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Give the smoothing operator for 3D meshes! Which weights can we use for this?
Smoothing Operator
Uniform Weights
Move vertices into center of gravity of its 1-ring neighbors. Performs normal and tangential smoothing. Leads to a regular distribution of vertices.
Cotangent Weights
Denoting the area of the 1-ring around
by 
, cotangent weights move into the direction of 
. Since in a planar configuration, moving does not change , is normal to the mesh. Thus, cotangent weights have linear precision. Cotangent weights mostly do normal smoothing. They can become negative for very long triangles. However, if the mesh is Delaunay, Cotangent weights are positive.
Mean Value Weights
where
and 
are the angles between the edge 
and the edges to the previous and next 1-ring neighbor, respectively. MVW have linear precision, they are always positive, but they are non-symmetric:
, in general
Uniform Weights
Move vertices into center of gravity of its 1-ring neighbors. Performs normal and tangential smoothing. Leads to a regular distribution of vertices.
Cotangent Weights
Denoting the area of the 1-ring around
by , cotangent weights move into the direction of . Since in a planar configuration, moving does not change , is normal to the mesh. Thus, cotangent weights have linear precision. Cotangent weights mostly do normal smoothing. They can become negative for very long triangles. However, if the mesh is Delaunay, Cotangent weights are positive.Mean Value Weights
where
and are the angles between the edge and the edges to the previous and next 1-ring neighbor, respectively. MVW have linear precision, they are always positive, but they are non-symmetric:, in general
Karteninfo:
Autor: janisborn
Oberthema: Informatik
Thema: Computergrafik
Schule / Uni: RWTH Aachen
Ort: Aachen
Veröffentlicht: 18.05.2022