Workshop on Barycentric Coordinates in Graphics Processing and Finite/Boundary Element Methods

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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.