I routinely scale non-circular variables using methods you can see [here](https://stats.stackexchange.com/questions/25894/changing-the-scale-of-a-variable-to-0-100). If I use the same methods with circular data, the cutoff creates issues, such as huge "jumps" in the data depending on the "direction" (decreasing/increasing) in which the data go while scaling... I hope it is clear enough. I read [here](https://stats.stackexchange.com/questions/544873/converting-a-circular-outcome-variable-to-a-linear-one) that maybe I am trying an impossible task?!

**Question: How can I scale a circular variable (e.g. the circular variable is in the range of 0-1 and I want to scale it in the range of 0.25-0.75)?**

(I use R)


**Edit:** I have a dataset consisting of check-in times of many individuals. They can check-in from 00:00 till 24:00 and I want to simultate their distribution if they have to check-in from 08:00 till 20:00.

I know that approximation is somewhat biased, but I would like to use it as a starting point. If I use the methods I linked, issues arise, e.g. if a check-in time is near the "cut-off/extremes", 1:59:59 will be transformed to 20:00, 2:00:01 will be transformed to 08:00, creating a huge "gap/jump" in the data because of mere seconds