Merge remote-tracking branch 'origin/master' into sparsev3

13 files changed, 177 insertions, 66 deletions

diff --git a/src/Alpha_complex/utilities/CMakeLists.txt b/src/Alpha_complex/utilities/CMakeLists.txt
index b12c9690..e76edc5f 100644
--- a/src/Alpha_complex/utilities/CMakeLists.txt
+++ b/src/Alpha_complex/utilities/CMakeLists.txt
@@ -23,7 +23,7 @@ if (NOT CGAL_WITH_EIGEN3_VERSION VERSION_LESS 4.11.0)
 
   add_test(NAME Alpha_complex_utilities_alpha_complex_3d COMMAND $<TARGET_FILE:alpha_complex_3d_persistence>
           "${CMAKE_SOURCE_DIR}/data/points/tore3D_300.off"
-          "-p" "2" "-m" "0.45" "-o" "alpha.pers")
+          "-p" "2" "-m" "0.45" "-o" "safe.pers")
 
   add_test(NAME Alpha_complex_utilities_exact_alpha_complex_3d COMMAND $<TARGET_FILE:alpha_complex_3d_persistence>
           "${CMAKE_SOURCE_DIR}/data/points/tore3D_300.off"
@@ -31,13 +31,13 @@ if (NOT CGAL_WITH_EIGEN3_VERSION VERSION_LESS 4.11.0)
 
   add_test(NAME Alpha_complex_utilities_safe_alpha_complex_3d COMMAND $<TARGET_FILE:alpha_complex_3d_persistence>
           "${CMAKE_SOURCE_DIR}/data/points/tore3D_300.off"
-          "-p" "2" "-m" "0.45" "-o" "safe.pers" "-s")
+          "-p" "2" "-m" "0.45" "-o" "fast.pers" "-f")
 
   if (DIFF_PATH)
     add_test(Alpha_complex_utilities_diff_alpha_complex_3d ${DIFF_PATH}
-            "exact.pers" "alpha.pers")
+            "exact.pers" "safe.pers")
     add_test(Alpha_complex_utilities_diff_alpha_complex_3d ${DIFF_PATH}
-            "safe.pers" "alpha.pers")
+            "fast.pers" "safe.pers")
   endif()
 
   add_test(NAME Alpha_complex_utilities_periodic_alpha_complex_3d_persistence COMMAND $<TARGET_FILE:alpha_complex_3d_persistence>
diff --git a/src/Alpha_complex/utilities/alpha_complex_3d_persistence.cpp b/src/Alpha_complex/utilities/alpha_complex_3d_persistence.cpp
index 19e608ad..09c84eb3 100644
--- a/src/Alpha_complex/utilities/alpha_complex_3d_persistence.cpp
+++ b/src/Alpha_complex/utilities/alpha_complex_3d_persistence.cpp
@@ -94,11 +94,11 @@ int main(int argc, char **argv) {
   int coeff_field_characteristic = 0;
   Filtration_value min_persistence = 0.;
   bool exact_version = false;
-  bool safe_version = false;
+  bool fast_version = false;
   bool weighted_version = false;
   bool periodic_version = false;
 
-  program_options(argc, argv, off_file_points, exact_version, safe_version, weight_file, cuboid_file, output_file_diag,
+  program_options(argc, argv, off_file_points, exact_version, fast_version, weight_file, cuboid_file, output_file_diag,
                   alpha_square_max_value, coeff_field_characteristic, min_persistence);
 
   std::vector<double> weights;
@@ -120,16 +120,16 @@ int main(int argc, char **argv) {
     periodic_version = true;
   }
 
