qtransform-representation.png
+
+ A QTransform object contains a 3 x 3 matrix. The \c dx and \c dy
+ elements specify horizontal and vertical translation. The \c m11
+ and \c m22 elements specify horizontal and vertical scaling. The
+ \c m21 and \c m12 elements specify horizontal and vertical \e shearing.
+ And finally, the \c m13 and \c m23 elements specify horizontal and vertical
+ projection, with \c m33 as an additional projection factor.
+
+ QTransform transforms a point in the plane to another point using the
+ following formulas:
+
+ \snippet doc/src/snippets/code/src_gui_painting_qtransform.cpp 0
+
+ The point \e (x, y) is the original point, and \e (x', y') is the
+ transformed point. \e (x', y') can be transformed back to \e (x,
+ y) by performing the same operation on the inverted() matrix.
+
+ The various matrix elements can be set when constructing the
+ matrix, or by using the setMatrix() function later on. They can also
+ be manipulated using the translate(), rotate(), scale() and
+ shear() convenience functions, The currently set values can be
+ retrieved using the m11(), m12(), m13(), m21(), m22(), m23(),
+ m31(), m32(), m33(), dx() and dy() functions.
+
+ Translation is the simplest transformation. Setting \c dx and \c
+ dy will move the coordinate system \c dx units along the X axis
+ and \c dy units along the Y axis. Scaling can be done by setting
+ \c m11 and \c m22. For example, setting \c m11 to 2 and \c m22 to
+ 1.5 will double the height and increase the width by 50%. The
+ identity matrix has \c m11, \c m22, and \c m33 set to 1 (all others are set
+ to 0) mapping a point to itself. Shearing is controlled by \c m12
+ and \c 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. Perspective transformation is achieved by carefully setting
+ both the projection factors and the scaling factors.
+
+ Here's the combined transformations example using basic matrix
+ operations:
+
+ \table 100%
+ \row
+ \o \inlineimage qtransform-combinedtransformation2.png
+ \o
+ \snippet doc/src/snippets/transform/main.cpp 2
+ \endtable
+
+ \sa QPainter, {The Coordinate System}, {demos/affine}{Affine
+ Transformations Demo}, {Transformations Example}
+*/
+
+/*!
+ \enum QTransform::TransformationType
+
+ \value TxNone
+ \value TxTranslate
+ \value TxScale
+ \value TxRotate
+ \value TxShear
+ \value TxProject
+*/
+
+/*!
+ Constructs an identity matrix.
+
+ All elements are set to zero except \c m11 and \c m22 (specifying
+ the scale) and \c m13 which are set to 1.
+
+ \sa reset()
+*/
+QTransform::QTransform()
+ : m_13(0), m_23(0), m_33(1)
+ , m_type(TxNone)
+ , m_dirty(TxNone)
+{
+
+}
+
+/*!
+ Constructs a matrix with the elements, \a h11, \a h12, \a h13,
+ \a h21, \a h22, \a h23, \a h31, \a h32, \a h33.
+
+ \sa setMatrix()
+*/
+QTransform::QTransform(qreal h11, qreal h12, qreal h13,
+ qreal h21, qreal h22, qreal h23,
+ qreal h31, qreal h32, qreal h33)
+ : affine(h11, h12, h21, h22, h31, h32),
+ m_13(h13), m_23(h23), m_33(h33)
+ , m_type(TxNone)
+ , m_dirty(TxProject)
+{
+
+}
+
+/*!
+ Constructs a matrix with the elements, \a h11, \a h12, \a h21, \a
+ h22, \a dx and \a dy.
+
+ \sa setMatrix()
+*/
+QTransform::QTransform(qreal h11, qreal h12, qreal h21,
+ qreal h22, qreal dx, qreal dy)
+ : affine(h11, h12, h21, h22, dx, dy),
+ m_13(0), m_23(0), m_33(1)
+ , m_type(TxNone)
+ , m_dirty(TxShear)
+{
+
+}
+
+/*!
+ \fn QTransform::QTransform(const QMatrix &matrix)
+
+ Constructs a matrix that is a copy of the given \a matrix.
+ Note that the \c m13, \c m23, and \c m33 elements are set to 0, 0,
+ and 1 respectively.
+ */
+QTransform::QTransform(const QMatrix &mtx)
+ : affine(mtx),
+ m_13(0), m_23(0), m_33(1)
+ , m_type(TxNone)
+ , m_dirty(TxShear)
+{
+
+}
+
+/*!
+ Returns the adjoint of this matrix.
+*/
+QTransform QTransform::adjoint() const
+{
+ qreal h11, h12, h13,
+ h21, h22, h23,
+ h31, h32, h33;
+ h11 = affine._m22*m_33 - m_23*affine._dy;
+ h21 = m_23*affine._dx - affine._m21*m_33;
+ h31 = affine._m21*affine._dy - affine._m22*affine._dx;
+ h12 = m_13*affine._dy - affine._m12*m_33;
+ h22 = affine._m11*m_33 - m_13*affine._dx;
+ h32 = affine._m12*affine._dx - affine._m11*affine._dy;
+ h13 = affine._m12*m_23 - m_13*affine._m22;
+ h23 = m_13*affine._m21 - affine._m11*m_23;
+ h33 = affine._m11*affine._m22 - affine._m12*affine._m21;
+
+ return QTransform(h11, h12, h13,
+ h21, h22, h23,
+ h31, h32, h33);
+}
+
+/*!
+ Returns the transpose of this matrix.
+*/
+QTransform QTransform::transposed() const
+{
+ QTransform t(affine._m11, affine._m21, affine._dx,
+ affine._m12, affine._m22, affine._dy,
+ m_13, m_23, m_33);
+ t.m_type = m_type;
+ t.m_dirty = m_dirty;
+ return t;
+}
+
+/*!
+ Returns an inverted copy of this matrix.
+
+ If the matrix is singular (not invertible), the returned matrix is
+ the identity matrix. If \a invertible is valid (i.e. not 0), its
+ value is set to true if the matrix is invertible, otherwise it is
+ set to false.
+
+ \sa isInvertible()
+*/
+QTransform QTransform::inverted(bool *invertible) const
+{
+ QTransform invert;
+ bool inv = true;
+ qreal det;
+
+ switch(type()) {
+ case TxNone:
+ break;
+ case TxTranslate:
+ invert.affine._dx = -affine._dx;
+ invert.affine._dy = -affine._dy;
+ break;
+ case TxScale:
+ inv = !qFuzzyCompare(affine._m11 + 1, 1);
+ inv &= !qFuzzyCompare(affine._m22 + 1, 1);
+ if (inv) {
+ invert.affine._m11 = 1 / affine._m11;
+ invert.affine._m22 = 1 / affine._m22;
+ invert.affine._dx = -affine._dx * invert.affine._m11;
+ invert.affine._dy = -affine._dy * invert.affine._m22;
+ }
+ break;
+ case TxRotate:
+ case TxShear:
+ invert.affine = affine.inverted(&inv);
+ break;
+ default:
+ // general case
+ det = determinant();
+ inv = !qFuzzyCompare(det + 1, 1);
+ if (inv)
+ invert = adjoint() / det;
+ break;
+ }
+
+ if (invertible)
+ *invertible = inv;
+
+ if (inv) {
+ // inverting doesn't change the type
+ invert.m_type = m_type;
+ invert.m_dirty = m_dirty;
+ }
+
+ return invert;
+}
+
+/*!
+ Moves the coordinate system \a dx along the x axis and \a dy along
+ the y axis, and returns a reference to the matrix.
