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24236Re: Pano2VR makes different default cubefaces

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  • fierodeval
    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?


      --- 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
      > 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
      > 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
      > 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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