diff --git a/docs/examples/05_PartOnDrop/Input/Edges_ico2562.txt b/docs/examples/05_PartOnDrop/Input/Edges_ico2562.txt
new file mode 100644
index 00000000..28c02f16
--- /dev/null
+++ b/docs/examples/05_PartOnDrop/Input/Edges_ico2562.txt
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diff --git a/docs/examples/05_PartOnDrop/Input/Vertices_ico2562.txt b/docs/examples/05_PartOnDrop/Input/Vertices_ico2562.txt
new file mode 100644
index 00000000..55fb6463
--- /dev/null
+++ b/docs/examples/05_PartOnDrop/Input/Vertices_ico2562.txt
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diff --git a/docs/examples/05_PartOnDrop/Output Example/Output.txt b/docs/examples/05_PartOnDrop/Output Example/Output.txt
new file mode 100644
index 00000000..1552b364
--- /dev/null
+++ b/docs/examples/05_PartOnDrop/Output Example/Output.txt	
@@ -0,0 +1,405 @@
+Mesh
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+ NumFaces  5120
+ NumEdges  7680
+ NumHEdges  15360
+Particles created = 95 Area Fraction =0.23750000000000004
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diff --git a/docs/examples/05_PartOnDrop/Output Example/Particle_on_Sphere_t980000.vtp b/docs/examples/05_PartOnDrop/Output Example/Particle_on_Sphere_t980000.vtp
new file mode 100644
index 00000000..863f3742
--- /dev/null
+++ b/docs/examples/05_PartOnDrop/Output Example/Particle_on_Sphere_t980000.vtp	
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diff --git a/docs/examples/05_PartOnDrop/Output Example/Particle_on_Sphere_t980000_edges.vtp b/docs/examples/05_PartOnDrop/Output Example/Particle_on_Sphere_t980000_edges.vtp
new file mode 100644
index 00000000..c2fcf72a
--- /dev/null
+++ b/docs/examples/05_PartOnDrop/Output Example/Particle_on_Sphere_t980000_edges.vtp	
@@ -0,0 +1,8161 @@
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+        </DataArray>
+      </Lines>
+      <Strips>
+        <DataArray type="Int64" Name="connectivity" format="ascii" RangeMin="0" RangeMax="2561">
+        </DataArray>
+        <DataArray type="Int64" Name="offsets" format="ascii" RangeMin="2" RangeMax="15360">
+        </DataArray>
+      </Strips>
+      <Polys>
+        <DataArray type="Int64" Name="connectivity" format="ascii" RangeMin="0" RangeMax="2561">
+        </DataArray>
+        <DataArray type="Int64" Name="offsets" format="ascii" RangeMin="2" RangeMax="15360">
+        </DataArray>
+      </Polys>
+    </Piece>
+  </PolyData>
+</VTKFile>
diff --git a/docs/examples/05_PartOnDrop/PartOnDrop.py b/docs/examples/05_PartOnDrop/PartOnDrop.py
new file mode 100644
index 00000000..f1709b2b
--- /dev/null
+++ b/docs/examples/05_PartOnDrop/PartOnDrop.py
@@ -0,0 +1,139 @@
+import pymembrane as mb
+import numpy as np
+import random
+
+vertex_file = './Input/Vertices_ico2562.txt'
+faces_file = './Input/Edges_ico2562.txt'
+
+# System
+system = mb.System()
+system.read_mesh_from_files(files={'vertices':vertex_file, 'faces':faces_file})
+
+faces = system.faces
+for face in faces:
+    face.type = 0
+system.setFaces(faces)
+edges = system.edges
+
+rad_particle=0.1
+overl_factor=2
+random.seed(0)  
+tot_hole_vertices=0
+vertices = system.vertices
+
+for vertex in vertices:
+    vertex.type=-1  #Initialize the system with no particles, then add particles in.
+    vertex.mass=-1  #Mass attribute is used to point to edge vertices in a set of vertices covered by a particle. 
+                    #Initialize it at -1.
+
+for vertex in vertices:
+    if random.random()<0.2:    # This factor varies the area fraction of droplet-attached particles. Note, that the 
+                               # generated particle area fraction depends on the random number sequence and will
+                               # slightly vary between runs (provided that the random.seed number is changed each time).
