The Smooth filter adjusts point coordinates using Laplacian smoothing. The effect is to "relax" the mesh, making the cells better shaped and the vertices more evenly distributed. Note that this filter operates on the lines, polygons, and triangle strips composing an instance of vtkPolyData. Vertex or poly-vertex cells are never modified.
The algorithm proceeds as follows. For each vertex v, a topological and geometric analysis is performed to determine which vertices are connected to v, and which cells are connected to v. Then, a connectivity array is constructed for each vertex. (The connectivity array is a list of lists of vertices that directly attach to each vertex.) Next, an iteration phase begins over all vertices. For each vertex v, the coordinates of v are modified according to an average of the connected vertices. (A relaxation factor is available to control the amount of displacement of v). The process repeats for each vertex. This pass over the list of vertices is a single iteration. Many iterations (generally around 20 or so) are repeated until the desired result is obtained.