Algebraic Representations in Computer-Aided Design for complEx Shapes
Marie Sklodowska-Curie European Training Network, Jan 2016 -- Dec 2019.
Members: ATHENA Research & Innovation Center (Greece, coordinator), U. Barcelona (Spain), INRIA (France), J. Kepler U. Linz (Austria), SINTEF (Norway), U. Strathclyde (UK), T.U. Wien (Austria), Evolute GmbH (Austria).
ARCADES aims at disrupting the traditional paradigm in Computer-Aided Design (CAD) by exploiting cutting-edge research in mathematics and algorithm design. Geometry is now a critical tool in a large number of key applications; somewhat surprisingly, however, several approaches of the CAD industry are outdated, and 3D geometry processing is becoming increasingly the weak link. This is alarming in sectors where CAD faces new challenges arising from fast point acquisition, big data, and mobile computing, but also in robotics, simulation, animation, fabrication and manufacturing where CAD strives to address crucial societal and market needs. The challenge taken up by ARCADES is to invert the trend of CAD industry lagging behind mathematical breakthroughs and to build the next generation of CAD software based on strong foundations from algebraic geometry, differential geometry, scientific computing, and algorithm design. Our game-changing methods lead to real-time modelers for architectural geometry and visualisation, to isogeometric and design-through-analysis software for shape optimisation, and marine design & hydrodynamics, and to tools for motion design, robot kinematics, path planning, and control of machining tools.
I4MS: Innovation for Manufacturing SMEs,
February 2015 -- January 2016.
Members: Helic S.A. (Leader), ATHENA Research & Innovation Center, European Sensor Systems (ESS), Arctur racunalniški inženirin (Slovenia).
We, at ATHENA, optimize the geometric modeling tools of HELIC, especially in what concerns scientific computing for grid usage and the cloud provided by Arctur. ESS, MEMS sensors producer, will use modeling and simulation tools by HELIC to investigate for possible detrimental self- and mutual- inductance effects on their sensor front-end designs, option previously not available due to high cost of modeling software.
Exploiting Structure in Polynomial Equation and System Solving for geOmetric and game mOdeling.
Excellence Programme, EU and Ministry of Development.
October 2012 -- September 2015.
ESPRESSO members: I. Emiris (PI), Y. Avrithis and R. Vidunas (Postdocs), A. Karasoulou (PhD student), E. Koutsoupias (U. Athens, U. Oxford), B. Mourrain (INRIA), P. Bro Miltersen (U. Aarhus).
The complexity of polynomial equation and system solving is often too high, hence the need for algorithms that exploit the structure of the problem, leading to complexity bounds in terms of its intrinsic rather than nominal hardness. Structure is multifarious: We consider the sparseness of the input, and reducing the problem to methods that operate on sparse objects. ESPRESSO focuses on two specific applications. The first is geometric modeling, where we have extensive experience and expect to obtain tangible and practical results, based on effective, publicly available implementations. Our second application uses algebraic tools to better model stochastic games with the goal of effectively computing finite or infinite game equilibria. Further info or visit the webpage.
Advanced Geometric Computing and Critical Applications (website)
January 2012 -- September 2015. Ministry of Education and EU (acks). Budget: 520,000 euro. GeomComp includes 3 Greek teams, namely:
- ErGA (coordinating), Dept Informatics & Telecoms, University of Athens. Faculty members: Ioannis Emiris (team leader), Dimitrios Gunopulos. The group includes Leonidas Palios (University of Ioannina), Euripides Markou (University of Thessaly).
- School of Naval Architecture and Marine Engineering, National Technical University of Athens. Faculty members: Panagiotis Kaklis (team leader), Alexandros Ginnis.
- Foundation for Research and Technology - Hellas (FORTH), Heraklio, Crete. Faculty members: Menelaos Karavelas (team leader), Vassilis Samoladas (Technical U. Crete).
GeomComp involves external partners, who include L. Guibas (Stanford University, USA) and E. Papadopoulou (U. Svizzera Italiana, Lugano, Switzerland).
The main topics include (details in Greek):
- Computational geometry and generalizations: convex geometry with extensions to higher dimensions and nonlinear objects, Voronoi diagrams in 2D with extensions to 3D and curved objects, visibility with linear obstacles with extensions to nonlinear obstacles, nearest-neighbor queries with extensions to data-mining, approximate geometric optimization with extensions to massive data.