+        overlaps=0
+        for vertex_j in vertices:
+            if vertex_j!=vertex and vertex_j.type!=-1:
+                dist_ij=((vertex.r.x-vertex_j.r.x)**2+(vertex.r.y-vertex_j.r.y)**2+(vertex.r.z-vertex_j.r.z)**2)**0.5;
+                if dist_ij<rad_particle*overl_factor:
+                    overlaps=1
+        if overlaps==0:    #If no overlap with other particles, "vertex" is chosen as a center of a new droplet-attached particle.
+            vertex.type = vertex.id   # The central vertex in a set of vertices covered by a particle has its type value 
+                                      # equal to its id. This "flag" allows the central vertices of each particle to be 
+                                      # distinguished from all other particles.
+            for vertex_j in vertices:
+                if vertex_j!=vertex and vertex_j.type==-1:
+                    dist_ij=((vertex.r.x-vertex_j.r.x)**2+(vertex.r.y-vertex_j.r.y)**2+(vertex.r.z-vertex_j.r.z)**2)**0.5;
+                    if dist_ij<rad_particle:    # vertex_j is covered by the particle centered at "vertex".
+                        vertex_j.type=vertex.id  # The type field of a vertex covered by a particle holds the id of the vertex which is at the center of the relevant particle.     
+            last_bndry_prt=-1                       
+            bndry_part_i=0
+            tot_hole_vertices+=1
+            for vertex_j in vertices:           # This loop is used to specially mark all edge vertices belonging to the same particle.
+                                                # These vertices typically interact with particle-free vertices, so that they are particularly important.
+                if vertex_j!=vertex and vertex_j.type==vertex.id:
+                    he_first=vertex_j._hedge
+                    he=he_first
+                    condition = True
+                    hole_bndry_vertex = False
+                    while condition:
+                        edge_index=system.halfedges[he].edge
+                        v1 = edges[edge_index].i
+                        v2 = edges[edge_index].j
+                        t1 = vertices[v1].type
+                        t2 = vertices[v2].type
+                        he_pair = system.halfedges[he].pair
+                        he = system.halfedges[he_pair].next
+                        condition = (he!=he_first)
+                        if ((t1<0 and t2>=0) or (t2<0 and t1>=0)):
+                            hole_bndry_vertex=True
+                    if hole_bndry_vertex :
+                        bndry_part_i=bndry_part_i+1
+                        if bndry_part_i==1:
+                            vertex.mass=vertex_j.id   # Use .mass attribute to point to "the first" edge vertex of the hole.
+                                                      # Then, each edge vertex points to the next edge vertex, using its .mass attribute.
+                                                      # The last edge vertex has mass=-1 (yet, it's type is equal to vertex.id, so that it is easily
+                                                      # distinguished from either free vertices or vertices covered by other particles.
+                        else:
+                            vertices[last_bndry_prt].mass=vertex_j.id
+                        last_bndry_prt=vertex_j.id
+system.setVertices(vertices)
+print(f"Particles created = {tot_hole_vertices} Area Fraction ={tot_hole_vertices*rad_particle**2/4}")   #Display the actual area fraction of surface-piercing particles.
+
+for edge in edges:
+    edge.type = 0
+
+system.setEdges(edges)
+
+compute = system.compute_mesh()
+
+edge_lengths = compute.edge_lengths()
+avg_edge_length= np.mean(edge_lengths)
+print(f"avg = {np.mean(edge_lengths)} max ={np.max(edge_lengths)} min = {np.min(edge_lengths)}")
+
+evolver = mb.Evolver(system)
+
+parameters = {"k" : {"0": str(2)},"l0": {"0": str(0.06955)},"J": {"0": str(0)},"Ea": {"0": str(0)}}
+
+evolver.add_force("Mesh>Limit", {"lmax": {"0": str(1.8*np.max(edge_lengths))},\
+                                  "lmin": {"0": str(0.7*np.min(edge_lengths))}})
+
+evolver.add_force("Mesh>HarmonicDye", parameters)
+evolver.add_force("Mesh>Bending", {"kappa":{"0":str(0.0001)}})
+
+evolver.add_integrator("Mesh>MonteCarlo>vertex>move", {"T":str(1e-5),"dr": str(0.001),"seed": str(123949)})
+evolver.add_integrator("Mesh>MonteCarlo>edge>flip", {"T":str(3.5e-4),"every step": "1"})
+
+#No global temperature is defined here. Two separate temperatures were defined for the two evolvers.
