Kan Yeuk Ming. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1994. / Chapter 1. --- INTRODUCTION --- p.1 / Chapter 1.1 --- Motivation --- p.1 / Chapter 1.2 --- Objectives --- p.2 / Chapter 1.3 --- Report Organization --- p.3 / Chapter 2. --- RETROSPECT OF NON-MANIFOLD SOLID MODELING --- p.5 / Chapter 2.1 --- Geometric Modeling --- p.5 / Chapter 2.2 --- Euclidean Space and Topological Space --- p.6 / Chapter 2.3 --- Domains of Solid and Non-Manifold Geometric Modeling --- p.8 / Chapter 2.3.1 --- r-set Domain --- p.8 / Chapter 2.3.2 --- Manifold Domain --- p.9 / Chapter 2.3.3 --- Adjacency Form of Topology --- p.11 / Chapter 2.3.4 --- Cell Complex --- p.13 / Chapter 2.4 --- Representation Schemes of Solid and Non-Manifold Geometric Modeling --- p.14 / Chapter 2.4.1 --- Spatial Decomposition --- p.14 / Chapter 2.4.2 --- Constructive Solid Geometry (CSG) --- p.15 / Chapter 2.4.3 --- Boundary Representations (B-rep) --- p.17 / Chapter 2.5 --- Summary --- p.20 / Chapter 3. --- BOOSTING UP THE SPEED OF BOOLEAN OPERATIONS --- p.21 / Chapter 3.1 --- Solid Modeling with Specialized Hardware --- p.22 / Chapter 3.1.1 --- Modeling with a 4x4 Determinant Processor --- p.22 / Chapter 3.1.2 --- Ray Casting Engine --- p.24 / Chapter 3.2 --- Solid Modeling with General Purposed Parallel Computer --- p.25 / Chapter 3.2.1 --- Modeling with Shared Memory Parallel Computer --- p.27 / Chapter 3.2.2 --- Modeling with SIMD Massively Parallel Computer --- p.27 / Chapter 3.2.3 --- Modeling with MIMD Distributed Memory Parallel Computer --- p.30 / Chapter 3.3 --- Summary --- p.33 / Chapter 4. --- OVERVIEW OF DECmpp 12000/Sx/8K --- p.34 / Chapter 4.1 --- System Architecture --- p.34 / Chapter 4.1.1 --- DECmpp Sx Front End --- p.34 / Chapter 4.1.2 --- DECmpp Sx Data Parallel Unit --- p.35 / Chapter 4.1.2.1 --- Array Control Unit --- p.35 / Chapter 4.1.2.2 --- Processor Element Array --- p.35 / Chapter 4.1.2.3 --- Processor Element Communication Mechanism --- p.36 / Chapter 4.2 --- DECmpp Sx Programming Language --- p.37 / Chapter 4.2.1 --- Variable Declarations --- p.37 / Chapter 4.2.2 --- Plural Pointers --- p.38 / Chapter 4.2.3 --- Processor Selection by Conditional Expressions --- p.39 / Chapter 4.2.4 --- Processor Element Communications --- p.39 / Chapter 4.3 --- Summary --- p.40 / Chapter 5. --- ARCHITECTURE OF THE NON-MANIFOLD GEOMETRIC MODELER --- p.41 / Chapter 6. --- SEQUENTIAL MODELER --- p.43 / Chapter 6.1 --- Sequential Half-Wedge structures (SHW) --- p.43 / Chapter 6.2 --- Incremental Topological Operators --- p.51 / Chapter 6.3 --- Sequential Boolean Operations --- p.58 / Chapter 6.3.1 --- Complementing the subtracted model --- p.59 / Chapter 6.3.2 --- Computing intersection of geometric entities --- p.59 / Chapter 6.3.3 --- Construction of sub-faces --- p.53 / Chapter 6.3.4 --- Extraction of resultant topological entities --- p.64 / Chapter 6.4 --- Summary --- p.67 / Chapter 7. --- PARALLEL MODELER --- p.68 / Chapter 7.1 --- Parallel Half-Wedge Structure (PHW) --- p.68 / Chapter 7.1.1 --- Pmodel structure --- p.69 / Chapter 7.1.1.1 --- Phwedge structure --- p.69 / Chapter 7.1.1.2 --- Psurface structure --- p.71 / Chapter 7.1.1.3 --- Pedge structure --- p.72 / Chapter 7.1.2 --- Pmav structure --- p.73 / Chapter 7.2 --- Parallel Boolean Operations --- p.74 / Chapter 7.2.1 --- Complementing the subtracted model --- p.75 / Chapter 7.2.2 --- Intersection computation --- p.79 / Chapter 7.2.2.1 --- Distributing geometric entities --- p.80 / Chapter 7.2.2.2 --- Vertex-Vertex intersection --- p.89 / Chapter 7.2.2.3 --- Vertex-Edge intersection --- p.89 / Chapter 7.2.2.4 --- Edge-Edge intersection --- p.89 / Chapter 7.2.2.5 --- Vertex-Face intersection --- p.90 / Chapter 7.2.2.6 --- Edge-Face intersection --- p.92 / Chapter 7.2.2.7 --- Face-Face intersection --- p.93 / Chapter 7.2.3 --- Constructing sub-faces --- p.98 / Chapter 7.2.4 --- Extraction and construction of resultant topological entities --- p.100 / Chapter 7.3 --- Summary --- p.106 / Chapter 8. --- THE PERFORMANCE OF PARALLEL HALF-WEDGE MODELER --- p.108 / Chapter 8.1 --- The performance of converting sequential to parallel structure --- p.111 / Chapter 8.2 --- The overall performance of parallel Boolean operations --- p.112 / Chapter 8.3 --- The percentage of execution time for individual stages of parallel Boolean operations --- p.119 / Chapter 8.4 --- The effect of inbalance loading to the performance of parallel Boolean operations --- p.121 / Chapter 8.5 --- Summary --- p.125 / Chapter 9. --- CONCLUSIONS AND SUGGESTIONS FOR FURTHER WORK --- p.126 / Chapter 9.1 --- Conclusions --- p.126 / Chapter 9.2 --- Suggestions for further work --- p.127 / APPENDIX / Chapter A. --- SEQUENTIAL HALF-WEDGE STRUCTURE --- p.A-1 / Chapter B. --- COMPUTATION SCHEME IN CHECKING A FACE LOCATING INSIDE THE FACES OF A SOLID --- p.A-3 / Chapter C. --- ALGORITHM IN FINDING A HALF-WEDGE WITH A DIRECTION CLOSEST FROM A REFERENCE HALF-WEDGE --- p.A-5 / Chapter D. --- PARALLEL HALF-WEDGE STRUCTURE --- p.A-7 / REFERENCES --- p.A-10

