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diff --git a/doc/Bitmap_cubical_complex/Gudhi_Cubical_Complex_doc.h b/doc/Bitmap_cubical_complex/Gudhi_Cubical_Complex_doc.h deleted file mode 100644 index d1836ef0..00000000 --- a/doc/Bitmap_cubical_complex/Gudhi_Cubical_Complex_doc.h +++ /dev/null @@ -1,117 +0,0 @@ -/* This file is part of the Gudhi Library. The Gudhi library - * (Geometric Understanding in Higher Dimensions) is a generic C++ - * library for computational topology. - * - * Author(s): Pawel Dlotko - * - * Copyright (C) 2015 Inria - * - * This program is free software: you can redistribute it and/or modify - * it under the terms of the GNU General Public License as published by - * the Free Software Foundation, either version 3 of the License, or - * (at your option) any later version. - * - * This program is distributed in the hope that it will be useful, - * but WITHOUT ANY WARRANTY; without even the implied warranty of - * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the - * GNU General Public License for more details. - * - * You should have received a copy of the GNU General Public License - * along with this program. If not, see <http://www.gnu.org/licenses/>. - */ - - -#ifndef DOC_GUDHI_CUBICAL_COMPLEX_COMPLEX_H_ -#define DOC_GUDHI_CUBICAL_COMPLEX_COMPLEX_H_ - -namespace Gudhi { - -namespace cubical_complex { - -/** \defgroup cubical_complex Cubical complex - * - * \author Pawel Dlotko - * - * @{ - * - - * Bitmap_cubical_complex is an example of a structured complex useful in computational mathematics (specially rigorous - * numerics) and image analysis. The presented implementation of cubical complexes is based on the following - * definition. - * - * An <em>elementary interval</em> is an interval of a form \f$ [n,n+1] \f$, or \f$[n,n]\f$, for \f$ n \in \mathcal{Z} - * \f$. The first one is called <em>non-degenerate</em>, while the second one is \a degenerate interval. A - * <em>boundary of a elementary interval</em> is a chain \f$\partial [n,n+1] = [n+1,n+1]-[n,n] \f$ in case of - * non-degenerated elementary interval and \f$\partial [n,n] = 0 \f$ in case of degenerate elementary interval. An - * <em>elementary cube</em> \f$ C \f$ is a product of elementary intervals, \f$C=I_1 \times \ldots \times I_n\f$. - * <em>Embedding dimension</em> of a cube is n, the number of elementary intervals (degenerate or not) in the product. - * A <em>dimension of a cube</em> \f$C=I_1 \times ... \times I_n\f$ is the number of non degenerate elementary - * intervals in the product. A <em>boundary of a cube</em> \f$C=I_1 \times \ldots \times I_n\f$ is a chain obtained - * in the following way: - * \f[\partial C = (\partial I_1 \times \ldots \times I_n) + (I_1 \times \partial I_2 \times \ldots \times I_n) + - * \ldots + (I_1 \times I_2 \times \ldots \times \partial I_n).\f] - * A <em>cubical complex</em> \f$\mathcal{K}\f$ is a collection of cubes closed under operation of taking boundary - * (i.e. boundary of every cube from the collection is in the collection). A cube \f$C\f$ in cubical complex - * \f$\mathcal{K}\f$ is <em>maximal</em> if it is not in a boundary of any other cube in \f$\mathcal{K}\f$. A \a - * support of a cube \f$C\f$ is the set in \f$\mathbb{R}^n\f$ occupied by \f$C\f$ (\f$n\f$ is the embedding dimension - * of \f$C\f$). - * - * Cubes may be equipped with a filtration values in which case we have filtered cubical complex. All the cubical - * complexes considered in this implementation are filtered cubical complexes (although, the range of a filtration may - * be a set of two elements). - * - * For further details and theory of cubical complexes, please consult \cite kaczynski2004computational as well as the - * following paper \cite peikert2012topological . - * - * \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 - * of so called bitmaps. Let \f$R = [b_1,e_1] \times \ldots \times [b_n,e_n]\f$, for \f$b_1,...b_n,e_1,...,e_n \in - * \mathbb{Z}\f$, \f$b_i \leq d_i\f$ be the considered rectangular region and let \f$\mathcal{K}\f$ be a filtered - * cubical complex having the rectangle \f$R\f$ as its support. Note that the structure of the coordinate system gives - * a way a lexicographical ordering of cells of \f$\mathcal{K}\f$. This ordering is a base of the presented - * bitmap-based implementation. In this implementation, the whole cubical complex is stored as a vector of the values - * of filtration. This, together with dimension of \f$\mathcal{K}\f$ and the sizes of \f$\mathcal{K}\f$ in all - * directions, allows to determine, dimension, neighborhood, boundary and coboundary of every cube \f$C \in - * \mathcal{K}\f$. - * - * \image html "Cubical_complex_representation.png" Cubical complex. - * - * Note that the cubical complex in the figure above is, in a natural way, a product of one dimensional cubical - * complexes in \f$\mathbb{R}\f$. The number of all cubes in each direction is equal \f$2n+1\f$, where \f$n\f$ is the - * number of maximal cubes in the considered direction. Let us consider a cube at the position \f$k\f$ in the bitmap. - * Knowing the sizes of the bitmap, by a series of modulo operation, we can determine which elementary intervals are - * 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 - * - * 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. 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$. Imposing periodic boundary - * conditions in the direction i, means that the left and the right side of a complex \f$ \mathcal{K} \f$ are - * 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 (see \ref FileFormatsPerseus). - * - * \section BitmapExamples Examples - * End user programs are available in example/Bitmap_cubical_complex and utilities/Bitmap_cubical_complex folders. - * - */ -/** @} */ // end defgroup cubical_complex - -} // namespace cubical_complex - -namespace Cubical_complex = cubical_complex; - -} // namespace Gudhi - -#endif // DOC_GUDHI_CUBICAL_COMPLEX_COMPLEX_H_ |