-  Gudhi::alpha_complex::complexity complexity = Gudhi::alpha_complex::complexity::FAST;
+  Gudhi::alpha_complex::complexity complexity = Gudhi::alpha_complex::complexity::SAFE;
   if (exact_version) {
-    if (safe_version) {
-      std::cerr << "You cannot set the exact and the safe version." << std::endl;
+    if (fast_version) {
+      std::cerr << "You cannot set the exact and the fast version." << std::endl;
       exit(-1);
     }
     complexity = Gudhi::alpha_complex::complexity::EXACT;
   }
-  if (safe_version) {
-    complexity = Gudhi::alpha_complex::complexity::SAFE;
+  if (fast_version) {
+    complexity = Gudhi::alpha_complex::complexity::FAST;
   }
 
   Simplex_tree simplex_tree;
@@ -258,7 +258,7 @@ int main(int argc, char **argv) {
   return 0;
 }
 
-void program_options(int argc, char *argv[], std::string &off_file_points, bool &exact, bool &safe,
+void program_options(int argc, char *argv[], std::string &off_file_points, bool &exact, bool &fast,
                      std::string &weight_file, std::string &cuboid_file, std::string &output_file_diag,
                      Filtration_value &alpha_square_max_value, int &coeff_field_characteristic,
                      Filtration_value &min_persistence) {
@@ -270,9 +270,9 @@ void program_options(int argc, char *argv[], std::string &off_file_points, bool
   po::options_description visible("Allowed options", 100);
   visible.add_options()("help,h", "produce help message")(
       "exact,e", po::bool_switch(&exact),
-      "To activate exact version of Alpha complex 3d (default is false, not available if safe is set)")(
-      "safe,s", po::bool_switch(&safe),
-      "To activate safe version of Alpha complex 3d (default is false, not available if exact is set)")(
+      "To activate exact version of Alpha complex 3d (default is false, not available if fast is set)")(
+      "fast,f", po::bool_switch(&fast),
+      "To activate fast version of Alpha complex 3d (default is false, not available if exact is set)")(
       "weight-file,w", po::value<std::string>(&weight_file)->default_value(std::string()),
       "Name of file containing a point weights. Format is one weight per line:\n  W1\n  ...\n  Wn ")(
       "cuboid-file,c", po::value<std::string>(&cuboid_file),
@@ -303,7 +303,7 @@ void program_options(int argc, char *argv[], std::string &off_file_points, bool
     std::cout << std::endl;
     std::cout << "Compute the persistent homology with coefficient field Z/pZ \n";
     std::cout << "of a 3D Alpha complex defined on a set of input points.\n";
-    std::cout << "3D Alpha complex can be exact or safe, weighted and/or periodic\n\n";
+    std::cout << "3D Alpha complex can be safe (by default) exact or fast, weighted and/or periodic\n\n";
     std::cout << "The output diagram contains one bar per line, written with the convention: \n";
     std::cout << "   p   dim b d \n";
     std::cout << "where dim is the dimension of the homological feature,\n";
diff --git a/src/Alpha_complex/utilities/alphacomplex.md b/src/Alpha_complex/utilities/alphacomplex.md
index 98f56802..50a39d32 100644
--- a/src/Alpha_complex/utilities/alphacomplex.md
+++ b/src/Alpha_complex/utilities/alphacomplex.md
@@ -107,6 +107,7 @@ It must be in the format described
 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**

 

diff --git a/src/Tangential_complex/doc/Intro_tangential_complex.h b/src/Tangential_complex/doc/Intro_tangential_complex.h
index f4fc8ac7..501f4a8b 100644
--- a/src/Tangential_complex/doc/Intro_tangential_complex.h
+++ b/src/Tangential_complex/doc/Intro_tangential_complex.h
@@ -35,9 +35,11 @@ namespace tangential_complex {
 
 \section tangentialdefinition Definition
 
-A Tangential Delaunay complex is a <a target="_blank" href="https://en.wikipedia.org/wiki/Simplicial_complex">simplicial complex</a>
+A Tangential Delaunay complex is a
+<a target="_blank" href="https://en.wikipedia.org/wiki/Simplicial_complex">simplicial complex</a>
 designed to reconstruct a \f$k\f$-dimensional smooth manifold embedded in \f$d\f$-dimensional Euclidean space. 
-The input is a point sample coming from an unknown manifold, which means that the points lie close to a structure of "small" intrinsic dimension.
+The input is a point sample coming from an unknown manifold, which means that the points lie close to a structure of
+"small" intrinsic dimension.
 The running time depends only linearly on the extrinsic dimension \f$ d \f$
 and exponentially on the intrinsic dimension \f$ k \f$.
 
