[PATCH] libcamera: geometry: Rename Rectangle's top-left corner

Jacopo Mondi jacopo.mondi at ideasonboard.com
Thu Sep 26 16:35:40 CEST 2024


Hi Harvey

On Thu, Sep 26, 2024 at 10:03:55PM GMT, Cheng-Hao Yang wrote:
> Hi Jacopo,
>
> On Thu, Sep 26, 2024 at 5:36 PM Jacopo Mondi
> <jacopo.mondi at ideasonboard.com> wrote:
> >
> > Hi Harvey
> >
> > On Thu, Sep 26, 2024 at 05:28:13PM GMT, Cheng-Hao Yang wrote:
> > > Hi Jacopo,
> > >
> > >
> > >
> > > On Thu, Sep 26, 2024, 4:38 PM Jacopo Mondi <jacopo.mondi at ideasonboard.com>
> > > wrote:
> > >
> > > > Hi Harvey
> > > >
> > > > On Thu, Sep 26, 2024 at 04:29:50PM GMT, Cheng-Hao Yang wrote:
> > > > > Hi Jacopo,
> > > > >
> > > > > On Thu, Sep 26, 2024, 4:03 PM Jacopo Mondi <
> > > > jacopo.mondi at ideasonboard.com>
> > > > > wrote:
> > > > >
> > > > > > Hi Harvey
> > > > > >
> > > > > > On Wed, Sep 25, 2024 at 03:09:38PM GMT, Cheng-Hao Yang wrote:
> > > > > > > Hi Jacopo,
> > > > > > >
> > > > > > > Thank you for the patch.
> > > > > > >
> > > > > > > On Wed, Sep 25, 2024 at 2:36 PM Umang Jain <
> > > > umang.jain at ideasonboard.com>
> > > > > > wrote:
> > > > > > > >
> > > > > > > > Hi Jacopo
> > > > > > > >
> > > > > > > > Thank you for the patch
> > > > > > > >
> > > > > > > > On 24/09/24 6:15 pm, Jacopo Mondi wrote:
> > > > > > > > > The libcamera::Rectangle class should allow defining rectangles
> > > > > > > > > regardless of the reference system where an instance is used in.
> > > > > > > > >
> > > > > > > > > However the class documentation assumes the reference system
> > > > origin
> > > > > > > > > point to be in the visual top-left side and that rectangles are
> > > > > > > > > constructed by specifying the top-left corner position and sizes.
> > > > > > > > >
> > > > > > > > > However this is ambiguous when using a different reference
> > > > system as,
> > > > > > > > > in example, constructing a rectangle (x, y, w, h) in the
> > > > following
> > > > > > > > > scenario, with the origin corner in the top-left position, would
> > > > > > require
> > > > > > > > > a negative decrement along the y-axis.
> > > > > > > > >
> > > > > > > > >           ^
> > > > > > > > >           |
> > > > > > > > >          y|      o------------------
> > > > > > > > >           |      |                 | h
> > > > > > > > >           |      |                 |
> > > > > > > > >           |      -------------------
> > > > > > > > >           |               w
> > > > > > > > >            ------------------------------->
> > > > > > > > >           (0,0)  x
> > > > > > > > >
> > > > > > > > > To remove ambiguities, drop references to the visual top-left
> > > > corner
> > > > > > and
> > > > > > > > > define the rectangle's origin corner as the corner closer to the
> > > > > > > > > reference system origin point, and specify the horizontal and
> > > > > > vertical
> > > > > > > > > dimensions always increment along their respective axis, as in
> > > > the
> > > > > > > > > following example.
> > > > > > > > >
> > > > > > > > >           ^
> > > > > > > > >           |
> > > > > > > > >           |      -------------------
> > > > > > > > >           |      ^                 | h
> > > > > > > > >           |      |                 |
> > > > > > > > >          y|      o---->-------------
> > > > > > > > >           |               w
> > > > > > > > >            ------------------------------->
> > > > > > > > >           (0,0)  x
> > > > > > > > >
> > > > > > > > >           (0,0)  x
> > > > > > > > >             ------------------------------>
> > > > > > > > >            |              w
> > > > > > > > >           y|     o---->-------------
> > > > > > > > >            |     |                 | h
> > > > > > > > >            |     v                 |
> > > > > > > > >            |     -------------------
> > > > > > > > >            |
> > > > > > > > >            V
> > > > > > > > >
> > > > > > > > > Also rename for consistency the Rectangle::topLeft() function to
> > > > > > > > > Rectangle::origin() and update its in-tree users.
