Blender 2.9+ update available:   Download EdgeTune for 2.8

This script is an implementation of the concept of sliding vertices around
   on edges.  It is used to finetune/redraw edges/edgeloops through the process of sliding
   vertices.  It can be used to slide anything anywhere.
   To my knowledge this is a new concept in 3D modelling. Try it and you will
   see how it can impact your modelling habits.
   You are able to tune vertices by sliding by freehand-redrawing them on the
   edges they are part of.
   

   This is version 2 of the script, implementing a new graphical user interface
   and having gone to a complete rewrite of the code,
   lifting almost all shortcomings of the old code.
   

   Documentation
   Put the script file in your scripts/addons directory. 
   Activate the script in User Preferences->AddOns->Mesh.

   

   The script will work on any vertice/edge/face-selection. 
   Make a selection, invoke script. (script only accessible when in EditMode).
   Find the EdgeTune button near the bottom of the Mesh Tools panel.
   

   The selection will be visualized in yellow.
   When limited visibility is on, EdgeTune will only select non-occluded
   verts/edges:  turn on Auto Occlusion in the panel to make EdgeTune change
   selection when user changes orientation, otherwise initial selection remains.
   Press and hold left-mouse button and draw freely across the in red
   visualized, so called "slide-edges".  
   The respective selected vertices will change position on the slide-edge to
   the new position you choose by moving over it with the left mouse-button
   pressed.

   Undo one step a time with Ctrl-Z.
   Press ENTER/RETURN to finalize the operation.

   Just press the right-mouse-button to cancel the script operation.

   Change orientation the standard Blender way.
   HINT: EdgeTune is also multi-vertex-slide.