@@ -46,17 +48,19 @@ An extensive description of the Tangential complex can be found in \cite tangent
 \subsection whatisthetc What is a Tangential Complex?
 
 Let us start with the description of the Tangential complex of a simple example, with \f$ k=1 \f$ and \f$ d=2 \f$.
-The input data is 4 points \f$ P \f$ located on a curve embedded in 2D.
+The point set \f$ \mathscr P \f$ is located on a closed curve embedded in 2D.
+Only 4 points will be displayed (more are required for PCA) to simplify the figures.
 \image html "tc_example_01.png" "The input"
-For each point \f$ p \f$, estimate its tangent subspace \f$ T_p \f$ (e.g. using PCA).
+For each point \f$ P \f$, estimate its tangent subspace \f$ T_P \f$ using PCA.
 \image html "tc_example_02.png" "The estimated normals"
-Let us add the Voronoi diagram of the points in orange. For each point \f$ p \f$, construct its star in the Delaunay triangulation of \f$ P \f$ restricted to \f$ T_p \f$.
+Let us add the Voronoi diagram of the points in orange. For each point \f$ P \f$, construct its star in the Delaunay
+triangulation of \f$ \mathscr P \f$ restricted to \f$ T_P \f$.
 \image html "tc_example_03.png" "The Voronoi diagram"
 The Tangential Delaunay complex is the union of those stars.
 
 In practice, neither the ambient Voronoi diagram nor the ambient Delaunay triangulation is computed.
-Instead, local \f$ k \f$-dimensional regular triangulations are computed with a limited number of points as we only need the star of each point.
-More details can be found in \cite tangentialcomplex2014.
+Instead, local \f$ k \f$-dimensional regular triangulations are computed with a limited number of points as we only
+need the star of each point. More details can be found in \cite tangentialcomplex2014.
 
 \subsection inconsistencies Inconsistencies
 
@@ -65,7 +69,7 @@ An inconsistency occurs when a simplex is not in the star of all its vertices.
 
 Let us take the same example.
 \image html "tc_example_07_before.png" "Before"
-Let us slightly move the tangent subspace \f$ T_q \f$
+Let us slightly move the tangent subspace \f$ T_Q \f$
 \image html "tc_example_07_after.png" "After"
 Now, the star of \f$ Q \f$ contains \f$ QP \f$, but the star of \f$ P \f$ does not contain \f$ QP \f$. We have an inconsistency.
 \image html "tc_example_08.png" "After"
diff --git a/src/Tangential_complex/include/gudhi/Tangential_complex.h b/src/Tangential_complex/include/gudhi/Tangential_complex.h
index 37cdf1b4..4a78127c 100644
--- a/src/Tangential_complex/include/gudhi/Tangential_complex.h
+++ b/src/Tangential_complex/include/gudhi/Tangential_complex.h
@@ -322,7 +322,11 @@ class Tangential_complex {
     for (std::size_t i = 0; i < m_points.size(); ++i) m_are_tangent_spaces_computed[i] = true;
   }
 
-  /// Computes the tangential complex.
+  /** \brief Computes the tangential complex.
+   *  \exception std::invalid_argument In debug mode, if the computed star dimension is too low. Try to set a bigger
+   *  maximal edge length value with `Tangential_complex::set_max_squared_edge_length` if
+   *  this happens.
+   */
   void compute_tangential_complex() {
 #ifdef GUDHI_TC_PERFORM_EXTRA_CHECKS
     std::cerr << red << "WARNING: GUDHI_TC_PERFORM_EXTRA_CHECKS is defined. "
@@ -1984,6 +1988,13 @@ class Tangential_complex {
     return os;
   }
 