> > > > > > > > >
> > > > > > > > > Signed-off-by: Jacopo Mondi <jacopo.mondi at ideasonboard.com>
> > > > > > > > > ---
> > > > > > > > >   include/libcamera/geometry.h                  |  2 +-
> > > > > > > > >   src/ipa/ipu3/algorithms/af.cpp                |  2 +-
> > > > > > > > >   src/libcamera/geometry.cpp                    | 85
> > > > > > ++++++++++++++-----
> > > > > > > > >   .../pipeline/rpi/common/pipeline_base.cpp     |  4 +-
> > > > > > > > >   src/py/libcamera/py_geometry.cpp              |  2 +-
> > > > > > > > >   test/geometry.cpp                             |  8 +-
> > > > > > > > >   6 files changed, 75 insertions(+), 28 deletions(-)
> > > > > > > > >
> > > > > > > > > diff --git a/include/libcamera/geometry.h
> > > > > > b/include/libcamera/geometry.h
> > > > > > > > > index 3e6f0f5d7fab..07cb0a7866fe 100644
> > > > > > > > > --- a/include/libcamera/geometry.h
> > > > > > > > > +++ b/include/libcamera/geometry.h
> > > > > > > > > @@ -277,7 +277,7 @@ public:
> > > > > > > > >               return { width, height };
> > > > > > > > >       }
> > > > > > > > >
> > > > > > > > > -     Point topLeft() const
> > > > > > > > > +     Point origin() const
> > > > > > > > >       {
> > > > > > > > >               return { x, y };
> > > > > > > > >       }
> > > > > > > > > diff --git a/src/ipa/ipu3/algorithms/af.cpp
> > > > > > b/src/ipa/ipu3/algorithms/af.cpp
> > > > > > > > > index cf68fb59c49b..1b707e9dd9ab 100644
> > > > > > > > > --- a/src/ipa/ipu3/algorithms/af.cpp
> > > > > > > > > +++ b/src/ipa/ipu3/algorithms/af.cpp
> > > > > > > > > @@ -155,7 +155,7 @@ int Af::configure(IPAContext &context, const
> > > > > > IPAConfigInfo &configInfo)
> > > > > > > > >        * - Return the AF ROI as metadata in the Request
> > > > > > > > >        */
> > > > > > > > >       Rectangle roi = gridSize.centeredTo(bds.center());
> > > > > > > > > -     Point start = roi.topLeft();
> > > > > > > > > +     Point start = roi.origin();
> > > > > > > > >
> > > > > > > > >       /* x_start and y_start should be even */
> > > > > > > > >       grid.x_start = utils::alignDown(start.x, 2);
> > > > > > > > > diff --git a/src/libcamera/geometry.cpp
> > > > b/src/libcamera/geometry.cpp
> > > > > > > > > index 000151364c7f..45ba81a99920 100644
> > > > > > > > > --- a/src/libcamera/geometry.cpp
> > > > > > > > > +++ b/src/libcamera/geometry.cpp
> > > > > > > > > @@ -593,11 +593,39 @@ std::ostream &operator<<(std::ostream &out,
> > > > > > const SizeRange &sr)
> > > > > > > > >    * \brief Describe a rectangle's position and dimensions
> > > > > > > > >    *
> > > > > > > > >    * Rectangles are used to identify an area of an image. They
> > > > are
> > > > > > specified by
> > > > > > > > > - * the coordinates of top-left corner and their horizontal and
> > > > > > vertical size.
> > > > > > > > > + * the coordinates of the corner closer to the reference
> > > > system's
> > > > > > origin point
> > > > > > > > > + * and by horizontal and vertical increments from there.
> > > > > > > > >    *
> > > > > > > > > - * The measure unit of the rectangle coordinates and size, as
> > > > well
> > > > > > as the
> > > > > > > > > - * reference point from which the Rectangle::x and Rectangle::y
> > > > > > displacements
> > > > > > > > > - * refers to, are defined by the context were rectangle is used.
> > > > > > > > > + * The corner closer to the reference system's origin point is
> > > > the
> > > > > > rectangle's
> > > > > > > > > + * origin corner.