+
+ \sa setMatrix()
+*/
+QTransform & QTransform::translate(qreal dx, qreal dy)
+{
+ switch(type()) {
+ case TxNone:
+ affine._dx = dx;
+ affine._dy = dy;
+ break;
+ case TxTranslate:
+ affine._dx += dx;
+ affine._dy += dy;
+ break;
+ case TxScale:
+ affine._dx += dx*affine._m11;
+ affine._dy += dy*affine._m22;
+ break;
+ case TxProject:
+ m_33 += dx*m_13 + dy*m_23;
+ // Fall through
+ case TxShear:
+ case TxRotate:
+ affine._dx += dx*affine._m11 + dy*affine._m21;
+ affine._dy += dy*affine._m22 + dx*affine._m12;
+ break;
+ }
+ m_dirty |= TxTranslate;
+ return *this;
+}
+
+/*!
+ Creates a matrix which corresponds to a translation of \a dx along
+ the x axis and \a dy along the y axis. This is the same as
+ QTransform().translate(dx, dy) but slightly faster.
+
+ \since 4.5
+*/
+QTransform QTransform::fromTranslate(qreal dx, qreal dy)
+{
+ QTransform transform(1, 0, 0, 1, dx, dy);
+ transform.m_dirty = TxTranslate;
+ return transform;
+}
+
+/*!
+ Scales the coordinate system by \a sx horizontally and \a sy
+ vertically, and returns a reference to the matrix.
+
+ \sa setMatrix()
+*/
+QTransform & QTransform::scale(qreal sx, qreal sy)
+{
+ switch(type()) {
+ case TxNone:
+ case TxTranslate:
+ affine._m11 = sx;
+ affine._m22 = sy;
+ break;
+ case TxProject:
+ m_13 *= sx;
+ m_23 *= sy;
+ // fall through
+ case TxRotate:
+ case TxShear:
+ affine._m12 *= sx;
+ affine._m21 *= sy;
+ // fall through
+ case TxScale:
+ affine._m11 *= sx;
+ affine._m22 *= sy;
+ break;
+ }
+ m_dirty |= TxScale;
+ return *this;
+}
+
+/*!
+ Creates a matrix which corresponds to a scaling of
+ \a sx horizontally and \a sy vertically.
+ This is the same as QTransform().scale(sx, sy) but slightly faster.
+
+ \since 4.5
+*/
+QTransform QTransform::fromScale(qreal sx, qreal sy)
+{
+ QTransform transform(sx, 0, 0, sy, 0, 0);
+ transform.m_dirty = TxScale;
+ return transform;
+}
+
+/*!
+ Shears the coordinate system by \a sh horizontally and \a sv
+ vertically, and returns a reference to the matrix.
+
+ \sa setMatrix()
+*/
+QTransform & QTransform::shear(qreal sh, qreal sv)
+{
+ switch(type()) {
+ case TxNone:
+ case TxTranslate:
+ affine._m12 = sv;
+ affine._m21 = sh;
+ break;
+ case TxScale:
+ affine._m12 = sv*affine._m22;
+ affine._m21 = sh*affine._m11;
+ break;
+ case TxProject: {
+ qreal tm13 = sv*m_23;
+ qreal tm23 = sh*m_13;
+ m_13 += tm13;
+ m_23 += tm23;
+ }
+ // fall through
+ case TxRotate:
+ case TxShear: {
+ qreal tm11 = sv*affine._m21;
+ qreal tm22 = sh*affine._m12;
+ qreal tm12 = sv*affine._m22;
+ qreal tm21 = sh*affine._m11;
+ affine._m11 += tm11; affine._m12 += tm12;
+ affine._m21 += tm21; affine._m22 += tm22;
+ break;
+ }
+ }
+ m_dirty |= TxShear;
+ return *this;
+}
+
+const qreal deg2rad = qreal(0.017453292519943295769); // pi/180
+const qreal inv_dist_to_plane = 1. / 1024.;
+
+/*!
+ \fn QTransform &QTransform::rotate(qreal angle, Qt::Axis axis)
+
+ Rotates the coordinate system counterclockwise by the given \a angle
+ about the specified \a axis and returns a reference to the matrix.
+
+ Note that if you apply a QTransform to a point defined in widget
+ coordinates, the direction of the rotation will be clockwise
+ because the y-axis points downwards.
+
+ The angle is specified in degrees.
+
+ \sa setMatrix()
+*/
+QTransform & QTransform::rotate(qreal a, Qt::Axis axis)
+{
+ qreal sina = 0;
+ qreal cosa = 0;
+ if (a == 90. || a == -270.)
+ sina = 1.;
+ else if (a == 270. || a == -90.)
+ sina = -1.;
+ else if (a == 180.)
+ cosa = -1.;
+ else{
+ qreal b = deg2rad*a; // convert to radians
+ sina = qSin(b); // fast and convenient
+ cosa = qCos(b);
+ }
+
+ if (axis == Qt::ZAxis) {
+ switch(type()) {
+ case TxNone:
+ case TxTranslate:
+ affine._m11 = cosa;
+ affine._m12 = sina;
+ affine._m21 = -sina;
+ affine._m22 = cosa;
+ break;
+ case TxScale: {
+ qreal tm11 = cosa*affine._m11;
+ qreal tm12 = sina*affine._m22;
+ qreal tm21 = -sina*affine._m11;
+ qreal tm22 = cosa*affine._m22;
+ affine._m11 = tm11; affine._m12 = tm12;
+ affine._m21 = tm21; affine._m22 = tm22;
+ break;
+ }
+ case TxProject: {
+ qreal tm13 = cosa*m_13 + sina*m_23;
+ qreal tm23 = -sina*m_13 + cosa*m_23;
+ m_13 = tm13;
+ m_23 = tm23;
+ // fall through
+ }
+ case TxRotate:
+ case TxShear: {
+ qreal tm11 = cosa*affine._m11 + sina*affine._m21;
+ qreal tm12 = cosa*affine._m12 + sina*affine._m22;
+ qreal tm21 = -sina*affine._m11 + cosa*affine._m21;
+ qreal tm22 = -sina*affine._m12 + cosa*affine._m22;
+ affine._m11 = tm11; affine._m12 = tm12;
+ affine._m21 = tm21; affine._m22 = tm22;
+ break;
+ }
+ }
+ m_dirty |= TxRotate;
+ } else {
+ QTransform result;
+ if (axis == Qt::YAxis) {
+ result.affine._m11 = cosa;
+ result.m_13 = -sina * inv_dist_to_plane;
+ } else {
+ result.affine._m22 = cosa;
+ result.m_23 = -sina * inv_dist_to_plane;
+ }
+ result.m_type = TxProject;
+ *this = result * *this;
+ }
+
+ return *this;
+}
+
+/*!
+ \fn QTransform & QTransform::rotateRadians(qreal angle, Qt::Axis axis)
+
+ Rotates the coordinate system counterclockwise by the given \a angle
+ about the specified \a axis and returns a reference to the matrix.
+
+ Note that if you apply a QTransform to a point defined in widget
+ coordinates, the direction of the rotation will be clockwise
+ because the y-axis points downwards.
+
+ The angle is specified in radians.
+
+ \sa setMatrix()
+*/
+QTransform & QTransform::rotateRadians(qreal a, Qt::Axis axis)
+{
+ qreal sina = qSin(a);
+ qreal cosa = qCos(a);
+
+ if (axis == Qt::ZAxis) {
+ switch(type()) {
+ case TxNone:
+ case TxTranslate:
+ affine._m11 = cosa;
+ affine._m12 = sina;
+ affine._m21 = -sina;
+ affine._m22 = cosa;
+ break;
+ case TxScale: {
+ qreal tm11 = cosa*affine._m11;
+ qreal tm12 = sina*affine._m22;
+ qreal tm21 = -sina*affine._m11;
+ qreal tm22 = cosa*affine._m22;
+ affine._m11 = tm11; affine._m12 = tm12;
+ affine._m21 = tm21; affine._m22 = tm22;
+ break;
+ }
+ case TxProject: {
+ qreal tm13 = cosa*m_13 + sina*m_23;
+ qreal tm23 = -sina*m_13 + cosa*m_23;
+ m_13 = tm13;
+ m_23 = tm23;
+ // fall through
+ }
+ case TxRotate:
+ case TxShear: {
+ qreal tm11 = cosa*affine._m11 + sina*affine._m21;
+ qreal tm12 = cosa*affine._m12 + sina*affine._m22;
+ qreal tm21 = -sina*affine._m11 + cosa*affine._m21;
+ qreal tm22 = -sina*affine._m12 + cosa*affine._m22;
+ affine._m11 = tm11; affine._m12 = tm12;
+ affine._m21 = tm21; affine._m22 = tm22;
+ break;
+ }
+ }
+ m_dirty |= TxRotate;
+ } else {
+ QTransform result;
+ if (axis == Qt::YAxis) {
+ result.affine._m11 = cosa;
+ result.m_13 = -sina * inv_dist_to_plane;
+ } else {
+ result.affine._m22 = cosa;
+ result.m_23 = -sina * inv_dist_to_plane;
+ }
+ result.m_type = TxProject;
+ *this = result * *this;
+ }
+ return *this;
+}
+
+/*!
