The objective of this award is to conduct a three-day workshop on the campus of Columbia University. The overarching theme of this workshop is to exploit the intimate connection between geometry-and-computations towards the development of more efficient and robust computational methods for the simulation of mechanics phenomena. Emanating from the work of Wachspress in 1975 (Wachspress basis functions on convex polygons), the ideas of barycentric coordinates and barycentric interpolation have been extended in recent years to arbitrary polygons in the plane and general polytopes in higher dimensions, which in turn has led to novel solutions in geometric processing and new applications in computational mechanics. The aims of the workshop include: to foster mutual exchanges and dialog between researchers in computer graphics and mechanics on emerging areas in the field of geometric-based computational methods; and to aid in promoting and advancing graduate education for the next generation of researchers in computational science and engineering. Tutorial sessions on generalized barycentric coordinates will be held on the first day of the workshop; the second day will include poster presentations by students; and the second and third days of the workshop will feature invited and contributed talks by leading experts in the fields. The research agenda for the workshop will be aimed at significantly advancing the state-of-the-art in computational mechanics and computer graphics.
The workshop will be strengthened by inviting a culturally diverse group of researchers and practitioners from academia, national laboratories, and industry. Travel awards will be offered to a number of graduate students as well, thereby enabling these researchers to frame their research using the latest computational techniques in their field. Efforts will be made to include participants from different levels (junior, senior) and from underrepresented groups in science and engineering. The main topics in the workshop will have broad impact in advancing simulation technology for applications in energy, defense, and manufacturing. The cross-disciplinary interactions between researchers from mechanics and graphics will also promote future collaborations and partnerships. The outcomes of the workshop will be crafted in a report, which will highlight current accomplishments, existing challenges and potential future research opportunities at the intersection of geometric methods and computer simulation of physical phenomena.
The past decade has seen a surge in the development of generalized barycentric coordinates for applications in geometry processing and finite elements. The advances in the respective fields, however, to a great extent have evolved independently. Recent applications of barycentric coordinates in areas such as mesh generation, error estimates, fracture simulations, and topology optimization highlight their potential and promise in simulation technology for applications in energy, defense and manufacturing. To draw closer connections and synergy between research in graphics and mechanics and to advance the state-of-the-art in computational mechanics, a workshop on generalized barycentric coordinates was held on the campus of Columbia University, New York, from July 25-27, 2012. The workshop was well-attended (53 participants), with participation from within the U.S. and abroad: attendees included researchers from academia, industry and the national laboratories (Livermore, Los Alamos, Sandia), and students and post-docs from U.S. academic institutions and abroad. The workshop included tutorial sessions, plenary lectures, invited talks, and a poster session. Tutorials on the basics of generalized barycentric coordinates were presented, and more recent research that highlighted applications in geometry processing and solid mechanics were also featured in the lectures given by the invited speakers. In closing, a panel discussion was held which highlighted current accomplishments, some of the existing challenges, and potential future research opportunities at the intersection of barycentric-based geometric methods and computer simulation of physical phenomena. Fellowship support was awarded to 24 students and post-docs from 15 universities within the U.S. and abroad to enable them to participate in this workshop. A poster competition was also held, which highlighted graduate and post-doctoral research. This workshop has brought together leading researchers to the U.S. to discuss new developments and future directions for the use of generalized barycentric coordinates, has promoted graduate training for the next generation of scientists in computational science and engineering, and has fostered connections between researchers and students with those from other countries and from the national laboratories, which will lead to new collaborations that will accelerate advances in this emerging field of research.
