…there is the N panel, which contains the control point values. These values are the location of the curve vertex.
I can rotate the curve vertex with the R key, but I can’t find where the actual angle values are in the UI. I can see that sometimes (can’t figure out which circumstances yet) that there is the Operator subpanel in the T panel shows things related to curve vertex transformations, but I can’t find the actual angle value anywhere.
Likewise, when I hit S and scale a curve vertex, the handles increase in size…but where are those values in the UI?
Ideally, I want to be able to set a curve so that it has the exact same rotation and scale as a previous point on the curve…but it doesn’t look possible unless I eyeball it.
The properties panel changes when you select the bezier handle vertices. They’re not based on angle, but rather on their location. (Arctan of rise/run should be able to calculate that angle from slope between the base vertex and the handle vertex.)
As for Alt-S that’s the radius property, and ctrl-T corresponds to tilt.
If you just want a certain angle, it’s possible to flatten along an axis by scaling to 0 while constraining to an axis, and then rotating the handles to the desired angle afterwards.
Yeah a lot of the path implementation could be a bit better. Even if it involved displaying properties the user couldn’t directly edit. Also note that Blender doesn’t have a built-in way of showing path length either. (Which is also very useful, yet somehow omitted.)