Eventi

CSF Workshop on Generalized Barycentric Coordinates in Computer Graphics and Computational Mechanics

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Centro Congressi Stefano Franscini, Monte Verità, Ascona, Switzerland

The CSF Workshop on Generalized Barycentric Coordinates in Computer Graphics and Computational Mechanics organized by Prof. Kai Hormann (USI) and N. Sukumar (UC Davis) will be held at Centro Congressi Stefano Franscini in Ascona, 11-14 November 2020.

Overview

Interpolating given discrete data with continuous functions in one or more variables is a fundamental problem in diverse fields of sciences and engineering. Barycentric coordinates, which were introduced by Möbius in 1827, still provide perhaps the most convenient way to linearly interpolate data prescribed at the vertices of an n-dimensional simplex. Barycentric interpolation is widely used in computer graphics, whereas such interpolating (basis) functions can also be adopted as trial and test approximations in finite and boundary element methods. Starting with the seminal work of Wachspress in 1975, 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 applications like mesh parametrization, image warping, mesh deformation, and finite/boundary element methods.

This workshop aims at fostering the interchange of researchers from computer graphics and computational mechanics on this exciting research topic. It is intended to provide greater synergy between these two fields so that a broader class of problems and associated solution strategies can be conceived. Moreover, this workshop will provide a forum for the novice as well as the expert to get acquainted with the latest research results and the potential use of generalized barycentric coordinates in different areas of science and engineering.

Topics

Some of the featured topics in the workshop are:

  • Barycentric and transfinite interpolation
  • Barycentric coordinates in computer graphics and geometry processing
  • Polygonal finite elements and boundary elements on polygons and polyhedra
  • Barycentric coordinates for mesh parametrization, image warping, mesh deformation, free-form modeling, character animation, and generalized Bézier surfaces
  • Barycentric coordinates in computational mathematics (e.g., rational interpolation, quadrature rules, collocated-solution for partial differential equations), solid mechanics (e.g., elasticity, topology optimization and fracture) and fluid mechanics (e.g., Stokes flow and Navier–Stokes equations)
  • Connections between barycentric coordinates, discrete differential geometry, and mimetic finite elements

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