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#include "qdatastream.h"

#include "qdebug.h"

#include "qmatrix.h"

#include "qregion.h"

#include "qpainterpath.h"

#include "qvariant.h"

#include <qmath.h>

#include <limits.h>

QT_BEGIN_NAMESPACE

/*!

    \class QMatrix

    \brief The QMatrix class specifies 2D transformations of a

    coordinate system.

    \obsolete

    \ingroup painting

    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 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, QMatrix provides the det() 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 {The 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

    \o \inlineimage qmatrix-simpletransformation.png

    \o

    \snippet doc/src/snippets/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

    \o \inlineimage qmatrix-combinedtransformation.png

    \o

    \snippet doc/src/snippets/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 doc/src/snippets/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

    \o \inlineimage qmatrix-combinedtransformation.png

    \o

    \snippet doc/src/snippets/matrix/matrix.cpp 2

    \endtable

    \sa QPainter, QTransform, {The Coordinate System}, 

    {demos/affine}{Affine Transformations Demo}, {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)

{

}

/*!

     Constructs a matrix that is a copy of the given \a matrix.

 */

QMatrix::QMatrix(const QMatrix &matrix)

    : _m11(matrix._m11)

    , _m12(matrix._m12)

    , _m21(matrix._m21)

    , _m22(matrix._m22)

    , _dx(matrix._dx)

    , _dy(matrix._dy)

{

}

/*!

    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 doc/src/snippets/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 doc/src/snippets/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

{