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

Chain-Based Representations for Solid and Physical Modeling

In this paper we show that the (co)chain complex associated with a decomposition of the computational domain, commonly called a mesh in computational science and engineering, can be represented by a block-bidiagonal matrix that we call the Hasse matrix. Moreover, we show that topology-preserving mesh refinements, produced by the action of (the simplest) Euler operators, can be reduced to multilinear transformations of the Hasse matrix representing the complex. Our main result is a new representation of the (co)chain complex underlying field computations, a representation that provides new insights into the transformations induced by local mesh refinements. Our approach is based on first principles and is general in that it applies to most representational domains that can be characterized as cell complexes, without any restrictions on their type, dimension, codimension, orientability, manifoldness, connectedness

Geometric Modeling of Cellular Materials for Additive Manufacturing in Biomedical Field: A Review

Advances in additive manufacturing technologies facilitate the fabrication of cellular materials that have tailored functional characteristics. The application of solid freeform fabrication techniques is especially exploited in designing scaffolds for tissue engineering. In this review, firstly, a classification of cellular materials from a geometric point of view is proposed; then, the main approaches on geometric modeling of cellular materials are discussed. Finally, an investigation on porous scaffolds fabricated by additive manufacturing technologies is pointed out. Perspectives in geometric modeling of scaffolds for tissue engineering are also proposed

Buildings and terrain unified – multidimensional dual data structure for GIS

© 2016 Wuhan University. 3D city models are widely used in many disciplines and applications, such as urban planning, disaster management, and environmental simulation. Usually, the terrain and embedded objects like buildings are taken into consideration. A consistent model integrating these elements is vital for GIS analysis, especially if the geometry is accompanied by the topological relations between neighboring objects. Such a model allows for more efficient and errorless analysis. The memory consumption is another crucial aspect when the wide area of a city is considered – light models are highly desirable. Three methods of the terrain representation using the geometrical–topological data structure – the dual half-edge – are proposed in this article. The integration of buildings and other structures like bridges with the terrain is also presented

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

What's the Situation with Intelligent Mesh Generation: A Survey and Perspectives

Intelligent Mesh Generation (IMG) represents a novel and promising field of research, utilizing machine learning techniques to generate meshes. Despite its relative infancy, IMG has significantly broadened the adaptability and practicality of mesh generation techniques, delivering numerous breakthroughs and unveiling potential future pathways. However, a noticeable void exists in the contemporary literature concerning comprehensive surveys of IMG methods. This paper endeavors to fill this gap by providing a systematic and thorough survey of the current IMG landscape. With a focus on 113 preliminary IMG methods, we undertake a meticulous analysis from various angles, encompassing core algorithm techniques and their application scope, agent learning objectives, data types, targeted challenges, as well as advantages and limitations. We have curated and categorized the literature, proposing three unique taxonomies based on key techniques, output mesh unit elements, and relevant input data types. This paper also underscores several promising future research directions and challenges in IMG. To augment reader accessibility, a dedicated IMG project page is available at \url{https://github.com/xzb030/IMG_Survey}

The dual half-edge-a topological primal/dual data structure and construction operators for modelling and manipulating cell complexes

© 2016 by the authors. There is an increasing need for building models that permit interior navigation, e.g., for escape route analysis. This paper presents a non-manifold Computer-Aided Design (CAD) data structure, the dual half-edge based on the Poincaré duality that expresses both the geometric representations of individual rooms and their topological relationships. Volumes and faces are expressed as vertices and edges respectively in the dual space, permitting a model just based on the storage of primal and dual vertices and edges. Attributes may be attached to all of these entities permitting, for example, shortest path queries between specified rooms, or to the exterior. Storage costs are shown to be comparable to other non-manifold models, and construction with local Euler-type operators is demonstrated with two large university buildings. This is intended to enhance current developments in 3D Geographic Information Systems for interior and exterior city modelling