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

该奖项的目的是在哥伦比亚大学校园内举办为期三天的研讨会。本次研讨会的首要主题是利用几何和计算之间的密切联系，为模拟力学现象开发更有效和更强大的计算方法。从Wachspress在1975年的工作（Wachspress凸多边形基函数）中产生，重心坐标和重心插值的思想近年来已经扩展到平面中的任意多边形和高维中的一般多面体，这反过来又导致了几何处理中的新解决方案和计算力学中的新应用。研讨会的目的包括：促进计算机图形学和力学研究人员之间在基于几何的计算方法领域的新兴领域的相互交流和对话;并帮助促进和推进计算科学和工程下一代研究人员的研究生教育。 讲习班的第一天将举行关于广义重心坐标的讨论会;第二天将包括学生的海报展示;讲习班的第二和第三天将邀请该领域的主要专家进行演讲。 研讨会的研究议程将旨在显著推进计算力学和计算机图形学的最新发展。将通过邀请来自学术界、国家实验室和工业界的一批文化多样的研究人员和从业人员来加强讲习班。旅行奖也将提供给一些研究生，从而使这些研究人员能够使用其领域的最新计算技术来构建他们的研究。将努力吸收不同级别（初级、高级）和理工科代表性不足群体的参与者。 研讨会的主要主题将对推进能源，国防和制造业应用的仿真技术产生广泛的影响。力学和图形学研究人员之间的跨学科互动也将促进未来的合作和伙伴关系。讲习班的成果将编写成一份报告，其中将突出强调几何方法和物理现象计算机模拟交叉领域的当前成就、现有挑战和未来潜在研究机会。

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.