A Dynamic Framework For Subdivision Surfaces

Abstract: Subdivision surfaces are extensively used to model smooth shapes of arbitrary topology. Recursive subdivision on a user-defined initial control mesh generates a visually pleasing smooth surface in the limit. However, users have to carefully select the intiail mesh and.or manipulate the control vertex positions at different levels of subdivision hierarchy to satisfy the functional and aesthetic requirements in the smooth limit surface. This modeling drawback results fromt eh lack of direct manipulation tools for the limit surface. In this dissertation, techniques from physics-based modeling are integrated with geometric subdivision methodology, and a dynamic framework is presented for direct manipulation of the smooth limit surface generated by the subdivision schemes using physics based "force" tools. In a typical subdivision scheme, the user starts with an initial control mesh which is refined recursively using a fixed set of subdivision rules, and a smooth surface is produced in the limit. Most often this limit surface does not have an analytic expression, and hence poses challenging problems in incorporating mass and damping distribution functions, internal deformation energy, forces, and other physical quantities required to develop a physics-based subdivision surface model. In this dissertation, local parameterization techniques suitable for embedding the geometric subdivision surface model in a physics-based modeling framework have been developed. Specific local parameterization techniques have been fully developed for the Catmull-Clark, modified butterfly and the Loop subdivision schemes. Techniques for assigning material properties to geometric subdivision surfaces are derived, and a motion equation for the dynamic model has been formulated using Lagrangian dynamics. Furthermore, advantages of the physics-based deformable models are incorporated into the conventional subdivision schemes, and a dynamic hierarchical control of this model is introduced. Finally, a multiresolution representation of the control mesh is developed and a unified approach for deriving subdivision surface-based finite elements is presented. The proposed dynamic framework enhances the applicability of the subdivision surfaces in modeling applications. It is also useful for hierarchical shape recovery from large range and volume data sets, as well as for non-rigid motion tracking from a temporal sequence of data sets. Multiresolution representation of the initial mesh controlling the smooth limit surface enables global and local editing of the shape as desired by the modeler. This dynamic framework has also been used for synthesizing natural terrain models from sparse elevation data. Dissertation Discovery Company and University of Florida are dedicated to making scholarly works more discoverable and accessible throughout the world. This dissertation, "A Dynamic Framework for Subdivision Surfaces" by Chhandomay Mandal, was obtained from University of Florida and is being sold with permission from the author. A digital copy of this work may also be found in the university's institutional repository, IR@UF. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation.

Since their first appearance in 1974, subdivision algorithms for generating surfaces of arbitrary topology have gained widespread popularity in computer graphics and are being evaluated in engineering applications. This development was complemented by ongoing efforts to develop appropriate mathematical tools for a thorough analysis, and today, many of the fascinating properties of subdivision are well understood. This book summarizes the current knowledge on the subject. It contains both meanwhile classical results as well as brand-new, unpublished material, such as a new framework for constructing C^2-algorithms. The focus of the book is on the development of a comprehensive mathematical theory, and less on algorithmic aspects. It is intended to serve researchers and engineers - both new to the beauty of the subject - as well as experts, academic teachers and graduate students or, in short, anybody who is interested in the foundations of this flourishing branch of applied geometry.

This book constitutes the refereed proceedings of the Second International Workshop on Articulated Motion and Deformable Objects, AMDO 2002, held in Palma de Mallorca, Spain in November 2002.The 21 revised full papers presented were carefully reviewed and selected for inclusion in the book. Among the topics addressed are geometric and physical deformable objects, motion analysis, articulated models and animation, visualization of deformable models, 3D recovery from motion, single or multiple human motion analysis and synthesis, applications of deformable models and motion analysis, face tracking, recovery and recognition models.

This book offers a comprehensive introduction to Subdivision Surface Modeling Technology focusing not only on fundamental theories but also on practical applications. It furthers readers’ understanding of the contacts between spline surfaces and subdivision surfaces, enabling them to master the Subdivision Surface Modeling Technology for analyzing subdivision surfaces. Subdivision surface modeling is a popular technology in the field of computer aided design (CAD) and computer graphics (CG) thanks to its ability to model meshes of any topology. The book also discusses some typical Subdivision Surface Modeling Technologies, such as interpolation, fitting, fairing, intersection, as well as trimming and interactive editing. It is a valuable tool, enabling readers to grasp the main technologies of subdivision surface modeling and use them in software development, which in turn leads to a better understanding of CAD/CG software operations.

This book contains the proceedings of the International Workshop on Volume Graphics 200 1 (VG'O I) which took place on June 21 and June 22 at Stony Brook, New York. This year's event was the second in the series, following a successful premiere in Swansea, Wales, in March 1999, and was co-sponsored by the IEEE Technical Committee on Visualization and Graphics (TC-VG) as well as EUROGRAPHICS. The Volume Graphics Workshop is held bi-annually and has been created to pro vide a forum for the exploration and advancement of volume-based techniques, beyond the scope of just volume visualization. It brings together researchers and practitioners both from academia and industry, from many parts of the world. Volume graphics is in the process of evolving into a general graphics technology, and the papers included in these proceedings are testimonial to the wide spectrum of unique applications and solu tions that volumetric representations are able to offer.

"This book provides research related to the concept of virtual reality and developing business models using this concept"--Provided by publisher.

3D Imaging, Analysis and Applications brings together core topics, both in terms of well-established fundamental techniques and the most promising recent techniques in the exciting field of 3D imaging and analysis. Many similar techniques are being used in a variety of subject areas and applications and the authors attempt to unify a range of related ideas. With contributions from high profile researchers and practitioners, the material presented is informative and authoritative and represents mainstream work and opinions within the community. Composed of three sections, the first examines 3D imaging and shape representation, the second, 3D shape analysis and processing, and the last section covers 3D imaging applications. Although 3D Imaging, Analysis and Applications is primarily a graduate text, aimed at masters-level and doctoral-level research students, much material is accessible to final-year undergraduate students. It will also serve as a reference text for professional academics, people working in commercial research and development labs and industrial practitioners.

With an A–Z format, this encyclopedia provides easy access to relevant information on all aspects of biometrics. It features approximately 250 overview entries and 800 definitional entries. Each entry includes a definition, key words, list of synonyms, list of related entries, illustration(s), applications, and a bibliography. Most entries include useful literature references providing the reader with a portal to more detailed information.