> > > > > > > > > + *
> > > > > > > > > + * \verbatim
> > > > > > > > > +
> > > > > > > > > +  o = origin corner
> > > > > > > > > +
> > > > > > > > > +         ^
> > > > > > > > > +         |
> > > > > > > > > +         |      -------------------
> > > > > > > > > +         |      ^                 |
> > > > > > > > > +         |      |                 |
> > > > > > > > > +         |      o---->-------------
> > > > > > > > > +         |
> > > > > > > > > +          ------------------------------->
> > > > > > > > > +         (0,0)
> > > > > > > > > +
> > > > > > > > > +         (0,0)
> > > > > > > > > +           ------------------------------->
> > > > > > > > > +          |
> > > > > > > > > +          |      o---->-------------
> > > > > > > > > +          |      |                 |
> > > > > > > > > +          |      v                 |
> > > > > > > > > +          |      -------------------
> > > > > > > > > +          |
> > > > > > > > > +          V
> > > > > > > > > +   \endverbatim
> > > > > > > > > + *
> > > > > > > > > + * The measure unit of the rectangle coordinates and size are
> > > > > > defined by the
> > > > > > > > > + * context were the rectangle is used.
> > > > > > > > >    */
> > > > > > > > >
> > > > > > > > >   /**
> > > > > > > > > @@ -608,35 +636,50 @@ std::ostream &operator<<(std::ostream &out,
> > > > > > const SizeRange &sr)
> > > > > > > > >   /**
> > > > > > > > >    * \fn Rectangle::Rectangle(int x, int y, const Size &size)
> > > > > > > > >    * \brief Construct a Rectangle with the given position and
> > > > size
> > > > > > > > > - * \param[in] x The horizontal coordinate of the top-left corner
> > > > > > > > > - * \param[in] y The vertical coordinate of the top-left corner
> > > > > > > > > + * \param[in] x The horizontal coordinate of the origin corner
> > > > > > > > > + * \param[in] y The vertical coordinate of the origin corner
> > > > > > > > >    * \param[in] size The size
> > > > > > > > > + *
> > > > > > > > > + * The rectangle's origin corner is the corner closer to the
> > > > > > reference system
> > > > > > > > > + * origin point (0, 0).
> > > > > > >
> > > > > > > I think we should stick to the previous description:
> > > > > > > `"origin" point defined as the point with the lower x and
> > > > > > > lower y of the rectangle`, as `x` and `y` are signed integers.
> > > > > > >
> > > > > > > If we only support coordinates that are positive or 0, which
> > > > > > > I'm not sure if it's the case, how about making the type to be
> > > > > > > `unsigned int`?
> > > > > > >
> > > > > >
> > > > > > To be honest I would rather make width and heigh signed to allow
> > > > > > constructing (x, y, -w, -h)
> > > > > >
> > > > > >
> > > > > >
> > > > > >
> > > > > >                -------------------
> > > > > >                |                 ^
> > > > > >                |            ------------->
> > > > > >                |           |     |
> > > > > >                ------<-----|-----o
> > > > > >                            |
> > > > > >                            |
> > > > > >                            V
> > > > > >
> > > > > > Not sure if it's useful or not though
> > > > > >
> > > > >
> > > > > Hmm... I find it pretty weird. What if all four corners have all negative
> > > > > coordinates?
> > > > >
> > > > >
> > > >
> > > > Don't know, maybe if the reference system where the rectangle is used
> > > > into has 4 planes and so an all-negative rectangle makes sense.
> > > >
> > > > My point is that we should allow users of this class to express
> > > > Rectangle in any context they plan to use them. Not sure if I'm going
> > > > overboard here or it makes sense.
> > > >
> > >
> > > Yeah I agree, while doesn't that mean the description doesn't fit all
> > > cases, like the corner closer to the reference system origin point of a
> > > rectangle that has all negative coordinates is actually the "bottom-right"
> >
> > This patch aims to remove all references to "top-left" or in general
> > to any visual reference exactly for that purpose. Or have I forgot any
> > ?
>
> In this c'tor `\fn Rectangle::Rectangle(int x, int y, const Size &size)`,
> the description of `x` and `y` are updated to "coordinates of the origin
> corner", where the origin corner is "the corner closer to the reference
> system origin point (0, 0)."
