Laplacian smoothing is an algorithm to
smooth
Smooth may refer to:
Mathematics
* Smooth function, a function that is infinitely differentiable; used in calculus and topology
* Smooth manifold, a differentiable manifold for which all the transition maps are smooth functions
* Smooth algebrai ...
a
polygonal mesh
In 3D computer graphics and solid modeling, a polygon mesh is a collection of , s and s that defines the shape of a polyhedral object. The faces usually consist of triangles (triangle mesh), quadrilaterals (quads), or other simple convex polyg ...
. 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
.
See also
*
Tutte embedding, an embedding of a planar mesh in which each vertex is already at the average of its neighbours' positions
References
Mesh generation
Geometry processing
{{geometry-stub