How to understand Plankton’s SplitFace SplitVertex and SplitEdge

Recently i found plankton’s splitface, splitvertex and splitedge are different with normal halfedge mesh. i have checked source code but i cannot still understand them in a geometry way. Does anyone help me?
Best wishes,

Now i think plankton just deal with the relationship of halfedge. But when i use these method i found the new inserted vertices were moved by something.
I just wanna understand this and have no other actual purposes. Could you please help me figure out it.