+  /** \brief Sets the maximal possible squared edge length for the edges in the triangulations.
+   *
+   * @param[in] max_squared_edge_length Maximal possible squared edge length.
+   *
+   * If the maximal edge length value is too low `Tangential_complex::compute_tangential_complex` will throw an
+   * exception in debug mode.
+   */
   void set_max_squared_edge_length(FT max_squared_edge_length) { m_max_squared_edge_length = max_squared_edge_length; }
 
  private:
diff --git a/src/Tangential_complex/test/test_tangential_complex.cpp b/src/Tangential_complex/test/test_tangential_complex.cpp
index 4e2d4f65..103b8b30 100644
--- a/src/Tangential_complex/test/test_tangential_complex.cpp
+++ b/src/Tangential_complex/test/test_tangential_complex.cpp
@@ -126,3 +126,33 @@ BOOST_AUTO_TEST_CASE(test_mini_tangential) {
   BOOST_CHECK(stree.num_vertices() == 4);
   BOOST_CHECK(stree.num_simplices() == 6);
 }
+
+#ifdef GUDHI_DEBUG
+BOOST_AUTO_TEST_CASE(test_basic_example_throw) {
+  typedef CGAL::Epick_d<CGAL::Dynamic_dimension_tag> Kernel;
+  typedef Kernel::FT FT;
+  typedef Kernel::Point_d Point;
+  typedef Kernel::Vector_d Vector;
+  typedef tc::Tangential_complex<Kernel, CGAL::Dynamic_dimension_tag,CGAL::Parallel_tag> TC;
+
+  const int INTRINSIC_DIM = 2;
+  const int AMBIENT_DIM = 3;
+  const int NUM_POINTS = 1000;
+
+  Kernel k;
+
+  // Generate points on a 2-sphere
+  CGAL::Random_points_on_sphere_d<Point> generator(AMBIENT_DIM, 3.);
+  std::vector<Point> points;
+  points.reserve(NUM_POINTS);
+  for (int i = 0; i < NUM_POINTS; ++i)
+    points.push_back(*generator++);
+
+  // Compute the TC
+  TC tc(points, INTRINSIC_DIM, k);
+  tc.set_max_squared_edge_length(0.01);
+  std::cout << "test_basic_example_throw - set_max_squared_edge_length(0.01) to make GUDHI_CHECK fail" << std::endl;
+  BOOST_CHECK_THROW(tc.compute_tangential_complex(), std::invalid_argument);
+
+}
+#endif
diff --git a/src/cmake/modules/GUDHI_third_party_libraries.cmake b/src/cmake/modules/GUDHI_third_party_libraries.cmake
index 7b0d350d..57ea7d14 100644
--- a/src/cmake/modules/GUDHI_third_party_libraries.cmake
+++ b/src/cmake/modules/GUDHI_third_party_libraries.cmake
@@ -148,6 +148,7 @@ if( PYTHONINTERP_FOUND )
   find_python_module("matplotlib")
   find_python_module("numpy")
   find_python_module("scipy")
+  find_python_module("sphinx")
 endif()
 
 if(NOT GUDHI_CYTHON_PATH)
@@ -157,20 +158,16 @@ endif(NOT GUDHI_CYTHON_PATH)
 option(WITH_GUDHI_CYTHON_RUNTIME_LIBRARY_DIRS "Build with setting runtime_library_dirs. Usefull when setting rpath is not allowed" ON)
 
