Are CLUI and TUI operating systems "two dimensional" and "GUI" operating systems "three dimentional"?

After using computers many years I think I can categorize operating systems to three main types by user interfaces (one operating system can have just one user interface or two or more user interfaces):

  1. CLUI: Command Line User Interface
  2. TUI: Textual User Interface (like Norton Commander and Midnight Commander)
  3. GUI: Graphical User Interface (like Windows, most modern Linux, macOS, etc).

But, I am not sure that this categorization is well defined.
What will make it well defined? Graphical dimensions?
Are CLUI and TUI operating systems “two dimensional” and “GUI” operating systems “three dimentional” (graphicwise)?

I had to look up TUI to find out what it was. Learned an interesting term, wikipedia calls it a “retronym” - ie a term invented after its actual use, to help distinguish it from a later technology (in this case, GUI). TUI was a brief but interesting part of the computing timeline, where we were still using character-based terminals, but the terminal manufacturers had added user-programmable character sequences that allowed programmatic addressing of a very low-rez (e.g. often 80x24 or 132x24) screen of characters, as well as special “graphical” characters like corners of boxes. I wrote a lot of programs on VMS at the time, using SMG to simulate a windowed environment, and they were quite slick looking compared to earlier command line programs.

That said, those TUI programs were no different from GUI programs in that they could only simulate 3D graphics on a 2D raster plane. It wasn’t until quite a while after we all had raster-addressable pixel screens, that 3D graphics started to be imbeded in the processor hardware then in separate co-processors, when you might use a term like “3D operating system”.

For my take, the items you mention are characteristics of User Interfaces and not of Operating Systems. If you’re trying to categorize operating systems, there are many categories other than the UI that would be distinguishing characteristics. “UI’s used on this OS” would be but one feature.

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