Implicit fairing of irregular meshes using diffusion and curvature flow
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Computer Aided Geometric Design
Spectral surface quadrangulation
ACM SIGGRAPH 2006 Papers
Laplace-Beltrami eigenfunctions for deformation invariant shape representation
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
A discrete scheme of Laplace-Beltrami operator and its convergence over quadrilateral meshes
Computers & Mathematics with Applications
Harmonic functions for quadrilateral remeshing of arbitrary manifolds
Computer Aided Geometric Design - Special issue: Geometry processing
Discrete surface modelling using partial differential equations
Computer Aided Geometric Design
Discrete Laplace--Beltrami operators and their convergence
Computer Aided Geometric Design
Discrete Laplacians on general polygonal meshes
ACM SIGGRAPH 2011 papers
Transactions on Edutainment IX
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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.