Laplacian smoothing

Laplacian smoothing is an algorithm to smooth a polygonal mesh. For each vertex in a mesh, a new position is chosen based on local information (such as the position of neighbors) and the vertex is moved there. In the case that a mesh is topologically a rectangular grid (that is, each internal vertex is connected to four neighbors) then this operation produces the Laplacian of the mesh.

More formally, the smoothing operation may be described per-vertex as:

Where ${\displaystyle N}$ is the number of adjacent vertices to node ${\displaystyle i}$, ${\displaystyle {\bar {x}}_{j}}$ is the position of the ${\displaystyle j}$-th adjacent vertex and ${\displaystyle {\bar {x}}_{i}}$ is the new position for node ${\displaystyle i}$.

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