Added support for six-parameter radial gradients.

The extended radial gradients conform to the radial gradient
specification in HTML 5 canvas.

Task-number: QTBUG-14075
Reviewed-by: Andreas Kling
(cherry picked from commit da55c1ea92474e989e5582b02815936bbf584405)

11 files changed, 343 insertions, 73 deletions

diff --git a/src/gui/painting/qbrush.cpp b/src/gui/painting/qbrush.cpp
index bf5764a609..3ff7eb84d0 100644
--- a/src/gui/painting/qbrush.cpp
+++ b/src/gui/painting/qbrush.cpp
@@ -840,6 +840,22 @@ const QGradient *QBrush::gradient() const
     return 0;
 }
 
+Q_GUI_EXPORT bool qt_isExtendedRadialGradient(const QBrush &brush)
+{
+    if (brush.style() == Qt::RadialGradientPattern) {
+        const QGradient *g = brush.gradient();
+        const QRadialGradient *rg = static_cast<const QRadialGradient *>(g);
+
+        if (!qFuzzyIsNull(rg->focalRadius()))
+            return true;
+
+        QPointF delta = rg->focalPoint() - rg->center();
+        if (delta.x() * delta.x() + delta.y() * delta.y() > rg->radius() * rg->radius())
+            return true;
+    }
+
+    return false;
+}
 
 /*!
     Returns true if the brush is fully opaque otherwise false. A brush
@@ -849,6 +865,7 @@ const QGradient *QBrush::gradient() const
     \i The alpha component of the color() is 255.
     \i Its texture() does not have an alpha channel and is not a QBitmap.
     \i The colors in the gradient() all have an alpha component that is 255.
+    \i It is an extended radial gradient.
     \endlist
 */
 
@@ -860,6 +877,9 @@ bool QBrush::isOpaque() const
     if (d->style == Qt::SolidPattern)
         return opaqueColor;
 
+    if (qt_isExtendedRadialGradient(*this))
+        return false;
+
     if (d->style == Qt::LinearGradientPattern
         || d->style == Qt::RadialGradientPattern
         || d->style == Qt::ConicalGradientPattern) {
@@ -1209,8 +1229,10 @@ QDataStream &operator>>(QDataStream &s, QBrush &b)
 
     \list
     \o \e Linear gradients interpolate colors between start and end points.
-    \o \e Radial gradients interpolate colors between a focal point and end
-        points on a circle surrounding it.
+    \o \e Simple radial gradients interpolate colors between a focal point
+        and end points on a circle surrounding it.
+    \o \e Extended radial gradients interpolate colors between a center and
+        a focal circle.
     \o \e Conical gradients interpolate colors around a center point.
     \endlist
 
@@ -1506,8 +1528,6 @@ void QGradient::setInterpolationMode(InterpolationMode mode)
     dummy = p;
 }
 
-#undef Q_DUMMY_ACCESSOR
-
 /*!
     \fn bool QGradient::operator!=(const QGradient &gradient) const
     \since 4.2
@@ -1541,7 +1561,7 @@ bool QGradient::operator==(const QGradient &gradient) const
             || m_data.radial.cy != gradient.m_data.radial.cy
             || m_data.radial.fx != gradient.m_data.radial.fx
             || m_data.radial.fy != gradient.m_data.radial.fy
-            || m_data.radial.radius != gradient.m_data.radial.radius)
+            || m_data.radial.cradius != gradient.m_data.radial.cradius)
             return false;
     } else { // m_type == ConicalGradient
         if (m_data.conical.cx != gradient.m_data.conical.cx
@@ -1747,10 +1767,17 @@ void QLinearGradient::setFinalStop(const QPointF &stop)
     \brief The QRadialGradient class is used in combination with QBrush to
     specify a radial gradient brush.
 
-    Radial gradients interpolate colors between a focal point and end
-    points on a circle surrounding it. Outside the end points the
-    gradient is either padded, reflected or repeated depending on the
-    currently set \l {QGradient::Spread}{spread} method:
+    Qt supports both simple and extended radial gradients.
+
+    Simple radial gradients interpolate colors between a focal point and end
+    points on a circle surrounding it. Extended radial gradients interpolate
+    colors between a focal circle and a center circle. Points outside the cone
+    defined by the two circles will be transparent. For simple radial gradients
+    the focal point is adjusted to lie inside the center circle, whereas the
+    focal point can have any position in an extended radial gradient.
+
+    Outside the end points the gradient is either padded, reflected or repeated
+    depending on the currently set \l {QGradient::Spread}{spread} method:
 
     \table
     \row
@@ -1795,9 +1822,14 @@ static QPointF qt_radial_gradient_adapt_focal_point(const QPointF &center,
 }
 
 /*!
-    Constructs a radial gradient with the given \a center, \a
+    Constructs a simple radial gradient with the given \a center, \a
     radius and \a focalPoint.
 