+ \fn bool QTransform::operator==(const QTransform &matrix) const
+ Returns true if this matrix is equal to the given \a matrix,
+ otherwise returns false.
+*/
+bool QTransform::operator==(const QTransform &o) const
+{
+#define qFZ qFuzzyCompare
+ return qFZ(affine._m11, o.affine._m11) && qFZ(affine._m12, o.affine._m12) && qFZ(m_13, o.m_13)
+ && qFZ(affine._m21, o.affine._m21) && qFZ(affine._m22, o.affine._m22) && qFZ(m_23, o.m_23)
+ && qFZ(affine._dx, o.affine._dx) && qFZ(affine._dy, o.affine._dy) && qFZ(m_33, o.m_33);
+#undef qFZ
+}
+
+/*!
+ \fn bool QTransform::operator!=(const QTransform &matrix) const
+ Returns true if this matrix is not equal to the given \a matrix,
+ otherwise returns false.
+*/
+bool QTransform::operator!=(const QTransform &o) const
+{
+ return !operator==(o);
+}
+
+/*!
+ \fn QTransform & QTransform::operator*=(const QTransform &matrix)
+ \overload
+
+ Returns the result of multiplying this matrix by the given \a
+ matrix.
+*/
+QTransform & QTransform::operator*=(const QTransform &o)
+{
+ TransformationType t = qMax(type(), o.type());
+ switch(t) {
+ case TxNone:
+ break;
+ case TxTranslate:
+ affine._dx += o.affine._dx;
+ affine._dy += o.affine._dy;
+ break;
+ case TxScale:
+ {
+ qreal m11 = affine._m11*o.affine._m11;
+ qreal m22 = affine._m22*o.affine._m22;
+
+ qreal m31 = affine._dx*o.affine._m11 + o.affine._dx;
+ qreal m32 = affine._dy*o.affine._m22 + o.affine._dy;
+
+ affine._m11 = m11;
+ affine._m22 = m22;
+ affine._dx = m31; affine._dy = m32;
+ break;
+ }
+ case TxRotate:
+ case TxShear:
+ {
+ qreal m11 = affine._m11*o.affine._m11 + affine._m12*o.affine._m21;
+ qreal m12 = affine._m11*o.affine._m12 + affine._m12*o.affine._m22;
+
+ qreal m21 = affine._m21*o.affine._m11 + affine._m22*o.affine._m21;
+ qreal m22 = affine._m21*o.affine._m12 + affine._m22*o.affine._m22;
+
+ qreal m31 = affine._dx*o.affine._m11 + affine._dy*o.affine._m21 + o.affine._dx;
+ qreal m32 = affine._dx*o.affine._m12 + affine._dy*o.affine._m22 + o.affine._dy;
+
+ affine._m11 = m11; affine._m12 = m12;
+ affine._m21 = m21; affine._m22 = m22;
+ affine._dx = m31; affine._dy = m32;
+ break;
+ }
+ case TxProject:
+ {
+ qreal m11 = affine._m11*o.affine._m11 + affine._m12*o.affine._m21 + m_13*o.affine._dx;
+ qreal m12 = affine._m11*o.affine._m12 + affine._m12*o.affine._m22 + m_13*o.affine._dy;
+ qreal m13 = affine._m11*o.m_13 + affine._m12*o.m_23 + m_13*o.m_33;
+
+ qreal m21 = affine._m21*o.affine._m11 + affine._m22*o.affine._m21 + m_23*o.affine._dx;
+ qreal m22 = affine._m21*o.affine._m12 + affine._m22*o.affine._m22 + m_23*o.affine._dy;
+ qreal m23 = affine._m21*o.m_13 + affine._m22*o.m_23 + m_23*o.m_33;
+
+ qreal m31 = affine._dx*o.affine._m11 + affine._dy*o.affine._m21 + m_33*o.affine._dx;
+ qreal m32 = affine._dx*o.affine._m12 + affine._dy*o.affine._m22 + m_33*o.affine._dy;
+ qreal m33 = affine._dx*o.m_13 + affine._dy*o.m_23 + m_33*o.m_33;
+
+ affine._m11 = m11; affine._m12 = m12; m_13 = m13;
+ affine._m21 = m21; affine._m22 = m22; m_23 = m23;
+ affine._dx = m31; affine._dy = m32; m_33 = m33;
+ }
+ }
+
+ m_dirty = t;
+ m_type = t;
+
+ return *this;
+}
+
+/*!
+ \fn QTransform QTransform::operator*(const QTransform &matrix) const
+ Returns the result of multiplying this matrix by the given \a
+ matrix.
+
+ Note that matrix multiplication is not commutative, i.e. a*b !=
+ b*a.
+*/
+QTransform QTransform::operator*(const QTransform &m) const
+{
+ QTransform result = *this;
+ result *= m;
+ return result;
+}
+
+/*!
+ \fn QTransform & QTransform::operator*=(qreal scalar)
+ \overload
+
+ Returns the result of performing an element-wise multiplication of this
+ matrix with the given \a scalar.
+*/
+
+/*!
+ \fn QTransform & QTransform::operator/=(qreal scalar)
+ \overload
+
+ Returns the result of performing an element-wise division of this
+ matrix by the given \a scalar.
+*/
+
+/*!
+ \fn QTransform & QTransform::operator+=(qreal scalar)
+ \overload
+
+ Returns the matrix obtained by adding the given \a scalar to each
+ element of this matrix.
+*/
+
+/*!
+ \fn QTransform & QTransform::operator-=(qreal scalar)
+ \overload
+
+ Returns the matrix obtained by subtracting the given \a scalar from each
+ element of this matrix.
+*/
+
+/*!
+ Assigns the given \a matrix's values to this matrix.
+*/
+QTransform & QTransform::operator=(const QTransform &matrix)
+{
+ affine._m11 = matrix.affine._m11;
+ affine._m12 = matrix.affine._m12;
+ affine._m21 = matrix.affine._m21;
+ affine._m22 = matrix.affine._m22;
+ affine._dx = matrix.affine._dx;
+ affine._dy = matrix.affine._dy;
+ m_13 = matrix.m_13;
+ m_23 = matrix.m_23;
+ m_33 = matrix.m_33;
+ m_type = matrix.m_type;
+ m_dirty = matrix.m_dirty;
+
+ return *this;
+}
+
+/*!
+ Resets the matrix to an identity matrix, i.e. all elements are set
+ to zero, except \c m11 and \c m22 (specifying the scale) which are
+ set to 1.
+
+ \sa QTransform(), isIdentity(), {QTransform#Basic Matrix
+ Operations}{Basic Matrix Operations}
+*/
+void QTransform::reset()
+{
+ affine._m11 = affine._m22 = m_33 = 1.0;
+ affine._m12 = m_13 = affine._m21 = m_23 = affine._dx = affine._dy = 0;
+ m_type = TxNone;
+ m_dirty = TxNone;
+}
+
+#ifndef QT_NO_DATASTREAM
+/*!
