De la Geometría Descriptiva a la Geometría Arquitectónica: aportaciones de autores clásicos al nuevo paradigma

The use of computation for architectural design, together with the application of digital fabrication techniques for materialisation, has brought a new paradigm where contributions by classic authors linked to Descriptive Geometry might seem inappropriate. This paper shows a case study of a full-scale prototype which proves how some of the classic geometric theorems and procedures can still play a role in the design computation era. Objectives: identify and analyse the usefulness of classic Descriptive Geometry contents within the computational design paradigm through the case study of a particular project. Methodology: Analysis of the conception, development and materialization processes, to identify the application and potential benefits of classic geometric contents. Results: at the different stages analysed, some classic geometric theorems and procedures were found to be useful and efficient. Practical implications: The implications of these findings involve both architectural practice and the academic sphere. Originality / value: Although initially bound to this case study, the methodology could be extrapolated to more complex projects to obtain more simple and efficient design algorithms.El uso de la computación en el diseño arquitectónico, junto con la aplicación de técnicas de fabricación digital para la materialización, ha traído un nuevo paradigma donde las aportaciones de los autores clásicos vinculados a la Geometría Descriptiva podrían parecer inadecuadas. Esta comunicación muestra un estudio de caso sobre un prototipo a escala natural que demuestra cómo algunos de los teoremas y trazados clásicos aún pueden tener un papel en la era de la computación. Objetivos: analizar la utilidad de contenidos de la Geometría Descriptiva clásica dentro del paradigma del diseño computacional a través del estudio de caso de un proyecto concreto. Metodología: Análisis de los procesos de concepción, desarrollo y materialización, para identificar la aplicación y beneficios potenciales de contenidos geométricos clásicos. Resultados: en las diferentes etapas analizadas, algunos procedimientos y teoremas geométricos clásicos resultaron ser útiles y eficientes. Repercusiones prácticas: Las repercusiones de los resultados obtenidos atañen tanto a la profesión arquitectónica como al ámbito académico. Originalidad / Valor: La metodología usada en este estudio de caso, podría extrapolarse a proyectos más complejos para obtener algoritmos de diseño más simples y eficiente

Volumetric Untrimming: Precise decomposition of trimmed trivariates into tensor products

3D objects, modeled using Computer Aided Geometric Design tools, are traditionally represented using a boundary representation (B-rep), and typically use spline functions to parameterize these boundary surfaces. However, recent development in physical analysis, in isogeometric analysis (IGA) in specific, necessitates a volumetric parametrization of the interior of the object. IGA is performed directly by integrating over the spline spaces of the volumetric spline representation of the object. Typically, tensor-product B-spline trivariates are used to parameterize the volumetric domain. A general 3D object, that can be modeled in contemporary B-rep CAD tools, is typically represented using trimmed B-spline surfaces. In order to capture the generality of the contemporary B-rep modeling space, while supporting IGA needs, Massarwi and Elber (2016) proposed the use of trimmed trivariates volumetric elements. However, the use of trimmed geometry makes the integration process more difficult since integration over trimmed B-spline basis functions is a highly challenging task. In this work, we propose an algorithm that precisely decomposes a trimmed B-spline trivariate into a set of (singular only on the boundary) tensor-product B-spline trivariates, that can be utilized to simplify the integration process in IGA. The trimmed B-spline trivariate is first subdivided into a set of trimmed B\'ezier trivariates, at all its internal knots. Then, each trimmed B\'ezier trivariate, is decomposed into a set of mutually exclusive tensor-product B-spline trivariates, that precisely cover the entire trimmed domain. This process, denoted untrimming, can be performed in either the Euclidean space or the parametric space of the trivariate. We present examples on complex trimmed trivariates' based geometry, and we demonstrate the effectiveness of the method by applying IGA over the (untrimmed) results.Comment: 18 pages, 32 figures. Contribution accepted in International Conference on Geometric Modeling and Processing (GMP 2019

Computer-Aided Geometry Modeling

Techniques in computer-aided geometry modeling and their application are addressed. Mathematical modeling, solid geometry models, management of geometric data, development of geometry standards, and interactive and graphic procedures are discussed. The applications include aeronautical and aerospace structures design, fluid flow modeling, and gas turbine design

State-of-the-art in aerodynamic shape optimisation methods

Aerodynamic optimisation has become an indispensable component for any aerodynamic design over the past 60 years, with applications to aircraft, cars, trains, bridges, wind turbines, internal pipe flows, and cavities, among others, and is thus relevant in many facets of technology. With advancements in computational power, automated design optimisation procedures have become more competent, however, there is an ambiguity and bias throughout the literature with regards to relative performance of optimisation architectures and employed algorithms. This paper provides a well-balanced critical review of the dominant optimisation approaches that have been integrated with aerodynamic theory for the purpose of shape optimisation. A total of 229 papers, published in more than 120 journals and conference proceedings, have been classified into 6 different optimisation algorithm approaches. The material cited includes some of the most well-established authors and publications in the field of aerodynamic optimisation. This paper aims to eliminate bias toward certain algorithms by analysing the limitations, drawbacks, and the benefits of the most utilised optimisation approaches. This review provides comprehensive but straightforward insight for non-specialists and reference detailing the current state for specialist practitioners

Point-based mathematics for computer-aided manufacture

This thesis demonstrates the feasibility of machining high quality sculptured surfaces directly from a point-based definition. The work is founded on the strategy of using a sparse set of points to characterise shape although it is assumed that an appropriately dense definition can be generated by the use of some unspecified high quality interpolation algorithm. This is in contrast to the conventional CAD/CAM approach where explicit parametric expressions are used to describe the part. The research is founded on the Inverse Offset Method (IOM) proposed by Kishinami; the algorithm is chosen because it possesses a number of desirable properties, most notably its versatility and robustness. The first fundamental contribution is an error analysis of the IOM that has not been published before, the analysis is dependent on the surface and cutter path point spacing, the tool radius and the local surface curvature. The accuracy of the error analysis is corroborated by the machining and measuring of a physical part. Furthermore it is established that the quality of the finished part produced by the IOM compares favourably with that produced by a commercial package for similar tolerances. The principal research achievement is the optimisation of the IOM to exploit the coherence of data ordered into sections. This results in the IOM generating cutter paths in a time period comparable to that of the commercial package without a reduction in the quality of the finished part. The last contribution made in this thesis is a report on the issues concerning the machining of point definitions derived from multi-surfaces. The work presented in this thesis offers an alternative strategy to the design and manufacture of free-form surfaces. The main benefits of adopting this strategy are gained because it removes the need to generate a parametric surface definition