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Laplacian smoothing

Algorithm to smooth a polygonal mesh From Wikipedia, the free encyclopedia

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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 neighbours) 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 neighbours) then this operation produces the Laplacian of the mesh.

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

Where is the number of adjacent vertices to node , is the position of the -th adjacent vertex and is the new position for node .[3]

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See also

  • Tutte embedding, an embedding of a planar mesh in which each vertex is already at the average of its neighbours' positions

References

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