/**************************************************************************** ** ** Copyright (C) 2016 The Qt Company Ltd. ** Contact: https://www.qt.io/licensing/ ** ** This file is part of the QtGui module of the Qt Toolkit. ** ** $QT_BEGIN_LICENSE:LGPL$ ** Commercial License Usage ** Licensees holding valid commercial Qt licenses may use this file in ** accordance with the commercial license agreement provided with the ** Software or, alternatively, in accordance with the terms contained in ** a written agreement between you and The Qt Company. For licensing terms ** and conditions see https://www.qt.io/terms-conditions. For further ** information use the contact form at https://www.qt.io/contact-us. ** ** GNU Lesser General Public License Usage ** Alternatively, this file may be used under the terms of the GNU Lesser ** General Public License version 3 as published by the Free Software ** Foundation and appearing in the file LICENSE.LGPL3 included in the ** packaging of this file. Please review the following information to ** ensure the GNU Lesser General Public License version 3 requirements ** will be met: https://www.gnu.org/licenses/lgpl-3.0.html. ** ** GNU General Public License Usage ** Alternatively, this file may be used under the terms of the GNU ** General Public License version 2.0 or (at your option) the GNU General ** Public license version 3 or any later version approved by the KDE Free ** Qt Foundation. The licenses are as published by the Free Software ** Foundation and appearing in the file LICENSE.GPL2 and LICENSE.GPL3 ** included in the packaging of this file. Please review the following ** information to ensure the GNU General Public License requirements will ** be met: https://www.gnu.org/licenses/gpl-2.0.html and ** https://www.gnu.org/licenses/gpl-3.0.html. ** ** $QT_END_LICENSE$ ** ****************************************************************************/ #include "qmatrix.h" #include "qdatastream.h" #include "qdebug.h" #include "qhashfunctions.h" #include "qregion.h" #include "qpainterpath.h" #include "qpainterpath_p.h" #include "qvariant.h" #include #include QT_BEGIN_NAMESPACE /*! \class QMatrix \brief The QMatrix class specifies 2D transformations of a coordinate system. \obsolete \ingroup painting \inmodule QtGui A matrix specifies how to translate, scale, shear or rotate the coordinate system, and is typically used when rendering graphics. QMatrix, in contrast to QTransform, does not allow perspective transformations. QTransform is the recommended transformation class in Qt. A QMatrix object can be built using the setMatrix(), scale(), rotate(), translate() and shear() functions. Alternatively, it can be built by applying \l {QMatrix#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 QMatrix 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. QMatrix provides the isIdentity() function which returns \c true if the matrix is the identity matrix, and the isInvertible() function which returns \c 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, QMatrix provides the determinant() function returning the matrix's determinant. Finally, the QMatrix 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 {Coordinate System}{coordinate system} documentation. QPainter has functions to translate, scale, shear and rotate the coordinate system without using a QMatrix. For example: \table 100% \row \li \inlineimage qmatrix-simpletransformation.png \li \snippet matrix/matrix.cpp 0 \endtable Although these functions are very convenient, it can be more efficient to build a QMatrix and call QPainter::setMatrix() if you want to perform more than a single transform operation. For example: \table 100% \row \li \inlineimage qmatrix-combinedtransformation.png \li \snippet matrix/matrix.cpp 1 \endtable \section1 Basic Matrix Operations \image qmatrix-representation.png A QMatrix 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. And finally, the \c m21 and \c m12 elements specify horizontal and vertical \e shearing. QMatrix transforms a point in the plane to another point using the following formulas: \snippet code/src_gui_painting_qmatrix.