The Loop Subdivision filter is an approximating subdivision scheme that creates four new triangles for each triangle in the mesh. The user can specify the NumberOfSubdivisions. Loop's subdivision scheme is described in: Loop, C., "Smooth Subdivision surfaces based on triangles,", Masters Thesis, University of Utah, August 1987. For a nice summary of the technique see, Hoppe, H., et. al, "Piecewise Smooth Surface Reconstruction,:, Proceedings of Siggraph 94 (Orlando, Florida, July 24-29, 1994). In COmputer Graphics Proceedings, Annual COnference Series, 1994, ACM SIGGRAPH, pp. 295-302.
The filter only operates on triangles. The filter approximates point data using the same scheme. New triangles create at a subdivision step will have the cell data of their parent cell.