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-rw-r--r--doc/Bitmap_cubical_complex/COPYRIGHT19
-rw-r--r--doc/Bitmap_cubical_complex/Cubical_complex_representation.ipe732
-rw-r--r--doc/Bitmap_cubical_complex/Cubical_complex_representation.pngbin19167 -> 0 bytes
-rw-r--r--doc/Bitmap_cubical_complex/Gudhi_Cubical_Complex_doc.h117
-rw-r--r--doc/Bitmap_cubical_complex/bitmapAllCubes.pngbin38944 -> 0 bytes
-rw-r--r--doc/Bitmap_cubical_complex/exampleBitmap.pngbin2549 -> 0 bytes
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diff --git a/doc/Bitmap_cubical_complex/COPYRIGHT b/doc/Bitmap_cubical_complex/COPYRIGHT
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index 2b14dcb9..00000000
--- a/doc/Bitmap_cubical_complex/COPYRIGHT
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@@ -1,19 +0,0 @@
-The files of this directory are 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/>.
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diff --git a/doc/Bitmap_cubical_complex/Cubical_complex_representation.png b/doc/Bitmap_cubical_complex/Cubical_complex_representation.png
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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
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-/* 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_
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