This dissertation describes a new topology analysis tool for a skeletal based geometric modeling system for conceptual design. Skeletal modeling is an approach to creating solid models in which the engineer designs with lower dimensional primitives such as points, lines, and triangles. The skeleton is then "skinned over" to create the surfaces of the three-dimensional object. In this research, convolution surfaces are used to provide the flesh to the skeleton. Convolution surfaces are generated by convolving a kernel function with a geometric field function to create an implicit surface. Certain properties of convolution surfaces make them attractive for skeletal modeling, including: (1) providing analytic solutions for various geometry primitives (including points, line segments, and triangles); (2) generating smooth surfaces; and (3) providing well-behaved blending. We assume that engineering designers expect the topology of a skeletal model to be identical to that of the underlying skeleton. However, the topology of convolution surfaces can change arbitrarily, making it difficult to predict the topology of the generated surface from knowledge of the topology of the skeleton. To address this issue, we apply Morse theory to analyze the topology of convolution surfaces by detecting the critical points of the surfaces. We developed an efficient and intelligent algorithm to find the critical points (CPs) by analyzing the skeleton. The critical points provide valuable information about the topology of the convolution surfaces. By tracking the CPs, we know where and what kind of topology changes happen when the threshold value reaches the critical value at the CP. Topology matching is done in two steps: (1) global topology is tested by comparing the Betti numbers (number of component, loops, and voids) of the skeleton and the generated convolution surfaces; (2) with matched Betti numbers, local topology is tested by comparing the location of each loop and void area between the skeleton and surfaces. If the topology does not match, appropriate heuristics for determining parameter values of the convolution surfaces are applied to force the surface topology to match that of the skeleton. A recommend threshold value is then provided to generate the topology matched convolution surfaces.

Thesis (Ph. D.)--University of Texas at Austin, 2007. / Vita. Includes bibliographical references.

Thesis (Ph.D.)--University of Alberta, 2010. / Title from PDF file main screen (viewed on July 2, 2010). A thesis submitted to the Faculty of Graduate Studies and Research in partial fulfillment of the requirements for the degree of Doctor of Philosophy, Department of Computing Science, University of Alberta. Includes bibliographical references.

Thesis (M.S.) University of Missouri-Columbia, 2006. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file viewed on (May 21, 2007) Vita. Includes bibliographical references.

This recommended "time planner" has been included so that you have some idea of how much time you will need for each of the lessons. One of the aims of this package is to ensure that teachers do not have to deviate more than is necessary from their normal Std 8 lessons on the structure and function of cells. However, teachers are asked to include the following introductory exercises when they teach the section on the cell. Please emphasis strongly (to the pupils) that this is NOT extra work irrelevant to the syllabus. These lessons are to assist them to develop skills which are absolutely essential for them to succeed as biology scholars. Thereafter the teaching is left to the teacher. However, teachers are asked to incorporate the worksheets on cell organelles. and other relevant exercises, into those lessons in which they deal with those organelles. As teachers will realise. the active involvement of pupils in the learning task inevitably means that more time is spent teaching that section of work. Thus some of the tasks are for pupils to complete at home. Teachers are asked to ensure that pupils do complete these exercises, and that they have some sort of follow-up in class, even if it is merely a class display of drawings which have been done

Thesis (Ph.D.)--Electrical and Computer Engineering, Georgia Institute of Technology, 2008. / Committee Chair: Allen R. Tannenbaum; Committee Member: Anthony J. Yezzi; Committee Member: Gregory Turk; Committee Member: Joel R. Jackson; Committee Member: Patricio A. Vela

