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Artificial Intelligence
Data Science
Algorithms
archimedes-Artificial Intelligence, Data Science, Algorithms-greece
greece
Algorithms
Data Science
Artificial Intelligence
[Archimedes Talks Series] (Geometric) Constraints Solving Using Multivariate Spline Functions
Dates
2024-09-16 11:30 - 14:00
Venue
Artemidos 1 - Amphitheater
Title: (Geometric) Constraints Solving Using Multivariate Spline Functions
Presenter: Professor Gershon Elber, CS, Technion*
Abstract:
We present a subdivision based paradigm to solve a set of (piecewise) rational constraints represented by multivariate (piecewise) rational spline functions. The constraints can be formulated as either inequalities or equalities (semi-algebraic sets). The presented solver is not only capable of finding all solutions, globally, but is also capable of handling solution spaces of dimensions larger than zero. A special care is taken to guarantee all roots are isolated via a single solution geometric test.
This solver was applied to a large variety of geometric problems above the (piecewise) rationals domain that will be discussed as part of the talk. This set includes point-curve and curve-curve bi-tangents, convex hulls and kernels of planar curves and 3-space surfaces, ray-traps (bouncing billiard balls) between planar curves, the 10th Apollonius problem (circle tangent to given three circles), bounding circles, bisectors and voronoi regions, mold design, visibility and accessibility, sweeps and envelopes, and self-intersection trimming in offset approximations of curves and surfaces.
Abstract:
We present a subdivision based paradigm to solve a set of (piecewise) rational constraints represented by multivariate (piecewise) rational spline functions. The constraints can be formulated as either inequalities or equalities (semi-algebraic sets). The presented solver is not only capable of finding all solutions, globally, but is also capable of handling solution spaces of dimensions larger than zero. A special care is taken to guarantee all roots are isolated via a single solution geometric test.
This solver was applied to a large variety of geometric problems above the (piecewise) rationals domain that will be discussed as part of the talk. This set includes point-curve and curve-curve bi-tangents, convex hulls and kernels of planar curves and 3-space surfaces, ray-traps (bouncing billiard balls) between planar curves, the 10th Apollonius problem (circle tangent to given three circles), bounding circles, bisectors and voronoi regions, mold design, visibility and accessibility, sweeps and envelopes, and self-intersection trimming in offset approximations of curves and surfaces.
Bio:
Gershon Elber is a professor in the Computer Science Department, Technion, Israel. His research interests span computer aided geometric design and computer graphics. Prof. Elber received a BSc in computer engineering and an MSc in computer science from the Technion, Israel in 1986 and 1987, respectively, and a PhD in computer science from the University of Utah, USA, in 1992. Prof. Elber had several academic and Technion appointments, including the deputy vice president for computing, Technion, 2010-2013, and a member and head of the Solid Modeling Association (the parent organization of the solid and physical modeling, SPM, conferences), 2008-2010. He is now the head of the Technion Additive Manufacturing Center. Prof. Elber has served on the editorial board of the Computer Aided Design, Computer Graphics Forum, The Visual Computer, Graphical Models, and the International Journal of Computational Geometry & Applications and has served in many conferences' program committees including Solid Modeling, Shape Modeling, Geometric Modeling and Processing, Pacific Graphics, Computer Graphics International, and Siggraph. Prof. Elber was one of the paper chairs of Solid Modeling 2003 and Solid Modeling 2004, one of the conference chairs of Solid and Physical Modeling 2010, the chair of GDM 2014, the conference co-chair of SIAM GD/SPM 2015, and the conference co-chair of SPM 2018. He has published over 250 papers in international conferences and journals, received 15 best paper awards, presented a dozen keynote plenary talks, and is one of the authors of a book titled "Geometric Modeling with Splines - An Introduction". Prof. Elber received the John Gregory Memorial Award, 2011, in "Appreciation for Outstanding Contributions in Geometric Modeling", the Solid Modeling Association pioneers award in 2016, the Bezier award in 2019, and the Kunii award in 2024.
* Some of this work has been conducted in collaboration with many others including Myung-Soo Kim, SNU, Korea, Elaine Cohen, University of Utah, USA, Tom Grandine, Boeing, USA, Ralph Martin, Cardiff, Michael Barton and Yong Joon Kim, Technion.
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Vision
To position Greece as a leading player in AI and Data Science
Mission
To build an AI Excellence Hub in Greece where the international research community can connect, groundbreaking ideas can thrive, and the next generation of scientists emerges, shaping a brighter future for Greece and the world
Welcome to ARCHIMEDES, a vibrant research hub connecting the global AI and Data Science research community fostering groundbreaking research in Greece and beyond. Its dedicated core team, comprising lead researchers, affiliated researchers, Post-Docs, PhDs and interns, is committed to advancing basic and applied research in Artificial Intelligence and its supporting disciplines, including Algorithms, Statistics, Learning Theory, and Game Theory organized around 8 core research areas. By collaborating with Greek and Foreign Universities and Research Institutes, ARCHIMEDES disseminates its research findings fostering knowledge exchange and providing enriching opportunities for students. Leveraging AI to address real-world challenges, ARCHIMEDES promotes innovation within the Greek ecosystem and extends its societal impact. Established in January 2022, as a research unit of the Athena Research Center with support from the Committee Greece 2021, ARCHIMEDES is funded for its first four years by the EU Recovery and Resilience Facility (RRF).
Archimedes and the Biomedical Research Foundation Share Latest Findings in AI and Medicine
4 March 2025
Archimedes and the Biomedical Research Foundation of the Academy of Athens successfully hosted a special collaborative session at the Panhellenic Working Group Seminars of the Hellenic Society of Cardiology. This session focused on innovative applications of artificial intelligence in medicine, with a particular emphasis on advancements in cardiology. Held on Friday, February 7, 2025, in Room MC2 of the Megaron Athens International Conference Centre, the event brought together leading experts to explore how artificial intelligence is transforming cardiovascular medicine.
Archimedes Reaches Milestone of 200 Publications
12 February 2025
Archimedes is proud to announce that its researchers have published over 200 scientific publications in top-tier conferences (NeurIPS, ICLR, ICML) and journals.Archimedes maintains a vibrant scientific community of over 130 researchers, including more than 60 senior researchers (faculty members from Greece and abroad), 12 postdoctoral fellows, and 55 PhD students, along with over 20 undergraduate interns from various disciplines.
Happy International Greek Language Day!
9 February 2025
Today, we celebrate the historical, cultural, and linguistic significance of the Greek language. While Standard Modern Greek often takes center stage, we at Archimedes - AI and Data Science Research Hub recognize the impressive diversity and great cultural significance of its numerous dialects. These dialects present both exciting opportunities and complex challenges for AI and Large Language Models (LLMs) because each one of them presents unique linguistic features and all of them are low resourced. That’s why we’re using cutting-edge AI to document, digitize, and analyze these invaluable linguistic treasures, ensuring their preservation and accessibility for generations to come.
Two Research Positions in Data Stream Management Systems & Big Data Management
7 February 2025
We are pleased to announce the availability of two research positions in data stream management systems and big data management, to be co-supervised by Assistant Professor Odysseas Papapetrou from the Eindhoven University of Technology (TU/e) in the Netherlands and Professor Minos Garofalakis from the Technical University of Crete in Greece.
The project “ARCHIMEDES Unit: Research in Artificial Intelligence, Data Science and Algorithms” with code OPS 5154714 is implemented by the National Recovery and Resilience Plan “Greece 2.0” and is funded by the European Union – NextGenerationEU.
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