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Subdivision and Its Applications in Solid Modeling and Signal Compression

专 业: Computational Mathematics  英文
关键词: Subd:v:son S:gnd Compress:on Sol d modeing
分类号: O24
形 态: 共 108 页 约 70,740 个字 约 3.384 M内容
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内容摘要


AbstractSubdivision for curves and surfaces has gained popularity in Computer Graphics and Computer Aided Geometric Designduring the past two decades, yet solid/volumetric subdivision has received much less attention。

In this dissertation, we design a hexahedralbased, approximation scheme。

According to the existing hexahedral-based, approximation scheme over simple or rough hexahedral meshes it is difficult to get the solid models which designers want to model without using some special rules。

We devise a set of solid subdivision rules to facilitate a simple subdivision procedure。

In principle, our solid subdivision process is a combination of simple linear subdivision and two rounds of averaging。

This process makes no restrictions on the local topology of the meshes。

Particularly, it can be applied without any change to meshes with non-manifold topology。

We have introduced free parameters to control the shape of models and offer more flexibility to design models over simple or rough meshes network。

Multiresolution analysis is a generalization of subdivision。

It is a representation which allows the user to change a high resolution to a lower one, in such a way that the original data can be reconstructed correctly。

A conventional approach to obtain an multiresolution representation is based on wavelets。

We have introduced ternary wavelets, based on an interpolating 4-point C2 ternary stationary subdivision scheme, for compressing fractal-like signals。

These wavelets are tightly squeezed and therefore they are more suitable for compressing fractal-like signals。

The error in compressing fractal-like signals by ternary wavelets is at least half less than the error given by existing wavelets。

However, for compressing regular signals we have further classified ternary wavelets into odd ternary and even ternary wavelets。

Our odd ternary wavelets are better in part for compressing both regular and fractal-like signals than other wavelets。

These ternary wavelets are locally supported, symmetric and stable。

The analysis and synthesis algorithms have linear time complexity。

A widely used, efficient and intuitive way to specify, represent and reason about curved,nonlinear geometry for design and modeling is the control polygon paradigm。

For many applications, e。

g。

, rendering, intersection testing or design, this raises the question just how well the control polygon approximates the exact curved and surface geometry。

In this dissertation, we answer this question。

We estimate error bounds between binary/ternary subdivision curves/surfaces and their control polygons after k-fold subdivision in terms of the maximal differences of the initial control point sequences and constants that depend on the subdivision mask。

The bound is independent of the process of subdivision and can be evaluated without recursive subdivision。

Our technique is independent of parameterizations therefore it can be easily and efficiently implemented……

全文目录


英文文摘
Acknowledgements
Chapter1 Introduction
1.1 Subdivision
1.1.1 Previous and related work
1.2 Multiresolution analysis and wavelets
1.2.1 Previous and related work
1.3 Error bounds
1.4 Contributions of this Dissertation
1.4.1 Solid subdivision
1.4.2 Wavelets
1.4.3 Error estimate
1.5 Outline of Dissertation
Chapter2 Background
2.1 Background on solid modeling
2.1.1 Multi-linear subdivision
2.1.2 Averaging operations
2.2 Background on wavelets
2.2.1 General formulation
Chapter3 A New Solid Subdivision Scheme
3.1 Motivations
3.2 The solid subdivision scheme
3.2.1 Multi-linear subdivision
3.2.2 Averaging operations
3.2.3 Boundaries and creases
3.3 Implementation of the scheme
3.4 Geometric meaning of parameters
3.5 Non-hexahedral initial meshes
3.6 Results and examples
3.7 Concluding remarks and future work
Chapter4 Ternary Wavelets and Its Applications to Signal Compression
4.1 Introduction
4.2 Modified interpolating 4-point ternary scheme
4.3 Ternary wavelets
4.4 Applications of ternary wavelets
4.5 Summary and future work
Chapter5 Estimating Error Bounds For Binary Subdivision Curves/Surfaces
5.1 The error bounds for subdivision curves
5.2 The error bounds for subdivision surfaces
5.3 Conclusions and further work
Chapter6 Estimating Error Bounds For Ternary Subdivision Curves/Surfaces
6.1 The error bounds for subdivision curves
6.2 The error bounds for subdivision surfaces
6.2.1 Definition and Notations
6.2.2 Main Result
6.3 Conclusions and further work
Chapter7 Summary
7.1 Solid subdivision
7.2 Wavelets
7.3 Error estimate
Bibliography
Publications

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