The objective of this thesis is to use the Majorana description of a spin-1 system to give a geometrical construction of a maximal set of Mutually Unbiased Bases (MUBs) and Symmetric Informationally Complete Positive Operator Valued Measures (SIC-POVMs) for this system. In the Majorana Approach, an arbitrary pure state of a spin-1 system is represented by a pair of points on the Reimann sphere, or a pair of unit vectors (known as Majorana vectors or M-vectors). Spin-1 states can be of three types: those whose vectors are parallel, those whose vectors are antiparallel and those whose vectors make an arbitrary angle. The types of bases possible for a spin-1 system are thus geometrically much more varied than for a spin-half system or qubit, which is the standard unit of information storage in most quantum protocols. Our derivation of the MUBs and SIC-POVMs proceeds from a recently derived expression for the squared overlap of two spin-1 states in terms of their M-vectors and the minimal additional set of assumptions that are needed. These assumptions include time-reversal invariance in the case of the MUBs and the requirement of three-fold symmetry in the case of the SIC-POVMs. The applications of these results to problems in quantum information are mentioned.

No description available.

We present two watermarking schemes for 3D meshes : - watermarking with geometrical invariant for fragile watermarking towards authentication and integrity purposes - watermarking in the geometrical spectral domain towards robust watermarking / Nous présentons deux schémas de tatouage pour maillages surfaciques 3D : - tatouage fragile par invariants géométriques pour l'authentification et l'intégrité - tatouage robuste dans l'espace de la décomposition spectrale

Thesis (Ph. D.)--University of Missouri-Columbia, 2003. / Typescript. Vita. Includes bibliographical references (leaf 177). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2003. / Typescript. Vita. Includes bibliographical references (leaf 177). Also available on the Internet.

Thesis (Ph. D.)--University of Hong Kong, 2000. / Includes bibliographical references (leaves 220-223).

Thesis (Ph. D.)--University of Washington, 2002. / Vita. Includes bibliographical references (p. 200-209).

The research evaluates the feasibility of assisting orthodontists to treat irregularities in teeth by computing the transformations to move each tooth to its ideal position. The intent is to help orthodontists craft a precise and specific treatment plan for each patient. Computation of the transformations is achieved through the use of a reverse engineering package, Geomagic Studio, and a three dimensional modeling program, Rhino3D. The inputs for finding the transformation are the patient's teeth mold and dental arch templates. A 3D laser scanner is used to form a point cloud data representation of the patient's teeth mold. Geomagic is used to construct a Non-Uniform Rational B-Spline surface for the mold. Rhino3D is used to manipulate this surface and compute the required transformations using the scripting platform, Rhinoscript, in Rhino3D. The steps in the process and the algorithms developed in Rhinoscript to compute the transformations are discussed. Three case studies are presented to demonstrate the process. / text

published_or_final_version / Mechanical Engineering / Doctoral / Doctor of Philosophy