"Trevor G Quayle" <Tin### [at] hotmailcom> wrote:
> "Bill Pragnell" <bil### [at] hotmailcom> wrote:
> > "Trevor G Quayle" <Tin### [at] hotmailcom> wrote:
> I don't know wheteher they preserve the information better or not for certain,
> but I do suspect that they make more efficient and uniform storing of the
> environment data.  They actually do contain more information than necessary, as
> they get spread apart towards the poles.  A true equal representation would be
> cos shaped progrssing from a width of 1 circumference at the equator to 0 at
> the poles.  Angular maps only occupy a circular portion of the square image and
> not all of this is efficiently used, as one progresses outward from the center
> (ie angle from viewing line increases), the number of pixels (circumference)
> increases linearly, whereas, to be equal, it should progress sin shaped.  For
> angles from 0 to 90, there are less pixels than ideal by up to 50%, from 90 to
> 180, there are more pixels than ideal, meaning less efficient storing of the
> data.
>
> -tgq

I did some strange math:

The lat/long format has an efficiency of ~64% (64% of the pixels it contains
carry unique, required information)

The angular format has a similar efficiency over the circular area itself, but
coupled with the inefficiency of the circular area over the square area of the
image gives a total efficiency of ~50% (only 50% of the pixels are unique and
usuable).  Add also to this that over the middle of the circle, there is a
total deficiency of about 27% (there are about 27% less pixels in this region
than needed) based on the 90deg circle pixel count. Conversely, if we assume
that the pixel count at/near the centre (0deg) of the angular map is
sufficient, such that tere is no inherent deficiency, then the map has a total
efficiency of ~32%.

I don't know if this makes much sense or is a valid assessment, nor how these
numbers are with reference to the data available from the original mirrorball
images, but it does seem to indicate that, mathematically speaking, the
lat/long format preserves the data better and more efficiently.

-tgq

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