+ \fn QDataStream &operator<<(QDataStream &stream, const QTransform &matrix)
+ \since 4.3
+ \relates QTransform
+
+ Writes the given \a matrix to the given \a stream and returns a
+ reference to the stream.
+
+ \sa {Format of the QDataStream Operators}
+*/
+QDataStream & operator<<(QDataStream &s, const QTransform &m)
+{
+ s << double(m.m11())
+ << double(m.m12())
+ << double(m.m13())
+ << double(m.m21())
+ << double(m.m22())
+ << double(m.m23())
+ << double(m.m31())
+ << double(m.m32())
+ << double(m.m33());
+ return s;
+}
+
+/*!
+ \fn QDataStream &operator>>(QDataStream &stream, QTransform &matrix)
+ \since 4.3
+ \relates QTransform
+
+ Reads the given \a matrix from the given \a stream and returns a
+ reference to the stream.
+
+ \sa {Format of the QDataStream Operators}
+*/
+QDataStream & operator>>(QDataStream &s, QTransform &t)
+{
+ double m11, m12, m13,
+ m21, m22, m23,
+ m31, m32, m33;
+
+ s >> m11;
+ s >> m12;
+ s >> m13;
+ s >> m21;
+ s >> m22;
+ s >> m23;
+ s >> m31;
+ s >> m32;
+ s >> m33;
+ t.setMatrix(m11, m12, m13,
+ m21, m22, m23,
+ m31, m32, m33);
+ return s;
+}
+
+#endif // QT_NO_DATASTREAM
+
+#ifndef QT_NO_DEBUG_STREAM
+QDebug operator<<(QDebug dbg, const QTransform &m)
+{
+ dbg.nospace() << "QTransform("
+ << "11=" << m.m11()
+ << " 12=" << m.m12()
+ << " 13=" << m.m13()
+ << " 21=" << m.m21()
+ << " 22=" << m.m22()
+ << " 23=" << m.m23()
+ << " 31=" << m.m31()
+ << " 32=" << m.m32()
+ << " 33=" << m.m33()
+ << ")";
+ return dbg.space();
+}
+#endif
+
+/*!
+ \fn QPoint operator*(const QPoint &point, const QTransform &matrix)
+ \relates QTransform
+
+ This is the same as \a{matrix}.map(\a{point}).
+
+ \sa QTransform::map()
+*/
+QPoint QTransform::map(const QPoint &p) const
+{
+ qreal fx = p.x();
+ qreal fy = p.y();
+
+ qreal x = 0, y = 0;
+
+ TransformationType t = type();
+ switch(t) {
+ case TxNone:
+ x = fx;
+ y = fy;
+ break;
+ case TxTranslate:
+ x = fx + affine._dx;
+ y = fy + affine._dy;
+ break;
+ case TxScale:
+ x = affine._m11 * fx + affine._dx;
+ y = affine._m22 * fy + affine._dy;
+ break;
+ case TxRotate:
+ case TxShear:
+ case TxProject:
+ x = affine._m11 * fx + affine._m21 * fy + affine._dx;
+ y = affine._m12 * fx + affine._m22 * fy + affine._dy;
+ if (t == TxProject) {
+ qreal w = 1./(m_13 * fx + m_23 * fy + m_33);
+ x *= w;
+ y *= w;
+ }
+ }
+ return QPoint(qRound(x), qRound(y));
+}
+
+
+/*!
+ \fn QPointF operator*(const QPointF &point, const QTransform &matrix)
+ \relates QTransform
+
+ Same as \a{matrix}.map(\a{point}).
+
+ \sa QTransform::map()
+*/
+
+/*!
+ \overload
+
+ Creates and returns a QPointF object that is a copy of the given point,
+ \a p, mapped into the coordinate system defined by this matrix.
+*/
+QPointF QTransform::map(const QPointF &p) const
+{
+ qreal fx = p.x();
+ qreal fy = p.y();
+
+ qreal x = 0, y = 0;
+
+ TransformationType t = type();
+ switch(t) {
+ case TxNone:
+ x = fx;
+ y = fy;
+ break;
+ case TxTranslate:
+ x = fx + affine._dx;
+ y = fy + affine._dy;
+ break;
+ case TxScale:
+ x = affine._m11 * fx + affine._dx;
+ y = affine._m22 * fy + affine._dy;
+ break;
+ case TxRotate:
+ case TxShear:
+ case TxProject:
+ x = affine._m11 * fx + affine._m21 * fy + affine._dx;
+ y = affine._m12 * fx + affine._m22 * fy + affine._dy;
+ if (t == TxProject) {
+ qreal w = 1./(m_13 * fx + m_23 * fy + m_33);
+ x *= w;
+ y *= w;
+ }
+ }
+ return QPointF(x, y);
+}
+
+/*!
+ \fn QPoint QTransform::map(const QPoint &point) const
+ \overload
+
+ Creates and returns a QPoint object that is a copy of the given \a
+ point, mapped into the coordinate system defined by this
+ matrix. Note that the transformed coordinates are rounded to the
+ nearest integer.
+*/
+
+/*!
+ \fn QLineF operator*(const QLineF &line, const QTransform &matrix)
+ \relates QTransform
+
+ This is the same as \a{matrix}.map(\a{line}).
+
+ \sa QTransform::map()
+*/
+
+/*!
+ \fn QLine operator*(const QLine &line, const QTransform &matrix)
+ \relates QTransform
+
+ This is the same as \a{matrix}.map(\a{line}).
+
+ \sa QTransform::map()
+*/
+
+/*!
+ \overload
+
+ Creates and returns a QLineF object that is a copy of the given line,
+ \a l, mapped into the coordinate system defined by this matrix.
+*/
+QLine QTransform::map(const QLine &l) const
+{
+ qreal fx1 = l.x1();
+ qreal fy1 = l.y1();
+ qreal fx2 = l.x2();
+ qreal fy2 = l.y2();
+
+ qreal x1 = 0, y1 = 0, x2 = 0, y2 = 0;
+
+ TransformationType t = type();
+ switch(t) {
+ case TxNone:
+ x1 = fx1;
+ y1 = fy1;
+ x2 = fx2;
+ y2 = fy2;
+ break;
+ case TxTranslate:
+ x1 = fx1 + affine._dx;
+ y1 = fy1 + affine._dy;
+ x2 = fx2 + affine._dx;
+ y2 = fy2 + affine._dy;
+ break;
+ case TxScale:
+ x1 = affine._m11 * fx1 + affine._dx;
+ y1 = affine._m22 * fy1 + affine._dy;
+ x2 = affine._m11 * fx2 + affine._dx;
+ y2 = affine._m22 * fy2 + affine._dy;
+ break;
+ case TxRotate:
+ case TxShear:
+ case TxProject:
+ x1 = affine._m11 * fx1 + affine._m21 * fy1 + affine._dx;
+ y1 = affine._m12 * fx1 + affine._m22 * fy1 + affine._dy;
+ x2 = affine._m11 * fx2 + affine._m21 * fy2 + affine._dx;
+ y2 = affine._m12 * fx2 + affine._m22 * fy2 + affine._dy;
+ if (t == TxProject) {
+ qreal w = 1./(m_13 * fx1 + m_23 * fy1 + m_33);
+ x1 *= w;
+ y1 *= w;
+ w = 1./(m_13 * fx2 + m_23 * fy2 + m_33);
+ x2 *= w;
+ y2 *= w;
+ }
+ }
+ return QLine(qRound(x1), qRound(y1), qRound(x2), qRound(y2));
+}
+
+/*!
+ \overload
+
+ \fn QLineF QTransform::map(const QLineF &line) const
+
+ Creates and returns a QLine object that is a copy of the given \a
+ line, mapped into the coordinate system defined by this matrix.
+ Note that the transformed coordinates are rounded to the nearest
+ integer.
