## 24233Re: [PanoToolsNG] Re: Pano2VR makes different default cubefaces

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• Nov 1, 2008
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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