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(), m21(), m22(), 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 and \c m22 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. Here's the combined transformations example using basic matrix operations: \table 100% \row \li \inlineimage qmatrix-combinedtransformation.png \li \snippet matrix/matrix.cpp 2 \endtable \sa QPainter, QTransform, {Coordinate System}, {painting/affine}{Affine Transformations Example}, {Transformations Example} */ // some defines to inline some code #define MAPDOUBLE(x, y, nx, ny) \ { \ qreal fx = x; \ qreal fy = y; \ nx = _m11*fx + _m21*fy + _dx; \ ny = _m12*fx + _m22*fy + _dy; \ } #define MAPINT(x, y, nx, ny) \ { \ qreal fx = x; \ qreal fy = y; \ nx = qRound(_m11*fx + _m21*fy + _dx); \ ny = qRound(_m12*fx + _m22*fy + _dy); \ } /***************************************************************************** QMatrix member functions *****************************************************************************/ /*! \fn QMatrix::QMatrix(Qt::Initialization) \internal */ /*! Constructs an identity matrix. All elements are set to zero except \c m11 and \c m22 (specifying the scale), which are set to 1. \sa reset() */ QMatrix::QMatrix() : _m11(1.) , _m12(0.) , _m21(0.) , _m22(1.) , _dx(0.) , _dy(0.) { } /*! Constructs a matrix with the elements, \a m11, \a m12, \a m21, \a m22, \a dx and \a dy. \sa setMatrix() */ QMatrix::QMatrix(qreal m11, qreal m12, qreal m21, qreal m22, qreal dx, qreal dy) : _m11(m11) , _m12(m12) , _m21(m21) , _m22(m22) , _dx(dx) , _dy(dy) { } #if QT_VERSION < QT_VERSION_CHECK(6, 0, 0) /*! Constructs a matrix that is a copy of the given \a matrix. */ QMatrix::QMatrix(const QMatrix &matrix) noexcept : _m11(matrix._m11) , _m12(matrix._m12) , _m21(matrix._m21) , _m22(matrix._m22) , _dx(matrix._dx) , _dy(matrix._dy) { } #endif /*! Sets the matrix elements to the specified values, \a m11, \a m12, \a m21, \a m22, \a dx and \a dy. Note that this function replaces the previous values. QMatrix provide the translate(), rotate(), scale() and shear() convenience functions to manipulate the various matrix elements based on the currently defined coordinate system. \sa QMatrix() */ void QMatrix::setMatrix(qreal m11, qreal m12, qreal m21, qreal m22, qreal dx, qreal dy) { _m11 = m11; _m12 = m12; _m21 = m21; _m22 = m22; _dx = dx; _dy = dy; } /*! \fn qreal QMatrix::m11() const Returns the horizontal scaling factor. \sa scale(), {QMatrix#Basic Matrix Operations}{Basic Matrix Operations} */ /*! \fn qreal QMatrix::m12() const Returns the vertical shearing factor. \sa shear(), {QMatrix#Basic Matrix Operations}{Basic Matrix Operations} */ /*! \fn qreal QMatrix::m21() const Returns the horizontal shearing factor. \sa shear(), {QMatrix#Basic Matrix Operations}{Basic Matrix Operations} */ /*! \fn qreal QMatrix::m22() const Returns the vertical scaling factor. \sa scale(), {QMatrix#Basic Matrix Operations}{Basic Matrix Operations} */ /*! \fn qreal QMatrix::dx() const Returns the horizontal translation factor. \sa translate(), {QMatrix#Basic Matrix Operations}{Basic Matrix Operations} */ /*! \fn qreal QMatrix::dy() const Returns the vertical translation factor. \sa translate(), {QMatrix#Basic Matrix Operations}{Basic Matrix Operations} */ /*! 