I once got kidded that my rectangular pattern is more like a race track.

Turns out my curved out corners (which is mostly due to flying closer in patterns) may actually be a safer way to do things.

https://www.aopa.org/News-and-Media/...lized-approach

The hypothesis to be studied is that in contrast with a rectangular pattern, a continuous turn from downwind to final may provide for increased stability, reduced pilot workload, and a constant bank angle throughout the maneuver, helping pilots better manage angle-of-attack variances. Additionally, the use of a continuous turning approach has the potential to reduce the likelihood of overshooting a runway during base-to-final turns, a scenario that has resulted in multiple stall/spin accidents due to aggressive corrective maneuvering. Depending on the results of the study, this procedure may serve as a mitigating technique to reduce the likelihood of loss-of-control accidents during the landing phase of flight.
I think they're going to hit into some problems with the study, owing to the difference in aircraft out there.

For little LSA aircraft like mine, I'm in the "continuous turn" camp (but still call base and final - let's not deviate too far from things), as low speeds make a closer half mile from the runway pattern better for a host of reasons. It also means less distance for turns, so the corners get chopped off.

Now, then, my friend's newly built KR2 is a hot little aircraft (on final he's exceeding my Vne), and if he flew my pattern he'd be dead. Naturally his pattern is much larger than mine, and so the standard rectangle is just fine, and has some advantages. With more than just a throttle, stick, and rudder to worry about, he has to do stuff with levers, wheels and pushy-pully things attached to his dash board and other parts of the cockpit, and that time is invaluable to him and the "corners" are mental cues that develop into muscle memory.