diff options
Diffstat (limited to 'src/Alpha_complex/doc')
| -rw-r--r-- | src/Alpha_complex/doc/Intro_alpha_complex.h | 14 | ||||
| -rw-r--r-- | src/Alpha_complex/doc/alpha_complex_representation.ipe | 6 | ||||
| -rw-r--r-- | src/Alpha_complex/doc/alpha_complex_representation.png | bin | 14606 -> 19568 bytes |
3 files changed, 10 insertions, 10 deletions
diff --git a/src/Alpha_complex/doc/Intro_alpha_complex.h b/src/Alpha_complex/doc/Intro_alpha_complex.h index 3c32a1e6..a8b1a106 100644 --- a/src/Alpha_complex/doc/Intro_alpha_complex.h +++ b/src/Alpha_complex/doc/Intro_alpha_complex.h @@ -31,8 +31,8 @@ namespace alpha_complex { * circumsphere is empty (the simplex is then said to be Gabriel), and as the minimum of the filtration * values of the codimension 1 cofaces that make it not Gabriel otherwise. * - * All simplices that have a filtration value strictly greater than a given alpha squared value are not inserted into - * the complex. + * All simplices that have a filtration value \f$ > \alpha^2 \f$ are removed from the Delaunay complex + * when creating the simplicial complex if it is specified. * * \image html "alpha_complex_representation.png" "Alpha-complex representation" * @@ -46,8 +46,8 @@ namespace alpha_complex { * \cite cgal:s-gkd-19b from CGAL as template parameter. * * \remark - * - When the simplicial complex is constructed with an infinite value of alpha, the complex is a Delaunay - * complex. + * - When an \f$\alpha\f$-complex is constructed with an infinite value of \f$ \alpha^2 \f$, the complex is a Delaunay + * complex (with special filtration values). * - For people only interested in the topology of the \ref alpha_complex (for instance persistence), * \ref alpha_complex is equivalent to the \ref cech_complex and much smaller if you do not bound the radii. * \ref cech_complex can still make sense in higher dimension precisely because you can bound the radii. @@ -135,13 +135,13 @@ namespace alpha_complex { * * \subsubsection nondecreasing Non decreasing filtration values * - * As the squared radii computed by CGAL are an approximation, it might happen that these alpha squared values do not - * quite define a proper filtration (i.e. non-decreasing with respect to inclusion). + * As the squared radii computed by CGAL are an approximation, it might happen that these \f$ \alpha^2 \f$ values do + * not quite define a proper filtration (i.e. non-decreasing with respect to inclusion). * We fix that up by calling `SimplicialComplexForAlpha::make_filtration_non_decreasing()`. * * \subsubsection pruneabove Prune above given filtration value * - * The simplex tree is pruned from the given maximum alpha squared value (cf. + * The simplex tree is pruned from the given maximum \f$ \alpha^2 \f$ value (cf. * `SimplicialComplexForAlpha::prune_above_filtration()`). * In the following example, the value is given by the user as argument of the program. * diff --git a/src/Alpha_complex/doc/alpha_complex_representation.ipe b/src/Alpha_complex/doc/alpha_complex_representation.ipe index e8096b93..40ff1d0f 100644 --- a/src/Alpha_complex/doc/alpha_complex_representation.ipe +++ b/src/Alpha_complex/doc/alpha_complex_representation.ipe @@ -1,7 +1,7 @@ <?xml version="1.0"?> <!DOCTYPE ipe SYSTEM "ipe.dtd"> -<ipe version="70107" creator="Ipe 7.1.10"> -<info created="D:20150603143945" modified="D:20160404172133"/> +<ipe version="70206" creator="Ipe 7.2.7"> +<info created="D:20150603143945" modified="D:20200110100102"/> <ipestyle name="basic"> <symbol name="arrow/arc(spx)"> <path stroke="sym-stroke" fill="sym-stroke" pen="sym-pen"> @@ -305,7 +305,7 @@ h 108.275 743.531 m 166.45 743.531 l </path> -<text matrix="1 0 0 1 142.618 -109.867" transformations="translations" pos="127.397 746.763" stroke="darkgray" type="label" width="6.41" height="4.289" depth="0" valign="baseline">$\alpha$</text> +<text matrix="1 0 0 1 126.618 -109.867" transformations="translations" pos="127.397 746.763" stroke="darkgray" type="label" width="45.707" height="9.041" depth="1.32" valign="baseline" style="math">\alpha = \sqrt{32.0}</text> <use matrix="1 0 0 1 -209.478 12.0238" name="mark/fdisk(sfx)" pos="300 720" size="normal" stroke="black" fill="white"/> <use matrix="1 0 0 1 -210.178 22.1775" name="mark/fdisk(sfx)" pos="280 660" size="normal" stroke="black" fill="white"/> <use matrix="1 0 0 1 -210.178 22.1775" name="mark/fdisk(sfx)" pos="370 690" size="normal" stroke="black" fill="white"/> diff --git a/src/Alpha_complex/doc/alpha_complex_representation.png b/src/Alpha_complex/doc/alpha_complex_representation.png Binary files differindex 7b81cd69..5ebb1e75 100644 --- a/src/Alpha_complex/doc/alpha_complex_representation.png +++ b/src/Alpha_complex/doc/alpha_complex_representation.png |