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 code/src_gui_painting_qmatrix.cpp 1 The point (x, y) is the original point, and (x', y') is the transformed point. \sa {QMatrix#Basic Matrix Operations}{Basic Matrix Operations} */ void QMatrix::map(qreal x, qreal y, qreal *tx, qreal *ty) const { MAPDOUBLE(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 QMatrix::map(int x, int y, int *tx, int *ty) const { MAPINT(x, y, *tx, *ty); } QRect QMatrix::mapRect(const QRect &rect) const { QRect result; if (_m12 == 0.0F && _m21 == 0.0F) { int x = qRound(_m11*rect.x() + _dx); int y = qRound(_m22*rect.y() + _dy); int w = qRound(_m11*rect.width()); int h = qRound(_m22*rect.height()); if (w < 0) { w = -w; x -= w; } if (h < 0) { h = -h; y -= h; } result = QRect(x, y, w, h); } else { // see mapToPolygon for explanations of the algorithm. qreal x0, y0; qreal x, y; MAPDOUBLE(rect.left(), rect.top(), x0, y0); qreal xmin = x0; qreal ymin = y0; qreal xmax = x0; qreal ymax = y0; MAPDOUBLE(rect.right() + 1, rect.top(), x, y); xmin = qMin(xmin, x); ymin = qMin(ymin, y); xmax = qMax(xmax, x); ymax = qMax(ymax, y); MAPDOUBLE(rect.right() + 1, rect.bottom() + 1, x, y); xmin = qMin(xmin, x); ymin = qMin(ymin, y); xmax = qMax(xmax, x); ymax = qMax(ymax, y); MAPDOUBLE(rect.left(), rect.bottom() + 1, x, y); xmin = qMin(xmin, x); ymin = qMin(ymin, y); xmax = qMax(xmax, x); ymax = qMax(ymax, y); result = QRect(qRound(xmin), qRound(ymin), qRound(xmax)-qRound(xmin), qRound(ymax)-qRound(ymin)); } return result; } /*! \fn QRectF QMatrix::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 code/src_gui_painting_qmatrix.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(), {QMatrix#Basic Matrix Operations}{Basic Matrix Operations} */ QRectF QMatrix::mapRect(const QRectF &rect) const { QRectF result; if (_m12 == 0.0F && _m21 == 0.0F) { qreal x = _m11*rect.x() + _dx; qreal y = _m22*rect.y() + _dy; qreal w = _m11*rect.width(); qreal h = _m22*rect.height(); if (w < 0) { w = -w; x -= w; } if (h < 0) { h = -h; y -= h; } result = QRectF(x, y, w, h); } else { qreal x0, y0; qreal x, y; MAPDOUBLE(rect.x(), rect.y(), x0, y0); qreal xmin = x0; qreal ymin = y0; qreal xmax = x0; qreal ymax = y0; MAPDOUBLE(rect.x() + rect.width(), rect.y(), x, y); xmin = qMin(xmin, x); ymin = qMin(ymin, y); xmax = qMax(xmax, x); ymax = qMax(ymax, y); MAPDOUBLE(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); MAPDOUBLE(rect.x(), rect.y() + rect.height(), x, y); xmin = qMin(xmin, x); ymin = qMin(ymin, y); xmax = qMax(xmax, x); ymax = qMax(ymax, y); result = QRectF(xmin, ymin, xmax-xmin, ymax - ymin); } return result; } /*! \fn QRect QMatrix::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. */ /*! \fn QPoint operator*(const QPoint &point, const QMatrix &matrix) \relates QMatrix This is the same as \a{matrix}.map(\a{point}). \sa QMatrix::map() */ QPoint QMatrix::map(const QPoint &p) const { qreal fx = p.x(); qreal fy = p.y(); return QPoint(qRound(_m11*fx + _m21*fy + _dx), qRound(_m12*fx + _m22*fy + _dy)); } /*! \fn QPointF operator*(const QPointF &point, const QMatrix &matrix) \relates QMatrix Same as \a{matrix}.map(\a{point}). \sa QMatrix::map() */ /*! \overload Creates and returns a QPointF object that is a copy of the given \a point, mapped into the coordinate system defined by this matrix. */ QPointF QMatrix::map(const QPointF &point) const { qreal fx = point.x(); qreal fy = point.y(); return QPointF(_m11*fx + _m21*fy + _dx, _m12*fx + _m22*fy + _dy); } /*! \fn QPoint QMatrix::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 QMatrix &matrix) \relates QMatrix This is the same as \a{matrix}.map(\a{line}). \sa