Tsui Ping Tim = 建築物埸景的三維重建 / 徐秉添. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 82-85). / Text in English; abstracts in English and Chinese. / Tsui Ping Tim = Jian zhu wu yi jing de san wei zhong jian / Xu Bingtian. / Acknowledgement --- p.ii / Abstract --- p.iii / Table of Content --- p.v / Chapter Chapter 1. --- Introduction --- p.1 / Chapter 1.1. --- A Brief Review on 3D Site Reconstruction --- p.1 / Chapter 1.2. --- Approach of the Project --- p.3 / Chapter 1.3. --- Organization of the Thesis --- p.4 / Chapter 1.3.1 --- The 3D Site Reconstruction --- p.4 / Chapter 1.3.2 --- The Conformal Point Theory --- p.5 / Chapter 1.4. --- Notations --- p.6 / Chapter Chapter 2. --- General System Overview --- p.7 / Chapter 2.1 --- Introduction --- p.7 / Chapter 2.2 --- Ground Reconstruction --- p.8 / Chapter 2.2.1 --- Planar Homography --- p.9 / Chapter 2.2.2 --- Determination of the Planar Homography --- p.10 / Chapter 2.3 --- Buildings and Cliff Reconstruction --- p.13 / Chapter 2.3.1 --- Correspondence Extraction --- p.14 / Chapter 2.3.2 --- Self-Calibration --- p.17 / Chapter 2.3.3 --- Extrinsic Parameters Estimation --- p.17 / Chapter 2.3.4 --- Scene Point Coordinates Computation --- p.18 / Chapter 2.3.5 --- Bundle Adjustment --- p.19 / Chapter 2.4 --- Object Assimilation --- p.19 / Chapter 2.5 --- Summary --- p.21 / Chapter Chapter 3. --- Camera Calibration --- p.22 / Chapter 3.1 --- Introduction --- p.22 / Chapter 3.2 --- Chapter Organization --- p.22 / Chapter 3.3 --- Brief Review of Camera Calibration --- p.23 / Chapter 3.4 --- Camera Intrinsic Parameters --- p.23 / Chapter 3.5 --- Difficulty of the Calibration Problem --- p.25 / Chapter 3.6 --- Non-automatic Calibration --- p.26 / Chapter 3.6.1 --- DLT --- p.26 / Chapter 3.6.2 --- Vanishing Points Approach --- p.26 / Chapter 3.6.3 --- Homography Approach --- p.28 / Chapter 3.7 --- Auto-Calibration --- p.29 / Chapter 3.7.1 --- Square Pixel with Known Principal Points --- p.30 / Chapter 3.7.2 --- Constant Camera Matrices --- p.31 / Chapter 3.8 --- Experiment --- p.33 / Chapter 3.8.1 --- Experimental Measurement --- p.33 / Chapter 3.8.2 --- Experimental Results --- p.34 / Chapter 3.9 --- Conclusion --- p.37 / Chapter Chapter 4. --- Bundle Adjustment --- p.38 / Chapter 4.1 --- Introduction --- p.38 / Chapter 4.2 --- Descent Direction and Gradient Method --- p.39 / Chapter 4.3 --- Problem Implementation --- p.40 / Chapter 4.4 --- Newton Method --- p.40 / Chapter 4.5 --- Gauss-Newton and Levenberg-Marquardt Method --- p.41 / Chapter 4.6 --- Linear Line Search --- p.43 / Chapter 4.7 --- Golden Section [38] --- p.44 / Chapter 4.8 --- Experiment --- p.47 / Chapter 4.9 --- Summary --- p.50 / Chapter Chapter 5. --- Site Reconstruction Review --- p.51 / Chapter 5.1. --- Introduction --- p.51 / Chapter 5.2. --- Chapter Organization --- p.51 / Chapter 5.3. --- Road Reconstruction --- p.51 / Chapter 5.4. --- Cliff Reconstruction --- p.54 / Chapter 5.5. --- Building Reconstruction --- p.56 / Chapter 5.6. --- Object Assimilation --- p.60 / Chapter 5.7. --- Gallery --- p.61 / Chapter 5.8. --- Application --- p.64 / Chapter Chapter 6. --- Conformal Point Theory --- p.65 / Chapter 6.1. --- Introduction --- p.65 / Chapter 6.2. --- Chapter Organization --- p.65 / Chapter 6.3. --- Hartley Conformal Point Theory --- p.66 / Chapter 6.3.1 --- Angle Measurement Making Use of the Conformal Point --- p.66 / Chapter 6.3.2 --- Position of the Conformal Point --- p.66 / Chapter 6.3.3 --- Proof of the Metric Measurement with the Conformal Point --- p.67 / Chapter 6.3.4 --- Limitation of Hartley's Theory --- p.69 / Chapter 6.4. --- The Discovery of Vanishing Line from 2 or More Images --- p.69 / Chapter 6.4.1 --- Parallax and Plane Stabilization --- p.70 / Chapter 6.4.2 --- Recovery of Vanishing Point by Ideal Plane Stabilization --- p.71 / Chapter 6.5 --- Determining the Infinite Homography and Angle Measurement --- p.73 / Chapter 6.5.1 --- "Four Corresponding Vanishing Points, 3 of which are of Orthogonal Directions" --- p.73 / Chapter 6.5.2 --- "Three Corresponding Orthogonal Point Pairs, and Known Epipoles" --- p.74 / Chapter 6.5.3 --- Known camera matrix and Four Distant Points --- p.74 / Chapter 6.6 --- Applications --- p.77 / Chapter 6.7 --- Conclusion --- p.77 / Chapter 6.8 --- Notes on Publication --- p.78 / Chapter Chapter 7. --- Conclusions --- p.79 / Chapter 7.1 --- Summary --- p.79 / Chapter 7.2 --- Conclusion and Future Work --- p.80 / Appendix A. References --- p.82 / Appendix B. Experiment Dataset --- p.86 / Chapter B.1. --- Introduction --- p.86 / Chapter B.2. --- Synthetic Dataset 1 (S1) --- p.87 / Chapter B.3. --- Synthetic Dataset 2 (S2) --- p.89 / Chapter B.4. --- Real Dataset 1 (Rl) --- p.91 / Chapter B.5. --- Real Dataset 2 (R2) --- p.92 / Chapter B.6. --- Real Dataset 3 (R3) --- p.93 / Appendix C. Mathematical Proof of Vanishing Line Detection by Infinite Plane Stabilization --- p.94

