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## 24236Re: Pano2VR makes different default cubefaces

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• Nov 1, 2008
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Yes, I understand. But when you speak about the "sqrt(2)", you are
speaking about the figure in the right of this image
http://www.devalvr.com/fiero/equicube.jpg . Te correct figure is in
the left and this figure is valid in the two directions.

Then, if I understand correctly, you say that the figure for
equirect->cube conversion is the left image and for cube->equirect is
the right image?

fiero

--- In PanoToolsNG@yahoogroups.com, Thomas Rauscher <yahoo@...> wrote:
>
> fierodeval wrote, On 01.11.2008 19:04 Uhr:
> > Hi Thomas,
> >
> > I saw this behavior too, if I open a 4000x2000 panorama, then the
> > default cubeface is width/4 = 1000. But if you use width/4 you are
> > loosing quality in all the cubeface, not only in the edges of the
> > cubeface. If I display a MOV with 1000x1000 cubefaces I see the same
> > quality than with a 3140x1570 equirect.
>
> But for the "best cube face possible" you have to think the other
> direction. You have to think of the necessary equirectangular to
produce
> these cube faces.
>
> Just imagine a cube face with black and white lines, each 1 pixel in
> width. To produce such a cube face with an equirectangular image the
> width would need to be tile size * pi * sqrt(2) to produce such a
> resolution.
>
> To simplify the problem for a moment just think of it in two dimension,
> looking onto the scene from the top. The equirectangular image is a
> circle and the cube faces build a square.
>
> To produce the highest possible resolution *in the corner* the circle
> needs to have a radius of (tile size / 2) * sqrt(2). The resulting
> circumference is now (square width / 2) * sqrt(2) * 2 * Pi = square
> width * sqrt(2) * Pi.
>
> If you look at this problem back in 3D the corner of the cube has a
> distance of (cube size / 2) * sqrt(3) and the sphere that hits this
cube
> exactly at the corner needs to have this radius. Fortunately the same
> amount of "stretching" happens from the equirectangular projection so
> not more resolution is needed as for a cylinder.
>
> > I don't understand when you say "loose quality in the center" or
> > "sharp line near the cube face". If you modify the cubeface you change
> > the quality in all the cubeface, not only in the center or in the
> > edge. Or maybe I did not understand anything?
>
> The equirectangular image of this size would provide a higher
resolution
> for the center of the cube face but as we want to produce a cube
face we
> reduce this portion by 1/sqrt(2) so approximately 3 pixels in the
> equirectangular would just produce 2 pixel on the cube face.
>
> As a conclusion: The formula to keep the resolution
>
> cube face size=equi width/Pi
>
> is only true in the equi -> cube direction. For the other direction
>
> equi width=cube face size * Pi * sqrt(2)
>
> would be true. As in the normal panorama workflow you start with an
> equirectangular and convert it to cubic (or extract a view) to patch
> stuff. In this process you are not adding high frequency information to
> the image so it is safe to convert the image back with just the
factor Pi.
>
> > Another issue about Pano2VR. I always ask me what is the practical
> > function of "Optimal" value for the cubeface. This value depends of
> > the window size, but almost all panoramas are shown with a percentage
> > size of the window, not a fixed size. And the existence of an optimal
> > cubesize for a display window size, avoid the possibility to do
> > zoom-in in the panorama, because the optimal value is calculated for a
> > resolution of 1:1 cubeface:screen. Is this correct?
>
> Yes. This is just a *hint*. If you plan a zoom in of x2 then you need
> the doubled tile size. Also if you use a percentage you can calculate a
> resolution for the target screen size.
>
> --
> MfG,
> Thomas
>
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