A butterfly subdivision scheme for surface interpolation with tension control
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Efficient, fair interpolation using Catmull-Clark surfaces
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Piecewise smooth surface reconstruction
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A unified approach to subdivision algorithms near extraordinary vertices
Computer Aided Geometric Design
Spherical wavelets: efficiently representing functions on the sphere
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Multiresolution analysis for surfaces of arbitrary topological type
Multiresolution analysis for surfaces of arbitrary topological type
Free-form deformations with lattices of arbitrary topology
SIGGRAPH '96 Proceedings of the 23rd 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)
The simplest subdivision scheme for smoothing polyhedra
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VIS '97 Proceedings of the 8th conference on Visualization '97
Analysis of Algorithms Generalizing B-Spline Subdivision
SIAM Journal on Numerical Analysis
Subdivision surfaces in character animation
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MAPS: multiresolution adaptive parameterization of surfaces
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Non-uniform recursive subdivision surfaces
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Exact evaluation of Catmull-Clark subdivision surfaces at arbitrary parameter values
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
ACM Transactions on Information Systems (TOIS)
Optimal triangular Haar bases for spherical data
VIS '99 Proceedings of the conference on Visualization '99: celebrating ten years
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Piecewise smooth subdivision surfaces with normal control
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Bicubic subdivision-surface wavelets for large-scale isosurface representation and visualization
Proceedings of the conference on Visualization '00
FEM-based subdivision solids for dynamic and haptic interaction
Proceedings of the sixth ACM symposium on Solid modeling and applications
Wavelet representation of contour sets
Proceedings of the conference on Visualization '01
Proceedings of the conference on Visualization '01
Multiresolution Analysis on Irregular Surface Meshes
IEEE Transactions on Visualization and Computer Graphics
Multiresolution modeling for scientific visualization
Multiresolution modeling for scientific visualization
An integrated approach to realize multi-resolution of B-rep model
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Technical Section: Multiresolutions numerically from subdivisions
Computers and Graphics
Mesh connection with RBF local interpolation and wavelet transform
Proceedings of the Third Symposium on Information and Communication Technology
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We present a biorthogonal wavelet construction based on Catmull-Clark-style subdivision volumes. Our wavelet transform is the three-dimensional extension of a previously developed construction of subdivision-surface wavelets that was used for multiresolution modeling of large-scale isosurfaces. Subdivision surfaces provide a flexible modeling tool for surfaces of arbitrary topology and for functions defined thereon. Wavelet representations add the ability to compactly represent large-scale geometries at multiple levels of detail. Our wavelet construction based on subdivision volumes extends these concepts to trivariate geometries, such as time-varying surfaces, free-form deformations, and solid models with non-uniform material properties. The domains of the repre-sented trivariate functions are defined by lattices composed of arbitrary polyhedral cells. These are recursively subdivided based on stationary rules converging to piecewise smooth limit-geometries. Sharp features and boundaries, defined by specific polygons, edges, and vertices of a lattice are explicitly represented using modified subdivision rules. Our wavelet transform provides the ability to reverse the subdivision process after a lattice has been re-shaped at a very fine level of detail, for example using an automatic fitting method. During this coarsening process all geometric detail is compactly stored in form of wavelet coefficients from which it can be reconstructed without loss.