No description available.

Chen, Yu. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 78-85). / Abstracts in English and Chinese. / Chapter 1 --- Introduction and Related Work --- p.1 / Chapter 1.1 --- Reconstruction from 2D Line Drawings and the Applications --- p.2 / Chapter 1.2 --- Previous Work on 3D Reconstruction from Single 2D Line Drawings --- p.4 / Chapter 1.3 --- Other Related Work on Interpretation of 2D Line Drawings --- p.5 / Chapter 1.3.1 --- Line Labeling and Superstrictness Problem --- p.6 / Chapter 1.3.2 --- CAD Reconstruction --- p.6 / Chapter 1.3.3 --- Modeling from Images --- p.6 / Chapter 1.3.4 --- Identifying Faces in the Line Drawings --- p.7 / Chapter 1.4 --- 3D Modeling Systems --- p.8 / Chapter 1.5 --- Research Problems and Our Contributions --- p.10 / Chapter 1.5.1 --- Recovering Complex Manifold Objects from Line Drawings --- p.10 / Chapter 1.5.2 --- The Vision-based Sketching System --- p.11 / Chapter 2 --- Reconstruction from Complex Line Drawings --- p.13 / Chapter 2.1 --- Introduction --- p.13 / Chapter 2.2 --- Assumptions and Terminology --- p.15 / Chapter 2.3 --- Separation of a Line Drawing --- p.17 / Chapter 2.3.1 --- Classification of Internal Faces --- p.18 / Chapter 2.3.2 --- Separating a Line Drawing along Internal Faces of Type 1 --- p.19 / Chapter 2.3.3 --- Detecting Internal Faces of Type 2 --- p.20 / Chapter 2.3.4 --- Separating a Line Drawing along Internal Faces of Type 2 --- p.28 / Chapter 2.4 --- 3D Reconstruction --- p.44 / Chapter 2.4.1 --- 3D Reconstruction from a Line Drawing --- p.44 / Chapter 2.4.2 --- Merging 3D Manifolds --- p.45 / Chapter 2.4.3 --- The Complete 3D Reconstruction Algorithm --- p.47 / Chapter 2.5 --- Experimental Results --- p.47 / Chapter 2.6 --- Summary --- p.52 / Chapter 3 --- A Vision-Based Sketching System for 3D Object Design --- p.54 / Chapter 3.1 --- Introduction --- p.54 / Chapter 3.2 --- The Sketching System --- p.55 / Chapter 3.3 --- 3D Geometry of the System --- p.56 / Chapter 3.3.1 --- Locating the Wand --- p.57 / Chapter 3.3.2 --- Calibration --- p.59 / Chapter 3.3.3 --- Working Space --- p.60 / Chapter 3.4 --- Wireframe Input and Object Editing --- p.62 / Chapter 3.5 --- Surface Generation --- p.63 / Chapter 3.5.1 --- Face Identification --- p.64 / Chapter 3.5.2 --- Planar Surface Generation --- p.65 / Chapter 3.5.3 --- Smooth Curved Surface Generation --- p.67 / Chapter 3.6 --- Experiments --- p.70 / Chapter 3.7 --- Summary --- p.72 / Chapter 4 --- Conclusion and Future Work --- p.74 / Chapter 4.1 --- Conclusion --- p.74 / Chapter 4.2 --- Future Work --- p.75 / Chapter 4.2.1 --- Learning-Based Line Drawing Reconstruction --- p.75 / Chapter 4.2.2 --- New Query Interface for 3D Object Retrieval --- p.75 / Chapter 4.2.3 --- Curved Object Reconstruction --- p.76 / Chapter 4.2.4 --- Improving the 3D Sketch System --- p.77 / Chapter 4.2.5 --- Other Directions --- p.77 / Bibliography --- p.78

Thesis (Ph.D.)--University of Texas at Dallas, 2008. / Includes vita. Includes bibliographical references (leaves 139-146)