+#evolver.set_global_temperature(str(1e-5))   
+
+snapshots = 10
+run_steps = 2000
+dump = system.dump() 
+dump.vtk("initial_mesh")
+for snapshot in range(1, snapshots):
+    acceptance = evolver.evolveMC(steps=run_steps)
+    compute = system.compute_mesh()
+    print(compute.energy(evolver)["edges"])
+    dump.vtk(f"Particle_on_Sphere_t{str(snapshot*run_steps)}")
+
+for snapshot in range(11, 50):
+    acceptance = evolver.evolveMC(steps=run_steps)
+    compute = system.compute_mesh()
+    print(compute.energy(evolver)["edges"])
+    dump.vtk(f"Particle_on_Sphere_t{str(snapshot*run_steps)}")
+
+Tinit=3.5e-4
+Tfin=1e-5
+Tstep=1e-5
+Nsteps=round((Tinit-Tfin)/Tstep+1)
+for Tcur_step in range(0,Nsteps):
+    Tcur=Tinit-Tstep*Tcur_step
+    evolver.delete_integrator("Mesh>MonteCarlo>edge>flip")
+    evolver.add_integrator("Mesh>MonteCarlo>edge>flip", {"T":str(Tcur),"every step": "1"})
+    for snapshot in range(151+(Tcur_step-1)*10, 151+Tcur_step*10):
+        acceptance = evolver.evolveMC(steps=run_steps)
+        compute = system.compute_mesh()
+        print(compute.energy(evolver)["edges"])
+        dump.vtk(f"Particle_on_Sphere_t{str(snapshot*run_steps)}")
+
+
diff --git a/docs/examples/06_SurfaceTension/initial_mesh_medium_faces.inp b/docs/examples/06_SurfaceTension/initial_mesh_medium_faces.inp
new file mode 100644
index 00000000..b76507ca
--- /dev/null
+++ b/docs/examples/06_SurfaceTension/initial_mesh_medium_faces.inp
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diff --git a/docs/examples/06_SurfaceTension/initial_mesh_medium_vertices.inp b/docs/examples/06_SurfaceTension/initial_mesh_medium_vertices.inp
new file mode 100644
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diff --git a/docs/examples/06_SurfaceTension/initial_mesh_refined_faces.inp b/docs/examples/06_SurfaceTension/initial_mesh_refined_faces.inp
new file mode 100644
index 00000000..f388ea89
--- /dev/null
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diff --git a/docs/examples/06_SurfaceTension/initial_mesh_refined_vertices.inp b/docs/examples/06_SurfaceTension/initial_mesh_refined_vertices.inp
new file mode 100644
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--- /dev/null
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diff --git a/docs/examples/06_SurfaceTension/initial_mesh_simple_faces.inp b/docs/examples/06_SurfaceTension/initial_mesh_simple_faces.inp
new file mode 100644
index 00000000..85ac74b5
--- /dev/null
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diff --git a/docs/examples/06_SurfaceTension/initial_mesh_simple_vertices.inp b/docs/examples/06_SurfaceTension/initial_mesh_simple_vertices.inp
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diff --git a/docs/examples/06_SurfaceTension/surface_tension.py b/docs/examples/06_SurfaceTension/surface_tension.py
new file mode 100644
index 00000000..58ba710e
--- /dev/null
+++ b/docs/examples/06_SurfaceTension/surface_tension.py
@@ -0,0 +1,98 @@
+import math
+import pymembrane as mb
+import numpy as np
+
+np.finfo(np.dtype("float64"))
+
+
+# Simulation of a droplet of water between two orthogonal cylindrical objects
+# contact angle defines wettability of the solids
+# radius defines cylinder radius relative to droplet radius
+# spacing defines spacing between the two cylinder (if too far from each other, nothing appends)
+#
+# saves mesh in a .ply file every snapshot and end mesh
+# return energy of the system at the end
+def orthogonal_cylinders(vertex_file, face_file, contact_angle=27, run_steps=4000, radius=15, spacing=1, max_snapshots=10):
