2011 | OriginalPaper | Buchkapitel
Mean Laplace–Beltrami Operator for Quadrilateral Meshes
verfasst von : Yunhui Xiong, Guiqing Li, Guoqiang Han
Erschienen in: Transactions on Edutainment V
Verlag: Springer Berlin Heidelberg
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This paper proposes a discrete approximation of Laplace-Beltrami operator for quadrilateral meshes which we name as mean Laplace-Beltrami operator (MLBO). Given vertex
p
and its quadrilateral 1-neighborhood
N
(
p
), the MLBO of
p
is defined as the average of the LBOs defined on all triangulations of
N
(
p
) and ultimately expressed as a linear combination of 1-neighborhood vertices. The operator is quite simple and numerically convergent. Its weights are symmetric, and easily modified to positive. Several examples are presented to show its applications.