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Algebraic Representations in Computer-Aided Design for complEx Shapes

Periodic Reporting for period 2 - ARCADES (Algebraic Representations in Computer-Aided Design for complEx Shapes)

Reporting period: 2018-01-01 to 2019-12-31

ARCADES supported Computer-Aided Design (CAD) industry by exploiting cutting-edge research in mathematics and algorithm design. Geometry is now a critical tool in a large number of key applications in which CAD strives to address crucial societal and market needs. The challenge taken up by ARCADES was to supply the CAD industry with recent mathematical breakthroughs so as to contribute to building the next generation of CAD software.

ARCADES put an emphasis in training the next generation of applied mathematicians, computer scientists and engineers, who became equipped with a double career advantage: excellent research training, and exposure to industrial research environments through a nexus of secondments among Universities, Research & Innovation Centers, and industrial teams. Our fellows have been endowed with an international culture and developed a strong network among themselves and with the other stakeholders of the project, thanks to the regular Network events.

The scientific results obtained by the ESRs of the Network are very promising. The CAD representation of complex shapes is expected to evolve considerably in the future as additive manufacturing supplants traditional (subtractive) manufacturing for many applications. This will also be driven by the trend towards increasingly integrated design as one sees in many applications (e.g. single surface ship hulls instead of a confederation of separate surfaces). This leads in turn to increased demand for high quality software to handle the additional complexity of the complex geometries. The technology developed in ARCADES may well prove to be disruptive to the entire CAD industry because of the advances being made in mathematical modelling and algorithm design. The innovations offered promise to be valuable to industry.
We strove to organise the managerial structure and the details of the implementation of our work plan. We have set up a mechanism that efficiently designed, implemented and monitored all activities within the project aiming at providing the best possible training to our fellows. This was complemented by a strong network, including industrial stakeholders as well, and an external Advisory Committee comprised of international academic and industrial leaders in the field who are external to ARCADES.

The recruitment procedure during the first year of the Project was very successful: all positions have been filled in with high quality candidates by Fall 2016. The fellows familiarised themselves to the new living and working environment, to the general scientific framework of their projects, and started producing research results. Most students have attended courses and seminars in their host institutions or in local universities. They participated at all 7 Network scientific training events where they also presented their research plan, research progress and results, in posters or by giving presentations. They all participated at the 3 Learning Weeks which focused on complementary training and have also completed at least two secondments each, typically one at an academic and one at an industrial member. Many students have organised short visits to research teams inside and outside the Network. The Project’s results have been communicated in over 250 dissemination activities such as conference/workshop presentations, publications in scientific journals, public lectures etc. These results include:
- Robust representations, and prototype implementations, relying on computer algebra tools for curved objects of low dimension in any ambient space.
- New tight bounds on the number of Euclidean embeddings of rigid objects in several unknown cases, and improved existing asymptotic bounds.
- Explored geometric aspects of parametrisations that led to new and faster algorithms; prototype implementations.
- A new approach to compute efficiently and robustly the distance between a point and a curve or surface, particularly well adapted for intensive distance computations on the same geometric model.
- New types of piecewise polynomial functions and new and efficient constructions of basis functions with important applications in geometric modelling and simulation.
- New results and software tools for motion design.
- New characterisation of the existence of distances that make certain planar mechanisms flexible by the existence of a certain colouring of the edges of the underlying graph.
- Novel methods addressing challenges in industrial applications for controlling the error, limiting computations and providing local refine-ability.
- A novel approach for switching between different representations of shapes based on clustering and approximate implicitization; an efficient method to approximate swept volumes.
- Enabling innovative ship design by developing parametric modellers which are able to generate reach design.
- Development of solvers of the wave resistance problem and the flow around lifting bodies with novel methodologies that seamlessly couple CAD representations with computational mechanics.
- An architectural application of geometric optimization, and a new computational approach to the geometric modelling of surfaces for the design and manufacturing of freeform facades.
"One of the main impacts has been to attract dynamic and scientifically strong students. They have been exposed to multi-disciplinary, multisectoral and versatile research environments, which will be a strong asset when seeking a job. During the recruitment process many young scientists were exposed to our problems and methodology, interacted with our senior scientists by presenting posters at our Recruitment event, and experienced an interesting interviewing procedure.
By the end of ARCADES, the ESRs have a significantly wider international academic and industrial network than most PhD-fellows, a view that is shared with the members of our Advisory Board. Some of our graduates are already integrated in European companies, while others have already started their academic career, thus strengthening the continent’s nexus of scientific research and technology transfer in the well-known triangle of Universities, research centres and industry.

ARCADES is becoming well known in the scientific community thanks to the organisation of Open Network events, our web portal, and our numerous publications. Societal impact is achieved throughout a series of public lectures and outreach activities.

Industrial impact is one of our primary goals. Our research and training program was designed by taking into account specific problems posed by our 5 industrial partners who also actively participated in Network events. The research of the students, through their industrial secondments, could be directly applied or tested on the field, and eventually could lead to innovative solutions or products, or enhance commercial tools. To this direction, it is notable that one PhD was hosted by an SME. Our industrial partners have used this interaction to strengthen their research activities and strongly wish to continue this collaboration beyond ARCADES

Some of our research is leading towards the development of specific innovations:
-Fabrication-aware smart geometric design.
-Big data approximation using locally refined splines.
-Approximate implicitisation using locally refined splines.
-Bridging the CAD-CAE gap for maritime industries (Key Innovator, Category: ""Exploration"", EU Radar Innovation Platform)."
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