 if(PYTHONINTERP_FOUND AND CYTHON_FOUND)
-  # Default found version 2
-  if(PYTHON_VERSION_MAJOR EQUAL 2)
+  if(SPHINX_FOUND)
     # Documentation generation is available through sphinx
     find_program( SPHINX_PATH sphinx-build )
-  elseif(PYTHON_VERSION_MAJOR EQUAL 3)
-    # No sphinx-build in Pyton3, just hack it
-    set(SPHINX_PATH "${PYTHON_EXECUTABLE}" "${CMAKE_CURRENT_SOURCE_DIR}/${GUDHI_CYTHON_PATH}/doc/python3-sphinx-build.py")
-  else()
-    message(FATAL_ERROR "ERROR: Try to compile the Cython interface. Python version ${PYTHON_VERSION_STRING} is not valid.")
-  endif(PYTHON_VERSION_MAJOR EQUAL 2)
-  # get PYTHON_SITE_PACKAGES relative path from a python command line
-  execute_process(
-    COMMAND "${PYTHON_EXECUTABLE}" -c "from distutils.sysconfig import get_python_lib; print (get_python_lib(prefix='', plat_specific=True))"
-    OUTPUT_VARIABLE PYTHON_SITE_PACKAGES
-    OUTPUT_STRIP_TRAILING_WHITESPACE)
+
+    if(NOT SPHINX_PATH)
+      if(PYTHON_VERSION_MAJOR EQUAL 3)
+        # In Python3, just hack sphinx-build if it does not exist
+        set(SPHINX_PATH "${PYTHON_EXECUTABLE}" "${CMAKE_CURRENT_SOURCE_DIR}/${GUDHI_CYTHON_PATH}/doc/python3-sphinx-build.py")
+      endif(PYTHON_VERSION_MAJOR EQUAL 3)
+    endif(NOT SPHINX_PATH)
+  endif(SPHINX_FOUND)
 endif(PYTHONINTERP_FOUND AND CYTHON_FOUND)
 
diff --git a/src/cython/cython/tangential_complex.pyx b/src/cython/cython/tangential_complex.pyx
index 4bb07076..293ef8cb 100644
--- a/src/cython/cython/tangential_complex.pyx
+++ b/src/cython/cython/tangential_complex.pyx
@@ -36,6 +36,7 @@ cdef extern from "Tangential_complex_interface.h" namespace "Gudhi":
         Tangential_complex_interface(int intrisic_dim, vector[vector[double]] points)
         # bool from_file is a workaround for cython to find the correct signature
         Tangential_complex_interface(int intrisic_dim, string off_file, bool from_file)
+        void compute_tangential_complex() except +
         vector[double] get_point(unsigned vertex)
         unsigned number_of_vertices()
         unsigned number_of_simplices()
@@ -43,6 +44,7 @@ cdef extern from "Tangential_complex_interface.h" namespace "Gudhi":
         unsigned number_of_inconsistent_stars()
         void create_simplex_tree(Simplex_tree_interface_full_featured* simplex_tree)
         void fix_inconsistencies_using_perturbation(double max_perturb, double time_limit)
+        void set_max_squared_edge_length(double max_squared_edge_length)
 
 # TangentialComplex python interface
 cdef class TangentialComplex:
@@ -92,6 +94,17 @@ cdef class TangentialComplex:
          """
         return self.thisptr != NULL
 
+    def compute_tangential_complex(self):
+        """This function computes the tangential complex.
+
+        Raises:
+            ValueError: In debug mode, if the computed star dimension is too
+                low. Try to set a bigger maximal edge length value with
+                :func:`~gudhi.Tangential_complex.set_max_squared_edge_length`
+                if this happens.
+        """
+        self.thisptr.compute_tangential_complex()
+
     def get_point(self, vertex):
         """This function returns the point corresponding to a given vertex.
 