+*/
+
+QLineF QTransform::map(const QLineF &l) const
+{
+ qreal fx1 = l.x1();
+ qreal fy1 = l.y1();
+ qreal fx2 = l.x2();
+ qreal fy2 = l.y2();
+
+ qreal x1 = 0, y1 = 0, x2 = 0, y2 = 0;
+
+ TransformationType t = type();
+ switch(t) {
+ case TxNone:
+ x1 = fx1;
+ y1 = fy1;
+ x2 = fx2;
+ y2 = fy2;
+ break;
+ case TxTranslate:
+ x1 = fx1 + affine._dx;
+ y1 = fy1 + affine._dy;
+ x2 = fx2 + affine._dx;
+ y2 = fy2 + affine._dy;
+ break;
+ case TxScale:
+ x1 = affine._m11 * fx1 + affine._dx;
+ y1 = affine._m22 * fy1 + affine._dy;
+ x2 = affine._m11 * fx2 + affine._dx;
+ y2 = affine._m22 * fy2 + affine._dy;
+ break;
+ case TxRotate:
+ case TxShear:
+ case TxProject:
+ x1 = affine._m11 * fx1 + affine._m21 * fy1 + affine._dx;
+ y1 = affine._m12 * fx1 + affine._m22 * fy1 + affine._dy;
+ x2 = affine._m11 * fx2 + affine._m21 * fy2 + affine._dx;
+ y2 = affine._m12 * fx2 + affine._m22 * fy2 + affine._dy;
+ if (t == TxProject) {
+ qreal w = 1./(m_13 * fx1 + m_23 * fy1 + m_33);
+ x1 *= w;
+ y1 *= w;
+ w = 1./(m_13 * fx2 + m_23 * fy2 + m_33);
+ x2 *= w;
+ y2 *= w;
+ }
+ }
+ return QLineF(x1, y1, x2, y2);
+}
+
+static QPolygonF mapProjective(const QTransform &transform, const QPolygonF &poly)
+{
+ if (poly.size() == 0)
+ return poly;
+
+ if (poly.size() == 1)
+ return QPolygonF() << transform.map(poly.at(0));
+
+ QPainterPath path;
+ path.addPolygon(poly);
+
+ path = transform.map(path);
+
+ QPolygonF result;
+ for (int i = 0; i < path.elementCount(); ++i)
+ result << path.elementAt(i);
+ return result;
+}
+
+
+/*!
+ \fn QPolygonF operator *(const QPolygonF &polygon, const QTransform &matrix)
+ \since 4.3
+ \relates QTransform
+
+ This is the same as \a{matrix}.map(\a{polygon}).
+
+ \sa QTransform::map()
+*/
+
+/*!
+ \fn QPolygon operator*(const QPolygon &polygon, const QTransform &matrix)
+ \relates QTransform
+
+ This is the same as \a{matrix}.map(\a{polygon}).
+
+ \sa QTransform::map()
+*/
+
+/*!
+ \fn QPolygonF QTransform::map(const QPolygonF &polygon) const
+ \overload
+
+ Creates and returns a QPolygonF object that is a copy of the given
+ \a polygon, mapped into the coordinate system defined by this
+ matrix.
+*/
+QPolygonF QTransform::map(const QPolygonF &a) const
+{
+ if (type() >= QTransform::TxProject)
+ return mapProjective(*this, a);
+
+ int size = a.size();
+ int i;
+ QPolygonF p(size);
+ const QPointF *da = a.constData();
+ QPointF *dp = p.data();
+
+ TransformationType t = type();
+ for(i = 0; i < size; ++i) {
+ MAP(da[i].xp, da[i].yp, dp[i].xp, dp[i].yp);
+ }
+ return p;
+}
+
+/*!
+ \fn QPolygon QTransform::map(const QPolygon &polygon) const
+ \overload
+
+ Creates and returns a QPolygon object that is a copy of the given
+ \a polygon, mapped into the coordinate system defined by this
+ matrix. Note that the transformed coordinates are rounded to the
+ nearest integer.
+*/
+QPolygon QTransform::map(const QPolygon &a) const
+{
+ if (type() >= QTransform::TxProject)
+ return mapProjective(*this, QPolygonF(a)).toPolygon();
+
+ int size = a.size();
+ int i;
+ QPolygon p(size);
+ const QPoint *da = a.constData();
+ QPoint *dp = p.data();
+
+ TransformationType t = type();
+ for(i = 0; i < size; ++i) {
+ qreal nx = 0, ny = 0;
+ MAP(da[i].xp, da[i].yp, nx, ny);
+ dp[i].xp = qRound(nx);
+ dp[i].yp = qRound(ny);
+ }
+ return p;
+}
+
+/*!
+ \fn QRegion operator*(const QRegion &region, const QTransform &matrix)
+ \relates QTransform
+
+ This is the same as \a{matrix}.map(\a{region}).
+
+ \sa QTransform::map()
+*/
+
+/*!
+ \fn QRegion QTransform::map(const QRegion &region) const
+ \overload
+
+ Creates and returns a QRegion object that is a copy of the given
+ \a region, mapped into the coordinate system defined by this matrix.
+
+ Calling this method can be rather expensive if rotations or
+ shearing are used.
+*/
+QRegion QTransform::map(const QRegion &r) const
+{
+ TransformationType t = type();
+ if (t == TxNone)
+ return r;
+ if (t == TxTranslate) {
+ QRegion copy(r);
+ copy.translate(qRound(affine._dx), qRound(affine._dy));
+ return copy;
+ }
+
+ extern QPainterPath qt_regionToPath(const QRegion &region);
+ QPainterPath p = map(qt_regionToPath(r));
+ return p.toFillPolygon(QTransform()).toPolygon();
+}
+
+struct QHomogeneousCoordinate
+{
+ qreal x;
+ qreal y;
+ qreal w;
+
+ QHomogeneousCoordinate() {}
+ QHomogeneousCoordinate(qreal x_, qreal y_, qreal w_) : x(x_), y(y_), w(w_) {}
+
+ const QPointF toPoint() const {
+ qreal iw = 1 / w;
+ return QPointF(x * iw, y * iw);
+ }
+};
+
+static inline QHomogeneousCoordinate mapHomogeneous(const QTransform &transform, const QPointF &p)
+{
+ QHomogeneousCoordinate c;
+ c.x = transform.m11() * p.x() + transform.m21() * p.y() + transform.m31();
+ c.y = transform.m12() * p.x() + transform.m22() * p.y() + transform.m32();
+ c.w = transform.m13() * p.x() + transform.m23() * p.y() + transform.m33();
+ return c;
+}
+
+static inline bool lineTo_clipped(QPainterPath &path, const QTransform &transform, const QPointF &a, const QPointF &b, bool needsMoveTo)
+{
+ QHomogeneousCoordinate ha = mapHomogeneous(transform, a);
+ QHomogeneousCoordinate hb = mapHomogeneous(transform, b);
+
+ if (ha.w < Q_NEAR_CLIP && hb.w < Q_NEAR_CLIP)
+ return false;
+
+ if (hb.w < Q_NEAR_CLIP) {
+ const qreal t = (Q_NEAR_CLIP - hb.w) / (ha.w - hb.w);
+
+ hb.x += (ha.x - hb.x) * t;
+ hb.y += (ha.y - hb.y) * t;
+ hb.w = qreal(Q_NEAR_CLIP);
+ } else if (ha.w < Q_NEAR_CLIP) {
+ const qreal t = (Q_NEAR_CLIP - ha.w) / (hb.w - ha.w);
+
+ ha.x += (hb.x - ha.x) * t;
+ ha.y += (hb.y - ha.y) * t;
+ ha.w = qreal(Q_NEAR_CLIP);
+
+ const QPointF p = ha.toPoint();
+ if (needsMoveTo) {
+ path.moveTo(p);
+ needsMoveTo = false;
+ } else {
+ path.lineTo(p);
+ }
+ }
+
+ if (needsMoveTo)
+ path.moveTo(ha.toPoint());
+
+ path.lineTo(hb.toPoint());
+
+ return true;
+}
+
+static inline bool cubicTo_clipped(QPainterPath &path, const QTransform &transform, const QPointF &a, const QPointF &b, const QPointF &c, const QPointF &d, bool needsMoveTo)
+{
+ const QHomogeneousCoordinate ha = mapHomogeneous(transform, a);
