SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
Spherical wavelets: efficiently representing functions on the sphere
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
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)
BLaC-Wavelets: a multiresolution analysis with non-nested spaces
Proceedings of the 7th conference on Visualization '96
View-dependent refinement of progressive meshes
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
VIS '97 Proceedings of the 8th conference on Visualization '97
Wavelets for computer graphics: theory and applications
Wavelets for computer graphics: theory and applications
A Pyramidal Data Structure for Triangle-Based Surface Description
IEEE Computer Graphics and Applications
Optimal triangular Haar bases for spherical data
VIS '99 Proceedings of the conference on Visualization '99: celebrating ten years
Bicubic subdivision-surface wavelets for large-scale isosurface representation and visualization
Proceedings of the conference on Visualization '00
Biorthogonal wavelets for subdivision volumes
Proceedings of the seventh ACM symposium on Solid modeling and applications
An Introduction to Wavelets for Scientific Visualization
Dagstuhl '97, Scientific Visualization
Wavelet-Based Multiresolution Analysis of Irregular Surface Meshes
IEEE Transactions on Visualization and Computer Graphics
Generalized B-Spline Subdivision-Surface Wavelets for Geometry Compression
IEEE Transactions on Visualization and Computer Graphics
Scale-separating operators for variational multiscale large eddy simulation of turbulent flows
Journal of Computational Physics
A view-dependent method for the multi-resolution representation of terrains with roads embedded
International Journal of Remote Sensing
Biorthogonal wavelets based on gradual subdivision of quadrilateral meshes
Computer Aided Geometric Design
ICCVG 2008 Proceedings of the International Conference on Computer Vision and Graphics: Revised Papers
The multiresolution analysis of triangle surface meshes with lifting scheme
MIRAGE'07 Proceedings of the 3rd international conference on Computer vision/computer graphics collaboration techniques
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Wavelet-based methods have proven their efficiency for the visualization at different levels of detail, progressive transmission, and compression of large data sets. The required core of all wavelet-based methods is a hierarchy of meshes that satisfies subdivision-connectivity: This hierarchy has to be the result of a subdivision process starting from a base mesh. Examples include quadtree uniform 2D meshes, octree uniform 3D meshes, or 4-to-1 split triangular meshes. In particular, the necessity of subdivision-connectivity prevents the application of wavelet-based methods on irregular triangular meshes. In this paper, a "wavelet-like" decomposition is introduced that works on piecewise constant data sets over irregular triangular surface meshes. The decomposition/reconstruction algorithms are based on an extension of wavelet-theory allowing hierarchical meshes without subdivision-connectivity property. Among others, this approach has the following features: It allows exact reconstruction of the data set, even for nonregular triangulations, and it extends previous results on Haar-wavelets over 4-to-1 split triangulations.