+    \note If the given focal point is outside the circle defined by the
+    center (\a cx, \a cy) and the \a radius it will be re-adjusted to
+    the intersection between the line from the center to the focal point
+    and the circle.
+
     \sa QGradient::setColorAt(), QGradient::setStops()
 */
 
@@ -1807,7 +1839,7 @@ QRadialGradient::QRadialGradient(const QPointF &center, qreal radius, const QPoi
     m_spread = PadSpread;
     m_data.radial.cx = center.x();
     m_data.radial.cy = center.y();
-    m_data.radial.radius = radius;
+    m_data.radial.cradius = radius;
 
     QPointF adapted_focal = qt_radial_gradient_adapt_focal_point(center, radius, focalPoint);
     m_data.radial.fx = adapted_focal.x();
@@ -1815,7 +1847,7 @@ QRadialGradient::QRadialGradient(const QPointF &center, qreal radius, const QPoi
 }
 
 /*!
-    Constructs a radial gradient with the given \a center, \a
+    Constructs a simple radial gradient with the given \a center, \a
     radius and the focal point in the circle center.
 
     \sa QGradient::setColorAt(), QGradient::setStops()
@@ -1826,16 +1858,21 @@ QRadialGradient::QRadialGradient(const QPointF &center, qreal radius)
     m_spread = PadSpread;
     m_data.radial.cx = center.x();
     m_data.radial.cy = center.y();
-    m_data.radial.radius = radius;
+    m_data.radial.cradius = radius;
     m_data.radial.fx = center.x();
     m_data.radial.fy = center.y();
 }
 
 
 /*!
-    Constructs a radial gradient with the given center (\a cx, \a cy),
+    Constructs a simple radial gradient with the given center (\a cx, \a cy),
     \a radius and focal point (\a fx, \a fy).
 
+    \note If the given focal point is outside the circle defined by the
+    center (\a cx, \a cy) and the \a radius it will be re-adjusted to
+    the intersection between the line from the center to the focal point
+    and the circle.
+
     \sa QGradient::setColorAt(), QGradient::setStops()
 */
 
@@ -1845,7 +1882,7 @@ QRadialGradient::QRadialGradient(qreal cx, qreal cy, qreal radius, qreal fx, qre
     m_spread = PadSpread;
     m_data.radial.cx = cx;
     m_data.radial.cy = cy;
-    m_data.radial.radius = radius;
+    m_data.radial.cradius = radius;
 
     QPointF adapted_focal = qt_radial_gradient_adapt_focal_point(QPointF(cx, cy),
                                                                  radius,
@@ -1856,7 +1893,7 @@ QRadialGradient::QRadialGradient(qreal cx, qreal cy, qreal radius, qreal fx, qre
 }
 
 /*!
-    Constructs a radial gradient with the center at (\a cx, \a cy) and the
+    Constructs a simple radial gradient with the center at (\a cx, \a cy) and the
     specified \a radius. The focal point lies at the center of the circle.
 
     \sa QGradient::setColorAt(), QGradient::setStops()
@@ -1867,14 +1904,14 @@ QRadialGradient::QRadialGradient(qreal cx, qreal cy, qreal radius)
     m_spread = PadSpread;
     m_data.radial.cx = cx;
     m_data.radial.cy = cy;
-    m_data.radial.radius = radius;
+    m_data.radial.cradius = radius;
     m_data.radial.fx = cx;
     m_data.radial.fy = cy;
 }
 
 
 /*!
-    Constructs a radial gradient with the center and focal point at
+    Constructs a simple radial gradient with the center and focal point at
     (0, 0) with a radius of 1.
 */
 QRadialGradient::QRadialGradient()
@@ -1883,11 +1920,51 @@ QRadialGradient::QRadialGradient()
     m_spread = PadSpread;
     m_data.radial.cx = 0;
     m_data.radial.cy = 0;
-    m_data.radial.radius = 1;
+    m_data.radial.cradius = 1;
     m_data.radial.fx = 0;
     m_data.radial.fy = 0;
 }
 
