Hellenica World

# .

Laplacian smoothing is an algorithm to smooth a polygonal mesh.[1][2] 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:

$$\bar{x}_{i}= \frac{1}{N} \sum_{j=1}^{N}\bar{x}_j$$

Where N is the number of adjacent vertices to node i and $$\bar{x}_{i}$$ is the new position for node i.[3]