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+.. GUDHI documentation master file, created by
+   sphinx-quickstart on Thu Jun 30 09:55:51 2016.
+   You can adapt this file completely to your liking, but it should at least
+   contain the root `toctree` directive.
+
+.. toctree::
+   :maxdepth: 2
+
+GUDHI's documentation
+#####################
+
+.. image:: img/Gudhi_banner.png
+   :align: center
+
+Introduction
+************
+
+The Gudhi library (Geometry Understanding in Higher Dimensions) is a generic
+open source C++ library for Computational Topology and Topological Data
+Analysis (TDA). The GUDHI library intends to help the development of new
+algorithmic solutions in TDA and their transfer to applications. It provides
+robust, efficient, flexible and easy to use implementations of
+state-of-the-art algorithms and data structures.
+
+The current release of the GUDHI library includes:
+
+* Data structures to represent, construct and manipulate simplicial complexes.
+* Algorithms to compute persistent homology and multi-field persistent homology.
+* Simplication of simplicial complexes by edge contraction.
+
+All data-structures are generic and several of their aspects can be
+parameterized via template classes. We refer to [14] for a detailed
+description of the design of the library.
+
+Data structures
+***************
+
+Alpha complex
+=============
+
+.. image:: img/alpha_complex_representation.png
+   :align: center
+
+Alpha_complex is a simplicial complex constructed from the finite cells of a
+Delaunay Triangulation.
+
+The filtration value of each simplex is computed as the square of the
+circumradius of the simplex if the 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.
+
+This package requires having CGAL version 4.7 or higher (4.8.1 is advised for
+better perfomances).
+
+* :ref:`alphacomplex`
+
+
+.. automodule:: gudhi
+   :members:
+   :undoc-members:
+   :show-inheritance:
+