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  ****************************************************************************/
  #ifndef QTRANSFORM_H
  #define QTRANSFORM_H
  
  #include <QtGui/qmatrix.h>
  #include <QtGui/qpainterpath.h>
  #include <QtGui/qpolygon.h>
  #include <QtGui/qregion.h>
  #include <QtGui/qwindowdefs.h>
  #include <QtCore/qline.h>
  #include <QtCore/qpoint.h>
  #include <QtCore/qrect.h>
  
  QT_BEGIN_NAMESPACE
  
  
  class QVariant;
  
  class Q_GUI_EXPORT QTransform
  {
  public:
      enum TransformationType {
          TxNone      = 0x00,
          TxTranslate = 0x01,
          TxScale     = 0x02,
          TxRotate    = 0x04,
          TxShear     = 0x08,
          TxProject   = 0x10
      };
  
      inline explicit QTransform(Qt::Initialization) : affine(Qt::Uninitialized) {}
      QTransform();
      QTransform(qreal h11, qreal h12, qreal h13,
                 qreal h21, qreal h22, qreal h23,
                 qreal h31, qreal h32, qreal h33 = 1.0);
      QTransform(qreal h11, qreal h12, qreal h21,
                 qreal h22, qreal dx, qreal dy);
      explicit QTransform(const QMatrix &mtx);
  
      bool isAffine() const;
      bool isIdentity() const;
      bool isInvertible() const;
      bool isScaling() const;
      bool isRotating() const;
      bool isTranslating() const;
  
      TransformationType type() const;
  
      inline qreal determinant() const;
      qreal det() const;
  
      qreal m11() const;
      qreal m12() const;
      qreal m13() const;
      qreal m21() const;
      qreal m22() const;
      qreal m23() const;
      qreal m31() const;
      qreal m32() const;
      qreal m33() const;
      qreal dx() const;
      qreal dy() const;
  
      void setMatrix(qreal m11, qreal m12, qreal m13,
                     qreal m21, qreal m22, qreal m23,
                     qreal m31, qreal m32, qreal m33);
  
      QTransform inverted(bool *invertible = 0) const;
      QTransform adjoint() const;
      QTransform transposed() const;
  
      QTransform &translate(qreal dx, qreal dy);
      QTransform &scale(qreal sx, qreal sy);
      QTransform &shear(qreal sh, qreal sv);
      QTransform &rotate(qreal a, Qt::Axis axis = Qt::ZAxis);
      QTransform &rotateRadians(qreal a, Qt::Axis axis = Qt::ZAxis);
  
      static bool squareToQuad(const QPolygonF &square, QTransform &result);
      static bool quadToSquare(const QPolygonF &quad, QTransform &result);
      static bool quadToQuad(const QPolygonF &one,
                             const QPolygonF &two,
                             QTransform &result);
  
      bool operator==(const QTransform &) const;
      bool operator!=(const QTransform &) const;
  
      QTransform &operator*=(const QTransform &);
      QTransform operator*(const QTransform &o) const;
  
      QTransform &operator=(const QTransform &);
  
      operator QVariant() const;
  
      void reset();
      QPoint       map(const QPoint &p) const;
      QPointF      map(const QPointF &p) const;
      QLine        map(const QLine &l) const;
      QLineF       map(const QLineF &l) const;
      QPolygonF    map(const QPolygonF &a) const;
      QPolygon     map(const QPolygon &a) const;
      QRegion      map(const QRegion &r) const;
      QPainterPath map(const QPainterPath &p) const;
      QPolygon     mapToPolygon(const QRect &r) const;
      QRect mapRect(const QRect &) const;
      QRectF mapRect(const QRectF &) const;
      void map(int x, int y, int *tx, int *ty) const;
      void map(qreal x, qreal y, qreal *tx, qreal *ty) const;
  
      const QMatrix &toAffine() const;
  
      QTransform &operator*=(qreal div);
      QTransform &operator/=(qreal div);
      QTransform &operator+=(qreal div);
      QTransform &operator-=(qreal div);
  
      static QTransform fromTranslate(qreal dx, qreal dy);
      static QTransform fromScale(qreal dx, qreal dy);
  
  private:
      inline QTransform(qreal h11, qreal h12, qreal h13,
                        qreal h21, qreal h22, qreal h23,
                        qreal h31, qreal h32, qreal h33, bool)
          : affine(h11, h12, h21, h22, h31, h32, true)
          , m_13(h13), m_23(h23), m_33(h33)
          , m_type(TxNone)
          , m_dirty(TxProject) {}
      inline QTransform(bool)
          : affine(true)
          , m_13(0), m_23(0), m_33(1)
          , m_type(TxNone)
          , m_dirty(TxNone) {}
      inline TransformationType inline_type() const;
      QMatrix affine;
      qreal   m_13;
      qreal   m_23;
      qreal   m_33;
  
      mutable uint m_type : 5;
      mutable uint m_dirty : 5;
  
      class Private;
      Private *d;
  };
  Q_DECLARE_TYPEINFO(QTransform, Q_MOVABLE_TYPE);
  
