Modeling objects using polar coordinates rather than cartesian coordinates? To make several vertices co-planar, the usual way is to use Scale = 0 along some convenient axis, but sometimes there is no convenient axis, e.g in this case were I placed the vertices using polar coordinates:

  

How to make the selected vertices co-planar again after they have been a bit disturbed. The target plane contains the global Y axis and the average angular position of the selected set.

I understand I could rotate the vertices around Y, so that they are roughly aligned with Z, then use Scale X = 0. That's what I do, but I'm looking now for a more accurate and less fastidious method.

In a more general way, is there a method (I assume this would be a addon) to facilitate work when dealing with object constructed by angle-distance rather than distance-distance. For example a method which would allow to move the selected vertices radially by the same specific distance (e.g. move each vertex away by 2 cm from the center of the object) while keeping their angular position unchanged?
This looks like a job for Custom Orientations. ('+' in the Orientation dropdown, after making a defining selection)


To flatten to a defined plane, select 3 vertices which define the plane, (or more, for an averaged normal), create a Custom Orientation from them, and with a suitable pivot point, SZ0. I usually set the pivot to 'Active Element', and make a vertex I want to lie in the plane active.
To translate elements in a defined direction, select 2 vertices which define the direction, and create a Custom Orientation from them. Then it's GY (optional numerical entry) on selected elements.
To straighten vertices to a line, select 2 vertices which define the line, and again, with a suitable pivot, it's SShiftY0


etc, etc.

If you do this a lot, it's probably worth creating a keyboard shortcut for the addition of a Custom Orientation, and maybe setting that operator to 'Overwrite Previous', and/or 'Use after Creation'.