+ const QHomogeneousCoordinate hb = mapHomogeneous(transform, b);
+ const QHomogeneousCoordinate hc = mapHomogeneous(transform, c);
+ const QHomogeneousCoordinate hd = mapHomogeneous(transform, d);
+
+ if (ha.w < Q_NEAR_CLIP && hb.w < Q_NEAR_CLIP && hc.w < Q_NEAR_CLIP && hd.w < Q_NEAR_CLIP)
+ return false;
+
+ if (ha.w >= Q_NEAR_CLIP && hb.w >= Q_NEAR_CLIP && hc.w >= Q_NEAR_CLIP && hd.w >= Q_NEAR_CLIP) {
+ if (needsMoveTo)
+ path.moveTo(ha.toPoint());
+
+ path.cubicTo(hb.toPoint(), hc.toPoint(), hd.toPoint());
+ return true;
+ }
+
+ if (lineTo_clipped(path, transform, a, b, needsMoveTo))
+ needsMoveTo = false;
+ if (lineTo_clipped(path, transform, b, c, needsMoveTo))
+ needsMoveTo = false;
+ if (lineTo_clipped(path, transform, c, d, needsMoveTo))
+ needsMoveTo = false;
+
+ return !needsMoveTo;
+}
+
+static QPainterPath mapProjective(const QTransform &transform, const QPainterPath &path)
+{
+ QPainterPath result;
+
+ QPointF last;
+ QPointF lastMoveTo;
+ bool needsMoveTo = true;
+ for (int i = 0; i < path.elementCount(); ++i) {
+ switch (path.elementAt(i).type) {
+ case QPainterPath::MoveToElement:
+ if (i > 0 && lastMoveTo != last)
+ lineTo_clipped(result, transform, last, lastMoveTo, needsMoveTo);
+
+ lastMoveTo = path.elementAt(i);
+ last = path.elementAt(i);
+ needsMoveTo = true;
+ break;
+ case QPainterPath::LineToElement:
+ if (lineTo_clipped(result, transform, last, path.elementAt(i), needsMoveTo))
+ needsMoveTo = false;
+ last = path.elementAt(i);
+ break;
+ case QPainterPath::CurveToElement:
+ if (cubicTo_clipped(result, transform, last, path.elementAt(i), path.elementAt(i+1), path.elementAt(i+2), needsMoveTo))
+ needsMoveTo = false;
+ i += 2;
+ last = path.elementAt(i);
+ break;
+ default:
+ Q_ASSERT(false);
+ }
+ }
+
+ if (path.elementCount() > 0 && lastMoveTo != last)
+ lineTo_clipped(result, transform, last, lastMoveTo, needsMoveTo);
+
+ return result;
+}
+
+/*!
+ \fn QPainterPath operator *(const QPainterPath &path, const QTransform &matrix)
+ \since 4.3
+ \relates QTransform
+
+ This is the same as \a{matrix}.map(\a{path}).
+
+ \sa QTransform::map()
+*/
+
+/*!
+ \overload
+
+ Creates and returns a QPainterPath object that is a copy of the
+ given \a path, mapped into the coordinate system defined by this
+ matrix.
+*/
+QPainterPath QTransform::map(const QPainterPath &path) const
+{
+ TransformationType t = type();
+ if (t == TxNone || path.isEmpty())
+ return path;
+
+ if (t >= TxProject)
+ return mapProjective(*this, path);
+
+ QPainterPath copy = path;
+ copy.detach();
+
+ if (t == TxTranslate) {
+ for (int i=0; i<path.elementCount(); ++i) {
+ QPainterPath::Element &e = copy.d_ptr->elements[i];
+ e.x += affine._dx;
+ e.y += affine._dy;
+ }
+ } else {
+ // Full xform
+ for (int i=0; i<path.elementCount(); ++i) {
+ QPainterPath::Element &e = copy.d_ptr->elements[i];
+ MAP(e.x, e.y, e.x, e.y);
+ }
+ }
+
+ return copy;
+}
+
+/*!
+ \fn QPolygon QTransform::mapToPolygon(const QRect &rectangle) const
+
+ Creates and returns a QPolygon representation of the given \a
+ rectangle, mapped into the coordinate system defined by this
+ matrix.
+
+ The rectangle's coordinates are transformed using the following
+ formulas:
+
+ \snippet doc/src/snippets/code/src_gui_painting_qtransform.cpp 1
+
+ Polygons and rectangles behave slightly differently when
+ transformed (due to integer rounding), so
+ \c{matrix.map(QPolygon(rectangle))} is not always the same as
+ \c{matrix.mapToPolygon(rectangle)}.
+
+ \sa mapRect(), {QTransform#Basic Matrix Operations}{Basic Matrix
+ Operations}
+*/
+QPolygon QTransform::mapToPolygon(const QRect &rect) const
+{
+ TransformationType t = type();
+
+ QPolygon a(4);
+ qreal x[4] = { 0, 0, 0, 0 }, y[4] = { 0, 0, 0, 0 };
+ if (t <= TxScale) {
+ x[0] = affine._m11*rect.x() + affine._dx;
+ y[0] = affine._m22*rect.y() + affine._dy;
+ qreal w = affine._m11*rect.width();
+ qreal h = affine._m22*rect.height();
+ if (w < 0) {
+ w = -w;
+ x[0] -= w;
+ }
+ if (h < 0) {
+ h = -h;
+ y[0] -= h;
+ }
+ x[1] = x[0]+w;
+ x[2] = x[1];
+ x[3] = x[0];
+ y[1] = y[0];
+ y[2] = y[0]+h;
+ y[3] = y[2];
+ } else {
+ qreal right = rect.x() + rect.width();
+ qreal bottom = rect.y() + rect.height();
+ MAP(rect.x(), rect.y(), x[0], y[0]);
+ MAP(right, rect.y(), x[1], y[1]);
+ MAP(right, bottom, x[2], y[2]);
+ MAP(rect.x(), bottom, x[3], y[3]);
+ }
+
+ // all coordinates are correctly, tranform to a pointarray
+ // (rounding to the next integer)
+ a.setPoints(4, qRound(x[0]), qRound(y[0]),
+ qRound(x[1]), qRound(y[1]),
+ qRound(x[2]), qRound(y[2]),
+ qRound(x[3]), qRound(y[3]));
+ return a;
+}
+
+/*!
+ Creates a transformation matrix, \a trans, that maps a unit square
+ to a four-sided polygon, \a quad. Returns true if the transformation
+ is constructed or false if such a transformation does not exist.
+
+ \sa quadToSquare(), quadToQuad()
+*/
+bool QTransform::squareToQuad(const QPolygonF &quad, QTransform &trans)
+{
+ if (quad.count() != 4)
+ return false;
+
+ qreal dx0 = quad[0].x();
+ qreal dx1 = quad[1].x();
+ qreal dx2 = quad[2].x();
+ qreal dx3 = quad[3].x();
+
+ qreal dy0 = quad[0].y();
+ qreal dy1 = quad[1].y();
+ qreal dy2 = quad[2].y();
+ qreal dy3 = quad[3].y();
+
+ double ax = dx0 - dx1 + dx2 - dx3;
+ double ay = dy0 - dy1 + dy2 - dy3;
+
+ if (!ax && !ay) { //afine transform
+ trans.setMatrix(dx1 - dx0, dy1 - dy0, 0,
+ dx2 - dx1, dy2 - dy1, 0,
+ dx0, dy0, 1);
+ } else {
+ double ax1 = dx1 - dx2;
+ double ax2 = dx3 - dx2;
+ double ay1 = dy1 - dy2;
+ double ay2 = dy3 - dy2;
+
+ /*determinants */
+ double gtop = ax * ay2 - ax2 * ay;
+ double htop = ax1 * ay - ax * ay1;
+ double bottom = ax1 * ay2 - ax2 * ay1;
+
+ double a, b, c, d, e, f, g, h; /*i is always 1*/
+
+ if (!bottom)
+ return false;
+
+ g = gtop/bottom;
+ h = htop/bottom;
+
+ a = dx1 - dx0 + g * dx1;
+ b = dx3 - dx0 + h * dx3;
+ c = dx0;
+ d = dy1 - dy0 + g * dy1;
+ e = dy3 - dy0 + h * dy3;
+ f = dy0;
+
+ trans.setMatrix(a, d, g,
+ b, e, h,
+ c, f, 1.0);
+ }
+
+ return true;
+}
+
+/*!
