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diff --git a/src/Coxeter_triangulation/test/manifold_tracing_test.cpp b/src/Coxeter_triangulation/test/manifold_tracing_test.cpp
new file mode 100644
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+++ b/src/Coxeter_triangulation/test/manifold_tracing_test.cpp
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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):       Siargey Kachanovich
+ *
+ *    Copyright (C) 2019 Inria
+ *
+ *    Modification(s):
+ *      - YYYY/MM Author: Description of the modification
+ */
+
+#define BOOST_TEST_DYN_LINK
+#define BOOST_TEST_MODULE "manifold_tracing"
+#include <boost/test/unit_test.hpp>
+#include <gudhi/Unitary_tests_utils.h>
+
+#include <iostream>
+
+#include <gudhi/Coxeter_triangulation.h>
+#include <gudhi/Functions/Function_Sm_in_Rd.h>
+#include <gudhi/Implicit_manifold_intersection_oracle.h>
+#include <gudhi/Manifold_tracing.h>
+
+using namespace Gudhi::coxeter_triangulation;
+
+BOOST_AUTO_TEST_CASE(manifold_tracing) {
+  // manifold without boundary
+  Function_Sm_in_Rd fun_sph(5.1111, 2);
+  auto oracle = make_oracle(fun_sph);
+  Coxeter_triangulation<> cox_tr(oracle.amb_d());
+  // cox_tr.change_offset(Eigen::VectorXd::Random(oracle.amb_d()));
+  
+  using MT = Manifold_tracing<Coxeter_triangulation<> >;
+  Eigen::VectorXd seed = fun_sph.seed();
+  std::vector<Eigen::VectorXd> seed_points(1, seed);
+  typename MT::Out_simplex_map out_simplex_map;
+  manifold_tracing_algorithm(seed_points, cox_tr, oracle, out_simplex_map);
+
+  for (auto si_pair: out_simplex_map) {
+    BOOST_CHECK ( si_pair.first.dimension() == oracle.function().cod_d() );
+    BOOST_CHECK ( si_pair.second.size() == (long int)oracle.function().amb_d() );
+  }
+  std::cout << "out_simplex_map.size() = " << out_simplex_map.size() << "\n";
+  BOOST_CHECK ( out_simplex_map.size() == 1140 );
+  
+
+  // manifold with boundary
+  Function_Sm_in_Rd fun_boundary(3.0, 2, fun_sph.seed());
+  auto oracle_with_boundary = make_oracle(fun_sph, fun_boundary);
+  typename MT::Out_simplex_map interior_simplex_map, boundary_simplex_map;
+  manifold_tracing_algorithm(seed_points, cox_tr, oracle_with_boundary, interior_simplex_map, boundary_simplex_map);
+  for (auto si_pair: interior_simplex_map) {
+    BOOST_CHECK ( si_pair.first.dimension() == oracle.function().cod_d() );
+    BOOST_CHECK ( si_pair.second.size() == (long int)oracle.function().amb_d() );
+  }
+  std::cout << "interior_simplex_map.size() = " << interior_simplex_map.size() << "\n";
+  BOOST_CHECK ( interior_simplex_map.size() == 96 );
+  for (auto si_pair: boundary_simplex_map) {
+    BOOST_CHECK ( si_pair.first.dimension() == oracle.function().cod_d()+1 );
+    BOOST_CHECK ( si_pair.second.size() == (long int)oracle.function().amb_d() );
+  }
+  std::cout << "boundary_simplex_map.size() = " << boundary_simplex_map.size() << "\n";
+  BOOST_CHECK ( boundary_simplex_map.size() == 55 );
+  
+}