qtransform.cpp

奇趣公司比较新的qt/emd版本

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#include "qtransform.h"

#include "qdatastream.h"
#include "qdebug.h"
#include "qmath_p.h"
#include "qmatrix.h"
#include "qregion.h"
#include "qpainterpath.h"
#include "qvariant.h"

#include <math.h>

#define MAPDOUBLE(x, y, nx, ny) \
{ \
    fx = x; \
    fy = y; \
    nx = affine._m11*fx + affine._m21*fy + affine._dx; \
    ny = affine._m12*fx + affine._m22*fy + affine._dy; \
    if (!isAffine()) { \
        qreal w = m_13*fx + m_23*fy + m_33; \
        w = 1/w; \
        nx *= w; \
        ny *= w; \
    }\
}

#define MAPINT(x, y, nx, ny) \
{ \
    fx = x; \
    fy = y; \
    nx = int(affine._m11*fx + affine._m21*fy + affine._dx); \
    ny = int(affine._m12*fx + affine._m22*fy + affine._dy); \
    if (!isAffine()) { \
        qreal w = m_13*fx + m_23*fy + m_33; \
        w = 1/w; \
        nx = int(nx*w); \
        ny = int(ny*w); \
    }\
}


/*!
    \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 perpective 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
    \quotefromfile snippets/transform/main.cpp
    \skipto SimpleTransformation::paintEvent
    \printuntil }
    \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
    \quotefromfile snippets/transform/main.cpp
    \skipto CombinedTransformation::paintEvent
    \printuntil }
    \endtable

    \section1 Basic Matrix Operations

    \image qmatrix-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. And
    finally, the \c m21 and \c m12 elements specify horizontal and
    vertical \e shearing.

    QTransform transforms a point in the plane to another point using the
    following formulas:

    \code
        x' = m11*x + m21*y + dx
        y' = m22*y + m12*x + dy
    \endcode

    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 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 qtransform-combinedtransformation2.png
    \o
    \quotefromfile snippets/transform/main.cpp
    \skipto BasicOperations::paintEvent
    \printuntil }
    \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;
    //### not a huge fan of this simplification but
    //    i'd like to keep m33 as 1.0
    //return QTransform(h11, h12, h13,
    //                  h21, h22, h23,
    //                  h31, h32, h33);
    h33 = 1/h33;
    return QTransform(h11*h33, h12*h33, h13*h33,
                      h21*h33, h22*h33, h23*h33,
                      h31*h33, h32*h33, 1.0);
}

/*!
    Returns the transpose of this matrix.
*/
QTransform QTransform::transposed() const
{
    return QTransform(affine._m11, affine._m21, affine._dx,
                      affine._m12, affine._m22, affine._dy,
                      m_13, m_23, m_33);
}

/*!
    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
{
    qreal det = determinant();
    if (qFuzzyCompare(det, qreal(0.0))) {
        if (invertible)
            *invertible = false;
        return QTransform();
    }
    if (invertible)
        *invertible = true;
    QTransform adjA = adjoint();
    QTransform invert = adjA / det;
    invert = QTransform(invert.m11()/invert.m33(), invert.m12()/invert.m33(), invert.m13()/invert.m33(),
                        invert.m21()/invert.m33(), invert.m22()/invert.m33(), invert.m23()/invert.m33(),
                        invert.m31()/invert.m33(), invert.m32()/invert.m33(), 1);
    // 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)
{
    if (type() != TxProject) {
        affine._dx += dx*affine._m11 + dy*affine._m21;
        affine._dy += dy*affine._m22 + dx*affine._m12;
    } else {
        QTransform translate;
        translate.affine._dx = dx;
        translate.affine._dy = dy;
        *this = translate * *this;
    }
    m_dirty |= TxTranslate;
    return *this;
}

/*!
    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)
{
    if (type() != TxProject) {
        affine._m11 *= sx;
        affine._m12 *= sx;
        affine._m21 *= sy;
        affine._m22 *= sy;
    } else {
        QTransform scale;
        scale.affine._m11 = sx;
        scale.affine._m22 = sy;
        *this = scale * *this;
    }
    m_dirty |= TxScale;
    return *this;
}

/*!
    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)
{
    if (type() != TxProject) {
        qreal tm11 = sv*affine._m21;
        qreal tm12 = sv*affine._m22;
        qreal tm21 = sh*affine._m11;
        qreal tm22 = sh*affine._m12;
        affine._m11 += tm11;
        affine._m12 += tm12;
        affine._m21 += tm21;
        affine._m22 += tm22;
    } else {
        QTransform shear;
        shear.affine._m12 = sv;
        shear.affine._m21 = sh;
        *this = shear * *this;
    }
    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) {
        if (type() != TxProject) {
            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;
        } else {
            QTransform result;
            result.affine._m11 = cosa;
            result.affine._m12 = sina;
            result.affine._m22 = cosa;
            result.affine._m21 = -sina;
            *this = result * *this;
        }
        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;
        }
        m_dirty = 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) {
        if (type() != TxProject) {
            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;
        } else {
            QTransform result;
            result.affine._m11 = cosa;
            result.affine._m12 = sina;
            result.affine._m22 = cosa;
            result.affine._m21 = -sina;
            *this = result * *this;
        }
        m_dirty |= TxRotate;
    } else {