+    
+    delta_gamma = math.cos(math.radians(contact_angle))
+    # Create a system 
+    box = mb.Box(10,10,10)
+    system = mb.System(box)
+    system.read_mesh_from_files(files={'vertices':vertex_file, 'faces':face_file})
+
+    # Create a dumper to export mesh
+    dump = system.dumper
+
+    # Create the evolver to run simulation
+    evolver = mb.Evolver(system)
+    compute = system.compute
+
+    # Add surface tension
+    evolver.add_force("Mesh>SurfaceTension", {"gamma": {"1": str(1.0), "2":str(delta_gamma)}})
+        
+    position = radius + spacing/2.0
+    
+    # Define how many cylinders in the simulation
+    # Then each is defined by an axis, a point on their axis, and their radius
+    evolver.add_force("Mesh>SubstrateCylinder", {"nb_cylinder": {"0": str(2.0)},
+                                                 "axis": {"0": str(1.0),"1": str(0.0), "2": str(0.0), "3": str(0), "4": str(0.0),"5": str(1.0)},
+                                                 "position": {"0": str(0.0), "1": str(-position), "2": str(0.0), "3": str(0.0), "4": str(position), "5": str(0.0)},
+                                                 "radius": {"0": str(radius), "1": str(radius)}})
+
+    initial_volume = compute.volume()
+    print("volume initial : {}".format(initial_volume))
+    # Add volume constraint (constant volume)
+    evolver.add_constraint("Mesh>Volume", {"V": str(initial_volume), "tol":str(initial_volume/100.0), "max_iter":str(1000)})
+
+    evolver.add_integrator("Mesh>Brownian>vertex>move", {"seed":"202208"})
+    
+    
+    #Note for the velocity brownian integrator we need to set the mass of each vertex
+    vertices = system.vertices
+    for vertex in vertices:
+        vertex.mass = 1.0
+        
+    system.vertices = vertices
+
+    dt = str(1e-3)
+    evolver.set_time_step(dt)
+
+    evolver.evolveMD(steps=1)
+    dump.ply("cyl_t0")
+    print("[start]-------------------------------------------")
+    not_converged = True
+    snapshot = 1
+    previous_contact_area = 0
+    previous_total_area = 0
+    while (not_converged):
+        evolver.evolveMD(steps=run_steps)
+        dump.ply("cyl_t" + str(snapshot))
+        contact_area = compute.area_typed(2)
+        total_area = compute.area()
+        
+        print("[snapshot_{}]-------------------------------------------(max {})".format(snapshot, max_snapshots))
+        if snapshot > max_snapshots or (abs(previous_contact_area - contact_area) < 0.1 and abs(previous_total_area - total_area) < 0.1):
+            not_converged = False
+        snapshot += 1
+        previous_contact_area = contact_area
+        previous_total_area = total_area
+        
+    name_type = "Results/"
+    
+    dump.ply(name_type+"r_{}_a_{}_s_{:.2f}".format(radius, contact_angle, spacing))
+    energy = compute.energy(evolver)['faces']
+    return energy
+
+#####################################################################################
+
+
+# for a faster simulation replace 'medium' by 'simple' (simpler inital mesh)
+# for a more precise simulation replace 'medium' by 'refined' (more complex inital mesh)
+vertex_file = 'initial_mesh_medium_vertices.inp'
+face_file = 'initial_mesh_medium_faces.inp'
+contact_angle = 27
+radius_cyl = 10
+fiber_spacing = 1.0
+
+energy = orthogonal_cylinders(vertex_file=vertex_file, face_file=face_file, contact_angle=contact_angle, radius=radius_cyl, spacing=fiber_spacing)
+print('energy = {:.3f}'.format(energy))
\ No newline at end of file
