Choosing nodes in parametric curve interpolation
Computer-Aided Design
Curves and surfaces for computer aided geometric design
Curves and surfaces for computer aided geometric design
Using parameters to increase smoothness of curves and surfaces generated by subdivision
Computer Aided Geometric Design
Deformable curve and surface finite-elements for free-form shape design
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Ten lectures on wavelets
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
Hierarchical spacetime control
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
Free-form shape design using triangulated surfaces
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
Hierarchical and variational geometric modeling with wavelets
I3D '95 Proceedings of the 1995 symposium on Interactive 3D graphics
Spherical wavelets: efficiently representing functions on the sphere
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Wavelet multiresolution representation of curves and surfaces
Graphical Models and Image Processing
A variational approach to subdivision
Computer Aided Geometric Design
Matrix computations (3rd ed.)
Designing Fair Curves and Surfaces: Shape Quality in Geometric Modeling and Computer-Aided Design
Designing Fair Curves and Surfaces: Shape Quality in Geometric Modeling and Computer-Aided Design
Stationary Subdivision
Subdivision Methods for Geometric Design: A Constructive Approach
Subdivision Methods for Geometric Design: A Constructive Approach
Bicubic subdivision-surface wavelets for large-scale isosurface representation and visualization
Proceedings of the conference on Visualization '00
EGRW '02 Proceedings of the 13th Eurographics workshop on Rendering
A cascadic geometric filtering approach to subdivision
Computer Aided Geometric Design
Multiresolution Constraints for Designing Subdivision Surfaces via Local Smoothing
PG '99 Proceedings of the 7th Pacific Conference on Computer Graphics and Applications
Opportunities for Subdivision-Based Multiresolution Modeling
PG '99 Proceedings of the 7th Pacific Conference on Computer Graphics and Applications
Geometric design of motions constrained by a contacting surface pair
Computer Aided Geometric Design
Generalized B-Spline Subdivision-Surface Wavelets for Geometry Compression
IEEE Transactions on Visualization and Computer Graphics
Energy-minimizing splines in manifolds
ACM SIGGRAPH 2004 Papers
Combining 4- and 3-direction subdivision
ACM Transactions on Graphics (TOG)
Locally adapted hierarchical basis preconditioning
ACM SIGGRAPH 2006 Papers
Towards flattenable mesh surfaces
Computer-Aided Design
Constrained variational refinement
Journal of Computational and Applied Mathematics
Temporal Computational Objects: A Process for Dynamic Surface Generation
ISVC '08 Proceedings of the 4th International Symposium on Advances in Visual Computing, Part II
Technical Section: Smooth reverse subdivision
Computers and Graphics
Surface interpolation of meshes by geometric subdivision
Computer-Aided Design
Curve subdivision with arc-length control
Computing - Geometric Modelling, Dagstuhl 2008
Construction of minimal subdivision surface with a given boundary
Computer-Aided Design
Smooth reverse Loop and Catmull-Clark subdivision
Graphical Models
Weighted progressive interpolation of Loop subdivision surfaces
Computer-Aided Design
Subdivision surfaces for scattered-data approximation
EGVISSYM'01 Proceedings of the 3rd Joint Eurographics - IEEE TCVG conference on Visualization
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Subdivision is a powerful paradigm for the generaton of curves and surfaces. It is easy to implement, computationally efficient, and useful in a variety of applications because of its intimate connection with multiresolution analysis. An important task in computer graphics and geometric modeling is the construction of curves that interpolate a griven set of points and minimize a fairness functional (variational design). In the context of subdivision, fairing leads to special schemes requiring the solution of a banded linear system at every subdivision step. We present several examples of such schemes including one that reproduces nonuniform interpolating cubic splines. Expressing the construction in terms of certain elementary operations we are able to embed variational subdivision in the lifting framework, a powerful technique to construct wavelet filter banks given a subdivision scheme. This allows us to extend the traditional lifting scheme for FIR filters to a certain class of IIR filters. Consquently, we how how to build variationally optimal curves and associated, stable wavelets in a straightforward fashion. The algorithms to perform the corresponding decomposition and reconstruction transformations are easy to implement and efficient enough for interactive applications.