A butterfly subdivision scheme for surface interpolation with tension control
ACM Transactions on Graphics (TOG)
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
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
Multiresolution analysis for surfaces of arbitrary topological type
ACM Transactions on Graphics (TOG)
Interactive multiresolution mesh editing
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
MAPS: multiresolution adaptive parameterization of surfaces
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Interactive multi-resolution modeling on arbitrary meshes
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
The lifting scheme: a construction of second generation wavelets
SIAM Journal on Mathematical Analysis
A multiresolution framework for variational subdivision
ACM Transactions on Graphics (TOG)
Multiresolution hierarchies on unstructured triangle meshes
Computational Geometry: Theory and Applications - Special issue on multi-resolution modelling and 3D geometry compression
Reversing subdivision rules: local linear conditions and observations on inner products
Journal of Computational and Applied Mathematics - Special issue/Dedicated to Prof. Larry L. Schumaker on the occasion of his 60th birthday
Bicubic subdivision-surface wavelets for large-scale isosurface representation and visualization
Proceedings of the conference on Visualization '00
Hierarchical B-spline refinement
SIGGRAPH '88 Proceedings of the 15th annual conference on Computer graphics and interactive techniques
Cut-and-paste editing of multiresolution surfaces
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
EGRW '02 Proceedings of the 13th Eurographics workshop on Rendering
Wavelets for Computer Graphics: A Primer, Part 1
IEEE Computer Graphics and Applications
Unlifted Loop Subdivision Wavelets
PG '04 Proceedings of the Computer Graphics and Applications, 12th Pacific Conference
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Biorthogonal loop-subdivision wavelets
Computing - Geometric modelling dagstuhl 2002
Technical Section: Multiresolution for curves and surfaces based on constraining wavelets
Computers and Graphics
Technical Section: Smooth reverse subdivision
Computers and Graphics
Sketch-based subdivision models
Proceedings of the 6th Eurographics Symposium on Sketch-Based Interfaces and Modeling
Image-assisted modeling from sketches
Proceedings of Graphics Interface 2010
A discrete approach to multiresolution curves and surfaces
Transactions on Computational Science VI
Local fairing with local inverse
Proceedings of Graphics Interface 2013
Special Section on Graphics Interface: Atlas of connectivity maps
Computers and Graphics
Connectivity editing for quad-dominant meshes
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
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In this paper we present a new multiresolution technique for general topology surfaces based on reversing subdivision with energy minimization. We first introduce a general reverse subdivision approach that starts from a trial set of biorthogonal multiresolution filters and refines the resulting coarse points using local masks. The refinement step tries to find a good approximation of the fine points while minimizing the local energy of the coarse points in a least-squares sense. This approach is then used to find smooth reverse of the Loop and Catmull-Clark subdivisions. We discuss the advantages of using this technique in various surface editing and synthesis applications.