diff --git a/pymembrane/cppmodule/CMakeLists.txt b/pymembrane/cppmodule/CMakeLists.txt
index d478b1f9..deb1785e 100644
--- a/pymembrane/cppmodule/CMakeLists.txt
+++ b/pymembrane/cppmodule/CMakeLists.txt
@@ -195,6 +195,11 @@ file(GLOB compute_HDRS ${INCLUDE_DIRS}/compute/*.hpp)
 file(GLOB compute_SRCS ${INCLUDE_DIRS}/compute/*.cpp)
 list(APPEND INCLUDE_DIRS_HDRS ${compute_HDRS})
 list(APPEND INCLUDE_DIRS_SRCS ${compute_SRCS})
+## mesh ##
+file(GLOB mesh_HDRS ${INCLUDE_DIRS}/mesh/*.hpp)
+file(GLOB mesh_SRCS ${INCLUDE_DIRS}/mesh/*.cpp)
+list(APPEND INCLUDE_DIRS_HDRS ${mesh_HDRS})
+list(APPEND INCLUDE_DIRS_SRCS ${mesh_SRCS})
 ## potentials ##
 file(GLOB potentials_HDRS ${INCLUDE_DIRS}/potentials/*.hpp)
 file(GLOB potentials_SRCS ${INCLUDE_DIRS}/potentials/*.cpp)
diff --git a/pymembrane/cppmodule/src/compute/computemesh.cpp b/pymembrane/cppmodule/src/compute/computemesh.cpp
index 483d96de..f1386e16 100644
--- a/pymembrane/cppmodule/src/compute/computemesh.cpp
+++ b/pymembrane/cppmodule/src/compute/computemesh.cpp
@@ -290,6 +290,7 @@ real ComputeMesh::meancurvature_vertex(const int &vertex_index)
     int first = he;
     do
     {
+
         // DO SOMETHING WITH THAT EDGE
         int edge_index = _system.halfedges[he].edge;
         if (_system.edges[edge_index].boundary == false)
@@ -500,6 +501,24 @@ real ComputeMesh::compute_mesh_area(void)
     return mesh_area;
 }
 
+real ComputeMesh::compute_area_typed(int type)
+{
+    real mesh_area = 0.0;
+    for (int face_index = 0; face_index < _system.Numfaces; face_index++)
+    {
+        int v1 = _system.faces[face_index].v1;
+        int v2 = _system.faces[face_index].v2;
+        int v3 = _system.faces[face_index].v3;
+        if (_system.vertices[v1].type != type || _system.vertices[v2].type != type || _system.vertices[v3].type != type)
+            continue;
+        
+        mesh_area += pymemb::compute_area_triangle_from_vertex(_system.vertices[v1].r, _system.vertices[v2].r, _system.vertices[v3].r, _system.get_box());
+    }
+
+    return mesh_area;
+}
+
+
 pymemb::vector<pymemb::vector<real>> ComputeMesh::compute_face_metric(void)
 {
     pymemb::vector<pymemb::vector<real>> metrics;
diff --git a/pymembrane/cppmodule/src/compute/computemesh.hpp b/pymembrane/cppmodule/src/compute/computemesh.hpp
index f8ebf17b..1b62a238 100644
--- a/pymembrane/cppmodule/src/compute/computemesh.hpp
+++ b/pymembrane/cppmodule/src/compute/computemesh.hpp
@@ -72,6 +72,9 @@ class ComputeMesh
     /// Computes the total surface area of the mesh.
     real compute_mesh_area(void);
 
+    /// Computes the surface area for a given type of vertex
+    real compute_area_typed(int type=1);
+
     /**
      * @brief Computes the area associated with each vertex in the mesh.
      * @return A vector containing areas for each vertex.
diff --git a/pymembrane/cppmodule/src/compute/pybind_export_compute.hpp b/pymembrane/cppmodule/src/compute/pybind_export_compute.hpp
index 2d7c090f..33c646cd 100644
--- a/pymembrane/cppmodule/src/compute/pybind_export_compute.hpp
+++ b/pymembrane/cppmodule/src/compute/pybind_export_compute.hpp
@@ -36,6 +36,9 @@ void export_ComputeMesh(py::module &m)
         .def("area", &ComputeMesh::compute_mesh_area, R"pbdoc(
             Compute the mesh area.
             )pbdoc")
+        .def("area_typed", &ComputeMesh::compute_area_typed, py::arg("type"), R"pbdoc(
+                Compute the mesh area for a given type.
+                )pbdoc")
         .def("face_metric", &ComputeMesh::compute_face_metric, R"pbdoc(
             Compute the face metric.
