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Diffstat (limited to 'src/python/doc/alpha_complex_user.rst')
| -rw-r--r-- | src/python/doc/alpha_complex_user.rst | 51 |
1 files changed, 24 insertions, 27 deletions
diff --git a/src/python/doc/alpha_complex_user.rst b/src/python/doc/alpha_complex_user.rst index 60319e84..d49f45b4 100644 --- a/src/python/doc/alpha_complex_user.rst +++ b/src/python/doc/alpha_complex_user.rst @@ -10,9 +10,9 @@ Definition .. include:: alpha_complex_sum.inc `AlphaComplex` is constructing a :doc:`SimplexTree <simplex_tree_ref>` using -`Delaunay Triangulation <http://doc.cgal.org/latest/Triangulation/index.html#Chapter_Triangulations>`_ -:cite:`cgal:hdj-t-19b` from `CGAL <http://www.cgal.org/>`_ (the Computational Geometry Algorithms Library -:cite:`cgal:eb-19b`). +`Delaunay Triangulation <http://doc.cgal.org/latest/Triangulation/index.html#Chapter_Triangulations>`_ +:cite:`cgal:hdj-t-19b` from the `Computational Geometry Algorithms Library <http://www.cgal.org/>`_ +:cite:`cgal:eb-19b`. Remarks ^^^^^^^ @@ -89,25 +89,28 @@ In order to build the alpha complex, first, a Simplex tree is built from the cel Filtration value computation algorithm ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ - **for** i : dimension :math:`\rightarrow` 0 **do** - **for all** :math:`\sigma` of dimension i - **if** filtration(:math:`\sigma`) is NaN **then** - filtration(:math:`\sigma`) = :math:`\alpha^2(\sigma)` - **end if** +.. code-block:: vim + + for i : dimension → 0 do + for all σ of dimension i + if filtration(σ) is NaN then + filtration(σ) = α²(σ) + end if + for all τ face of σ do // propagate alpha filtration value + if filtration(τ) is not NaN then + filtration(τ) = min( filtration(τ), filtration(σ) ) + else + if τ is not Gabriel for σ then + filtration(τ) = filtration(σ) + end if + end if + end for + end for + end for + + make_filtration_non_decreasing() + prune_above_filtration() - *//propagate alpha filtration value* - - **for all** :math:`\tau` face of :math:`\sigma` - **if** filtration(:math:`\tau`) is not NaN **then** - filtration(:math:`\tau`) = filtration(:math:`\sigma`) - **end if** - **end for** - **end for** - **end for** - - make_filtration_non_decreasing() - - prune_above_filtration() Dimension 2 ^^^^^^^^^^^ @@ -203,9 +206,3 @@ the program output is: [4, 5, 6] -> 22.74 [3, 6] -> 30.25 -CGAL citations -============== - -.. bibliography:: ../../biblio/how_to_cite_cgal.bib - :filter: docnames - :style: unsrt |