[css-borders-4] Consider continuous as a corner-shape

[noamr]

We've closed #10993 with the resolution to go with superellipses rather than with continuous rounded corners ("apple style").
Opening this issue to keep the option open to add this corner shape in the future, as it provides a style that differs from squircles.
See aforementioned issue for more context.

[tabatkins]

So 'continuous' is some sort of "round, but with c2 continuity", right? Because round (and squircle/etc) abruptly changes from 0 to non-zero curvature when you enter the border-radius zone. (Maybe it's "squircle with c2 continuity"?)

What's the actual math behind this? @smfr?

[smfr]

continuous actually eats into the "flat" part of the edge to achieve a smooth curvature change. You can see this at https://noamr.github.io/squircle-testbed/ (see the source for the bezier construction).

[PeterNjeim]

Forgive me if I'm wrong, but I've been experimenting with that website and it seems like I can recreate any border-radius of the continuous version by multiplying the border-radius by 1.16 and setting the K value to -1 of the superellipse, making it redundant.

Images

[smfr]

They are pretty close but not exact (easier to see in light mode).