Name
Abstract | ||
|---|---|---|
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. |
Year | DOI | Venue |
|---|---|---|
2005 | 10.1145/1198555.1198664 | Symposium on Geometry Processing |
Keywords | Field | DocType |
gaussian curvature,discrete willmore flow,ab initio discrete formulation,associated gradient flow,non-shrinking surface smoothing,willmore energy,surface restoration,discrete setting,bius symmetry,relevant gradient expression,discrete willmore energy,discrete differential geometry,geometric model,geometric flow,gradient flow,linear approximation,digital geometry | Discretization,Discrete differential geometry,Mathematical optimization,Geometric flow,Hessian matrix,Digital geometry,Linearization,Mathematics,Willmore energy,Gaussian curvature | Conference |
ISBN | Citations | PageRank |
3-905673-24-X | 43 | 2.18 |
References | Authors | |
13 | 2 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Alexander I. Bobenko | 1 | 182 | 17.20 |
| Peter Schröder | 2 | 5825 | 467.77 |