Propriétés topologiques pour la modélisation géométrique de domaines d'études comportant des singularités non-variétés

L’étude de comportement mécanique de structures et/ou d’écoulements s’appuie fréquemment sur des modèles géométriques perçus comme des assemblages de volumes, surfaces, lignes, connectés entre eux et comportant des singularités non-variétés. Une classification d’objets comportant des singularités non-variétés et des propriétés topologiques globales sont présentées pour accroître l’efficacité des modeleurs et la génération des contraintes de maillages

Topologic: tools to explore architectural topology

Buildings enclose and partition space and are built from assemblies of connected components. The many different forms of spatial and material partitioning and connectedness found within buildings can be represented by topology. This paper introduces the ‘Topologic’ software library which integrates a number of architecturally relevant topological concepts into a unified application toolkit. The goal of the Topologic toolkit is to support the creation of the lightest, most understandable conceptual models of architectural topology. The formal language of topology is well-matched to the data input requirements for applications such as energy simulation and structural analysis. In addition, the ease with which these lightweight topological models can be modified encourages design exploration and performance simulation at the conceptual design phase. A challenging and equally interesting question is how can the formal language of topology be used to represent architectural concepts of space which have previously been described in rather speculative and subjective terms

Characteristics of 3D solid modeling software libraries for non-manifold modeling

The aim of this paper is to provide a review of the characteristics of 3D solid modeling software libraries – otherwise known as ’geometric modeling kernels’ in non-manifold applications. ’Non-manifold’ is a geometric topology term that means ’to allow any combination of vertices, edges, surfaces and volumes to exist in a single logical body’. In computational architectural design, the use of non-manifold topology can enhance the representation of space as it provides topological clarity, allowing architects to better design, analyze and reason about buildings. The review is performed in two parts. The review is performed in two parts. The first part includes a comparison of the topological entities’ terminology and hierarchy as used within commercial applications, kernels, and within published academic research. The second part proposes an evaluation framework to explore the kernels’ support for non-manifold topology, including their capability to represent a non-manifold structure, and in performing non-regular Boolean operations, which are suitable for non-manifold modeling

Representing and Understanding Non-Manifold Objects

Solid Modeling is a well-established field. The significance of the contributions of this field is visible in the availability of abundant commercial and free modeling tools for the applications of CAD, animation, visualization etc. There are various approaches to modeling shapes. A common problem to all of them however, is the handling of non-manifold shapes. Manifold shapes are shapes with the property of topological ``smoothness'' at the local neighbourhood of every point. Objects that contain one or more points that lack this smoothness are all considered non-manifold. Non-manifold objects form a huge catagory of shapes. In the field of solid modeling, solutions typically limit the application domain to manifold shapes. Where the occurrence of non-manifold shapes is inevitable, they are often processed at a high cost. The lack of understanding on the nature of non-manifold shapes is the main cause of it. There is a tremendous gap between the well-established mathematical theories in topology and the materialization of such knowledge in the discrete combinatorial domain of computer science and engineering. The motivation of this research is to bridge this gap between the two. We present a characterization of non-manifoldness in 3D simplicial shapes. Based on this characterization, we propose data structures to address the applicational needs for the representation of 3D simplicial complexes with mixed dimensions and non-manifold connectivities, which is an area that is greatly lacking in the literature. The availability of a suitable data structure makes the structural analysis of non-manifold shapes feasible. We address the problem of non-manifold shape understanding through a structural analysis that is based on decomposition