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
Two Step Time Discretization of Willmore Flow
Proceedings of the 13th IMA International Conference on Mathematics of Surfaces XIII
Technical Section: Context-aware mesh smoothing for biomedical applications
Computers and Graphics
Partial differential equations for interpolation and compression of surfaces
MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces
Can Mean-Curvature Flow be Modified to be Non-singular?
Computer Graphics Forum
| Hi-index | 0.00 |
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.