  /******* inlines *****/
  inline QTransform::TransformationType QTransform::inline_type() const
  {
      if (m_dirty == TxNone)
          return static_cast<TransformationType>(m_type);
      return type();
  }
  
  inline bool QTransform::isAffine() const
  {
      return inline_type() < TxProject;
  }
  inline bool QTransform::isIdentity() const
  {
      return inline_type() == TxNone;
  }
  
  inline bool QTransform::isInvertible() const
  {
      return !qFuzzyIsNull(determinant());
  }
  
  inline bool QTransform::isScaling() const
  {
      return type() >= TxScale;
  }
  inline bool QTransform::isRotating() const
  {
      return inline_type() >= TxRotate;
  }
  
  inline bool QTransform::isTranslating() const
  {
      return inline_type() >= TxTranslate;
  }
  
  inline qreal QTransform::determinant() const
  {
      return affine._m11*(m_33*affine._m22-affine._dy*m_23) -
          affine._m21*(m_33*affine._m12-affine._dy*m_13)+affine._dx*(m_23*affine._m12-affine._m22*m_13);
  }
  inline qreal QTransform::det() const
  {
      return determinant();
  }
  inline qreal QTransform::m11() const
  {
      return affine._m11;
  }
  inline qreal QTransform::m12() const
  {
      return affine._m12;
  }
  inline qreal QTransform::m13() const
  {
      return m_13;
  }
  inline qreal QTransform::m21() const
  {
      return affine._m21;
  }
  inline qreal QTransform::m22() const
  {
      return affine._m22;
  }
  inline qreal QTransform::m23() const
  {
      return m_23;
  }
  inline qreal QTransform::m31() const
  {
      return affine._dx;
  }
  inline qreal QTransform::m32() const
  {
      return affine._dy;
  }
  inline qreal QTransform::m33() const
  {
      return m_33;
  }
  inline qreal QTransform::dx() const
  {
      return affine._dx;
  }
  inline qreal QTransform::dy() const
  {
      return affine._dy;
  }
  
  inline QTransform &QTransform::operator*=(qreal num)
  {
      if (num == 1.)
          return *this;
      affine._m11 *= num;
      affine._m12 *= num;
      m_13        *= num;
      affine._m21 *= num;
      affine._m22 *= num;
      m_23        *= num;
      affine._dx  *= num;
      affine._dy  *= num;
      m_33        *= num;
      if (m_dirty < TxScale)
          m_dirty = TxScale;
      return *this;
  }
  inline QTransform &QTransform::operator/=(qreal div)
  {
      if (div == 0)
          return *this;
      div = 1/div;
      return operator*=(div);
  }
  inline QTransform &QTransform::operator+=(qreal num)
  {
      if (num == 0)
          return *this;
      affine._m11 += num;
      affine._m12 += num;
      m_13        += num;
      affine._m21 += num;
      affine._m22 += num;
      m_23        += num;
      affine._dx  += num;
      affine._dy  += num;
      m_33        += num;
      m_dirty     = TxProject;
      return *this;
  }
  inline QTransform &QTransform::operator-=(qreal num)
  {
      if (num == 0)
          return *this;
      affine._m11 -= num;
      affine._m12 -= num;
      m_13        -= num;
      affine._m21 -= num;
      affine._m22 -= num;
      m_23        -= num;
      affine._dx  -= num;
      affine._dy  -= num;
      m_33        -= num;
      m_dirty     = TxProject;
      return *this;
  }
  
  inline bool qFuzzyCompare(const QTransform& t1, const QTransform& t2)
  {
      return qFuzzyCompare(t1.m11(), t2.m11())
          && qFuzzyCompare(t1.m12(), t2.m12())
          && qFuzzyCompare(t1.m13(), t2.m13())
          && qFuzzyCompare(t1.m21(), t2.m21())
          && qFuzzyCompare(t1.m22(), t2.m22())
          && qFuzzyCompare(t1.m23(), t2.m23())
          && qFuzzyCompare(t1.m31(), t2.m31())
          && qFuzzyCompare(t1.m32(), t2.m32())
          && qFuzzyCompare(t1.m33(), t2.m33());
  }
  
  
  /****** stream functions *******************/
  #ifndef QT_NO_DATASTREAM
  Q_GUI_EXPORT QDataStream &operator<<(QDataStream &, const QTransform &);
  Q_GUI_EXPORT QDataStream &operator>>(QDataStream &, QTransform &);
  #endif
  
  #ifndef QT_NO_DEBUG_STREAM
  Q_GUI_EXPORT QDebug operator<<(QDebug, const QTransform &);
  #endif
  /****** end stream functions *******************/
  
  // mathematical semantics
  inline QPoint operator*(const QPoint &p, const QTransform &m)
  { return m.map(p); }
  inline QPointF operator*(const QPointF &p, const QTransform &m)
  { return m.map(p); }
  inline QLineF operator*(const QLineF &l, const QTransform &m)
  { return m.map(l); }
  inline QLine operator*(const QLine &l, const QTransform &m)
  { return m.map(l); }
  inline QPolygon operator *(const QPolygon &a, const QTransform &m)
  { return m.map(a); }
  inline QPolygonF operator *(const QPolygonF &a, const QTransform &m)
  { return m.map(a); }
  inline QRegion operator *(const QRegion &r, const QTransform &m)
  { return m.map(r); }
  inline QPainterPath operator *(const QPainterPath &p, const QTransform &m)
  { return m.map(p); }
  
  inline QTransform operator *(const QTransform &a, qreal n)
  { QTransform t(a); t *= n; return t; }
  inline QTransform operator /(const QTransform &a, qreal n)
  { QTransform t(a); t /= n; return t; }
  inline QTransform operator +(const QTransform &a, qreal n)
  { QTransform t(a); t += n; return t; }
  inline QTransform operator -(const QTransform &a, qreal n)
  { QTransform t(a); t -= n; return t; }
  
  QT_END_NAMESPACE
  
  #endif // QTRANSFORM_H
  