@@ -152,3 +165,16 @@ cdef class TangentialComplex:
         """
         self.thisptr.fix_inconsistencies_using_perturbation(max_perturb,
                                                             time_limit)
+
+    def set_max_squared_edge_length(self, max_squared_edge_length):
+        """Sets the maximal possible squared edge length for the edges in the
+        triangulations.
+
+        :param max_squared_edge_length: Maximal possible squared edge length.
+        :type max_squared_edge_length: double
+
+        If the maximal edge length value is too low
+        :func:`~gudhi.Tangential_complex.compute_tangential_complex`
+        will throw an exception in debug mode.
+        """
+        self.thisptr.set_max_squared_edge_length(max_squared_edge_length)
diff --git a/src/cython/doc/installation.rst b/src/cython/doc/installation.rst
index 040f6b4a..855dea44 100644
--- a/src/cython/doc/installation.rst
+++ b/src/cython/doc/installation.rst
@@ -7,24 +7,23 @@ Installation
 
 Compiling
 *********
-The library uses c++11 and requires `Boost <https://www.boost.org/>`_ ≥ 1.56.0
-and `CMake <https://www.cmake.org/>`_   ≥ 3.1.
+The library uses c++11 and requires `Boost <https://www.boost.org/>`_ ≥ 1.56.0,
+`CMake <https://www.cmake.org/>`_   ≥ 3.1  to generate makefiles, and
+`Cython <https://www.cython.org/>`_ to compile the GUDHI Python module.
 It is a multi-platform library and compiles on Linux, Mac OSX and Visual
 Studio 2015.
-It also requires cmake to generate makefiles, and cython to compile the
-library.
 
 On `Windows <https://wiki.python.org/moin/WindowsCompilers>`_ , only Python
 3.5 and 3.6 are available because of the required Visual Studio version.
 
-On other systems, if you have several Python/cython installed, the version 2.X
+On other systems, if you have several Python/Cython installed, the version 2.X
 will be used by default, but you can force it by adding
 :code:`-DPython_ADDITIONAL_VERSIONS=3` to the cmake command.
 
-GUDHI Cythonization
-===================
+GUDHI Python module compilation
+===============================
 
-To build the GUDHI cython module, run the following commands in a terminal:
+To build the GUDHI Python module, run the following commands in a terminal:
 
 .. code-block:: bash
 
@@ -32,7 +31,28 @@ To build the GUDHI cython module, run the following commands in a terminal:
     mkdir build
     cd build/
     cmake ..
-    make cython
+    cd cython
+    make
+
+GUDHI Python module installation
+================================
+
+Once the compilation succeeds, one can add the GUDHI Python module path to the
+PYTHONPATH:
+
+.. code-block:: bash
+
+    # For windows, you have to set PYTHONPATH environment variable
+    export PYTHONPATH='$PYTHONPATH:/path-to-gudhi/build/cython'
+
+Or install it definitely in your Python packages folder:
+
+.. code-block:: bash
+
+    cd /path-to-gudhi/build/cython
+    # May require sudo or administrator privileges
+    make install
+
 
 Test suites
 ===========
@@ -45,7 +65,7 @@ following command in a terminal:
     cd /path-to-gudhi/build/cython
     # For windows, you have to set PYTHONPATH environment variable
     export PYTHONPATH='$PYTHONPATH:/path-to-gudhi/build/cython'
-    ctest -R py_test
+    make test
 
 Debugging issues
 ================
@@ -54,7 +74,7 @@ If tests fail, please check your PYTHONPATH and try to :code:`import gudhi`
 and check the errors.
 The problem can come from a third-party library bad link or installation.
 
-If :code:`import gudhi` succeeds, please have a look to debug informations:
+If :code:`import gudhi` succeeds, please have a look to debug information:
 
 .. code-block:: python
 
@@ -105,13 +125,17 @@ A complete configuration would be :
 Documentation
 =============
 