>
> As currently libcamera::Size takes only non-negative width and height,
> take rectangle [(-3, -3), (-3, -1), (-1, -3), (-1, -1)] as the example, you
> can find that the only valid way to construct this rectangle as
> libcamera::Rectangle is `{x = -3, y = -3, size = {2, 2}}`. However, this
> doesn't fit with your updated description, as the corner closer to the
> reference system origin point (0, 0) is actually (-1, -1), instead of
> (-3, -3).
>

You're right. Let's take a step back though. If we have a 4 planes reference
system, we always have a visual top-left indeed. As the 4 planes have
negative and positive coordinates, we can describe with absolute
positions the rectangle and all points in the system.

The problem at hands now is relevant for 1-planes reference systems,
that can be oriented differently, in example with the origin point
being in top-left or bottom-left positions, as per the examples above.
In this case I think we agree that "top-left" is ambiguous. The x and
y coordinates are always positive in the case with a single plane.

I think we should also be concerned with 1 plane reference systems and
move forward with this patch that removes references to the visual
"top-left" and assumes increments in width and height are always
positive.

> >
> > > corner, and currently libcamera::Size only allows non-negative width and
> > > height [1].
> >
> > True, Size uses unsigned int. I don't think it's a big deal and I'm
> > not proposing to introduce a new constructor with signed width and
> > height now, but my point is that if the need arises we can now do
> > that.
> >
> > >
> > > [1]:
> > > https://git.libcamera.org/libcamera/libcamera.git/tree/include/libcamera/geometry.h#n65
> > >
> > >
> > > > >
> > > > >
> > > > > >
> > > > > > > BR,
> > > > > > > Harvey
> > > > > > >
> > > > > > >
> > > > > > > > >    */
> > > > > > > > >
> > > > > > > > >   /**
> > > > > > > > >    * \fn Rectangle::Rectangle(int x, int y, unsigned int width,
> > > > > > unsigned int height)
> > > > > > > > >    * \brief Construct a Rectangle with the given position and
> > > > size
> > > > > > > > > - * \param[in] x The horizontal coordinate of the top-left corner
> > > > > > > > > - * \param[in] y The vertical coordinate of the top-left corner
> > > > > > > > > + * \param[in] x The horizontal coordinate of the origin corner
> > > > > > > > > + * \param[in] y The vertical coordinate of the origin corner
> > > > > > > > >    * \param[in] width The width
> > > > > > > > >    * \param[in] height The height
> > > > > > > > > + *
> > > > > > > > > + * The rectangle's origin corner is the corner closer to the
> > > > > > reference system
> > > > > > > > > + * origin point (0, 0).
> > > > > > > > >    */
> > > > > > > > >
> > > > > > > > >   /**
> > > > > > > > >    * \fn Rectangle::Rectangle(const Size &size)
> > > > > > > > > - * \brief Construct a Rectangle of \a size with its top left
> > > > corner
> > > > > > located
> > > > > > > > > + * \brief Construct a Rectangle of \a size with its origin
> > > > corner
> > > > > > located
> > > > > > > > >    * at (0,0)
> > > > > > > > >    * \param[in] size The desired Rectangle size
> > > > > > > > > + *
> > > > > > > > > + * The rectangle's origin corner is the corner closer to the
> > > > > > reference system
> > > > > > > > > + * origin point (0, 0).
> > > > > > > > >    */
> > > > > > > > >
> > > > > > > > >   /**
> > > > > > > > >    * \var Rectangle::x
> > > > > > > > > - * \brief The horizontal coordinate of the rectangle's top-left
> > > > > > corner
> > > > > > > > > + * \brief The horizontal coordinate of the rectangle's origin
> > > > corner
> > > > > > > > > + *
> > > > > > > > > + * The rectangle's origin corner is the corner closer to the
> > > > > > reference system
> > > > > > > > > + * origin point (0, 0).
> > > > > > > > >    */
> > > > > > > > >
> > > > > > > > >   /**
> > > > > > > > >    * \var Rectangle::y
> > > > > > > > > - * \brief The vertical coordinate of the rectangle's top-left
> > > > corner
> > > > > > > > > + * \brief The vertical coordinate of the rectangle's origin
> > > > corner
> > > > > > > > > + *
> > > > > > > > > + * The rectangle's origin corner is the corner closer to the
> > > > > > reference system
> > > > > > > > > + * origin point (0, 0).
