Multiresolution analysis and wavelets provide useful and efficient tools for representing functions at multiple levels of detail. Wavelet representations have been used in a broad range of applications, including image compression, physical simulation, hierarchical optimization, and numerical analysis.
In this dissertation, I present a new class of wavelets, based on subdivision surfaces, that radically extends the class of representable functions. Whereas previous two-dimensional methods were restricted to functions defined on $\IR\sp2,$ the subdivision wavelets developed here may be applied to functions defined on compact surfaces of arbitrary topological type.
The wavelets developed in this dissertation depend upon a generalization of the standard notion of multiresolution analysis. Rather than developing wavelets from scales and translates over regular domains, they are based on refinable scaling functions. Because these wavelets are built over subdivision surfaces, they may be used to model piecewise linear functions (such as polyhedral surfaces), tangent-plane smooth ($C\sp1$) functions, or piecewise smooth functions with discontinuities.
I present several applications of this work, including smooth level-of-detail control for graphics rendering, compression of geometric models, and animation previewing. The resulting algorithms are shown to run quite efficiently in most cases.
As shapes in computer graphics and modeling become increasingly complex, the techniques developed here provide a powerful and efficient means to extract and simplify essential detail, at the same time eliminating redundant information.
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- Phan A, Raffin R and Daniel M Mesh connection with RBF local interpolation and wavelet transform Proceedings of the 3rd Symposium on Information and Communication Technology, (81-90)
- Pang M, Sheng Y, Sourin A, Castro G and Ugail H Reconstructing multiresolution mesh for web visualization based on PDE resampling Transactions on computational science XII, (36-55)
- Bertram M Wavelet analysis for progressive meshes Proceedings of the 23rd Spring Conference on Computer Graphics, (161-167)
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- Jessl J, Bertram M and Hagen H Web-based progressive geometry transmission using subdivision-surface wavelets Proceedings of the tenth international conference on 3D Web technology, (29-35)
- Bertram M, Duchaineau M, Hamann B and Joy K (2004). Generalized B-Spline Subdivision-Surface Wavelets for Geometry Compression, IEEE Transactions on Visualization and Computer Graphics, 10:3, (326-338), Online publication date: 1-May-2004.
- Valette S and Prost R (2004). Wavelet-Based Multiresolution Analysis of Irregular Surface Meshes, IEEE Transactions on Visualization and Computer Graphics, 10:2, (113-122), Online publication date: 1-Mar-2004.
- Valette S and Prost R (2004). Wavelet-Based Progressive Compression Scheme for Triangle Meshes, IEEE Transactions on Visualization and Computer Graphics, 10:2, (123-129), Online publication date: 1-Mar-2004.
- Lin J, Chuang J, Lin C and Chen C Consistent parametrization by quinary subdivision for remeshing and mesh metamorphosis Proceedings of the 1st international conference on Computer graphics and interactive techniques in Australasia and South East Asia, (151-158)
- Bertram M Biorthogonal wavelets for subdivision volumes Proceedings of the seventh ACM symposium on Solid modeling and applications, (72-82)
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- Bertram M, Duchaineau M, Hamann B and Joy K Bicubic subdivision-surface wavelets for large-scale isosurface representation and visualization Proceedings of the conference on Visualization '00, (389-396)
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- Gross M, Staadt O and Gatti R (1996). Efficient Triangular Surface Approximations Using Wavelets and Quadtree Data Structures, IEEE Transactions on Visualization and Computer Graphics, 2:2, (130-143), Online publication date: 1-Jun-1996.
- MacCracken R and Joy K Free-form deformations with lattices of arbitrary topology Proceedings of the 23rd annual conference on Computer graphics and interactive techniques, (181-188)
- Certain A, Popovic J, DeRose T, Duchamp T, Salesin D and Stuetzle W Interactive multiresolution surface viewing Proceedings of the 23rd annual conference on Computer graphics and interactive techniques, (91-98)
- Hoppe H Progressive meshes Proceedings of the 23rd annual conference on Computer graphics and interactive techniques, (99-108)
- Eck M, DeRose T, Duchamp T, Hoppe H, Lounsbery M and Stuetzle W Multiresolution analysis of arbitrary meshes Proceedings of the 22nd annual conference on Computer graphics and interactive techniques, (173-182)
- Schröder P and Sweldens W Spherical wavelets Proceedings of the 22nd annual conference on Computer graphics and interactive techniques, (161-172)
Index Terms
- Multiresolution analysis for surfaces of arbitrary topological type
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