Abstract geometry for design in an empirical modelling context

We review research from an agenda set out in a previous paper, which investigated the application of definitive programming principles to the implementation of CAD systems. This has led us to the development of a new Empirical Modelling paradigm. We outline the principles of Empirical Modelling, and explain and illustrate the significance and potential role of definitive notations for shape such as CADNO, Eden CAD and HyperJazz in this context. We also describe the motivation for Empirical Modelling as a modelling method for open development that can assist the integration of geometric modelling, non-geometric modelling, and meta-modelling aspects of concurrent engineering

Geometric continuous patch complexes

A theory of geometric continuity of arbitrary order is presented. Conditions of geometric continuity at a vertex where a number of patches meet are investigated. Geometric continuous patch complexes are introduced as the appropriate setting for the representation of surfaces in CAGD. The theory is applied to the modelling of closed surfaces and the fitting of triangular patches into a geometric continuous patch complex

Hypergraph Modelling for Geometric Model Fitting

In this paper, we propose a novel hypergraph based method (called HF) to fit and segment multi-structural data. The proposed HF formulates the geometric model fitting problem as a hypergraph partition problem based on a novel hypergraph model. In the hypergraph model, vertices represent data points and hyperedges denote model hypotheses. The hypergraph, with large and "data-determined" degrees of hyperedges, can express the complex relationships between model hypotheses and data points. In addition, we develop a robust hypergraph partition algorithm to detect sub-hypergraphs for model fitting. HF can effectively and efficiently estimate the number of, and the parameters of, model instances in multi-structural data heavily corrupted with outliers simultaneously. Experimental results show the advantages of the proposed method over previous methods on both synthetic data and real images.Comment: Pattern Recognition, 201

Development of a novel 3D simulation modelling system for distributed manufacturing

This paper describes a novel 3D simulation modelling system for supporting our distributed machine design and control paradigm with respect to simulating and emulating machine behaviour on the Internet. The system has been designed and implemented using Java2D and Java3D. An easy assembly concept of drag-and-drop assembly has been realised and implemented by the introduction of new connection features (unified interface assembly features) between two assembly components (modules). The system comprises a hierarchical geometric modeller, a behavioural editor, and two assemblers. During modelling, designers can combine basic modelling primitives with general extrusions and integrate CAD geometric models into simulation models. Each simulation component (module) model can be visualised and animated in VRML browsers. It is reusable. This makes machine design re-configurable and flexible. A case study example is given to support our conclusions

A geometric framework for modelling similarity search

The aim of this paper is to propose a geometric framework for modelling similarity search in large and multidimensional data spaces of general nature, which seems to be flexible enough to address such issues as analysis of complexity, indexability, and the `curse of dimensionality.' Such a framework is provided by the concept of the so-called similarity workload, which is a probability metric space $\Omega$ (query domain) with a distinguished finite subspace $X$ (dataset), together with an assembly of concepts, techniques, and results from metric geometry. They include such notions as metric transform, \e-entropy, and the phenomenon of concentration of measure on high-dimensional structures. In particular, we discuss the relevance of the latter to understanding the curse of dimensionality. As some of those concepts and techniques are being currently reinvented by the database community, it seems desirable to try and bridge the gap between database research and the relevant work already done in geometry and analysis.Comment: 11 pages, LaTeX 2.

A survey of partial differential equations in geometric design

YesComputer aided geometric design is an area where the improvement of surface generation techniques is an everlasting demand since faster and more accurate geometric models are required. Traditional methods for generating surfaces were initially mainly based upon interpolation algorithms. Recently, partial differential equations (PDE) were introduced as a valuable tool for geometric modelling since they offer a number of features from which these areas can benefit. This work summarises the uses given to PDE surfaces as a surface generation technique togethe

As-Built 3D Heritage City Modelling to Support Numerical Structural Analysis: Application to the Assessment of an Archaeological Remain

Terrestrial laser scanning is a widely used technology to digitise archaeological, architectural and cultural heritage. This allows for modelling the assets’ real condition in comparison with traditional data acquisition methods. This paper, based on the case study of the basilica in the Baelo Claudia archaeological ensemble (Tarifa, Spain), justifies the need of accurate heritage modelling against excessively simplified approaches in order to support structural safety analysis. To do this, after validating the 3Dmeshing process frompoint cloud data, the semi-automatic digital reconstitution of the basilica columns is performed. Next, a geometric analysis is conducted to calculate the structural alterations of the columns. In order to determine the structural performance, focusing both on the accuracy and suitability of the geometric models, static and modal analyses are carried out by means of the finite element method (FEM) on three different models for the most unfavourable column in terms of structural damage: (1) as-built (2) simplified and (3) ideal model without deformations. Finally, the outcomes show that the as-built modelling enhances the conservation status analysis of the 3D heritage city (in terms of realistic compliance factor values), although further automation still needs to be implemented in the modelling process

Including widespread geometry formats in semantic graphs using RDF literals

The exchange of building data involves both geometric and non-geometric data. A promising Linked Data approach is to embed data from existing geometry formats inside Resource Description Framework (RDF) literals. Based on a study of relevant specifications and related work, this toolset-independent approach was found suitable for the exchange of geometric construction data. To implement the approach in practice, the File Ontology for Geometry formats (FOG) and accompanying modelling method is developed. In a proof-of-concept web application that uses FOG, is demonstrated how geometry descriptions of different existing formats are automatically recognised and parsed

Additive versus multiplicative parameters - applications in economics and finance

In this paper, we pay our attention to geometric parameters and their applications in economics and finance. We discuss the multiplicative models in which a geometric mean and a geometric standard deviation are more natural than arithmetic ones. We give two examples from Warsaw Stock Exchange in 1995--2009 and from a bid of 52-week treasury bills in 1992--2009 in Poland as an illustrative example. For distributions having applications in finance and insurance we give their multiplicative parameters as well as their estimations. We consider, among others, heavy-tailed distributions such as lognormal and Pareto distribution, applied to modelling of large losses