+/*!
+    \since 4.8
+
+    Constructs an extended radial gradient with the given \a center, \a
+    centerRadius, \a focalPoint, and \a focalRadius.
+*/
+QRadialGradient::QRadialGradient(const QPointF &center, qreal centerRadius, const QPointF &focalPoint, qreal focalRadius)
+{
+    m_type = RadialGradient;
+    m_spread = PadSpread;
+    m_data.radial.cx = center.x();
+    m_data.radial.cy = center.y();
+    m_data.radial.cradius = centerRadius;
+
+    m_data.radial.fx = focalPoint.x();
+    m_data.radial.fy = focalPoint.y();
+    setFocalRadius(focalRadius);
+}
+
+/*!
+    \since 4.8
+
+    Constructs an extended radial gradient with the given \a center, \a
+    centerRadius, \a focalPoint, and \a focalRadius.
+    Constructs a radial gradient with the given center (\a cx, \a cy),
+    center radius \a centerRadius, focal point (\a fx, \a fy), and
+    focal radius \a focalRadius.
+*/
+QRadialGradient::QRadialGradient(qreal cx, qreal cy, qreal centerRadius, qreal fx, qreal fy, qreal focalRadius)
+{
+    m_type = RadialGradient;
+    m_spread = PadSpread;
+    m_data.radial.cx = cx;
+    m_data.radial.cy = cy;
+    m_data.radial.cradius = centerRadius;
+
+    m_data.radial.fx = fx;
+    m_data.radial.fy = fy;
+    setFocalRadius(focalRadius);
+}
 
 /*!
     Returns the center of this radial gradient in logical coordinates.
@@ -1932,13 +2009,15 @@ void QRadialGradient::setCenter(const QPointF &center)
 /*!
     Returns the radius of this radial gradient in logical coordinates.
 
+    Equivalent to centerRadius()
+
     \sa QGradient::stops()
 */
 
 qreal QRadialGradient::radius() const
 {
     Q_ASSERT(m_type == RadialGradient);
-    return m_data.radial.radius;
+    return m_data.radial.cradius;
 }
 
 
@@ -1947,13 +2026,81 @@ qreal QRadialGradient::radius() const
 
     Sets the radius of this radial gradient in logical coordinates
     to \a radius
+
+    Equivalent to setCenterRadius()
 */
 void QRadialGradient::setRadius(qreal radius)
 {
     Q_ASSERT(m_type == RadialGradient);
-    m_data.radial.radius = radius;
+    m_data.radial.cradius = radius;
+}
+
+/*!
+    \since 4.8
+
+    Returns the center radius of this radial gradient in logical
+    coordinates.
+
+    \sa QGradient::stops()
+*/
+qreal QRadialGradient::centerRadius() const
+{
+    Q_ASSERT(m_type == RadialGradient);
+    return m_data.radial.cradius;
+}
+
+/*
+   \since 4.8
+
+   Sets the center radius of this radial gradient in logical coordinates
+   to \a radius
+*/
+void QRadialGradient::setCenterRadius(qreal radius)
+{
+    Q_ASSERT(m_type == RadialGradient);
+    m_data.radial.cradius = radius;
+}
+
+/*!
+    \since 4.8
+
+    Returns the focal radius of this radial gradient in logical
+    coordinates.
+
+    \sa QGradient::stops()
+*/
+qreal QRadialGradient::focalRadius() const
+{
+    Q_ASSERT(m_type == RadialGradient);
+    Q_DUMMY_ACCESSOR
+
+    // mask away low three bits
+    union { float f; quint32 i; } u;
+    u.i = i & ~0x07;
+    return u.f;
 }
 
+/*
+   \since 4.8
+
+   Sets the focal radius of this radial gradient in logical coordinates
+   to \a radius
+*/
+void QRadialGradient::setFocalRadius(qreal radius)
+{
+    Q_ASSERT(m_type == RadialGradient);
+    Q_DUMMY_ACCESSOR
+
+    // Since there's no QGradientData, we only have the dummy void * to
+    // store additional data in. The three lowest bits are already
+    // taken, thus we cut the three lowest bits from the significand
+    // and store the radius as a float.
+    union { float f; quint32 i; } u;
+    u.f = float(radius);
+    // add 0x04 to round up when we drop the three lowest bits
+    i |= (u.i + 0x04) & ~0x07;
+    dummy = p;
+}
 
 /*!
     Returns the focal point of this radial gradient in logical
@@ -2193,4 +2340,6 @@ void QConicalGradient::setAngle(qreal angle)
     \sa setTransform()
 */
 
+#undef Q_DUMMY_ACCESSOR
+
 QT_END_NAMESPACE
diff --git a/src/gui/painting/qbrush.h b/src/gui/painting/qbrush.h
index 8b313196db..d914c8c5b1 100644
--- a/src/gui/painting/qbrush.h
+++ b/src/gui/painting/qbrush.h
@@ -255,6 +255,7 @@ private:
     friend class QLinearGradient;
     friend class QRadialGradient;
     friend class QConicalGradient;
+    friend class QBrush;
 