QMatrix::map() */ /*! \fn QLine operator*(const QLine &line, const QMatrix &matrix) \relates QMatrix This is the same as \a{matrix}.map(\a{line}). \sa QMatrix::map() */ /*! \overload Creates and returns a QLineF object that is a copy of the given \a line, mapped into the coordinate system defined by this matrix. */ QLineF QMatrix::map(const QLineF &line) const { return QLineF(map(line.p1()), map(line.p2())); } /*! \overload 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. */ QLine QMatrix::map(const QLine &line) const { return QLine(map(line.p1()), map(line.p2())); } /*! \fn QPolygonF operator *(const QPolygonF &polygon, const QMatrix &matrix) \relates QMatrix This is the same as \a{matrix}.map(\a{polygon}). \sa QMatrix::map() */ /*! \fn QPolygon operator*(const QPolygon &polygon, const QMatrix &matrix) \relates QMatrix This is the same as \a{matrix}.map(\a{polygon}). \sa QMatrix::map() */ QPolygon QMatrix::map(const QPolygon &a) const { int size = a.size(); int i; QPolygon p(size); const QPoint *da = a.constData(); QPoint *dp = p.data(); for(i = 0; i < size; i++) { MAPINT(da[i].x(), da[i].y(), dp[i].rx(), dp[i].ry()); } return p; } /*! \fn QPolygonF QMatrix::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 QMatrix::map(const QPolygonF &a) const { int size = a.size(); int i; QPolygonF p(size); const QPointF *da = a.constData(); QPointF *dp = p.data(); for(i = 0; i < size; i++) { MAPDOUBLE(da[i].xp, da[i].yp, dp[i].xp, dp[i].yp); } return p; } /*! \fn QPolygon QMatrix::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. */ /*! \fn QRegion operator*(const QRegion ®ion, const QMatrix &matrix) \relates QMatrix This is the same as \a{matrix}.map(\a{region}). \sa QMatrix::map() */ extern QPainterPath qt_regionToPath(const QRegion ®ion); /*! \fn QRegion QMatrix::map(const QRegion ®ion) 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 QMatrix::map(const QRegion &r) const { if (_m11 == 1.0 && _m22 == 1.0 && _m12 == 0.0 && _m21 == 0.0) { // translate or identity if (_dx == 0.0 && _dy == 0.0) // Identity return r; QRegion copy(r); copy.translate(qRound(_dx), qRound(_dy)); return copy; } QPainterPath p = map(qt_regionToPath(r)); return p.toFillPolygon().toPolygon(); } /*! \fn QPainterPath operator *(const QPainterPath &path, const QMatrix &matrix) \relates QMatrix This is the same as \a{matrix}.map(\a{path}). \sa QMatrix::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 QMatrix::map(const QPainterPath &path) const { if (path.isEmpty()) return QPainterPath(); QPainterPath copy = path; // Translate or identity if (_m11 == 1.0 && _m22 == 1.0 && _m12 == 0.0 && _m21 == 0.0) { // Translate if (_dx != 0.0 || _dy != 0.0) { copy.detach(); for (int i=0; ielements[i]; e.x += _dx; e.y += _dy; } } // Full xform } else { copy.detach(); for (int i=0; ielements[i]; qreal fx = e.x, fy = e.y; e.x = _m11*fx + _m21*fy + _dx; e.y = _m12*fx + _m22*fy + _dy; } } return copy; } /*! \fn QPolygon QMatrix::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 code/src_gui_painting_qmatrix.cpp 3 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(), {QMatrix#Basic Matrix Operations}{Basic Matrix Operations} */ QPolygon QMatrix::mapToPolygon(const QRect &rect) const { QPolygon a(4); qreal x[4], y[4]; if (_m12 == 0.0F && _m21 == 0.0F) { x[0] = _m11*rect.x() + _dx; y[0] = _m22*rect.y() + _dy; qreal w = _m11*rect.width(); qreal h = _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(); MAPDOUBLE(rect.x(), rect.y(), x[0], y[0]); MAPDOUBLE(right, rect.y(), x[1], y[1]); MAPDOUBLE(right, bottom, x[2], y[2]); MAPDOUBLE(rect.x(), bottom, x[3], y[3]); } #if 0 int i; for(i = 0; i< 4; i++) qDebug("coords(%d) = (%f/%f) (%d/%d)", i, x[i], y[i], qRound(x[i]), qRound(y[i])); qDebug("width=%f, height=%f", qSqrt((x[1]-x[0])*(x[1]-x[0]) + (y[1]-y[0])*(y[1]-y[0])), qSqrt((x[0]-x[3])*(x[0]-x[3]) + (y[0]-y[3])*(y[0]-y[3]))); #endif // 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; } /*! 