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Diffstat (limited to 'src/Alpha_complex/utilities/alphacomplex.md')
| -rw-r--r-- | src/Alpha_complex/utilities/alphacomplex.md | 146 |
1 files changed, 53 insertions, 93 deletions
diff --git a/src/Alpha_complex/utilities/alphacomplex.md b/src/Alpha_complex/utilities/alphacomplex.md index 0fe98837..50a39d32 100644 --- a/src/Alpha_complex/utilities/alphacomplex.md +++ b/src/Alpha_complex/utilities/alphacomplex.md @@ -12,15 +12,18 @@ Leave the lines above as it is required by the web site generator 'Jekyll' ## alpha_complex_persistence ##
-This program computes the persistent homology with coefficient field Z/pZ of the dD alpha complex built from a dD point cloud.
+This program computes the persistent homology with coefficient field Z/pZ of
+the dD alpha complex built from a dD point cloud.
The output diagram contains one bar per line, written with the convention:
```
p dim birth death
```
-where `dim` is the dimension of the homological feature, `birth` and `death` are respectively the birth and death of the feature,
-and `p` is the characteristic of the field *Z/pZ* used for homology coefficients (`p` must be a prime number).
+where `dim` is the dimension of the homological feature, `birth` and `death`
+are respectively the birth and death of the feature, and `p` is the
+characteristic of the field *Z/pZ* used for homology coefficients (`p` must be
+a prime number).
**Usage**
@@ -29,15 +32,20 @@ and `p` is the characteristic of the field *Z/pZ* used for homology coefficients ```
where
-`<input OFF file>` is the path to the input point cloud in [nOFF ASCII format](http://www.geomview.org/docs/html/OFF.html).
+`<input OFF file>` is the path to the input point cloud in
+[nOFF ASCII format](http://www.geomview.org/docs/html/OFF.html).
**Allowed options**
* `-h [ --help ]` Produce help message
-* `-o [ --output-file ]` Name of file in which the persistence diagram is written. Default print in standard output.
-* `-r [ --max-alpha-square-value ]` (default = inf) Maximal alpha square value for the Alpha complex construction.
-* `-p [ --field-charac ]` (default = 11) Characteristic p of the coefficient field Z/pZ for computing homology.
-* `-m [ --min-persistence ]` (default = 0) Minimal lifetime of homology feature to be recorded. Enter a negative value to see zero length intervals.
+* `-o [ --output-file ]` Name of file in which the persistence diagram is
+written. Default print in standard output.
+* `-r [ --max-alpha-square-value ]` (default = inf) Maximal alpha square value
+for the Alpha complex construction.
+* `-p [ --field-charac ]` (default = 11) Characteristic p of the
+coefficient field Z/pZ for computing homology.
+* `-m [ --min-persistence ]` (default = 0) Minimal lifetime of homology feature
+to be recorded. Enter a negative value to see zero length intervals.
**Example**
@@ -51,13 +59,26 @@ N.B.: ## alpha_complex_3d_persistence ##
-This program computes the persistent homology with coefficient field Z/pZ of the 3D alpha complex built from a 3D point cloud. The output diagram contains one bar per line, written with the convention:
+This program computes the persistent homology with coefficient field Z/pZ of
+the 3D alpha complex built from a 3D point cloud.
+One can use exact computation. It is slower, but it is necessary when points
+are on a grid for instance.
+Alpha complex 3d can be weighted and/or periodic (refer to the
+[CGAL's 3D Periodic Triangulations User Manual](
+https://doc.cgal.org/latest/Periodic_3_triangulation_3/index.html)
+for more details).
+
+The output diagram contains
+one bar per line, written with the convention:
```
p dim birth death
```
-where `dim` is the dimension of the homological feature, `birth` and `death` are respectively the birth and death of the feature, and `p` is the characteristic of the field *Z/pZ* used for homology coefficients (`p` must be a prime number).
+where `dim` is the dimension of the homological feature, `birth` and `death`
+are respectively the birth and death of the feature, and `p` is the
+characteristic of the field *Z/pZ* used for homology coefficients (`p` must be
+a prime number).
**Usage**
@@ -65,14 +86,28 @@ where `dim` is the dimension of the homological feature, `birth` and `death` are alpha_complex_3d_persistence [options] <input OFF file>
```
-where `<input OFF file>` is the path to the input point cloud in [nOFF ASCII format](http://www.geomview.org/docs/html/OFF.html).
+where `<input OFF file>` is the path to the input point cloud in
+[nOFF ASCII format](http://www.geomview.org/docs/html/OFF.html).
**Allowed options**
* `-h [ --help ]` Produce help message
-* `-o [ --output-file ]` Name of file in which the persistence diagram is written. Default print in standard output.
-* `-p [ --field-charac ]` (default=11) Characteristic p of the coefficient field Z/pZ for computing homology.