     Type m_type;
     Spread m_spread;
@@ -264,7 +265,7 @@ private:
             qreal x1, y1, x2, y2;
         } linear;
         struct {
-            qreal cx, cy, fx, fy, radius;
+            qreal cx, cy, fx, fy, cradius;
         } radial;
         struct {
             qreal cx, cy, angle;
@@ -303,6 +304,9 @@ public:
     QRadialGradient(const QPointF &center, qreal radius);
     QRadialGradient(qreal cx, qreal cy, qreal radius);
 
+    QRadialGradient(const QPointF &center, qreal centerRadius, const QPointF &focalPoint, qreal focalRadius);
+    QRadialGradient(qreal cx, qreal cy, qreal centerRadius, qreal fx, qreal fy, qreal focalRadius);
+
     QPointF center() const;
     void setCenter(const QPointF &center);
     inline void setCenter(qreal x, qreal y) { setCenter(QPointF(x, y)); }
@@ -313,6 +317,12 @@ public:
 
     qreal radius() const;
     void setRadius(qreal radius);
+
+    qreal centerRadius() const;
+    void setCenterRadius(qreal radius);
+
+    qreal focalRadius() const;
+    void setFocalRadius(qreal radius);
 };
 
 
diff --git a/src/gui/painting/qdrawhelper.cpp b/src/gui/painting/qdrawhelper.cpp
index 09610ed795..360292c4d7 100644
--- a/src/gui/painting/qdrawhelper.cpp
+++ b/src/gui/painting/qdrawhelper.cpp
@@ -1406,23 +1406,47 @@ static void QT_FASTCALL getRadialGradientValues(RadialGradientValues *v, const Q
 {
     v->dx = data->gradient.radial.center.x - data->gradient.radial.focal.x;
     v->dy = data->gradient.radial.center.y - data->gradient.radial.focal.y;
-    v->a = data->gradient.radial.radius*data->gradient.radial.radius - v->dx*v->dx - v->dy*v->dy;
+
+    v->dr = data->gradient.radial.center.radius - data->gradient.radial.focal.radius;
+    v->sqrfr = data->gradient.radial.focal.radius * data->gradient.radial.focal.radius;
+
+    v->a = v->dr * v->dr - v->dx*v->dx - v->dy*v->dy;
+    v->inv2a = 1 / (2 * v->a);
+
+    v->extended = !qFuzzyIsNull(data->gradient.radial.focal.radius) || v->a <= 0;
 }
 
 class RadialFetchPlain
 {
 public:
-    static inline void fetch(uint *buffer, uint *end, const QSpanData *data, qreal det, qreal delta_det,
-                             qreal delta_delta_det, qreal b, qreal delta_b)
+    static inline void fetch(uint *buffer, uint *end, const Operator *op, const QSpanData *data, qreal det,
+                             qreal delta_det, qreal delta_delta_det, qreal b, qreal delta_b)
     {
-        while (buffer < end) {
-            *buffer = qt_gradient_pixel(&data->gradient, (det > 0 ? qSqrt(det) : 0) - b);
+        if (op->radial.extended) {
+            while (buffer < end) {
+                quint32 result = 0;
+                if (det >= 0) {
+                    qreal w = qSqrt(det) - b;
+                    if (data->gradient.radial.focal.radius + op->radial.dr * w >= 0)
+                        result = qt_gradient_pixel(&data->gradient, w);
+                }
 
-            det += delta_det;
-            delta_det += delta_delta_det;
-            b += delta_b;
+                *buffer = result;
 
-            ++buffer;
+                det += delta_det;
+                delta_det += delta_delta_det;
+                b += delta_b;
+
+                ++buffer;
+            }
+        } else {
+            while (buffer < end) {
+                *buffer++ = qt_gradient_pixel(&data->gradient, qSqrt(det) - b);
+
+                det += delta_det;
+                delta_det += delta_delta_det;
+                b += delta_b;
+            }
         }
     }
 };
diff --git a/src/gui/painting/qdrawhelper_neon.cpp b/src/gui/painting/qdrawhelper_neon.cpp
index 7eb2f09d7a..e673dd9861 100644
--- a/src/gui/painting/qdrawhelper_neon.cpp
+++ b/src/gui/painting/qdrawhelper_neon.cpp
@@ -985,6 +985,8 @@ public:
     static inline Float32x4 v_sqrt(Float32x4 x) { Float32x4 y = vrsqrteq_f32(x); y = vmulq_f32(y, vrsqrtsq_f32(x, vmulq_f32(y, y))); return vmulq_f32(x, y); }
 
     static inline Int32x4 v_toInt(Float32x4 x) { return vcvtq_s32_f32(x); }
+
+    static inline Int32x4 v_greaterOrEqual(Float32x4 a, Float32x4 b) { return vcge_f32(a, b); }
 };
 
