Mathematics Colloquia and Seminars

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Description

Barycentric coordinates provide the most convenient way to linearly interpolate data prescribed at the vertices of an n-dimensional simplex. In recent years, the ideas of barycentric coordinates and barycentric interpolation have been extended to arbitrary planar polygons and to general polytopes in higher dimensions. This has led to novel solutions in applications such as mesh parametrization, image warping and mesh deformation in geometry processing and fracture and topology optimization in solid mechanics. In this talk, I will give an overview of the use of generalized barycentric coordinates in finite element computations, with emphasis on their construction, a few theoretical results, and an extension to quadratically precise coordinates on planar polygons using the maximum-entropy principle.