-* `-m [ --min-persistence ]` (default = 0) Minimal lifetime of homology feature to be recorded. Enter a negative value to see zero length intervals.
+* `-o [ --output-file ]` Name of file in which the persistence diagram is
+written. Default print in standard output.
+* `-r [ --max-alpha-square-value ]` (default = inf) Maximal alpha square value
+for the Alpha complex construction.
+* `-p [ --field-charac ]` (default=11) Characteristic p of the coefficient
+field Z/pZ for computing homology.
+* `-m [ --min-persistence ]` (default = 0) Minimal lifetime of homology feature
+to be recorded. Enter a negative value to see zero length intervals.
+* `-c [ --cuboid-file ]` is the path to the file describing the periodic domain.
+It must be in the format described
+[here]({{ site.officialurl }}/doc/latest/fileformats.html#FileFormatsIsoCuboid).
+* `-w [ --weight-file ]` is the path to the file containing the weights of the
+points (one value per line).
+* `-e [ --exact ]` for the exact computation version (not compatible with
+weight and periodic version).
+* `-f [ --fast ]` for the fast computation version.
**Example**
@@ -84,82 +119,7 @@ N.B.: * `alpha_complex_3d_persistence` only accepts OFF files in dimension 3.
* Filtration values are alpha square values.
-
-
-## exact_alpha_complex_3d_persistence ##
-
-Same as `alpha_complex_3d_persistence`, but using exact computation.
-It is slower, but it is necessary when points are on a grid for instance.
-
-
-
-## weighted_alpha_complex_3d_persistence ##
-
-Same as `alpha_complex_3d_persistence`, but using weighted points.
-
-**Usage**
-
-```
- weighted_alpha_complex_3d_persistence [options] <input OFF file> <weights input file>
-```
-
-where
-
-* `<input OFF file>` is the path to the input point cloud in [nOFF ASCII format](http://www.geomview.org/docs/html/OFF.html).
-* `<input weights file>` is the path to the file containing the weights of the points (one value per line).
-
-**Allowed options**
-
-* `-h [ --help ]` Produce help message
-* `-o [ --output-file ]` Name of file in which the persistence diagram is written. Default print in standard output.
-* `-p [ --field-charac ]` (default=11) Characteristic p of the coefficient field Z/pZ for computing homology.
-* `-m [ --min-persistence ]` (default = 0) Minimal lifetime of homology feature to be recorded. Enter a negative value to see zero length intervals.
-
-**Example**
-
-```
- weighted_alpha_complex_3d_persistence ../../data/points/tore3D_300.off ../../data/points/tore3D_300.weights -p 2 -m 0.45
-```
-
-
-N.B.:
-
-* Weights values are explained on CGAL [Alpha shape](https://doc.cgal.org/latest/Alpha_shapes_3/index.html#title0)
-and [Regular triangulation](https://doc.cgal.org/latest/Triangulation_3/index.html#Triangulation3secclassRegulartriangulation) documentation.
-* Filtration values are alpha square values.
-
-
-## periodic_alpha_complex_3d_persistence ##
-Same as `alpha_complex_3d_persistence`, but using periodic alpha shape 3d.
-Refer to the [CGAL's 3D Periodic Triangulations User Manual](https://doc.cgal.org/latest/Periodic_3_triangulation_3/index.html) for more details.
-
-**Usage**
-
-```
- periodic_alpha_complex_3d_persistence [options] <input OFF file> <cuboid file>
-```
-
-where
-
-* `<input OFF file>` is the path to the input point cloud in [nOFF ASCII format](http://www.geomview.org/docs/html/OFF.html).
-* `<cuboid file>` is the path to the file describing the periodic domain. It must be in the format described
-[here](/doc/latest/fileformats.html#FileFormatsIsoCuboid).
-
-**Allowed options**
-
-* `-h [ --help ]` Produce help message
-* `-o [ --output-file ]` Name of file in which the persistence diagram is written. Default print in standard output.
-* `-p [ --field-charac ]` (default=11) Characteristic p of the coefficient field Z/pZ for computing homology.
-* `-m [ --min-persistence ]` (default = 0) Minimal lifetime of homology feature to be recorded. Enter a negative value to see zero length intervals
-
-
-**Example**
-
-```
-periodic_alpha_complex_3d_persistence ../../data/points/grid_10_10_10_in_0_1.off ../../data/points/iso_cuboid_3_in_0_1.txt -p 3 -m 1.0
-```
-
-N.B.:
-
-* Cuboid file must be in the format described [here](/doc/latest/fileformats.html#FileFormatsIsoCuboid).
-* Filtration values are alpha square values.
+* Weights values are explained on CGAL
+[Alpha shape](https://doc.cgal.org/latest/Alpha_shapes_3/index.html#title0)
+and
+[Regular triangulation](https://doc.cgal.org/latest/Triangulation_3/index.html#Triangulation3secclassRegulartriangulation) documentation.
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