A SURFACE (red) directly faces an invisible middle vector which vector can be changed between a fixed line (blue) and another line (green) whose angle can be varied by the number slider, rotating about the Point common to the two lines (Gh file attached).
This works over the whole arc (pale magenta) … except that it is not a continuously smooth motion. At about a tenth of the way from either of the two arc ends, the red square shudders and flicks from one orientation to another.
The question is please, can this be made smooth and continuous?
I understand it may involve either advanced rotation logic or quaternions, which are beyond me …
The Angles ~ .gh (49.1 KB)
I bet!
And me!
BUT, purely from guessing + not really sure I follow—does this look correct (see blue groups):
The Angles ~.gh (98.8 KB)
*Btw, I think the title in your definition (Rotating a line from side to side…) is more precise for the purposes of reaching other curious minds. I like “Angle tangle”, though 
René,
Thank you!
It looks correct and it works with those new-fangled components.
I’m going to have to study how you did that!
I’m grateful for your effort to wrangle and to untangle the mangled angles.
You’ve probably helped others too; many thanks.
Clive
Alternatively, and mainly because I truly don’t know what the ‘start’ position (for the red square) should be, this simplifies the fina{n}gling:
The Angles ~~.gh (47.1 KB)
Just in case,
Cheers!
In my screenshot, the mid-position of the lever didn’t make it clear, sorry; the start position for the lever and hence the red square, should be on the left side, as indeed you had it in your video.