+ \fn bool QTransform::quadToSquare(const QPolygonF &quad, QTransform &trans)
+
+ Creates a transformation matrix, \a trans, that maps a four-sided polygon,
+ \a quad, to a unit square. Returns true if the transformation is constructed
+ or false if such a transformation does not exist.
+
+ \sa squareToQuad(), quadToQuad()
+*/
+bool QTransform::quadToSquare(const QPolygonF &quad, QTransform &trans)
+{
+ if (!squareToQuad(quad, trans))
+ return false;
+
+ bool invertible = false;
+ trans = trans.inverted(&invertible);
+
+ return invertible;
+}
+
+/*!
+ Creates a transformation matrix, \a trans, that maps a four-sided
+ polygon, \a one, to another four-sided polygon, \a two.
+ Returns true if the transformation is possible; otherwise returns
+ false.
+
+ This is a convenience method combining quadToSquare() and
+ squareToQuad() methods. It allows the input quad to be
+ transformed into any other quad.
+
+ \sa squareToQuad(), quadToSquare()
+*/
+bool QTransform::quadToQuad(const QPolygonF &one,
+ const QPolygonF &two,
+ QTransform &trans)
+{
+ QTransform stq;
+ if (!quadToSquare(one, trans))
+ return false;
+ if (!squareToQuad(two, stq))
+ return false;
+ trans *= stq;
+ //qDebug()<<"Final = "<<trans;
+ return true;
+}
+
+/*!
+ Sets the matrix elements to the specified values, \a m11,
+ \a m12, \a m13 \a m21, \a m22, \a m23 \a m31, \a m32 and
+ \a m33. Note that this function replaces the previous values.
+ QMatrix provides the translate(), rotate(), scale() and shear()
+ convenience functions to manipulate the various matrix elements
+ based on the currently defined coordinate system.
+
+ \sa QTransform()
+*/
+
+void QTransform::setMatrix(qreal m11, qreal m12, qreal m13,
+ qreal m21, qreal m22, qreal m23,
+ qreal m31, qreal m32, qreal m33)
+{
+ affine._m11 = m11; affine._m12 = m12; m_13 = m13;
+ affine._m21 = m21; affine._m22 = m22; m_23 = m23;
+ affine._dx = m31; affine._dy = m32; m_33 = m33;
+ m_type = TxNone;
+ m_dirty = TxProject;
+}
+
+QRect QTransform::mapRect(const QRect &rect) const
+{
+ TransformationType t = type();
+ if (t <= TxScale) {
+ int x = qRound(affine._m11*rect.x() + affine._dx);
+ int y = qRound(affine._m22*rect.y() + affine._dy);
+ int w = qRound(affine._m11*rect.width());
+ int h = qRound(affine._m22*rect.height());
+ if (w < 0) {
+ w = -w;
+ x -= w;
+ }
+ if (h < 0) {
+ h = -h;
+ y -= h;
+ }
+ return QRect(x, y, w, h);
+ } else if (t < TxProject) {
+ // see mapToPolygon for explanations of the algorithm.
+ qreal x0 = 0, y0 = 0;
+ qreal x, y;
+ MAP(rect.left(), rect.top(), x0, y0);
+ qreal xmin = x0;
+ qreal ymin = y0;
+ qreal xmax = x0;
+ qreal ymax = y0;
+ MAP(rect.right() + 1, rect.top(), x, y);
+ xmin = qMin(xmin, x);
+ ymin = qMin(ymin, y);
+ xmax = qMax(xmax, x);
+ ymax = qMax(ymax, y);
+ MAP(rect.right() + 1, rect.bottom() + 1, x, y);
+ xmin = qMin(xmin, x);
+ ymin = qMin(ymin, y);
+ xmax = qMax(xmax, x);
+ ymax = qMax(ymax, y);
+ MAP(rect.left(), rect.bottom() + 1, x, y);
+ xmin = qMin(xmin, x);
+ ymin = qMin(ymin, y);
+ xmax = qMax(xmax, x);
+ ymax = qMax(ymax, y);
+ return QRect(qRound(xmin), qRound(ymin), qRound(xmax)-qRound(xmin), qRound(ymax)-qRound(ymin));
+ } else {
+ QPainterPath path;
+ path.addRect(rect);
+ return map(path).boundingRect().toRect();
+ }
+}
+
+/*!
+ \fn QRectF QTransform::mapRect(const QRectF &rectangle) const
+
+ Creates and returns a QRectF object that is a copy of the given \a
+ rectangle, mapped into the coordinate system defined by this
+ matrix.
+
+ The rectangle's coordinates are transformed using the following
+ formulas:
+
+ \snippet doc/src/snippets/code/src_gui_painting_qtransform.cpp 2
+
+ If rotation or shearing has been specified, this function returns
+ the \e bounding rectangle. To retrieve the exact region the given
+ \a rectangle maps to, use the mapToPolygon() function instead.
+
+ \sa mapToPolygon(), {QTransform#Basic Matrix Operations}{Basic Matrix
+ Operations}
+*/
+QRectF QTransform::mapRect(const QRectF &rect) const
+{
+ TransformationType t = type();
+ if (t <= TxScale) {
+ qreal x = affine._m11*rect.x() + affine._dx;
+ qreal y = affine._m22*rect.y() + affine._dy;
+ qreal w = affine._m11*rect.width();
+ qreal h = affine._m22*rect.height();
+ if (w < 0) {
+ w = -w;
+ x -= w;
+ }
+ if (h < 0) {
+ h = -h;
+ y -= h;
+ }
+ return QRectF(x, y, w, h);
+ } else if (t < TxProject) {
+ qreal x0 = 0, y0 = 0;
+ qreal x, y;
+ MAP(rect.x(), rect.y(), x0, y0);
+ qreal xmin = x0;
+ qreal ymin = y0;
+ qreal xmax = x0;
+ qreal ymax = y0;
+ MAP(rect.x() + rect.width(), rect.y(), x, y);
+ xmin = qMin(xmin, x);
+ ymin = qMin(ymin, y);
+ xmax = qMax(xmax, x);
+ ymax = qMax(ymax, y);
+ MAP(rect.x() + rect.width(), rect.y() + rect.height(), x, y);
+ xmin = qMin(xmin, x);
+ ymin = qMin(ymin, y);
+ xmax = qMax(xmax, x);
+ ymax = qMax(ymax, y);
+ MAP(rect.x(), rect.y() + rect.height(), x, y);
+ xmin = qMin(xmin, x);
+ ymin = qMin(ymin, y);
+ xmax = qMax(xmax, x);
+ ymax = qMax(ymax, y);
+ return QRectF(xmin, ymin, xmax-xmin, ymax - ymin);
+ } else {
+ QPainterPath path;
+ path.addRect(rect);
+ return map(path).boundingRect();
+ }
+}
+
+/*!
+ \fn QRect QTransform::mapRect(const QRect &rectangle) const
+ \overload
+
+ Creates and returns a QRect object that is a copy of the given \a
+ rectangle, mapped into the coordinate system defined by this
+ matrix. Note that the transformed coordinates are rounded to the
+ nearest integer.
+*/
+
+/*!
+ Maps the given coordinates \a x and \a y into the coordinate
+ system defined by this matrix. The resulting values are put in *\a
+ tx and *\a ty, respectively.
