FreeLists / openbeos / [openbeos] Re: The Scientific Method aka Bresenham NewsletterArticle

[Michael Noisternig <michael.noisternig@xxxxxxxxx>]

> are you imposing that the division need be performed on _each_ iteration?
>
> y = y1 + (y2-y1)*x/(x2-x1)
>
> is a linear function
>
> y = ax + b
>
> to keep the error within the precisional error margins of the media used (i.e. 
> not to have
> any additional cumulative error) all you need to do is to use a non-incremental 
> evaluator,
> and you end up with 1x multiplication and 1x addition per iteration, no 
> unit-errors
> whatsoever*, and last but not least you end up with no conditions in the inner 
> loop.

Actually it makes no difference whether you do it Mr. Phipps' way or 
your linear function way because the _absolute_ error is the same in 
both cases. The multiplication in your linear function also multiplies 
the error in the LSB which then is the same as the accumulated error by 
subsequent additions.