A butterfly subdivision scheme for surface interpolation with tension control
ACM Transactions on Graphics (TOG)
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Piecewise smooth surface reconstruction
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
A unified approach to subdivision algorithms near extraordinary vertices
Computer Aided Geometric Design
A signal processing approach to fair surface design
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Interpolating Subdivision for meshes with arbitrary topology
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
A variational approach to subdivision
Computer Aided Geometric Design
A multiresolution framework for variational subdivision
ACM Transactions on Graphics (TOG)
Implicit fairing of irregular meshes using diffusion and curvature flow
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Discrete Anisotropic Curve Shortening Flow
SIAM Journal on Numerical Analysis
A Method for Analysis of C1-Continuity of Subdivision Surfaces
SIAM Journal on Numerical Analysis
Anisotropic Geometric Diffusion in Surface Processing
VISUALIZATION '00 Proceedings of the 11th IEEE Visualization 2000 Conference (VIS 2000)
Stationary subdivision and multiresolution surface representations
Stationary subdivision and multiresolution surface representations
Computer Aided Geometric Design
Geometric fairing of irregular meshes for free-form surface design
Computer Aided Geometric Design
Sparse matrix solvers on the GPU: conjugate gradients and multigrid
ACM SIGGRAPH 2003 Papers
Combining 4- and 3-direction subdivision
ACM Transactions on Graphics (TOG)
Modeling with multiresolution subdivision surfaces
ACM SIGGRAPH 2006 Courses
Sparse matrix solvers on the GPU: conjugate gradients and multigrid
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
International Journal of Computer Applications in Technology
Two Step Time Discretization of Willmore Flow
Proceedings of the 13th IMA International Conference on Mathematics of Surfaces XIII
Surface interpolation of meshes by geometric subdivision
Computer-Aided Design
Construction of minimal subdivision surface with a given boundary
Computer-Aided Design
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A new approach to subdivision based on the evolution of surfaces under curvature motion is presented. Such an evolution can be understood as a natural geometric filter process where time corresponds to the filter width. Thus, subdivision can be interpreted as the application of a geometric filter on an initial surface. The concrete scheme is a model of such a filtering based on a successively improved spatial approximation starting with some initial coarse mesh and leading to a smooth limit surface.In every subdivision step the underlying grid is refined by some regular refinement rule and a linear finite element problem is either solved exactly or, especially on fine grid levels, one confines to a small number of smoothing steps within the corresponding iterative linear solver. The approach closely connects subdivision to surface fairing concerning the geometric smoothing and to cascadic multigrid methods with respect to the actual numerical procedure. The derived method does not distinguish between different valences of nodes nor between different mesh refinement types. Furthermore, the method comes along with a new approach for the theoretical treatment of subdivision.