What is the mathematics behind inkscape's power stroke path effect interpolator_type and interpolator_beta attributes?
Not a direct answer, but I can shed light on adding and removing pink control points using the GUI:

initially PowerStrok gives you 3 pink control points.
CTRL-Click on one of them duplicates it. Drag it along the path to a new position.
CTRL-ALT-Click removes the clicked one (don't remove all)
ALT-Click on a pink control point opens a text entry for exact coordinates.