diff options
Diffstat (limited to 'src/Cech_complex/doc/Intro_cech_complex.h')
-rw-r--r-- | src/Cech_complex/doc/Intro_cech_complex.h | 15 |
1 files changed, 7 insertions, 8 deletions
diff --git a/src/Cech_complex/doc/Intro_cech_complex.h b/src/Cech_complex/doc/Intro_cech_complex.h index ec0d35e2..a1d6f5dd 100644 --- a/src/Cech_complex/doc/Intro_cech_complex.h +++ b/src/Cech_complex/doc/Intro_cech_complex.h @@ -33,7 +33,7 @@ namespace cech_complex { * * @{ * - * \section cechdefinition Cech complex definition + * \section cechdefinition Čech complex definition * * Cech_complex * <a target="_blank" href="https://en.wikipedia.org/wiki/%C4%8Cech_cohomology">(Wikipedia)</a> is a @@ -42,7 +42,8 @@ namespace cech_complex { * from it. * The input shall be a point cloud in an Euclidean space. * - * The filtration value of each edge of the `Gudhi::Proximity_graph` is computed from `Gudhi::Radius_distance` function. + * The filtration value of each edge of the `Gudhi::Proximity_graph` is computed from + * `Gudhi::Minimal_enclosing_ball_radius` function. * * All edges that have a filtration value strictly greater than a user given maximal radius value, \f$max\_radius\f$, * are not inserted into the complex. @@ -51,8 +52,8 @@ namespace cech_complex { * * \image html "cech_one_skeleton.png" "Cech complex proximity graph representation" * - * When creating a simplicial complex from this proximity graph, Cech inserts the proximity graph into the simplicial - * complex data structure, and then expands the simplicial complex when required. + * When creating a simplicial complex from this proximity graph, Cech_complex inserts the proximity graph into the + * simplicial complex data structure, and then expands the simplicial complex when required. * * On this example, as edges \f$(x,y)\f$, \f$(y,z)\f$ and \f$(z,y)\f$ are in the complex, the minimal ball radius * containing the points \f$(x,y,z)\f$ is computed. @@ -62,7 +63,7 @@ namespace cech_complex { * * And so on for higher dimensions. * - * \image html "cech_complex_representation.png" "Cech complex expansion" + * \image html "cech_complex_representation.png" "Čech complex expansion" * * The minimal ball radius computation is insured by * <a target="_blank" href="https://people.inf.ethz.ch/gaertner/subdir/software/miniball.html"> @@ -78,8 +79,6 @@ namespace cech_complex { * <a href="_cech_complex_2cech_complex_step_by_step_8cpp-example.html"> * cech_complex_step_by_step.cpp</a> example, where the graph construction over the Simplex_tree is more detailed. * - * \section cechpointsdistance Point cloud - * * \subsection cechpointscloudexample Example from a point cloud * * This example builds the proximity graph from the given points, and maximal radius values. @@ -89,7 +88,7 @@ namespace cech_complex { * * \include Cech_complex/cech_complex_example_from_points.cpp * - * When launching (Cech maximal distance between 2 points is 1., is expanded until dimension 2): + * When launching (maximal enclosing ball radius is 1., is expanded until dimension 2): * * \code $> ./Cech_complex_example_from_points * \endcode |