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 QMatrix(), isIdentity(), {QMatrix#Basic Matrix Operations}{Basic Matrix Operations} */ void QMatrix::reset() { _m11 = _m22 = 1.0; _m12 = _m21 = _dx = _dy = 0.0; } /*! \fn bool QMatrix::isIdentity() const Returns \c true if the matrix is the identity matrix, otherwise returns \c false. \sa reset() */ /*! 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() */ QMatrix &QMatrix::translate(qreal dx, qreal dy) { _dx += dx*_m11 + dy*_m21; _dy += dy*_m22 + dx*_m12; return *this; } /*! \fn QMatrix &QMatrix::scale(qreal sx, qreal sy) Scales the coordinate system by \a sx horizontally and \a sy vertically, and returns a reference to the matrix. \sa setMatrix() */ QMatrix &QMatrix::scale(qreal sx, qreal sy) { _m11 *= sx; _m12 *= sx; _m21 *= sy; _m22 *= sy; return *this; } /*! Shears the coordinate system by \a sh horizontally and \a sv vertically, and returns a reference to the matrix. \sa setMatrix() */ QMatrix &QMatrix::shear(qreal sh, qreal sv) { qreal tm11 = sv*_m21; qreal tm12 = sv*_m22; qreal tm21 = sh*_m11; qreal tm22 = sh*_m12; _m11 += tm11; _m12 += tm12; _m21 += tm21; _m22 += tm22; return *this; } const qreal deg2rad = qreal(0.017453292519943295769); // pi/180 /*! \fn QMatrix &QMatrix::rotate(qreal degrees) Rotates the coordinate system the given \a degrees counterclockwise. Note that if you apply a QMatrix to a point defined in widget coordinates, the direction of the rotation will be clockwise because the y-axis points downwards. Returns a reference to the matrix. \sa setMatrix() */ QMatrix &QMatrix::rotate(qreal a) { 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); } qreal tm11 = cosa*_m11 + sina*_m21; qreal tm12 = cosa*_m12 + sina*_m22; qreal tm21 = -sina*_m11 + cosa*_m21; qreal tm22 = -sina*_m12 + cosa*_m22; _m11 = tm11; _m12 = tm12; _m21 = tm21; _m22 = tm22; return *this; } /*! \fn bool QMatrix::isInvertible() const Returns \c true if the matrix is invertible, otherwise returns \c false. \sa inverted() */ /*! \since 4.6 \fn qreal QMatrix::determinant() const Returns the matrix's determinant. */ /*! 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() */ QMatrix QMatrix::inverted(bool *invertible) const { qreal dtr = determinant(); if (dtr == 0.0) { if (invertible) *invertible = false; // singular matrix return QMatrix(true); } else { // invertible matrix if (invertible) *invertible = true; qreal dinv = 1.0/dtr; return QMatrix((_m22*dinv), (-_m12*dinv), (-_m21*dinv), (_m11*dinv), ((_m21*_dy - _m22*_dx)*dinv), ((_m12*_dx - _m11*_dy)*dinv), true); } } /*! \fn bool QMatrix::operator==(const QMatrix &matrix) const Returns \c true if this matrix is equal to the given \a matrix, otherwise returns \c false. */ bool QMatrix::operator==(const QMatrix &m) const { return _m11 == m._m11 && _m12 == m._m12 && _m21 == m._m21 && _m22 == m._m22 && _dx == m._dx && _dy == m._dy; } /*! \since 5.6 \relates QMatrix Returns the hash value for \a key, using \a seed to seed the calculation. */ uint qHash(const QMatrix &key, uint seed) noexcept { QtPrivate::QHashCombine hash; seed = hash(seed, key.m11()); seed = hash(seed, key.m12()); seed = hash(seed, key.m21()); seed = hash(seed, key.m22()); seed = hash(seed, key.dx()); seed = hash(seed, key.dy()); return seed; } /*! \fn bool QMatrix::operator!=(const QMatrix &matrix) const Returns \c true if this matrix is not equal to the given \a matrix, otherwise returns \c false. */ bool QMatrix::operator!