             )pbdoc")
diff --git a/pymembrane/cppmodule/src/constraints/constraintvolume.cpp b/pymembrane/cppmodule/src/constraints/constraintvolume.cpp
index d52f9393..eab93b8a 100644
--- a/pymembrane/cppmodule/src/constraints/constraintvolume.cpp
+++ b/pymembrane/cppmodule/src/constraints/constraintvolume.cpp
@@ -59,9 +59,13 @@ void ConstraintVolume::compute_gradient(void)
                 r1 = _system.vertices[v1].r;
                 r2 = _system.vertices[v2].r;
 
+                real angle = pymemb::compute_angle_vertex(r, r1, r2);
+                angle = angle/(M_PI);
+
                 //compute the volume in an atomic operation
                 nt = pymemb::compute_normal_triangle(r, r1, r2);
-                m_value+= vdot(r, nt) / 6.0 / 3.0;
+                m_value+= (vdot(r, nt) / 6.0 )*angle;
+                //old version:  m_value+= vdot(r, nt) / 6.0 / 3.0;
 
                 //compute the volume gradient
                 Nx += (r1.y * r2.z - r2.y * r1.z);
diff --git a/pymembrane/cppmodule/src/dumper/dumper.cpp b/pymembrane/cppmodule/src/dumper/dumper.cpp
index 4e57091c..32818f4b 100644
--- a/pymembrane/cppmodule/src/dumper/dumper.cpp
+++ b/pymembrane/cppmodule/src/dumper/dumper.cpp
@@ -54,3 +54,33 @@ void DumperClass::mesh_txt(const std::string &file_name, const bool &ffaces, con
         }
     }
 }
+
+
+void DumperClass::mesh_inp(const std::string &file_name)
+{
+
+    auto vertices = _system.get_vertices();
+    auto faces = _system.get_faces();
+
+    int Numvertices = vertices.size();
+    int Numfaces = faces.size();
+    std::ofstream vFile(file_name + "_vertices.inp", std::ios::out);
+    if(vFile.is_open())
+    {
+        for(int i=0; i<Numvertices; i++) {
+            vFile << vertices[i].id << " " << vertices[i].r.x << " "
+            << vertices[i].r.y << " " << vertices[i].r.z << " "
+            << vertices[i].type << std::endl;
+        }
+    }
+
+    std::ofstream fFile(file_name + "_faces.inp", std::ios::out);
+    if(fFile.is_open())
+    {
+        for(int i=0; i<Numfaces; i++) {
+            fFile << faces[i].id << " " << faces[i].v1 << " "
+            << faces[i].v2 << " " << faces[i].v3 << " "
+            << 1 << " " << faces[i].type << std::endl;
+        }
+    }
+}
diff --git a/pymembrane/cppmodule/src/dumper/dumper.hpp b/pymembrane/cppmodule/src/dumper/dumper.hpp
index 53eb0f3a..bcfe4124 100644
--- a/pymembrane/cppmodule/src/dumper/dumper.hpp
+++ b/pymembrane/cppmodule/src/dumper/dumper.hpp
@@ -30,6 +30,7 @@ class DumperClass
     }
     void mesh_vtk_periodic(const std::string &file_name);
     void mesh_ply(const std::string &file_name);
+    void mesh_inp(const std::string &file_name);
     void mesh_ply_periodic(const std::string &file_name){}
     
     void mesh_json(const std::string &file_name, const bool &ffaces, const bool &fvertices);
diff --git a/pymembrane/cppmodule/src/dumper/dumper_vis.cpp b/pymembrane/cppmodule/src/dumper/dumper_vis.cpp
index c92cdbc4..dfe4bbe0 100644
--- a/pymembrane/cppmodule/src/dumper/dumper_vis.cpp
+++ b/pymembrane/cppmodule/src/dumper/dumper_vis.cpp
@@ -82,6 +82,7 @@ void DumperClass::mesh_vertices_faces(const std::string &file_name)
     vtkSmartPointer<vtkDoubleArray> vnormal = vtkSmartPointer<vtkDoubleArray>::New();
     vtkSmartPointer<vtkDoubleArray> guassian_curv = vtkSmartPointer<vtkDoubleArray>::New();
     vtkSmartPointer<vtkDoubleArray> mean_curv = vtkSmartPointer<vtkDoubleArray>::New();
+    vtkSmartPointer<vtkDoubleArray> spin = vtkSmartPointer<vtkDoubleArray>::New();
 
     vtkSmartPointer<vtkPolygon> triangle_vtk = vtkSmartPointer<vtkPolygon>::New();
     vtkSmartPointer<vtkIntArray> ids_vtk = vtkSmartPointer<vtkIntArray>::New();
@@ -152,6 +153,9 @@ void DumperClass::mesh_vertices_faces(const std::string &file_name)
     guassian_curv->SetNumberOfComponents(1);
