Martin Krastev wrote:
"Michael Noisternig" <michael.noisternig@xxxxxxxxx> wrote:
Whether it's a _serious_ problem is probably subjective. Fact is that the slope code doesn't draw the line entirely correctly.
hmm, i'd say exactly the opposite - it's a fact that one of the fundamental problems of fractional arithmetics is LSB errors,
whereas whethert the slope code draws correctly is rather subjective :)
[snip]
I'll do it explicitely for your linear function y = ax + b: a = 1/10 <-- a < 1/10 due to finite number of digits y = a*5 + 0 <-- y < 0.5 --> round(y) = 0
yes, if the only place you use round() is for the float->int conversion
As I already said, if you round 'a' to the LSB then it becomes > 1/10 and when you draw the line backwards 'y' evaluates to 0 again.
see my comments at the end of this post.
Evaluating this point by the division variant or by Bresenham's algorithm gives you the right answer 1!
hmm, would you elaborate why the division variant would produce 1?
as above: (5*1)/10 + 0 = 0.5 (exactly!), round(0.5) = 1 or reverse: (-5*1)/10 + 1 = 0.5
ok, i formulated my question erroneously (as the division variant does produce .5 indeed). what i actually meant to say was: why do you think that in general the division variant is more accurate than the slope variant? but if all you meant is that it just handles consistently the '.5-transient' cases then yes - it does. but it's prone to the finite representation problem of fractionals just as well (i.e. (2*1)/10 is as erroneously represented in fp as 2 * 1/10 is)
(500*1001)/1000 = 500500/1000 = 500.5, round -> 501 500*(1001/1000) = 500*1.000999... = 500.4999..., round -> = 500 1001/1000 + 1001/1000 + ... (500 times) = 500.4999..., round -> = 500
but let's get back to the order invariance question. and the fact is the question is pretty much non-standing. why? because line plotters often, and in some particular cases _mandatory_, draw lines in one direction only, regardless of the order the verices were passed in. i.e. lines are treated not as vectors but as non-directional primitives, and as such line plotters are free to decide in what order to draw them. so, what finally matters w/ line plotters/edge evaluators is numerical precision, which condition i believe we both agree is well satisfied.
-blu
ps:
"Michael Noisternig" <michael.noisternig@xxxxxxxxx> wrote:
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.
the absolute error would be the same if we can guarantee that the slope is a always a _rational_ number.
