SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Filtering, Segmentation, and Depth
Filtering, Segmentation, and Depth
A cascadic geometric filtering approach to subdivision
Computer Aided Geometric Design
Fair Triangle Mesh Generation with Discrete Elastica
GMP '02 Proceedings of the Geometric Modeling and Processing — Theory and Applications (GMP'02)
A finite element method for surface restoration with smooth boundary conditions
Computer Aided Geometric Design
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
Galerkin Finite Element Methods for Parabolic Problems (Springer Series in Computational Mathematics)
A parametric finite element method for fourth order geometric evolution equations
Journal of Computational Physics
G1 surface modelling using fourth order geometric flows
Computer-Aided Design
On a linear programming approach to the discrete willmore boundary value problem and generalizations
Proceedings of the 7th international conference on Curves and Surfaces
Robust fairing via conformal curvature flow
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
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Based on a natural approach for the time discretization of gradient flows a new time discretization for discrete Willmore flow of polygonal curves and triangulated surfaces is proposed. The approach is variational and takes into account an approximation of the L 2-distance between the surface at the current time step and the unknown surface at the new time step as well as a fully implicity approximation of the Willmore functional at the new time step. To evaluate the Willmore energy on the unknown surface of the next time step, we first ask for the solution of a inner, secondary variational problem describing a time step of mean curvature motion. The time discrete velocity deduced from the solution of the latter problem is regarded as an approximation of the mean curvature vector and enters the approximation of the actual Willmore functional. To solve the resulting nested variational problem in each time step numerically relaxation theory from PDE constraint optimization are taken into account. The approach is applied to polygonal curves and triangular surfaces and is independent of the co-dimension. Various numerical examples underline the stability of the new scheme, which enables time steps of the order of the spatial grid size.