     mean_curv->SetName("MeanCurvature");
     mean_curv->SetNumberOfComponents(1);
+    spin->SetName("spin");
+    spin->SetNumberOfComponents(1);
+    
     //Compute the mean and the gaussian curvature
     auto compute_mesh = _system.get_compute_mesh();
     auto curvatures = _system.compute_mesh.compute_mesh_curvature();
@@ -291,6 +295,7 @@ void DumperClass::mesh_vertices_faces(const std::string &file_name)
         }
         guassian_curv->InsertNextValue(curvatures["gaussian"][i]);
         mean_curv->InsertNextValue(curvatures["mean"][i]);
+        spin->InsertNextValue(vertices[i].spin);
     }
     polydata_vtk->SetPoints(vertices_vtk);
     polydata_vtk->GetPointData()->AddArray(ids_vtk);
@@ -302,6 +307,8 @@ void DumperClass::mesh_vertices_faces(const std::string &file_name)
     polydata_vtk->GetPointData()->AddArray(vnormal);
     polydata_vtk->GetPointData()->AddArray(guassian_curv);
     polydata_vtk->GetPointData()->AddArray(mean_curv);
+    polydata_vtk->GetPointData()->AddArray(spin);
+
     ///USER DATA
     for (auto vtk_user_data : vertex_data_vtk)
         polydata_vtk->GetPointData()->AddArray(vtk_user_data);
@@ -526,6 +533,7 @@ void DumperClass::mesh_vtk_periodic(const std::string &file_name)
     vtkSmartPointer<vtkDoubleArray> vnormal = vtkSmartPointer<vtkDoubleArray>::New();
     vtkSmartPointer<vtkDoubleArray> guassian_curv = vtkSmartPointer<vtkDoubleArray>::New();
     vtkSmartPointer<vtkDoubleArray> mean_curv = vtkSmartPointer<vtkDoubleArray>::New();
+    vtkSmartPointer<vtkDoubleArray> spin = vtkSmartPointer<vtkDoubleArray>::New();
 
     vtkSmartPointer<vtkPolygon> triangle_vtk = vtkSmartPointer<vtkPolygon>::New();
     vtkSmartPointer<vtkIntArray> ids_vtk = vtkSmartPointer<vtkIntArray>::New();
@@ -574,6 +582,8 @@ void DumperClass::mesh_vtk_periodic(const std::string &file_name)
     guassian_curv->SetNumberOfComponents(1);
     mean_curv->SetName("MeanCurvature");
     mean_curv->SetNumberOfComponents(1);
+    spin->SetName("spin");
+    spin->SetNumberOfComponents(1);
     //Compute the mean and the gaussian curvature
     auto compute_mesh = _system.get_compute_mesh();
     auto curvatures = _system.compute_mesh.compute_mesh_curvature();
@@ -681,6 +691,7 @@ void DumperClass::mesh_vtk_periodic(const std::string &file_name)
         vnormal->InsertNextTuple(norm);
         guassian_curv->InsertNextValue(curvatures["gaussian"][i]);
         mean_curv->InsertNextValue(curvatures["mean"][i]);
+        spin->InsertNextValue(vertices[i].spin);
     }
     polydata_vtk->SetPoints(vertices_vtk);
     polydata_vtk->GetPointData()->AddArray(ids_vtk);
@@ -692,6 +703,7 @@ void DumperClass::mesh_vtk_periodic(const std::string &file_name)
     polydata_vtk->GetPointData()->AddArray(vnormal);
     polydata_vtk->GetPointData()->AddArray(guassian_curv);
     polydata_vtk->GetPointData()->AddArray(mean_curv);
+    polydata_vtk->GetPointData()->AddArray(spin);
     // Write the file
     vtkSmartPointer<vtkXMLPolyDataWriter> writer = vtkSmartPointer<vtkXMLPolyDataWriter>::New();
     writer->SetFileName(file_name2.c_str());
diff --git a/pymembrane/cppmodule/src/dumper/pybind_export_dumper.hpp b/pymembrane/cppmodule/src/dumper/pybind_export_dumper.hpp
index 8518f785..779a93b3 100644
--- a/pymembrane/cppmodule/src/dumper/pybind_export_dumper.hpp
+++ b/pymembrane/cppmodule/src/dumper/pybind_export_dumper.hpp
@@ -12,6 +12,7 @@ void export_DumperClass(py::module &m)
         .def("json", &DumperClass::mesh_json, "dump the mesh (vertices and faces) in json format", py::arg("filename"), py::arg("faces")=true, py::arg("vertices")=true)
         .def("ply", &DumperClass::mesh_ply, "dump the mesh (vertices and faces) in ply format", py::arg("filename"))