> > > > > > > > >    */
> > > > > > > > >
> > > > > > > > >   /**
> > > > > > > > > @@ -683,9 +726,13 @@ Point Rectangle::center() const
> > > > > > > > >    */
> > > > > > > > >
> > > > > > > > >   /**
> > > > > > > > > - * \fn Point Rectangle::topLeft() const
> > > > > > > > > - * \brief Retrieve the coordinates of the top left corner of
> > > > this
> > > > > > Rectangle
> > > > > > > > > - * \return The Rectangle's top left corner
> > > > > > > > > + * \fn Point Rectangle::origin() const
> > > > > > > > > + * \brief Retrieve the coordinates of the origin corner of this
> > > > > > Rectangle
> > > > > > > > > + *
> > > > > > > > > + * The rectangle's origin corner is the corner closer to the
> > > > > > reference system
> > > > > > > > > + * origin point (0, 0).
> > > > > > > > > + *
> > > > > > > > > + * \return The Rectangle's origin corner
> > > > > > > >
> > > > > > > > I think you can drop "corner" from "origin corner"
> > > > > > > >
> > > > > > > > Probably throughout the patch:
> > > > > > > >      s/origin corner/origin/
> > > > > > > >
> > > > > > > > Otherwise, LGTM
> > > > > > > >
> > > > > > > > Reviewed-by: Umang Jain <umang.jain at ideasonboard.com>
> > > > > > > > >    */
> > > > > > > > >
> > > > > > > > >   /**
> > > > > > > > > @@ -740,15 +787,15 @@ Rectangle &Rectangle::translateBy(const
> > > > Point
> > > > > > &point)
> > > > > > > > >    */
> > > > > > > > >   Rectangle Rectangle::boundedTo(const Rectangle &bound) const
> > > > > > > > >   {
> > > > > > > > > -     int topLeftX = std::max(x, bound.x);
> > > > > > > > > -     int topLeftY = std::max(y, bound.y);
> > > > > > > > > +     int originX = std::max(x, bound.x);
> > > > > > > > > +     int originY = std::max(y, bound.y);
> > > > > > > > >       int bottomRightX = std::min<int>(x + width, bound.x +
> > > > > > bound.width);
> > > > > > > > >       int bottomRightY = std::min<int>(y + height, bound.y +
> > > > > > bound.height);
> > > > > > > > >
> > > > > > > > > -     unsigned int newWidth = std::max(bottomRightX - topLeftX,
> > > > 0);
> > > > > > > > > -     unsigned int newHeight = std::max(bottomRightY - topLeftY,
> > > > 0);
> > > > > > > > > +     unsigned int newWidth = std::max(bottomRightX - originX,
> > > > 0);
> > > > > > > > > +     unsigned int newHeight = std::max(bottomRightY - originY,
> > > > 0);
> > > > > > > > >
> > > > > > > > > -     return { topLeftX, topLeftY, newWidth, newHeight };
> > > > > > > > > +     return { originX, originY, newWidth, newHeight };
> > > > > > > > >   }
> > > > > > > > >
> > > > > > > > >   /**
> > > > > > > > > diff --git a/src/libcamera/pipeline/rpi/common/pipeline_base.cpp
> > > > > > b/src/libcamera/pipeline/rpi/common/pipeline_base.cpp
> > > > > > > > > index 3041fd1ed9fd..8d2440026689 100644
> > > > > > > > > --- a/src/libcamera/pipeline/rpi/common/pipeline_base.cpp
> > > > > > > > > +++ b/src/libcamera/pipeline/rpi/common/pipeline_base.cpp
> > > > > > > > > @@ -1289,7 +1289,7 @@ Rectangle CameraData::scaleIspCrop(const
> > > > > > Rectangle &ispCrop) const
> > > > > > > > >        */
> > > > > > > > >       Rectangle nativeCrop =
> > > > > > ispCrop.scaledBy(sensorInfo_.analogCrop.size(),
> > > > > > > > >
> > > > > >  sensorInfo_.outputSize);
> > > > > > > > > -     nativeCrop.translateBy(sensorInfo_.analogCrop.topLeft());
> > > > > > > > > +     nativeCrop.translateBy(sensorInfo_.analogCrop.origin());
> > > > > > > > >       return nativeCrop;
> > > > > > > > >   }
> > > > > > > > >
> > > > > > > > > @@ -1303,7 +1303,7 @@ void CameraData::applyScalerCrop(const
> > > > > > ControlList &controls)
> > > > > > > > >                       nativeCrop = { 0, 0, 1, 1 };
