Laplacian smoothing: Difference between revisions
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'''Laplacian smoothing''' is an algorithm to [[smoothing|smooth]] a [[Polygon mesh|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. |
'''Laplacian smoothing''' is an algorithm to [[smoothing|smooth]] a [[Polygon mesh|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. |
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More formally, the smoothing operation may be described per-vertex as: |
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<math>x_{i}= \frac{1}{N} \sum_{j=0}^{N}x_j </math> |
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Where <math>N</math> is the number of adjacent vertices to node <math>i</math><ref>[[#Glen05|Glen et. al. 2005]]</ref>. |
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==External links== |
==External links== |
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* http://www.andrew.cmu.edu/user/sowen/abstracts/Fi464.html |
* http://www.andrew.cmu.edu/user/sowen/abstracts/Fi464.html |
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==References== |
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{{cite book |title=Mesh enhancement |last=Hansen |first=Glen A. |last2=Douglass |first2=R.W |first3=Andrew |last3=Zardecki |year=2005 |publisher=Imperial College Press |page=404 |ref=Glen05}} |
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[[Category:Geometric algorithms]] |
[[Category:Geometric algorithms]] |
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Revision as of 19:08, 8 April 2009
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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 is the number of adjacent vertices to node [1].
External links
References
Hansen, Glen A.; Douglass, R.W; Zardecki, Andrew (2005). Mesh enhancement. Imperial College Press. p. 404.
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