From: Tab Atkins Jr. <jackalmage@gmail.com>
Date: Fri, 15 Nov 2013 10:58:26 -0800
Message-ID: <CAAWBYDC3yydcOPsfBw-uyAoyWVKW_vtGLouQdmip_vYrc9Qp3g@mail.gmail.com>
To: Lea Verou <lea@verou.me>
Cc: Andrew Fedoniouk <news@terrainformatica.com>, www-style list <www-style@w3.org>, fantasai <fantasai.lists@inkedblade.net>, Peter Linss <plinss@csswg.org>, "L. David Baron" <dbaron@dbaron.org>
```On Fri, Nov 15, 2013 at 10:18 AM, Lea Verou <lea@verou.me> wrote:
> Sooo, after some discussion at TPAC after the recent F2F, some of us
> (fantasai, dbaron, plinss, me) decided that even though the edge cases about
> precision aren't that big of a problem, the currently defined behaviour
> results in abruptness when border-radius interpolates from 0 to any positive
> value. Therefore, we think the spread rounding should be changed to be
> defined as:
>
>
> where x = border-radius / spread and ratio() is a continuous strictly
> increasing function that is 0 when border-radius is 0 and becomes 1 after a
> certain point. Therefore, it would still be 0 at 0 and mostly the same for
> small differences between the border-radius and the spread size, but would
> progressively increase when the border-radius is considerably smaller than
>
> We tried many functions for what ratio() could be [1], and I made a demo of
> the three best ones that you can find here [2]. We think Cubic works best,
> which is 1 + (x-1)^3 in [0,1] and 1 when x > 1. Not only this makes
> interpolation smoother, but it also is more aesthetically pleasing, which
> reduces the need for manual ”filleting” (as demonstrated in [3]).
>
> We’d appreciate some feedback about the ratio() function. Perhaps someone
> can think of a better one? My demo supports entering a custom one (in JS
> syntax) so you can experiment there.
> The requirements are:
> - It needs to go through (0,0) and (1,1)
> - Its derivative at (1,1) should be 0
> - It needs to be fast to compute and easy for humans to understand
>
> [1]:

Cool!  I was thinking of coding up this same thing, so I'm glad you did it!

Hyperbolic seems to violate the requirements - it only approaches
(1,1) asymptotically.  (And for the Box.constant value you're using on
the page, it doesn't even really get close - it ends at (1, .8).
Using a constant of 4 seems to do better - it at least hits .91.)

Of the presented choices, I like both Arc and Cubic equally.  I'll
defer to your judgement and agree with Cubic, then.

~TJ
```
Received on Friday, 15 November 2013 18:59:14 UTC

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