Surface tiling, as well as its counterpart in 3D, i.e. volume tiling, is a fundamental research problem in the subject of computer graphics and geometric modeling, which has found applications in numerous areas, such as computer-aided design (CAD), physical simulation, realtime rendering and architectural modeling. The objective of surface tiling is to compute discrete mesh representations for given surfaces which are often required to possess some desirable geometric properties. Likewise, volume tiling focuses on the study of discretizing a given 3D volume with complex boundary into a set of high-quality volumetric elements. This thesis starts with the study of computing optimal sampling for parametric surfaces, that is, decompose the surface into quad patches such that 1) each quad patch should have their sides with equal length; and 2) the shapes and sizes of all the quad patches should be the same as much as possible. Then, the similar idea is applied to the discrete case, i.e. optimizing the face elements of a quad mesh surface with the goal of making it possess, as much as possible, face elements of desired shapes and sizes. This thesis further studies the computation of hexagonal tiling on free-form surfaces, where the planarity of the faces is more concerned. Free-form meshes with planar hexagonal faces, to be called P-Hex meshes, provide a useful surface representation in discrete differential geometry and are demanded in architectural design for representing surfaces built with planar glass/metal panels. We study the geometry of P-Hex meshes and present an algorithm for computing a free-form P-Hex mesh of a specified shape. Lastly, this thesis progresses to 3D volume case and proposes an automatic method for generating boundary-aligned all-hexahedron meshes with high quality, which possess nice numerical properties, such as a reduced number of elements and high approximation accuracy in physical simulation and mechanical engineering. / published_or_final_version / Computer Science / Doctoral / Doctor of Philosophy

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

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Chan, Pui Lam. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 72-75). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts also in Chinese.

The concept of intelligent CAD systems to assist a designer in automating the design process has been discussed for years. It has been recognized that knowledge engineering techniques and the study of design theory can provide certain solutions to this approach. A major issue in developing intelligent CAD systems for geometric modeling is the integration of the design geometry with the representation of the design constraints. Current commercial computer aided design (CAD) systems are used primarily for recording the results of the design process. Using conventional CAD systems, a design engineer either must create the geometry of the design object with precise coordinates and dimensions, or start his design from an existing geometry of a previous design. It is difficult to propagate a dimensional change throughout an entire model -- especially solid models. This rigidity imposed by conventional CAD systems discourages a designer from exploring different approaches in creating a novel product. / Ph. D.

In an integrated design environment, the common thread between the different design stages is usually the geometric model of the part. However, the requirements for the geometric definition of the design is usually different for each stage. The transformation of data between these different stages is essential for the success of the integrated design environment. For example, conceptual design systems usually deal with geometric dimensional parameters (e.g. length, radius, etc.) whereas preliminary design systems frequently require the geometry definition to be in the form of surface models. This dissertation presents the necessity and scope of creating and implementing methodologies to obtain dimensional geometric parameters from the surface description of an object. Since the study of geometric modeling and parametric surfaces is a new field, few classical methods are applicable. Methods and algorithms for the extraction of various geometry parameters are created. A few methods to pre-process and manipulate these surfaces before the parameter extraction methods can be applied are outlined. One of the most important applications of parameter extraction is in the field of aircraft design. There are two important aspects of geometry data conversion in the design cycle. The first is the conversion from conceptual CAD models to CFD compatible models. The second is the conversion from surface representations of CFD models to obtain component parameters (e.g. wing span, fuselage fineness ratio, moments of inertia, etc.). The methods created in this dissertation are used to extract geometric parameters of importance in aircraft design. This enables the design cycle to be complete and promotes integrated design. These methods have been implemented in the aircraft design software, ACSYNT. Examples of the conversion of data from B-spline surface models to dimensional geometric parameters using these methods are included. The emphasis of this dissertation is on non-uniform B-spline surfaces. Methods for obtaining geometric parameters from aircraft models described by characteristic points are also considered briefly. / Ph. D.