Summary ReportThe 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, topology optimization, image warping, and character animation highlight their potential and promise in simulation technology for applications in energy, defense, manufacturing, and entertainment. There is a need to have a common forum to draw closer connections between research in computer graphics and computational mechanics, which will aid in advancing the state-of-the-art in both fields.
Sponsored by the U.S. National Science Foundation, a workshop on generalized barycentric coordinates in geometry processing and finite element computations 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 US 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. The opening lecture was delivered by Dr. Eugene Wachspress, whose 1975 book A Rational Finite Element Basis laid the foundations for extending finite element computations to polygonal and polyhedral elements, and has led to sustained interest and development of generalized barycentric coordinates in computer graphics and computational mechanics. 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.
Fellowship SupportFellowship support was awarded to 24 students and post-docs from 15 universities within the US 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 US 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.
Best Poster AwardA poster session for students was organized on the second day of the workshop, and the best three posters were recognized with book awards. The awardees are:
- Dmitry Anisimov (Università della Svizzera italiana, Lugano): Blended barycentric coordinates
- Arun Lal Gain (University of Illinois, Urbana-Champaign): Structural topology optimization employing the Allen--Cahn evolution equation on unstructured polygonal meshes
- Andrea Tagliasacchi (Simon Fraser University, Burnaby): Mean curvature skeletons