- Nonlinear computational geometry, Computer-aided geometric design, and Geometric modeling, including the development of the required mathematical tools.
- Software development and applications to critical questions in structural bioinformatics, molecular modeling, and industrial design, such as VLSI and ship design.
CG Learning: Computational Geometry Learning
European FET-Open STREP project, November 2010 -- October 2013. It includes 7 Universities and one Research Institute. The tasks of ErGA are: High-dimensional polytopes, silhouettes and projections. General-dimensional kernel for CGAL and the Orientation predicate. Approximate nearest neighbor search and the related data structures.
SAGA: ShApes, Geometry and Algebra
European Marie Curie Initial Training Network (FP7). November 2008 -- October 2012. It includes 5 Universities, 3 Research Institutes, and 2 Companies, and its aim is to advance the mathematical and algorithmic foundations of CAD technology, by exploiting results and techniques from different fields, such as Computer Algebra, Algebraic Geometry, Numeric Computation, and Theory of Algorithms. The ErGA PhD fellow is Tatjana Kalinka, the postdoc fellow is Thang Luu Ba, and PhD student Angelos Mantzaflaris has visited ErGA from INRIA Sophia-Antipolis. There are SAGA training events, open to participants outside the Network: November 2008, in Castro Urdiales, Spain. March 2010 in Auron, France. October 2010 in Kolympari, Greece. September 2011 at Vilnius, Lithuania. October 2012 at Trento, Italy.
Algorithms for robotic platforms in physiotherapy
Project ΠΕΝΕΔ, "Algorithm design and software development for parallel robotic mechanisms and applications to physiotherapy", 1/7/05 - 31/12/10. Joint funding by Ministry of Development, and "Reflexion Ltd". PhD students: Christos Konaxis, Christos Sirseloudis, and Elias Tsigaridas. Engineer: Artemis Maglara. Collaboration with Instituto de Automatica Industrial (Madrid), INRIA (Sophia-Antipolis), Institute of Computer Science (FORTH, Heraklio). The aim of the project is to study and design a robotic platform for the rehabilitation of patients with kinetic problems and with posible remote control capabilities. For this purpose the kinematics of the foot are extensively studied and useful results are extracted such as the foot axes of rotaion, workspace, velocities, accelerations and forces that must be handled by a robotic device. Identification / calibration techniques are also studied in order to compute the specific kinematics parameters of the patient's foot. A new hybrid parallel / serial robotic platform is proposed and its parametric design is carried out in order to follow the foot movemets. Ancillary algebraic and numeric algorithms are developed.
ACS: Algorithms for Complex Shapes
IST-STREP (Open FET) FP6 project (greek/english summary) 1/5/05-30/4/08. Arrangements, Voronoi diagrams of ellipses (PhD by G.Tzoumas), visibility in curved art galleries, CGAL algebraic kernel, operations on complex shapes, predicates' implementation, algebraic benchmarking, CGAL-Python.
Figure by T. Kakargias, using a map of Greece from the Cartography Laboratory, National Technical University of Athens.
Αlgorithms for curves and surfaces
Efficient algorithms and implementations for the representation and manipulation of curves and surfaces. Project ENTER, Greek Ministry of Development. Visitor scientist: Ilias Kotsireas (W. Laurier Univ., Waterloo, Canada). Collaboration with company "MP & Associates". 2006-08.
Projects by the Research Council of the National and Kapodistrian University of Athens.
Team association (Equipe Associe'e) with the GALAAD Group of INRIA Sophia-Antipolis, France, 1/03-12/07.
"Design and development of geometric algorithms for curved objects", (περίληψη, summary). Funding by Greek Ministry of Education, 4/04-12/07. Arrangements of curved objects, Voronoi diagrams, approximation algorithms for visibility. Postdoctoral researcher: E.Markou.
Arrangements of curved objects, towards quadric surfaces in 3-D. ARCADIA project, with Loria-Nancy and INRIA Sophia-Antipolis. 1/1/05-31/12/06.
Calibration of Parallel platforms and applications in space robots. Bilateral PLATON project with the COPRIN Group of INRIA Sophia-Antipolis, France, 1/04-8/06.