Computing barycentric coordinates in Tensor Product Cells#246
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Computing barycentric coordinates in Tensor Product Cells#246
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…ts of different sizes
…ion to handle nested tensor-product cells + added tests
…ation works properly for symbolic points
…ds to work on different array shapes
…xpressions representing point sets
…rately with singleton contractions
…ons work on GEM tensor expressions
…_barycentric_coordinates in tp cells
Co-authored-by: Pablo Brubeck <brubeck@protonmail.com>
…plicies and tensor product cells
… sub-entities of simplicies + added notes + modified test checking facet ordering of bary coords on tp cells
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This is the first part of PR #245 concerning changes to FIAT only. In particular, I have extended FIAT to enable the computation of barycentric coordinates on tensor product cells.
The main distinction lies in how barycentric coordinates are represented in simplicies vs tensor product cells. For simplicies, there is one barycentric coordinate per vertex so the default ordering of these coordinates follows the vertex ordering. For tensor product cells, there is one barycentric coordinate per facet so the natural ordering is that of facets.
First, to enable facet ordering in simplicies, I have added a facet ordering permutation in
SimplicialComplex.compute_barycentric_coordinates. Then, since barycentric coordinates in tensor product cells are computed recursively on each factor, having facet ordering on the simplicies that form each factor ensure that we obtain facet ordering on the tensor-product cell as a whole.