On Tue, Aug 16, 2022 at 2:09 PM <neit...@gaertner.de> wrote: > circle =. cos j. sin > square =. cos j.&* sin > > squircle =. (square + circle) % 2: NB. your "mean" of the functions.
I thought of trying that, but... it leaves out the "closest distance" part. Perhaps the thought would have been that for each radius position, we want to find a minimum distance between that point and the square (which matches the distance between that point and the circle -- I think some constraint on the relationship between these two distances is required to keep the positions from being ambiguous, and "equal distance" is probably the simplest that allows a curve be specified). Of course, ... that also would mean that parts of the square nearest the corners would never be included. But I think that approach would also introduce "direction discontinuities" at locations corresponding to the four "corner angles" (because the contribution from the square would still jump between the two sides of the corner). Still... like I mentioned before... this approach is not actually mentioned in the wikipedia writeup on "squircles". And I guess your plot is as good of an illustration as any of the nature of this kind of approach. FYI, -- Raul ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
