Spaces of Simplicial Shapes

  • Jon Eivind VatneEmail author
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 126)


When discussing shapes of simplices, e.g. in connection with mesh generation and finite element methods, it is important to have a suitable space parametrizing the shapes. In particular, degenerations of different types can appear as boundary components in various ways. For triangles, we will present two natural parametrizing sets that highlight two different types of degenerations, and then combine the properties into a new parametrizing space that allows a good basis for understanding both types of degenerations. The combined space is constructed by the process of blowing up, which in this simple case is introduction of polar coordinates. For tetrahedra, there are many different types of degenerations. In this short paper we will only give one example of what can be achieved by blowing up a natural model, namely to pull apart the two tetrahedral degenerating types known as slivers and caps.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Western Norway University of Applied SciencesDepartment of Computing, Mathematics and PhysicsBergenNorway

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