In this thesis we present a general framework of geometric partial differential equations from the viewpoint of geometric energy functional. The proposed geometric functional involves the Gaussian curvature, the mean curvature and the squared norms of their gradients. The geometric partial differential equations are given as the Euler-Lagrangian Equations of the geometric energy functionals by using the calculus of variation method. As a special example, we focus on Gaussian curvature related geometric energy functionals and the corresponding partial differential equations. We present three numerical methods to solve the resulting geometric partial differential equations: the direct discretization method, the finite element method and the level set method. We test these numerical schemes with a large class of geometric models. Potential applications of our proposed geometric partial differential equations include mesh optimization, surface smoothing, surface blending, surface restoration and physical simulation. Finally, we point out some possible directions of future work including singular analysis of the derived geometric partial differential equations and numerical error estimates of our numerical schemes. / Yan, Yinhui. / "September 2008." / Adviser: Kwong Chung Piney. / Source: Dissertation Abstracts International, Volume: 73-01, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 121-134). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web.

by Leung Kin Lap. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references (leaves 70-72). / ACKNOWLEDGEMENTS --- p.I / ABSTRACT --- p.II / TABLE OF CONTENTS --- p.III / TABLE OF FIGURES --- p.IV / Chapter Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Contributions of the thesis --- p.2 / Chapter 1.2 --- Organization of the thesis --- p.4 / Chapter Chapter 2 --- Previous Work --- p.5 / Chapter 2.1 --- An overview of 3-D interpretation --- p.5 / Chapter 2.1.1 --- Multiple-View Clues --- p.5 / Chapter 2.1.2 --- Single-View Clues --- p.6 / Chapter 2.2 --- Line Drawing Interpretation --- p.7 / Chapter 2.2.1 --- Qualitative Interpretation --- p.7 / Chapter 2.2.2 --- Quantitative Interpretation --- p.10 / Chapter 2.3 --- Previous Methods of Quantitative Interpretation by Optimization --- p.12 / Chapter 2.3.1 --- Extremum Principle for Shape from Contour --- p.12 / Chapter 2.3.2 --- MSDA Algorithm --- p.14 / Chapter 2.4 --- Comments on Previous Work on Line Drawing Interpretation --- p.17 / Chapter Chapter 3 --- An Iterative Clustering Procedure for Imperfect Line Drawings --- p.18 / Chapter 3.1 --- Shape Constraints --- p.19 / Chapter 3.2 --- Problem Formulation --- p.20 / Chapter 3.3 --- Solution Steps --- p.25 / Chapter 3.4 --- Nearest-Neighbor Clustering Algorithm --- p.37 / Chapter 3.5 --- Discussion --- p.38 / Chapter Chapter 4 --- Experimental Results --- p.40 / Chapter 4.1 --- Synthetic Line Drawings --- p.40 / Chapter 4.2 --- Real Line Drawing --- p.42 / Chapter 4.2.1 --- Recovery of real images --- p.42 / Chapter Chapter 5 --- Conclusion and Future Work --- p.65 / Appendix A --- p.67 / Chapter A. 1 --- Gradient Space Concept --- p.67 / Chapter A. 2 --- Shading of images --- p.69 / Appendix B --- p.70

Typescript, etc. / Digitized by Kansas Correctional Industries

Thesis. 1978. M.S.--Massachusetts Institute of Technology. Dept. of Architecture. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ROTCH. / Bibliography: leaves 56-57. / by Andrew Lippman. / M.S.

Bibliography: leaves 173-176.

Thesis (M.E.E.)--University of Delaware, 2006. / Principal faculty advisor: Kenneth E. Barner, Dept. of Electrical and Computer Engineering. Includes bibliographical references.

The virtual worlds of Computer Graphics are populated by geometric objects, called models. Researchers have addressed the problem of synthesizing models automatically. Traditional modeling approaches often require a user to guide the synthesis process and to look after the geometry being synthesized, but user attention is expensive, and reducing user interaction is therefore desirable. I present a scheme for the automatic creation of geometry by deforming surfaces. My scheme includes a novel surface representation; it is an explicit representation consisting of points and edges, but it is not a traditional polygonal mesh. The novel surface representation is paired with a resampling policy to control the surface density and its evolution during deformation. The surface deforms with velocities assigned to its points through a set of deformation operators. Deformation operators avoid the manual computation and assignment of velocities, the operators allow a user to interactively assign velocities with minimal effort. Additionally, Petri nets are used to automatically deform a surface by mimicking a user assigning deformation operators. Furthermore, I present an algorithm to translate from the novel surface representations to a polygonal mesh. I demonstrate the utility of my model generation scheme with a gallery of models created automatically. The scheme's surface representation and resampling policy enables a surface to deform without requiring a user to control the deformation; self-intersections and hole creation are automatically prevented. The generated models show that my scheme is well suited to create organic-like models, whose surfaces have smooth transitions between surface features, but can also produce other kinds of models. My scheme allows a user to automatically generate varied instances of richly detailed models with minimal user interaction.

The virtual worlds of Computer Graphics are populated by geometric objects, called models. Researchers have addressed the problem of synthesizing models automatically. Traditional modeling approaches often require a user to guide the synthesis process and to look after the geometry being synthesized, but user attention is expensive, and reducing user interaction is therefore desirable. I present a scheme for the automatic creation of geometry by deforming surfaces. My scheme includes a novel surface representation; it is an explicit representation consisting of points and edges, but it is not a traditional polygonal mesh. The novel surface representation is paired with a resampling policy to control the surface density and its evolution during deformation. The surface deforms with velocities assigned to its points through a set of deformation operators. Deformation operators avoid the manual computation and assignment of velocities, the operators allow a user to interactively assign velocities with minimal effort. Additionally, Petri nets are used to automatically deform a surface by mimicking a user assigning deformation operators. Furthermore, I present an algorithm to translate from the novel surface representations to a polygonal mesh. I demonstrate the utility of my model generation scheme with a gallery of models created automatically. The scheme's surface representation and resampling policy enables a surface to deform without requiring a user to control the deformation; self-intersections and hole creation are automatically prevented. The generated models show that my scheme is well suited to create organic-like models, whose surfaces have smooth transitions between surface features, but can also produce other kinds of models. My scheme allows a user to automatically generate varied instances of richly detailed models with minimal user interaction.

The implementation of autonomous, flocking crowds of background characters in the feature film “Robots” is discussed. The techniques for obstacle avoidance and goal seeking are described. An overview of the implementation of the system as part of the production pipeline for the film is also provided.

In this work we describe the design and implementation of a general framework for visualizing and editing motion planning environments, problem instances, and their solutions. The motion planning problem consists of finding a valid path between a start and a goal configuration for a movable object. The workspace is, in traditional robotics and animation applications, composed of one or more objects (called obstacles) that cannot overlap with the robot. As even the simplest motion planning problems have been shown to be in- tractable, most practical approaches to motion planning use randomization and/or compute approximate solutions. While the tool we present allows the manipulation and evaluation of planner solutions and the animation of any path found by any plan- ner, it is specialized for a class of randomized planners called probabilistic roadmap methods (PRMs). PRMs are roadmap-based methods that generate a graph or roadmap where the nodes represent collision-free configurations and the edges represent feasible paths between those configurations. PRMs typically consist of two phases: roadmap con- struction, where a roadmap is built, and query, where the start and goal configura- tions are connected to the roadmap and then a path is extracted using graph search techniques.