From: Tab Atkins Jr. <jackalmage@gmail.com>

Date: Fri, 16 Jul 2010 13:17:16 -0700

Message-ID: <AANLkTinbgBUnzQzzJDxaXhArlg8d0D3Mc_SDEtWBnI4c@mail.gmail.com>

To: Brad Kemper <brad.kemper@gmail.com>

Cc: Aryeh Gregor <Simetrical+w3c@gmail.com>, "L. David Baron" <dbaron@dbaron.org>, Simon Fraser <smfr@me.com>, Brendan Kenny <bckenny@gmail.com>, www-style list <www-style@w3.org>

Date: Fri, 16 Jul 2010 13:17:16 -0700

Message-ID: <AANLkTinbgBUnzQzzJDxaXhArlg8d0D3Mc_SDEtWBnI4c@mail.gmail.com>

To: Brad Kemper <brad.kemper@gmail.com>

Cc: Aryeh Gregor <Simetrical+w3c@gmail.com>, "L. David Baron" <dbaron@dbaron.org>, Simon Fraser <smfr@me.com>, Brendan Kenny <bckenny@gmail.com>, www-style list <www-style@w3.org>

On Thu, Jul 15, 2010 at 6:36 PM, Tab Atkins Jr. <jackalmage@gmail.com> wrote: > As a contribution to the discussion, here's a hand-rolled > implementation of gaussian blur you can play with to get a sense for > how exactly it works. > > http://www.xanthir.com/etc/blurplay/ > > It appears that just halving the length gives a good sigma for lengths > 40px or less, but that approximation gradually becomes worse as the > blur gets larger (you gradually want something larger than half the > length). > > ~TJ > > (By the way, I can see why gaussians are so sucky to work with. I was > getting detectable floating-point errors nearly the entire time, which > were visible to the naked eye once the stdev topped 30 or so. I had > to contort my computations to keep decent accuracy.) So, it turns out the errors weren't due to floating-point precision. I hadn't realized that CanvasPixelArray takes an Octet instead of a Number, and so I was losing a lot of precision due to the automatic flooring that was happening. Tweaking my algorithm slightly produces ideal results with no contortions necessary. Now, the relationship between stdev and blur length is clear. Amazingly enough, if we define the length as "the distance from the edge where it reaches 98% transparency", then the stdev we need to produce that is just half the length. Yup, just divide the length by 2 and you have the appropriate stdev to feed the guassian. This relationship holds basically perfectly all the way from 0 to 100stdevs (that is, 0 to 200px blur length). This approximation eventually fails, but I don't know if that's an actual divergence or just actual floating point errors finally catching up to me. I'd want to run this with some infinite-precision arithmetic to verify. So, we have a relatively easy specification - just say that the blur must approximate a gaussian with a stdev of half the blur length. Then we can put up a little bit of language defining ranges that the approximation must fall within, which we were already planning on. I'm gonna call this problem solved, then. ~TJReceived on Friday, 16 July 2010 20:18:09 GMT

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