 const uint * QT_FASTCALL qt_fetch_radial_gradient_neon(uint *buffer, const Operator *op, const QSpanData *data,
diff --git a/src/gui/painting/qdrawhelper_p.h b/src/gui/painting/qdrawhelper_p.h
index a92f68613d..e93d7361e3 100644
--- a/src/gui/painting/qdrawhelper_p.h
+++ b/src/gui/painting/qdrawhelper_p.h
@@ -191,7 +191,11 @@ struct RadialGradientValues
 {
     qreal dx;
     qreal dy;
+    qreal dr;
+    qreal sqrfr;
     qreal a;
+    qreal inv2a;
+    bool extended;
 };
 
 struct Operator;
@@ -239,12 +243,13 @@ struct QRadialGradientData
     struct {
         qreal x;
         qreal y;
+        qreal radius;
     } center;
     struct {
         qreal x;
         qreal y;
+        qreal radius;
     } focal;
-    qreal radius;
 };
 
 struct QConicalGradientData
@@ -381,12 +386,6 @@ static inline qreal qRadialDeterminant(qreal a, qreal b, qreal c)
     return (b * b) - (4 * a * c);
 }
 
-// function to evaluate real roots
-static inline qreal qRadialRealRoots(qreal a, qreal b, qreal detSqrt)
-{
-    return (-b + detSqrt)/(2 * a);
-}
-
 template <class RadialFetchFunc>
 const uint * QT_FASTCALL qt_fetch_radial_gradient_template(uint *buffer, const Operator *op, const QSpanData *data,
                                                            int y, int x, int length)
@@ -394,7 +393,7 @@ const uint * QT_FASTCALL qt_fetch_radial_gradient_template(uint *buffer, const O
     // avoid division by zero
     if (qFuzzyIsNull(op->radial.a)) {
         extern void (*qt_memfill32)(quint32 *dest, quint32 value, int count);
-        qt_memfill32(buffer, data->gradient.colorTable[0], length);
+        qt_memfill32(buffer, 0, length);
         return buffer;
     }
 
@@ -415,7 +414,7 @@ const uint * QT_FASTCALL qt_fetch_radial_gradient_template(uint *buffer, const O
         const qreal delta_rx = data->m11;
         const qreal delta_ry = data->m12;
 
-        qreal b = 2*(rx * op->radial.dx + ry * op->radial.dy);
+        qreal b = 2*(op->radial.dr*data->gradient.radial.focal.radius + rx * op->radial.dx + ry * op->radial.dy);
         qreal delta_b = 2*(delta_rx * op->radial.dx + delta_ry * op->radial.dy);
         const qreal b_delta_b = 2 * b * delta_b;
         const qreal delta_b_delta_b = 2 * delta_b * delta_b;
@@ -433,31 +432,45 @@ const uint * QT_FASTCALL qt_fetch_radial_gradient_template(uint *buffer, const O
 
         inv_a *= inv_a;
 
-        qreal det = (bb + 4 * op->radial.a * rxrxryry) * inv_a;
+        qreal det = (bb - 4 * op->radial.a * (op->radial.sqrfr - rxrxryry)) * inv_a;
         qreal delta_det = (b_delta_b + delta_bb + 4 * op->radial.a * (rx_plus_ry + delta_rxrxryry)) * inv_a;
         const qreal delta_delta_det = (delta_b_delta_b + 4 * op->radial.a * delta_rx_plus_ry) * inv_a;
 
-        RadialFetchFunc::fetch(buffer, end, data, det, delta_det, delta_delta_det, b, delta_b);
+        RadialFetchFunc::fetch(buffer, end, op, data, det, delta_det, delta_delta_det, b, delta_b);
     } else {
         qreal rw = data->m23 * (y + qreal(0.5))
                    + data->m33 + data->m13 * (x + qreal(0.5));
-        if (!rw)
-            rw = 1;
+
         while (buffer < end) {
-            qreal gx = rx/rw - data->gradient.radial.focal.x;
-            qreal gy = ry/rw - data->gradient.radial.focal.y;
-            qreal b  = 2*(gx*op->radial.dx + gy*op->radial.dy);
-            qreal det = qRadialDeterminant(op->radial.a, b , -(gx*gx + gy*gy));
-            qreal s = qRadialRealRoots(op->radial.a, b, (det > 0 ? qSqrt(det) : 0));
+            if (rw == 0) {
+                *buffer = 0;
+            } else {
+                qreal invRw = 1 / rw;
+                qreal gx = rx * invRw - data->gradient.radial.focal.x;
+                qreal gy = ry * invRw - data->gradient.radial.focal.y;
+                qreal b  = 2*(op->radial.dr*data->gradient.radial.focal.radius + gx*op->radial.dx + gy*op->radial.dy);
+                qreal det = qRadialDeterminant(op->radial.a, b, op->radial.sqrfr - (gx*gx + gy*gy));
+
+                quint32 result = 0;
+                if (det >= 0) {
+                    qreal detSqrt = qSqrt(det);
+
+                    qreal s0 = (-b - detSqrt) * op->radial.inv2a;
+                    qreal s1 = (-b + detSqrt) * op->radial.inv2a;
+
+                    qreal s = qMax(s0, s1);
 
