From 9899ae167f281d10b1684dfcd02c6838c5bf28df Mon Sep 17 00:00:00 2001 From: Gard Spreemann Date: Fri, 2 Feb 2018 13:51:45 +0100 Subject: GUDHI 2.1.0 as released by upstream in a tarball. --- .../Gudhi_Cubical_Complex_doc.h | 56 +++------------------- 1 file changed, 7 insertions(+), 49 deletions(-) (limited to 'doc/Bitmap_cubical_complex/Gudhi_Cubical_Complex_doc.h') diff --git a/doc/Bitmap_cubical_complex/Gudhi_Cubical_Complex_doc.h b/doc/Bitmap_cubical_complex/Gudhi_Cubical_Complex_doc.h index 5963caa3..a5d7b60f 100644 --- a/doc/Bitmap_cubical_complex/Gudhi_Cubical_Complex_doc.h +++ b/doc/Bitmap_cubical_complex/Gudhi_Cubical_Complex_doc.h @@ -63,7 +63,7 @@ namespace cubical_complex { * For further details and theory of cubical complexes, please consult \cite kaczynski2004computational as well as the * following paper \cite peikert2012topological . * - * \section cubicalcomplexdatastructure Data structure. + * \section cubicalcomplexdatastructure Data structure * * The implementation of Cubical complex provides a representation of complexes that occupy a rectangular region in * \f$\mathbb{R}^n\f$. This extra assumption allows for a memory efficient way of storing cubical complexes in a form @@ -85,37 +85,14 @@ namespace cubical_complex { * present in the product that gives the cube \f$C\f$. In a similar way, we can compute boundary and the coboundary of * each cube. Further details can be found in the literature. * - * \section inputformat Input Format. + * \section inputformat Input Format * * In the current implantation, filtration is given at the maximal cubes, and it is then extended by the lower star * filtration to all cubes. There are a number of constructors that can be used to construct cubical complex by users * who want to use the code directly. They can be found in the \a Bitmap_cubical_complex class. * Currently one input from a text file is used. It uses a format used already in Perseus software - * (http://www.sas.upenn.edu/~vnanda/perseus/) by Vidit Nanda. - * Below we are providing a description of the format. The first line contains a number d begin the dimension of the - * bitmap (2 in the example below). Next d lines are the numbers of top dimensional cubes in each dimensions (3 and 3 - * in the example below). Next, in lexicographical order, the filtration of top dimensional cubes is given (1 4 6 8 - * 20 4 7 6 5 in the example below). - * - * - * \image html "exampleBitmap.png" "Example of a input data." - * - * The input file for the following complex is: - * \verbatim -2 -3 -3 -1 -4 -6 -8 -20 -4 -7 -6 -5 -\endverbatim - + * (http://www.sas.upenn.edu/~vnanda/perseus/) by Vidit Nanda. The file format is described here: \ref FileFormatsPerseus. + * * \section PeriodicBoundaryConditions Periodic boundary conditions * Often one would like to impose periodic boundary conditions to the cubical complex. Let \f$ I_1\times ... \times * I_n \f$ be a box that is decomposed with a cubical complex \f$ \mathcal{K} \f$. Imposing periodic boundary @@ -123,30 +100,11 @@ namespace cubical_complex { * considered the same. In particular, if for a bitmap \f$ \mathcal{K} \f$ periodic boundary conditions are imposed * in all directions, then complex \f$ \mathcal{K} \f$ became n-dimensional torus. One can use various constructors * from the file Bitmap_cubical_complex_periodic_boundary_conditions_base.h to construct cubical complex with periodic - * boundary conditions. One can also use Perseus style input files. To indicate periodic boundary conditions in a - * given direction, then number of top dimensional cells in this direction have to be multiplied by -1. For instance: - - *\verbatim -2 --3 -3 -1 -4 -6 -8 -20 -4 -7 -6 -5 -\endverbatim - - * Indicate that we have imposed periodic boundary conditions in the direction x, but not in the direction y. - + * boundary conditions. One can also use Perseus style input files (see \ref FileFormatsPerseus). + * * \section BitmapExamples Examples - * End user programs are available in example/Bitmap_cubical_complex folder. + * End user programs are available in example/Bitmap_cubical_complex and utilities/Bitmap_cubical_complex folders. * - * \copyright GNU General Public License v3. */ /** @} */ // end defgroup cubical_complex -- cgit v1.2.3