Computing Canonical Polygonal Schemata with Generalized Maps

International audienceThis paper shows that a well-known algorithm proposed to compute the canonical polygonal schema of a surface can be transferred onto a 2-dimensional generalized map. We show that transformation rules on polygonal schemata can be achieved in O(1) with generalized maps, which can help optimizing existing algorithms

TREE-D-SEEK: A Framework for Retrieving Three-Dimensional Scenes

In this dissertation, a strategy and framework for retrieving 3D scenes is proposed. The strategy is to retrieve 3D scenes based on a unified approach for indexing content from disparate information sources and information levels. The TREE-D-SEEK framework implements the proposed strategy for retrieving 3D scenes and is capable of indexing content from a variety of corpora at distinct information levels. A semantic annotation model for indexing 3D scenes in the TREE-D-SEEK framework is also proposed. The semantic annotation model is based on an ontology for rapid prototyping of 3D virtual worlds. With ongoing improvements in computer hardware and 3D technology, the cost associated with the acquisition, production and deployment of 3D scenes is decreasing. As a consequence, there is a need for efficient 3D retrieval systems for the increasing number of 3D scenes in corpora. An efficient 3D retrieval system provides several benefits such as enhanced sharing and reuse of 3D scenes and 3D content. Existing 3D retrieval systems are closed systems and provide search solutions based on a predefined set of indexing and matching algorithms Existing 3D search systems and search solutions cannot be customized for specific requirements, type of information source and information level. In this research, TREE-D-SEEK—an open, extensible framework for retrieving 3D scenes—is proposed. The TREE-D-SEEK framework is capable of retrieving 3D scenes based on indexing low level content to high-level semantic metadata. The TREE-D-SEEK framework is discussed from a software architecture perspective. The architecture is based on a common process flow derived from indexing disparate information sources. Several indexing and matching algorithms are implemented. Experiments are conducted to evaluate the usability and performance of the framework. Retrieval performance of the framework is evaluated using benchmarks and manually collected corpora. A generic, semantic annotation model is proposed for indexing a 3D scene. The primary objective of using the semantic annotation model in the TREE-D-SEEK framework is to improve retrieval relevance and to support richer queries within a 3D scene. The semantic annotation model is driven by an ontology. The ontology is derived from a 3D rapid prototyping framework. The TREE-D-SEEK framework supports querying by example, keyword based and semantic annotation based query types for retrieving 3D scenes

Mathematical techniques for shape modelling in computer graphics: A distance-based approach.

This research is concerned with shape modelling in computer graphics. The dissertation provides a review of the main research topics and developments in shape modelling and discusses current visualisation techniques required for the display of the models produced. In computer graphics surfaces are normally defined using analytic functions. Geometry however, supplies many shapes without providing their analytic descriptions. These are defined implicitly through fundamental relationships between primitive geometrical objects. Transferring this approach in computer graphics, opens new directions in shape modelling by enabling the definition of new objects or supplying a rigorous alternative to analytical definitions of objects with complex analytical descriptions. We review, in this dissertation, relevant works in the area of implicit modelling. Based on our observations on the shortcomings of these works, we develop an implicit modelling approach which draws on a seminal technique in this area: the distance based object definition. We investigate the principles, potential and applications of this technique both in conceptual terms (modelling aspects) and on technical merit (visualisation issues). This is the context of this PhD research. The conceptual and technological frameworks developed are presented in terms of a comprehensive investigation of an object's constituent primitives and modelling constraints on the one hand, and software visualisation platforms on the other. Finally, we adopt a critical perspective of our work to discuss possible directions for further improvements and exploitation for the modelling approach we have developed

Formalizing graphical notations

The thesis describes research into graphical notations for software engineering, with a principal interest in ways of formalizing them. The research seeks to provide a theoretical basis that will help in designing both notations and the software tools that process them. The work starts from a survey of literature on notation, followed by a review of techniques for formal description and for computational handling of notations. The survey concentrates on collecting views of the benefits and the problems attending notation use in software development; the review covers picture description languages, grammars and tools such as generic editors and visual programming environments. The main problem of notation is found to be a lack of any coherent, rigorous description methods. The current approaches to this problem are analysed as lacking in consensus on syntax specification and also lacking a clear focus on a defined concept of notated expression. To address these deficiencies, the thesis embarks upon an exploration of serniotic, linguistic and logical theory; this culminates in a proposed formalization of serniosis in notations, using categorial model theory as a mathematical foundation. An argument about the structure of sign systems leads to an analysis of notation into a layered system of tractable theories, spanning the gap between expressive pictorial medium and subject domain. This notion of 'tectonic' theory aims to treat both diagrams and formulae together. The research gives details of how syntactic structure can be sketched in a mathematical sense, with examples applying to software development diagrams, offering a new solution to the problem of notation specification. Based on these methods, the thesis discusses directions for resolving the harder problems of supporting notation design, processing and computer-aided generic editing. A number of future research areas are thereby opened up. For practical trial of the ideas, the work proceeds to the development and partial implementation of a system to aid the design of notations and editors. Finally the thesis is evaluated as a contribution to theory in an area which has not attracted a standard approach

The design and analysis of boundary data structures

The thesis is concerned with the efficient interrogation of CAD data. CAD data finds use in diverse range of applications which necessitates extension and integration of the CAD data base. By an exhaustive categorization of such application requirements and analysis of various CAD techniques, it is shown that boundary data structures are the most suitable in CAD, CAM and advanced robotic applications. Several boundary data structures have been proposed since the classic Winged edge data structure, these aimed at reducing the storage requirement and increasing information retrieval speeds. In this thesis methodologies are developed which enable us to discover compact and fast access time schemes and analyze and fine tune for individual applications. We demonstrate how the application of the optimality concepts can lead us to the discovery of more efficient data structures than popular data structures. All the boundary data structures proposed to date have been based on the underlying assumption that all the data resides in main memory. We show that in an integrated CAD environment (characterized by virtual a memory environment or a data base environment), these data structures are inefficient in both storage and time. We propose a new data structure shaped like A which is the most compact as well as more efficient in access time, under certain conditions of real memory and virtual memory. Experiments reveal a paradoxical phenomenon: access time increases with storage, violating the classic law of storage vs. time. Recently non-manifold boundary geometric modeling has become popular to meet the growing needs such as uniform treatment of wire frame, surface and solid modeling and design by features. We introduce a uniform terminology and notation to distinguish and critically analyze several non-manifold boundary data structures. It is hoped to fulfill the need for a ready reference for the design of efficient boundary data structures. The other aspects dealt with are the validity and conversion of Boundary data structures. To verify the concepts developed, in practice, a whole suite of fast algorithms have been implemented for model manipulation, visualization and data conversion

History of Mathematics: Models and Visualization in the Mathematical and Physical Sciences

This workshop brought together historians of mathematics and science as well as mathematicians to explore important historical developments connected with models and visual elements in the mathematical and physical sciences. It addressed the larger question of what has been meant by a model, a notion that has seldom been subjected to careful historical study. Most of the talks dealt with case studies from the period 1800 to 1950 that covered a number of analytical, geometrical, mechanical, astronomical, and physical phenomena. The workshop also considered the role of visual thinking as a component of mathematical creativity and understanding