Method for fairing B-spline surfaces
Computer-Aided Design
Free-form shape design using triangulated surfaces
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
Multiresolution analysis of arbitrary meshes
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Implicit fairing of irregular meshes using diffusion and curvature flow
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Computation of open Willmore-type surfaces
Applied Numerical Mathematics
CHARMS: a simple framework for adaptive simulation
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Fair Triangle Mesh Generation with Discrete Elastica
GMP '02 Proceedings of the Geometric Modeling and Processing — Theory and Applications (GMP'02)
Simulation of clothing with folds and wrinkles
Proceedings of the 2003 ACM SIGGRAPH/Eurographics symposium on Computer animation
Proceedings of the 2003 ACM SIGGRAPH/Eurographics symposium on Computer animation
Global conformal surface parameterization
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Geometric surface processing via normal maps
ACM Transactions on Graphics (TOG)
A finite element method for surface restoration with smooth boundary conditions
Computer Aided Geometric Design
Geometric fairing of irregular meshes for free-form surface design
Computer Aided Geometric Design
Computing surface hyperbolic structure and real projective structure
Proceedings of the 2006 ACM symposium on Solid and physical modeling
Proceedings of the 4th international conference on Computer graphics and interactive techniques in Australasia and Southeast Asia
3D distance transform adaptive filtering for smoothing and denoising triangle meshes
Proceedings of the 4th international conference on Computer graphics and interactive techniques in Australasia and Southeast Asia
Discrete quadratic curvature energies
ACM SIGGRAPH 2006 Courses
Geometric modeling based on triangle meshes
ACM SIGGRAPH 2006 Courses
Computing geodesic spectra of surfaces
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Computing general geometric structures on surfaces using Ricci flow
Computer-Aided Design
FiberMesh: designing freeform surfaces with 3D curves
ACM SIGGRAPH 2007 papers
Volume-controlled surface fairing
ACM SIGGRAPH 2007 sketches
A quadratic bending model for inextensible surfaces
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Generalized surface flows for mesh processing
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Constraint-based fairing of surface meshes
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Discrete quadratic curvature energies
Computer Aided Geometric Design
Fast, robust, and faithful methods for detecting crest lines on meshes
Computer Aided Geometric Design
Integral invariants for robust geometry processing
Computer Aided Geometric Design
Temporal Computational Objects: A Process for Dynamic Surface Generation
ISVC '08 Proceedings of the 4th International Symposium on Advances in Visual Computing, Part II
Local and Nonlocal Discrete Regularization on Weighted Graphs for Image and Mesh Processing
International Journal of Computer Vision
Curvature estimation over smooth polygonal meshes using the half tube formula
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
A multistep approach to restoration of locally undersampled meshes
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
Noise removal based on the variation of digitized energy
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
Modeling and computation of two phase geometric biomembranes using surface finite elements
Journal of Computational Physics
Semantic 3D Media and Content: Surface partial matching and application to archaeology
Computers and Graphics
ACM SIGGRAPH 2011 papers
Spin transformations of discrete surfaces
ACM SIGGRAPH 2011 papers
A level-set method for skinning animated particle data
SCA '11 Proceedings of the 2011 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
Learning shape and texture characteristics of CT tree-in-bud opacities for CAD systems
MICCAI'11 Proceedings of the 14th international conference on Medical image computing and computer-assisted intervention - Volume Part III
Smoothing of meshes and point clouds using weighted geometry-aware bases
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
On a linear programming approach to the discrete willmore boundary value problem and generalizations
Proceedings of the 7th international conference on Curves and Surfaces
Computer Graphics Forum
Robust fairing via conformal curvature flow
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Multiscale geometric modeling of macromolecules I: Cartesian representation
Journal of Computational Physics
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The Willmore energy of a surface, ∫(H2 -- K) dA, as a function of mean and Gaussian curvature, captures the deviation of a surface from (local) sphericity. As such this energy and its associated gradient flow play an important role in digital geometry processing, geometric modeling, and physical simulation. In this paper we consider a discrete Willmore energy and its flow. In contrast to traditional approaches it is not based on a finite element discretization, but rather on an ab initio discrete formulation which preserves the Möbius symmetries of the underlying continuous theory in the discrete setting. We derive the relevant gradient expressions including a linearization (approximation of the Hessian), which are required for non-linear numerical solvers. As examples we demonstrate the utility of our approach for surface restoration, n-sided hole filling, and non-shrinking surface smoothing.