+
+ The coordinates are transformed using the following formulas:
+
+ \snippet doc/src/snippets/code/src_gui_painting_qtransform.cpp 3
+
+ The point (x, y) is the original point, and (x', y') is the
+ transformed point.
+
+ \sa {QTransform#Basic Matrix Operations}{Basic Matrix Operations}
+*/
+void QTransform::map(qreal x, qreal y, qreal *tx, qreal *ty) const
+{
+ TransformationType t = type();
+ MAP(x, y, *tx, *ty);
+}
+
+/*!
+ \overload
+
+ Maps the given coordinates \a x and \a y into the coordinate
+ system defined by this matrix. The resulting values are put in *\a
+ tx and *\a ty, respectively. Note that the transformed coordinates
+ are rounded to the nearest integer.
+*/
+void QTransform::map(int x, int y, int *tx, int *ty) const
+{
+ TransformationType t = type();
+ qreal fx = 0, fy = 0;
+ MAP(x, y, fx, fy);
+ *tx = qRound(fx);
+ *ty = qRound(fy);
+}
+
+/*!
+ Returns the QTransform cast to a QMatrix.
+ */
+const QMatrix &QTransform::toAffine() const
+{
+ return affine;
+}
+
+/*!
+ Returns the transformation type of this matrix.
+
+ The transformation type is the highest enumeration value
+ capturing all of the matrix's transformations. For example,
+ if the matrix both scales and shears, the type would be \c TxShear,
+ because \c TxShear has a higher enumeration value than \c TxScale.
+
+ Knowing the transformation type of a matrix is useful for optimization:
+ you can often handle specific types more optimally than handling
+ the generic case.
+ */
+QTransform::TransformationType QTransform::type() const
+{
+ if (m_dirty >= m_type) {
+ if (m_dirty > TxShear && (!qFuzzyCompare(m_13 + 1, 1) || !qFuzzyCompare(m_23 + 1, 1)))
+ m_type = TxProject;
+ else if (m_dirty > TxScale && (!qFuzzyCompare(affine._m12 + 1, 1) || !qFuzzyCompare(affine._m21 + 1, 1))) {
+ const qreal dot = affine._m11 * affine._m12 + affine._m21 * affine._m22;
+ if (qFuzzyCompare(dot + 1, 1))
+ m_type = TxRotate;
+ else
+ m_type = TxShear;
+ } else if (m_dirty > TxTranslate && (!qFuzzyCompare(affine._m11, 1) || !qFuzzyCompare(affine._m22, 1) || !qFuzzyCompare(m_33, 1)))
+ m_type = TxScale;
+ else if (m_dirty > TxNone && (!qFuzzyCompare(affine._dx + 1, 1) || !qFuzzyCompare(affine._dy + 1, 1)))
+ m_type = TxTranslate;
+ else
+ m_type = TxNone;
+
+ m_dirty = TxNone;
+ }
+
+ return static_cast<TransformationType>(m_type);
+}
+
+/*!
+
+ Returns the transform as a QVariant.
+*/
+QTransform::operator QVariant() const
+{
+ return QVariant(QVariant::Transform, this);
+}
+
+
+/*!
+ \fn bool QTransform::isInvertible() const
+
+ Returns true if the matrix is invertible, otherwise returns false.
+
+ \sa inverted()
+*/
+
+/*!
+ \fn qreal QTransform::det() const
+
+ Returns the matrix's determinant.
+*/
+
+
+/*!
+ \fn qreal QTransform::m11() const
+
+ Returns the horizontal scaling factor.
+
+ \sa scale(), {QTransform#Basic Matrix Operations}{Basic Matrix
+ Operations}
+*/
+
+/*!
+ \fn qreal QTransform::m12() const
+
+ Returns the vertical shearing factor.
+
+ \sa shear(), {QTransform#Basic Matrix Operations}{Basic Matrix
+ Operations}
+*/
+
+/*!
+ \fn qreal QTransform::m21() const
+
+ Returns the horizontal shearing factor.
+
+ \sa shear(), {QTransform#Basic Matrix Operations}{Basic Matrix
+ Operations}
+*/
+
+/*!
+ \fn qreal QTransform::m22() const
+
+ Returns the vertical scaling factor.
+
+ \sa scale(), {QTransform#Basic Matrix Operations}{Basic Matrix
+ Operations}
+*/
+
+/*!
+ \fn qreal QTransform::dx() const
+
+ Returns the horizontal translation factor.
+
+ \sa m31(), translate(), {QTransform#Basic Matrix Operations}{Basic Matrix
+ Operations}
+*/
+
+/*!
+ \fn qreal QTransform::dy() const
+
+ Returns the vertical translation factor.
+
+ \sa translate(), {QTransform#Basic Matrix Operations}{Basic Matrix
+ Operations}
+*/
+
+
+/*!
+ \fn qreal QTransform::m13() const
+
+ Returns the horizontal projection factor.
+
+ \sa translate(), {QTransform#Basic Matrix Operations}{Basic Matrix
+ Operations}
+*/
+
+
+/*!
+ \fn qreal QTransform::m23() const
+
+ Returns the vertical projection factor.
+
+ \sa translate(), {QTransform#Basic Matrix Operations}{Basic Matrix
+ Operations}
+*/
+
+/*!
+ \fn qreal QTransform::m31() const
+
+ Returns the horizontal translation factor.
+
+ \sa dx(), translate(), {QTransform#Basic Matrix Operations}{Basic Matrix
+ Operations}
+*/
+
+/*!
+ \fn qreal QTransform::m32() const
+
+ Returns the vertical translation factor.
+
+ \sa dy(), translate(), {QTransform#Basic Matrix Operations}{Basic Matrix
+ Operations}
+*/
+
+/*!
+ \fn qreal QTransform::m33() const
+
+ Returns the division factor.
+
+ \sa translate(), {QTransform#Basic Matrix Operations}{Basic Matrix
+ Operations}
+*/
+
+/*!
+ \fn qreal QTransform::determinant() const
+
+ Returns the matrix's determinant.
+*/
+
+/*!
+ \fn bool QTransform::isIdentity() const
+
+ Returns true if the matrix is the identity matrix, otherwise
+ returns false.
+
+ \sa reset()
+*/
+
+/*!
+ \fn bool QTransform::isAffine() const
+
+ Returns true if the matrix represent an affine transformation,
+ otherwise returns false.
+*/
+
+/*!
+ \fn bool QTransform::isScaling() const
+
+ Returns true if the matrix represents a scaling
+ transformation, otherwise returns false.
+
+ \sa reset()
+*/
+
+/*!
+ \fn bool QTransform::isRotating() const
+
+ Returns true if the matrix represents some kind of a
+ rotating transformation, otherwise returns false.
+
+ \sa reset()
+*/
+
+/*!
+ \fn bool QTransform::isTranslating() const
+
+ Returns true if the matrix represents a translating
+ transformation, otherwise returns false.
+
+ \sa reset()
+*/
+
+// returns true if the transform is uniformly scaling
+// (same scale in x and y direction)
+// scale is set to the max of x and y scaling factors
+Q_GUI_EXPORT
+bool qt_scaleForTransform(const QTransform &transform, qreal *scale)
+{
+ if (transform.type() <= QTransform::TxTranslate) {
+ *scale = 1;
+ return true;
+ } else if (transform.type() == QTransform::TxScale) {
+ const qreal xScale = qAbs(transform.m11());
+ const qreal yScale = qAbs(transform.m22());
+ *scale = qMax(xScale, yScale);
+ return qFuzzyCompare(xScale, yScale);
+ }
+
+ const qreal xScale = transform.m11() * transform.m11()
+ + transform.m21() * transform.m21();
+ const qreal yScale = transform.m12() * transform.m12()
+ + transform.m22() * transform.m22();
+ *scale = qSqrt(qMax(xScale, yScale));
+ return transform.type() == QTransform::TxRotate && qFuzzyCompare(xScale, yScale);
+}
+
+QT_END_NAMESPACE