-            *buffer = qt_gradient_pixel(&data->gradient, s);
+                    if (data->gradient.radial.focal.radius + op->radial.dr * s >= 0)
+                        result = qt_gradient_pixel(&data->gradient, s);
+                }
+
+                *buffer = result;
+            }
 
             rx += data->m11;
             ry += data->m12;
             rw += data->m13;
-            if (!rw) {
-                rw += data->m13;
-            }
+
             ++buffer;
         }
     }
@@ -469,8 +482,8 @@ template <class Simd>
 class QRadialFetchSimd
 {
 public:
-    static inline void fetch(uint *buffer, uint *end, const QSpanData *data, qreal det, qreal delta_det,
-                             qreal delta_delta_det, qreal b, qreal delta_b)
+    static void fetch(uint *buffer, uint *end, const Operator *op, const QSpanData *data, qreal det,
+                      qreal delta_det, qreal delta_delta_det, qreal b, qreal delta_b)
     {
         typename Simd::Vect_buffer_f det_vec;
         typename Simd::Vect_buffer_f delta_det4_vec;
@@ -490,6 +503,9 @@ public:
         const typename Simd::Float32x4 v_delta_delta_det6 = Simd::v_dup(6 * delta_delta_det);
         const typename Simd::Float32x4 v_delta_b4 = Simd::v_dup(4 * delta_b);
 
+        const typename Simd::Float32x4 v_r0 = Simd::v_dup(data->gradient.radial.focal.radius);
+        const typename Simd::Float32x4 v_dr = Simd::v_dup(op->radial.dr);
+
         const typename Simd::Float32x4 v_min = Simd::v_dup(0.0f);
         const typename Simd::Float32x4 v_max = Simd::v_dup(GRADIENT_STOPTABLE_SIZE-1.5f);
         const typename Simd::Float32x4 v_half = Simd::v_dup(0.5f);
@@ -501,10 +517,15 @@ public:
 
         const typename Simd::Int32x4 v_reflect_limit = Simd::v_dup(2 * GRADIENT_STOPTABLE_SIZE - 1);
 
+        const int extended_mask = op->radial.extended ? 0x0 : ~0x0;
+
 #define FETCH_RADIAL_LOOP_PROLOGUE \
         while (buffer < end) { \
+            typename Simd::Vect_buffer_i v_buffer_mask; \
+            v_buffer_mask.v = Simd::v_greaterOrEqual(det_vec.v, v_min); \
             const typename Simd::Float32x4 v_index_local = Simd::v_sub(Simd::v_sqrt(Simd::v_max(v_min, det_vec.v)), b_vec.v); \
             const typename Simd::Float32x4 v_index = Simd::v_add(Simd::v_mul(v_index_local, v_table_size_minus_one), v_half); \
+            v_buffer_mask.v = Simd::v_and(v_buffer_mask.v, Simd::v_greaterOrEqual(Simd::v_add(v_r0, Simd::v_mul(v_dr, v_index_local)), v_min)); \
             typename Simd::Vect_buffer_i index_vec;
 #define FETCH_RADIAL_LOOP_CLAMP_REPEAT \
             index_vec.v = Simd::v_and(v_repeat_mask, Simd::v_toInt(v_index));
@@ -519,21 +540,26 @@ public:
             delta_det4_vec.v = Simd::v_add(delta_det4_vec.v, v_delta_delta_det16); \
             b_vec.v = Simd::v_add(b_vec.v, v_delta_b4); \
             for (int i = 0; i < 4; ++i) \
-                *buffer++ = data->gradient.colorTable[index_vec.i[i]]; \
+                *buffer++ = (extended_mask | v_buffer_mask.i[i]) & data->gradient.colorTable[index_vec.i[i]]; \
         }
 
