Representable range mini-rant

This is about representation of data, specifically with respects to 
closed intervals, and using fixed point representation.

For example, representing components for normals, you need the range 
[-1,1]. (let's ignore the dropping of components for compression reasons 
for now) Same thing with various tree coordinates (if you allow the 
topmost coordinate value), vertex components, and pretty much any other 
quantity. This gets annoying when you are dealing with fixed point data.

This is perhaps made most famous with the color->byte conversion, where 
255 means 1.0. The problem with this is that you can't exactly represent 
the midpoint (0.5 maps to 127.5, in this case). If all you want to do is 
representing the midpoint, you can throw away the top value, and 
represent 1.0 using 254, and thus 0.5 as 127. For example, with sound 
samples, and geo-measurement data, it's common to make -32768 mean "no 
data" or "invalid", and normalize -32767 to 32767 as the peak-to-peak 
range. However, then you run into the same problem with mid-midpoints, 
which isn't so much a problem for colors (or audio samples), but a whole 
other kettle of fish for trees of various kinds, or vertex values that 
need to quantize into some tree-based structure.

What I find myself doing is repersenting the midpoint and the two 
endpoints, and throwing away almost a whole bit of precision. For 
example, to represent 0..1 using 8 bits, I'd represent 0 as 0, and 1 as 
128, and then "throwing away" data in the range 129-255. For data that 
needs more precision, I'd represent it using 16 bits, with 32768 being 
1.0 and 0 being 0.0, and ignoring values 32769 through 65535.

It just annoys me that I leave almost a whole bit (6 dB!) of dynamic 
range un-used, but for these cases (closed ranges, must support 
subdivision) I really don't see any better option.

Comments?

Cheers,

          / h+


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