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Algebraic Representations in Computer-Aided Design for complEx Shapes

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Capturing the essence of 3D objects spurs innovative design and efficient manufacturing

While computer-aided design (CAD) has become a booming business, finding the right balance between speed and accuracy has been a challenge. A wealth of new algorithms incorporating the latest mathematical advances has bridged the gap for applications from freeform architecture to marine design.

Fundamental Research icon Fundamental Research

Computers have revolutionised our ability to solve complex problems. However, exploiting their full potential necessitates lean, yet sophisticated, algorithms to capture the minimally necessary information for high accuracy without slowing computation time. EU funding of the ARCADES project supported the creation of a Marie Skłodowska-Curie Innovative Training Network (ITN) that has accomplished this. Numerous advanced CAD algorithms and tools will enhance European competitiveness in critical applications. “In contrast to traditional doctoral programmes, the ITN exposes fellows to an international network of academic environments and industrial partners. This unique opportunity supported ARCADES’ development of novel methods for CAD software that integrate the latest mathematical breakthroughs,” explains ARCADES coordinator Ioannis Emiris of Athena – Research and Innovation Centre in Information, Communication and Knowledge Technologies and the National and Kapodistrian University of Athens.

Curved surfaces and complex mobility on land and sea

In hydrodynamics and marine design, young researchers developed new isogeometric modellers and solvers that seamlessly and directly couple CAD models with computational mechanics and finite element analysis. A novel T-splines-based parametric modeller (TshipPM for complex ship forms) integrates over 20 design parameters, and efficiently and robustly generates a comprehensive set of design alternatives of high-quality ship hulls. TshipPM is now ready for commercialisation. In addition, during a fellow’s secondment to ARCADES’ industrial partner ITI, decisive steps were taken to exploit the representation in ITI's principal software product, CADfix. Emiris adds: “The work of two fellows on CAD in maritime industries was put on the map, so to speak, by the EU Innovation Radar.” ARCADES’ fellows also developed intuitive interactive CAD tools to support architects and engineers in the design and manufacturing of curved facades and freeform architectural surfaces of materials including glass. Work undertaken in conjunction with ARCADES member Evolute has already been implemented and adapted by several industry leaders. Emiris continues: “Our digital design framework that combines geometric modelling and optimisation, physical simulation and deep learning, surpassed our original goals. In addition to supporting design, it provides feedback relative to production costs.” Exploring the potential of modern machine learning techniques for 3D-shape learning has earned a starring role in the new ITN GRAPES. Yet another key area of significant advances is the study of rigid objects with prescribed degrees of freedom for the design of robots, machine tools and even molecular kinematics. During a fellow’s secondment at industrial partner TopSolid (formerly Missler Software), some of the methods were integrated in the flagship commercial software family ‘TopSolid’. Further, prototype software including modelling algorithms for controlling machining tools is currently being evaluated by ARCADES associated partner RISC Software.

Spreading the news – and the bright minds behind it

ARCADES’ outcomes have been communicated via over 250 activities including scientific presentations and publications, public lectures and science fairs. “Our fellows have become a very tight community of exceptional young scientists. Many are moving into research positions in other European countries. This international mindset will further the fellows’ careers, the CAD field and the industries it supports,” Emiris concludes. The global CAD market is expected to generate revenue of nearly USD 19 billion by 2030. ARCADES’ best and brightest will be key players.


ARCADES, CAD, TopSolid, robots, TshipPM, geometric modelling, ship hulls, freeform architecture, computational mechanics, CADfix

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