Minimal roughness property of the Delaunay triangulation
Computer Aided Geometric Design
Implicit fairing of irregular meshes using diffusion and curvature flow
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Least squares conformal maps for automatic texture atlas generation
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Global conformal surface parameterization
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Convergence of the Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes
SIAM Journal on Numerical Analysis
Discrete calculus methods for diffusion
Journal of Computational Physics
Discrete laplace operators: no free lunch
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Discrete quadratic curvature energies
Computer Aided Geometric Design
A Discrete Laplace–Beltrami Operator for Simplicial Surfaces
Discrete & Computational Geometry
A Monotonicity Property for Weighted Delaunay Triangulations
Discrete & Computational Geometry
A discrete scheme of Laplace-Beltrami operator and its convergence over quadrilateral meshes
Computers & Mathematics with Applications
Discrete laplace operator on meshed surfaces
Proceedings of the twenty-fourth annual symposium on Computational geometry
Discrete Laplace--Beltrami operators and their convergence
Computer Aided Geometric Design
Spectral conformal parameterization
SGP '08 Proceedings of the Symposium on Geometry Processing
A spectral characterization of the Delaunay triangulation
Computer Aided Geometric Design
Convergence, stability, and discrete approximation of Laplace spectra
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Mean Laplace-Beltrami operator for quadrilateral meshes
Transactions on edutainment V
SMI 2012: Full Spectral computations on nontrivial line bundles
Computers and Graphics
Shape-Up: Shaping Discrete Geometry with Projections
Computer Graphics Forum
SMI 2013: Heat diffusion kernel and distance on surface meshes and point sets
Computers and Graphics
Geodesics in heat: A new approach to computing distance based on heat flow
ACM Transactions on Graphics (TOG)
Surface- and volume-based techniques for shape modeling and analysis
SIGGRAPH Asia 2013 Courses
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While the theory and applications of discrete Laplacians on triangulated surfaces are well developed, far less is known about the general polygonal case. We present here a principled approach for constructing geometric discrete Laplacians on surfaces with arbitrary polygonal faces, encompassing non-planar and non-convex polygons. Our construction is guided by closely mimicking structural properties of the smooth Laplace--Beltrami operator. Among other features, our construction leads to an extension of the widely employed cotan formula from triangles to polygons. Besides carefully laying out theoretical aspects, we demonstrate the versatility of our approach for a variety of geometry processing applications, embarking on situations that would have been more difficult to achieve based on geometric Laplacians for simplicial meshes or purely combinatorial Laplacians for general meshes.