=(const QMatrix &m) const { return _m11 != m._m11 || _m12 != m._m12 || _m21 != m._m21 || _m22 != m._m22 || _dx != m._dx || _dy != m._dy; } /*! \fn QMatrix &QMatrix::operator *=(const QMatrix &matrix) \overload Returns the result of multiplying this matrix by the given \a matrix. */ QMatrix &QMatrix::operator *=(const QMatrix &m) { qreal tm11 = _m11*m._m11 + _m12*m._m21; qreal tm12 = _m11*m._m12 + _m12*m._m22; qreal tm21 = _m21*m._m11 + _m22*m._m21; qreal tm22 = _m21*m._m12 + _m22*m._m22; qreal tdx = _dx*m._m11 + _dy*m._m21 + m._dx; qreal tdy = _dx*m._m12 + _dy*m._m22 + m._dy; _m11 = tm11; _m12 = tm12; _m21 = tm21; _m22 = tm22; _dx = tdx; _dy = tdy; return *this; } /*! \fn QMatrix QMatrix::operator *(const QMatrix &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. */ QMatrix QMatrix::operator *(const QMatrix &m) const { qreal tm11 = _m11*m._m11 + _m12*m._m21; qreal tm12 = _m11*m._m12 + _m12*m._m22; qreal tm21 = _m21*m._m11 + _m22*m._m21; qreal tm22 = _m21*m._m12 + _m22*m._m22; qreal tdx = _dx*m._m11 + _dy*m._m21 + m._dx; qreal tdy = _dx*m._m12 + _dy*m._m22 + m._dy; return QMatrix(tm11, tm12, tm21, tm22, tdx, tdy, true); } #if QT_VERSION < QT_VERSION_CHECK(6, 0, 0) /*! Assigns the given \a matrix's values to this matrix. */ QMatrix &QMatrix::operator=(const QMatrix &matrix) noexcept { _m11 = matrix._m11; _m12 = matrix._m12; _m21 = matrix._m21; _m22 = matrix._m22; _dx = matrix._dx; _dy = matrix._dy; return *this; } #endif /*! \since 4.2 Returns the matrix as a QVariant. */ QMatrix::operator QVariant() const { return QVariant(QVariant::Matrix, this); } Q_GUI_EXPORT QPainterPath operator *(const QPainterPath &p, const QMatrix &m) { return m.map(p); } /***************************************************************************** QMatrix stream functions *****************************************************************************/ #ifndef QT_NO_DATASTREAM /*! \fn QDataStream &operator<<(QDataStream &stream, const QMatrix &matrix) \relates QMatrix Writes the given \a matrix to the given \a stream and returns a reference to the stream. \sa {Serializing Qt Data Types} */ QDataStream &operator<<(QDataStream &s, const QMatrix &m) { if (s.version() == 1) { s << (float)m.m11() << (float)m.m12() << (float)m.m21() << (float)m.m22() << (float)m.dx() << (float)m.dy(); } else { s << double(m.m11()) << double(m.m12()) << double(m.m21()) << double(m.m22()) << double(m.dx()) << double(m.dy()); } return s; } /*! \fn QDataStream &operator>>(QDataStream &stream, QMatrix &matrix) \relates QMatrix Reads the given \a matrix from the given \a stream and returns a reference to the stream. \sa {Serializing Qt Data Types} */ QDataStream &operator>>(QDataStream &s, QMatrix &m) { if (s.version() == 1) { float m11, m12, m21, m22, dx, dy; s >> m11; s >> m12; s >> m21; s >> m22; s >> dx; s >> dy; m.setMatrix(m11, m12, m21, m22, dx, dy); } else { double m11, m12, m21, m22, dx, dy; s >> m11; s >> m12; s >> m21; s >> m22; s >> dx; s >> dy; m.setMatrix(m11, m12, m21, m22, dx, dy); } return s; } #endif // QT_NO_DATASTREAM #ifndef QT_NO_DEBUG_STREAM QDebug operator<<(QDebug dbg, const QMatrix &m) { QDebugStateSaver saver(dbg); dbg.nospace() << "QMatrix(" << "11=" << m.m11() << " 12=" << m.m12() << " 21=" << m.m21() << " 22=" << m.m22() << " dx=" << m.dx() << " dy=" << m.dy() << ')'; return dbg; } #endif /*! \fn bool qFuzzyCompare(const QMatrix& m1, const QMatrix& m2) \relates QMatrix \since 4.6 \brief The qFuzzyCompare function is for comparing two matrices using a fuzziness factor. Returns \c true if \a m1 and \a m2 are equal, allowing for a small fuzziness factor for floating-point comparisons; false otherwise. */ QT_END_NAMESPACE