-To build the documentation, `sphinx-doc <http://http://www.sphinx-doc.org>`_ is
-required. Please refer to *conf.py* file to see which
-`sphinx-doc <http://http://www.sphinx-doc.org>`_ modules are required to
-generate the documentation. Run the following commands in a terminal:
+To build the documentation, `sphinx-doc <http://www.sphinx-doc.org>`_ and
+`sphinxcontrib-bibtex <https://sphinxcontrib-bibtex.readthedocs.io>`_ are
+required. As the documentation is auto-tested, `CGAL`_, `Eigen3`_,
+`Matplotlib`_, `NumPy`_ and `SciPy`_ are also mandatory to build the
+documentation.
+
+Run the following commands in a terminal:
 
 .. code-block:: bash
 
+    cd /path-to-gudhi/build/cython
     make sphinx
 
 Optional third-party library
@@ -127,7 +151,7 @@ The :doc:`Alpha complex </alpha_complex_user>`,
 C++ library which provides easy access to efficient and reliable geometric
 algorithms.
 
-Having CGAL,  the Computational Geometry Algorithms Library, version 4.7.0 or
+Having CGAL, the Computational Geometry Algorithms Library, version 4.7.0 or
 higher installed is recommended. The procedure to install this library
 according to your operating system is detailed
 `here <http://doc.cgal.org/latest/Manual/installation.html>`_.
diff --git a/src/cython/doc/tangential_complex_user.rst b/src/cython/doc/tangential_complex_user.rst
index 5ce69e86..ebfe1e29 100644
--- a/src/cython/doc/tangential_complex_user.rst
+++ b/src/cython/doc/tangential_complex_user.rst
@@ -23,8 +23,10 @@ What is a Tangential Complex?
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
 
 Let us start with the description of the Tangential complex of a simple
-example, with :math:`k = 1` and :math:`d = 2`. The input data is 4 points
-:math:`P` located on a curve embedded in 2D.
+example, with :math:`k = 1` and :math:`d = 2`. The point set
+:math:`\mathscr P` is located on a closed curve embedded in 2D.
+Only 4 points will be displayed (more are required for PCA) to simplify the
+figures.
 
 .. figure:: ../../doc/Tangential_complex/tc_example_01.png
     :alt: The input
@@ -32,8 +34,7 @@ example, with :math:`k = 1` and :math:`d = 2`. The input data is 4 points
 
     The input
 
-For each point :math:`p`, estimate its tangent subspace :math:`T_p` (e.g.
-using PCA). 
+For each point :math:`P`, estimate its tangent subspace :math:`T_P` using PCA.
 
 .. figure:: ../../doc/Tangential_complex/tc_example_02.png
     :alt: The estimated normals
@@ -43,8 +44,8 @@ using PCA).
 
 
 Let us add the Voronoi diagram of the points in orange. For each point
-:math:`p`, construct its star in the Delaunay triangulation of :math:`P`
-restricted to :math:`T_p`.
+:math:`P`, construct its star in the Delaunay triangulation of
+:math:`\mathscr P` restricted to :math:`T_P`.
 
 .. figure:: ../../doc/Tangential_complex/tc_example_03.png
     :alt: The Voronoi diagram
@@ -72,7 +73,7 @@ Let us take the same example.
 
     Before
 
-Let us slightly move the tangent subspace :math:`T_q`
+Let us slightly move the tangent subspace :math:`T_Q`
 
 .. figure:: ../../doc/Tangential_complex/tc_example_07_after.png
     :alt: After
@@ -128,6 +129,7 @@ This example builds the Tangential complex of point set read in an OFF file.
     import gudhi
     tc = gudhi.TangentialComplex(intrisic_dim = 1,
         off_file=gudhi.__root_source_dir__ + '/data/points/alphacomplexdoc.off')
+    tc.compute_tangential_complex()
     result_str = 'Tangential contains ' + repr(tc.num_simplices()) + \
         ' simplices - ' + repr(tc.num_vertices()) + ' vertices.'
     print(result_str)
@@ -175,6 +177,7 @@ simplices.
    import gudhi
    tc = gudhi.TangentialComplex(intrisic_dim = 1,
        points=[[0.0, 0.0], [1.0, 0.0], [0.0, 1.0], [1.0, 1.0]])
+   tc.compute_tangential_complex()
    result_str = 'Tangential contains ' + repr(tc.num_vertices()) + ' vertices.'
    print(result_str)
 
