>>> I am not sure you can do it accurately with integer math at all, given
>>> that there's a "portion of a pixel" involved in there somewhere. At best
>>> you'd be working in scaled fixed-point.
>>
>> You realise that all of the quantities involved are rational, right? And
>> that a rational number is just two integers?
>
> But in the end you want to paint a pixel a particular color, which is a
> /single/ integer. That's where the precision you might be able to keep
> with rational representation ultimately breaks down.

That's where the precision with ANY POSSIBLE REPRESENTATION will break 
down. :-P

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