-        if (data->gradient.spread == QGradient::RepeatSpread) {
-            FETCH_RADIAL_LOOP_PROLOGUE
-            FETCH_RADIAL_LOOP_CLAMP_REPEAT
-            FETCH_RADIAL_LOOP_EPILOGUE
-        } else if (data->gradient.spread == QGradient::ReflectSpread) {
-            FETCH_RADIAL_LOOP_PROLOGUE
-            FETCH_RADIAL_LOOP_CLAMP_REFLECT
-            FETCH_RADIAL_LOOP_EPILOGUE
-        } else {
-            FETCH_RADIAL_LOOP_PROLOGUE
-            FETCH_RADIAL_LOOP_CLAMP_PAD
-            FETCH_RADIAL_LOOP_EPILOGUE
+#define FETCH_RADIAL_LOOP(FETCH_RADIAL_LOOP_CLAMP) \
+        FETCH_RADIAL_LOOP_PROLOGUE \
+        FETCH_RADIAL_LOOP_CLAMP \
+        FETCH_RADIAL_LOOP_EPILOGUE
+
+        switch (data->gradient.spread) {
+        case QGradient::RepeatSpread:
+            FETCH_RADIAL_LOOP(FETCH_RADIAL_LOOP_CLAMP_REPEAT)
+            break;
+        case QGradient::ReflectSpread:
+            FETCH_RADIAL_LOOP(FETCH_RADIAL_LOOP_CLAMP_REFLECT)
+            break;
+        case QGradient::PadSpread:
+            FETCH_RADIAL_LOOP(FETCH_RADIAL_LOOP_CLAMP_PAD)
+            break;
+        default:
+            Q_ASSERT(false);
         }
     }
 };
diff --git a/src/gui/painting/qdrawhelper_sse2.cpp b/src/gui/painting/qdrawhelper_sse2.cpp
index 542d845dde..fdab95fdda 100644
--- a/src/gui/painting/qdrawhelper_sse2.cpp
+++ b/src/gui/painting/qdrawhelper_sse2.cpp
@@ -522,6 +522,8 @@ public:
     static inline Float32x4 v_sqrt(Float32x4 x) { return _mm_sqrt_ps(x); }
 
     static inline Int32x4 v_toInt(Float32x4 x) { return _mm_cvttps_epi32(x); }
+
+    static inline Int32x4 v_greaterOrEqual(Float32x4 a, Float32x4 b) { return (__m128i)_mm_cmpgt_ps(a, b); }
 };
 
 const uint * QT_FASTCALL qt_fetch_radial_gradient_sse2(uint *buffer, const Operator *op, const QSpanData *data,
diff --git a/src/gui/painting/qpaintengine_mac.cpp b/src/gui/painting/qpaintengine_mac.cpp
index c6d061dea8..6dcc3cc9fc 100644
--- a/src/gui/painting/qpaintengine_mac.cpp
+++ b/src/gui/painting/qpaintengine_mac.cpp
@@ -1546,8 +1546,9 @@ void QCoreGraphicsPaintEnginePrivate::setFillBrush(const QPointF &offset)
                 QPointF center(radialGrad->center());
                 QPointF focal(radialGrad->focalPoint());
                 qreal radius = radialGrad->radius();
+                qreal focalRadius = radialGrad->focalRadius();
                 shading = CGShadingCreateRadial(colorspace, CGPointMake(focal.x(), focal.y()),
-                                                0.0, CGPointMake(center.x(), center.y()), radius, fill_func, false, true);
+                                                focalRadius, CGPointMake(center.x(), center.y()), radius, fill_func, false, true);
             }
 
             CGFunctionRelease(fill_func);
diff --git a/src/gui/painting/qpaintengine_raster.cpp b/src/gui/painting/qpaintengine_raster.cpp
index 8486adb64a..2119e307d7 100644
--- a/src/gui/painting/qpaintengine_raster.cpp
+++ b/src/gui/painting/qpaintengine_raster.cpp
@@ -5282,10 +5282,11 @@ void QSpanData::setup(const QBrush &brush, int alpha, QPainter::CompositionMode
             QPointF center = g->center();
             radialData.center.x = center.x();
             radialData.center.y = center.y();
+            radialData.center.radius = g->centerRadius();
             QPointF focal = g->focalPoint();
             radialData.focal.x = focal.x();
             radialData.focal.y = focal.y();
-            radialData.radius = g->radius();
+            radialData.focal.radius = g->focalRadius();
         }
         break;
 
diff --git a/src/gui/painting/qpaintengineex.cpp b/src/gui/painting/qpaintengineex.cpp
index 509fb77d25..7f601eb755 100644
--- a/src/gui/painting/qpaintengineex.cpp
+++ b/src/gui/painting/qpaintengineex.cpp
@@ -1012,4 +1012,50 @@ void QPaintEngineEx::updateState(const QPaintEngineState &)
     // do nothing...
 }
 