diff --git a/src/cython/example/tangential_complex_plain_homology_from_off_file_example.py b/src/cython/example/tangential_complex_plain_homology_from_off_file_example.py
index 0f8f5e80..536517d1 100755
--- a/src/cython/example/tangential_complex_plain_homology_from_off_file_example.py
+++ b/src/cython/example/tangential_complex_plain_homology_from_off_file_example.py
@@ -50,6 +50,7 @@ with open(args.file, 'r') as f:
         print("TangentialComplex creation from points read in a OFF file")
         
         tc = gudhi.TangentialComplex(intrisic_dim = args.intrisic_dim, off_file=args.file)
+        tc.compute_tangential_complex()
         st = tc.create_simplex_tree()
     
         message = "Number of simplices=" + repr(st.num_simplices())
diff --git a/src/cython/include/Tangential_complex_interface.h b/src/cython/include/Tangential_complex_interface.h
index 71418886..c4ddbdbe 100644
--- a/src/cython/include/Tangential_complex_interface.h
+++ b/src/cython/include/Tangential_complex_interface.h
@@ -49,8 +49,6 @@ class Tangential_complex_interface {
     Dynamic_kernel k;
 
     tangential_complex_ = new TC(points, intrisic_dim, k);
-    tangential_complex_->compute_tangential_complex();
-    num_inconsistencies_ = tangential_complex_->number_of_inconsistent_simplices();
   }
 
   Tangential_complex_interface(int intrisic_dim, const std::string& off_file_name, bool from_file = true) {
@@ -60,14 +58,17 @@ class Tangential_complex_interface {
     std::vector<Point_d> points = off_reader.get_point_cloud();
 
     tangential_complex_ = new TC(points, intrisic_dim, k);
-    tangential_complex_->compute_tangential_complex();
-    num_inconsistencies_ = tangential_complex_->number_of_inconsistent_simplices();
   }
 
   ~Tangential_complex_interface() {
     delete tangential_complex_;
   }
 
+  void compute_tangential_complex() {
+    tangential_complex_->compute_tangential_complex();
+    num_inconsistencies_ = tangential_complex_->number_of_inconsistent_simplices();
+  }
+
   std::vector<double> get_point(unsigned vh) {
     std::vector<double> vd;
     if (vh < tangential_complex_->number_of_vertices()) {
@@ -104,7 +105,11 @@ class Tangential_complex_interface {
     simplex_tree->initialize_filtration();
   }
 
- private:
+  void set_max_squared_edge_length(double max_squared_edge_length) {
+    tangential_complex_->set_max_squared_edge_length(max_squared_edge_length);
+  }
+
+private:
   TC* tangential_complex_;
   TC::Num_inconsistencies num_inconsistencies_;
 };
diff --git a/src/cython/test/test_tangential_complex.py b/src/cython/test/test_tangential_complex.py
index 5385a0d3..5c62f278 100755
--- a/src/cython/test/test_tangential_complex.py
+++ b/src/cython/test/test_tangential_complex.py
@@ -32,6 +32,15 @@ def test_tangential():
     tc = TangentialComplex(intrisic_dim = 1, points=point_list)
     assert tc.__is_defined() == True
     assert tc.num_vertices() == 4
+    assert tc.num_simplices() == 0
+    assert tc.num_inconsistent_simplices() == 0
+    assert tc.num_inconsistent_stars() == 0
+
+    tc.compute_tangential_complex()
+    assert tc.num_vertices() == 4
+    assert tc.num_simplices() == 4
+    assert tc.num_inconsistent_simplices() == 0
+    assert tc.num_inconsistent_stars() == 0
 
     st = tc.create_simplex_tree()
     assert st.__is_defined() == True