> > > > > > > > >
> > > > > > > > >               /* Create a version of the crop scaled to ISP
> > > > (camera
> > > > > > mode) pixels. */
> > > > > > > > > -             Rectangle ispCrop =
> > > > > > nativeCrop.translatedBy(-sensorInfo_.analogCrop.topLeft());
> > > > > > > > > +             Rectangle ispCrop =
> > > > > > nativeCrop.translatedBy(-sensorInfo_.analogCrop.origin());
> > > > > > > > >               ispCrop.scaleBy(sensorInfo_.outputSize,
> > > > > > sensorInfo_.analogCrop.size());
> > > > > > > > >
> > > > > > > > >               /*
> > > > > > > > > diff --git a/src/py/libcamera/py_geometry.cpp
> > > > > > b/src/py/libcamera/py_geometry.cpp
> > > > > > > > > index c7e303609427..8dee365b25dd 100644
> > > > > > > > > --- a/src/py/libcamera/py_geometry.cpp
> > > > > > > > > +++ b/src/py/libcamera/py_geometry.cpp
> > > > > > > > > @@ -105,7 +105,7 @@ void init_py_geometry(py::module &m)
> > > > > > > > >               .def_property_readonly("is_null",
> > > > &Rectangle::isNull)
> > > > > > > > >               .def_property_readonly("center",
> > > > &Rectangle::center)
> > > > > > > > >               .def_property_readonly("size", &Rectangle::size)
> > > > > > > > > -             .def_property_readonly("topLeft",
> > > > &Rectangle::topLeft)
> > > > > > > > > +             .def_property_readonly("origin",
> > > > &Rectangle::origin)
> > > > > > > > >               .def("scale_by", &Rectangle::scaleBy)
> > > > > > > > >               .def("translate_by", &Rectangle::translateBy)
> > > > > > > > >               .def("bounded_to", &Rectangle::boundedTo)
> > > > > > > > > diff --git a/test/geometry.cpp b/test/geometry.cpp
> > > > > > > > > index 64169206ad16..a4ee6f6e167a 100644
> > > > > > > > > --- a/test/geometry.cpp
> > > > > > > > > +++ b/test/geometry.cpp
> > > > > > > > > @@ -363,16 +363,16 @@ protected:
> > > > > > > > >                       return TestFail;
> > > > > > > > >               }
> > > > > > > > >
> > > > > > > > > -             /* Rectangle::size(), Rectangle::topLeft() and
> > > > > > Rectangle::center() tests */
> > > > > > > > > +             /* Rectangle::size(), Rectangle::origin() and
> > > > > > Rectangle::center() tests */
> > > > > > > > >               if (Rectangle(-1, -2, 3, 4).size() != Size(3, 4) ||
> > > > > > > > >                   Rectangle(0, 0, 100000, 200000).size() !=
> > > > > > Size(100000, 200000)) {
> > > > > > > > >                       cout << "Rectangle::size() test failed" <<
> > > > > > endl;
> > > > > > > > >                       return TestFail;
> > > > > > > > >               }
> > > > > > > > >
> > > > > > > > > -             if (Rectangle(1, 2, 3, 4).topLeft() != Point(1, 2)
> > > > ||
> > > > > > > > > -                 Rectangle(-1, -2, 3, 4).topLeft() != Point(-1,
> > > > > > -2)) {
> > > > > > > > > -                     cout << "Rectangle::topLeft() test failed"
> > > > <<
> > > > > > endl;
> > > > > > > > > +             if (Rectangle(1, 2, 3, 4).origin() != Point(1, 2)
> > > > ||
> > > > > > > > > +                 Rectangle(-1, -2, 3, 4).origin() != Point(-1,
> > > > -2))
> > > > > > {
> > > > > > > > > +                     cout << "Rectangle::origin() test failed"
> > > > <<
> > > > > > endl;
> > > > > > > > >                       return TestFail;
> > > > > > > > >               }
> > > > > > > > >
> > > > > > > > > --
> > > > > > > > > 2.46.1
> > > > > > > > >
> > > > > > > >
> > > > > > >
> > > > > > >
> > > > > > > --
> > > > > > > BR,
> > > > > > > Harvey Yang
> > > > > >
> > > >
>
>
>
> --
> BR,
> Harvey Yang


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