User:Ctralie/sandbox

Laplacian smoothing is an algorithm to smooth a polygonal mesh, or to smoothly interpolate function values across the surface via diffusion. 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:


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

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