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diff --git a/src/GudhUI/utils/Critical_points.h b/src/GudhUI/utils/Critical_points.h
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+/*    This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT.
+ *    See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details.
+ *    Author(s):       David Salinas
+ *
+ *    Copyright (C) 2014 Inria
+ *
+ *    Modification(s):
+ *      - YYYY/MM Author: Description of the modification
+ */
+
+#ifndef UTILS_CRITICAL_POINTS_H_
+#define UTILS_CRITICAL_POINTS_H_
+
+#include <deque>
+#include <utility>  // for pair<>
+#include <algorithm>  // for sort
+
+#include "utils/Edge_contractor.h"
+
+/**
+ * Iteratively tries to anticollapse smallest edge non added so far.
+ * If its link is contractible then no topological change and else possible topological change.
+ *
+ * todo do a sparsification with some parameter eps while growing
+ */
+template<typename SkBlComplex> class Critical_points {
+ private:
+  SkBlComplex filled_complex_;
+  const SkBlComplex& input_complex_;
+  double max_length_;
+  std::ostream& stream_;
+
+ public:
+  typedef typename SkBlComplex::Vertex_handle Vertex_handle;
+  typedef typename SkBlComplex::Edge_handle Edge_handle;
+  typedef typename std::pair<Vertex_handle, Vertex_handle> Edge;
+
+  /**
+   * @brief check all pair of points with length smaller than max_length
+   */
+  Critical_points(const SkBlComplex& input_complex, std::ostream& stream, double max_length) :
+      input_complex_(input_complex), max_length_(max_length), stream_(stream) {
+    std::deque<Edge> edges;
+    auto vertices = input_complex.vertex_range();
+    for (auto p = vertices.begin(); p != vertices.end(); ++p) {
+      filled_complex_.add_vertex(input_complex.point(*p));
+      for (auto q = p; ++q != vertices.end(); /**/)
+        if (squared_eucl_distance(input_complex.point(*p), input_complex.point(*q)) < max_length_ * max_length_)
+          edges.emplace_back(*p, *q);
+    }
+
+    std::sort(edges.begin(), edges.end(),
+              [&](Edge e1, Edge e2) {
+                return squared_edge_length(e1) < squared_edge_length(e2);
+              });
+
+    anti_collapse_edges(edges);
+  }
+
+ private:
+  double squared_eucl_distance(const Point& p1, const Point& p2) const {
+    return Geometry_trait::Squared_distance_d()(p1, p2);
+  }
+
+  void anti_collapse_edges(const std::deque<Edge>& edges) {
+    unsigned pos = 0;
+    for (Edge e : edges) {
+      std::cout << "edge " << pos++ << "/" << edges.size() << "\n";
+      auto eh = filled_complex_.add_edge_without_blockers(e.first, e.second);
+      int is_contractible(is_link_reducible(eh));
+
+      switch (is_contractible) {
+        case 0:
+          stream_ << "alpha=" << std::sqrt(squared_edge_length(e)) << " topological change" << std::endl;
+          break;
+        case 2:
+          stream_ << "alpha=" << std::sqrt(squared_edge_length(e)) << " maybe a topological change" << std::endl;
+          break;
+        default:
+          break;
+      }
+    }
+  }
+
+  // 0 -> not
+  // 1 -> yes
+  // 2 -> maybe
+
+  int is_link_reducible(Edge_handle e) {
+    auto link = filled_complex_.link(e);
+
+    if (link.empty())
+      return 0;
+
+    Edge_contractor<Complex> contractor(link, link.num_vertices() - 1);
+    (void)contractor;
+
+    if (link.num_connected_components() > 1)
+      // one than more CC -> not contractible
+      return 0;
+
+    if (link.num_vertices() == 1)
+      // reduced to one point -> contractible
+      return 1;
+    else
+      // we dont know
+      return 2;
+  }
+
+  double squared_edge_length(Edge_handle e) const {
+    return squared_eucl_distance(input_complex_.point(input_complex_.first_vertex(e)),
+                                 input_complex_.point(input_complex_.second_vertex(e)));
+  }
+
+  double squared_edge_length(Edge e) const {
+    return squared_eucl_distance(input_complex_.point(e.first), input_complex_.point(e.second));
+  }
+};
+
+#endif  // UTILS_CRITICAL_POINTS_H_