+Q_GUI_EXPORT QPainterPath qt_painterPathFromVectorPath(const QVectorPath &path)
+{
+    const qreal *points = path.points();
+    const QPainterPath::ElementType *types = path.elements();
+
+    QPainterPath p;
+    if (types) {
+        int id = 0;
+        for (int i=0; i<path.elementCount(); ++i) {
+            switch(types[i]) {
+            case QPainterPath::MoveToElement:
+                p.moveTo(QPointF(points[id], points[id+1]));
+                id+=2;
+                break;
+            case QPainterPath::LineToElement:
+                p.lineTo(QPointF(points[id], points[id+1]));
+                id+=2;
+                break;
+            case QPainterPath::CurveToElement: {
+                QPointF p1(points[id], points[id+1]);
+                QPointF p2(points[id+2], points[id+3]);
+                QPointF p3(points[id+4], points[id+5]);
+                p.cubicTo(p1, p2, p3);
+                id+=6;
+                break;
+            }
+            case QPainterPath::CurveToDataElement:
+                ;
+                break;
+            }
+        }
+    } else {
+        p.moveTo(QPointF(points[0], points[1]));
+        int id = 2;
+        for (int i=1; i<path.elementCount(); ++i) {
+            p.lineTo(QPointF(points[id], points[id+1]));
+            id+=2;
+        }
+    }
+    if (path.hints() & QVectorPath::WindingFill)
+        p.setFillRule(Qt::WindingFill);
+
+    return p;
+}
+
+
 QT_END_NAMESPACE
diff --git a/src/gui/painting/qpainter.cpp b/src/gui/painting/qpainter.cpp
index 6c588cf32e..7130fbf07d 100644
--- a/src/gui/painting/qpainter.cpp
+++ b/src/gui/painting/qpainter.cpp
@@ -504,8 +504,12 @@ void QPainterPrivate::draw_helper(const QPainterPath &originalPath, DrawOperatio
 
     q->save();
     state->matrix = QTransform();
-    state->dirtyFlags |= QPaintEngine::DirtyTransform;
-    updateState(state);
+    if (extended) {
+        extended->transformChanged();
+    } else {
+        state->dirtyFlags |= QPaintEngine::DirtyTransform;
+        updateState(state);
+    }
     engine->drawImage(absPathRect,
                  image,
                  QRectF(0, 0, absPathRect.width(), absPathRect.height()),
@@ -688,11 +692,14 @@ void QPainterPrivate::updateInvMatrix()
     invMatrix = state->matrix.inverted();
 }
 
+extern bool qt_isExtendedRadialGradient(const QBrush &brush);
+
 void QPainterPrivate::updateEmulationSpecifier(QPainterState *s)
 {
     bool alpha = false;
     bool linearGradient = false;
     bool radialGradient = false;
+    bool extendedRadialGradient = false;
     bool conicalGradient = false;
     bool patternBrush = false;
     bool xform = false;
@@ -724,6 +731,7 @@ void QPainterPrivate::updateEmulationSpecifier(QPainterState *s)
                            (brushStyle == Qt::LinearGradientPattern));
         radialGradient = ((penBrushStyle == Qt::RadialGradientPattern) ||
                            (brushStyle == Qt::RadialGradientPattern));
+        extendedRadialGradient = radialGradient && (qt_isExtendedRadialGradient(penBrush) || qt_isExtendedRadialGradient(s->brush));
         conicalGradient = ((penBrushStyle == Qt::ConicalGradientPattern) ||
                             (brushStyle == Qt::ConicalGradientPattern));
         patternBrush = (((penBrushStyle > Qt::SolidPattern
@@ -807,7 +815,7 @@ void QPainterPrivate::updateEmulationSpecifier(QPainterState *s)
         s->emulationSpecifier &= ~QPaintEngine::LinearGradientFill;
 
     // Radial gradient emulation
-    if (radialGradient && !engine->hasFeature(QPaintEngine::RadialGradientFill))
+    if (extendedRadialGradient || (radialGradient && !engine->hasFeature(QPaintEngine::RadialGradientFill)))
         s->emulationSpecifier |= QPaintEngine::RadialGradientFill;
     else
         s->emulationSpecifier &= ~QPaintEngine::RadialGradientFill;
diff --git a/src/gui/painting/qpainter.h b/src/gui/painting/qpainter.h
index e8cc3a6bdb..601c386059 100644
--- a/src/gui/painting/qpainter.h
+++ b/src/gui/painting/qpainter.h
@@ -553,6 +553,7 @@ private:
     friend class QPaintEngine;
     friend class QPaintEngineExPrivate;
     friend class QOpenGLPaintEngine;
+    friend class QVGPaintEngine;
     friend class QX11PaintEngine;
     friend class QX11PaintEnginePrivate;
     friend class QWin32PaintEngine;