         .def("txt", &DumperClass::mesh_txt, "dump the mesh (vertices and faces) in text format", py::arg("filename"), py::arg("faces")=true, py::arg("vertices")=true)
+        .def("inp", &DumperClass::mesh_inp, "dump the mesh (vertices and faces) in inp format", py::arg("filename"))
         .def("setvtkLegacyFormat", &DumperClass::setvtkLegacyFormat, "set the vtk legacy format flag")
         
         .def("user_data_vertex", (void (DumperClass::*)(const std::string&, std::vector<real>&)) & DumperClass::user_vertex_data, "dump user data on vertices")
diff --git a/pymembrane/cppmodule/src/evolver/evolverclass.cpp b/pymembrane/cppmodule/src/evolver/evolverclass.cpp
index a2d9f256..5cd23384 100644
--- a/pymembrane/cppmodule/src/evolver/evolverclass.cpp
+++ b/pymembrane/cppmodule/src/evolver/evolverclass.cpp
@@ -12,6 +12,7 @@
 #include "../integrators/montercarlo_swap_vertex.hpp"
 #include "../integrators/montercarlo_swap_edge.hpp"
 #include "../integrators/montercarlo_flip_edge.hpp"
+#include "../integrators/montercarlo_spin_vertex.hpp"
 
 // here we include all the Minimizers
 #include "../minimizer/fire.hpp"
@@ -105,6 +106,11 @@ void EvolverClass::add_integrator(const std::string &name, std::map<std::string,
         mesh_integrator_montecarlo_list[name] = std::make_shared<MonteCarloIntegratorFlipEdge>(_system, mesh_force_list);
         mesh_integrator_montecarlo_list[name]->set_property(parameters);
     }
+    else if (name.compare("Mesh>MonteCarlo>vertex>spin") == 0)
+    {
+        mesh_integrator_montecarlo_list[name] = std::make_shared<MonteCarloIntegratorSpinVertex>(_system, mesh_force_list);
+        mesh_integrator_montecarlo_list[name]->set_property(parameters);
+    }
     else
         py::print(name, " integrator not found");
 }
@@ -160,8 +166,11 @@ void EvolverClass::set_global_temperature(const std::string &value)
 }
 void EvolverClass::evolve_mesh_md(const int &mdsteps)
 {
+    MeshOperations mesh_op(_system);
+
     for (auto step = 0; step < mdsteps; step++)
-    {
+    {   
+        //std::cout << step << "/" << mdsteps << std::endl;
         // Perform the preintegration step, i.e., step before forces and torques are computed
         this->evolve_mesh_prestep();
 
@@ -173,6 +182,10 @@ void EvolverClass::evolve_mesh_md(const int &mdsteps)
 
         // Perform the second step of integration
         this->evolve_mesh_poststep();
+
+        enforce_mesh_constraints();
+        mesh_op.adapt_mesh();
+        mesh_op.refine_mesh_edge_flip();
     }
 }
 
diff --git a/pymembrane/cppmodule/src/evolver/evolverclass.hpp b/pymembrane/cppmodule/src/evolver/evolverclass.hpp
index 564262b3..e88dc453 100644
--- a/pymembrane/cppmodule/src/evolver/evolverclass.hpp
+++ b/pymembrane/cppmodule/src/evolver/evolverclass.hpp
@@ -32,6 +32,7 @@
 namespace py = pybind11;
 
 #include "../system/systemclass.hpp"
+#include "../mesh/meshoperations.hpp"
 #include "../potentials/computeforceclass.hpp"
 #include "../integrators/integratorclass.hpp"
 #include "../integrators/montecarlointegrator.hpp"
@@ -49,6 +50,10 @@ namespace py = pybind11;
 #include "../potentials/potentialLineTension.hpp"
 #include "../potentials/potentialConstantAreaTriangle.hpp"
 #include "../potentials/potentialSubstrate.hpp"
+#include "../potentials/potentialIsing.hpp"
+#include "../potentials/potentialHarmonicDye.hpp"
+#include "../potentials/potentialSurfaceTension.hpp"
+#include "../potentials/potentialSubstrateCylinder.hpp"
 
 
 class EvolverClass
@@ -107,6 +112,26 @@ class EvolverClass
             mesh_force_list[name] = std::make_unique<ComputeVertexSubstrateEnergy>(_system);
             mesh_force_list[name]->set_property(parameters);
         }
+        else if (name.compare("Mesh>Ising") == 0)
+        {
+            mesh_force_list[name] = std::make_unique<ComputeVertexFerromagneticEnergy>(_system);
+            mesh_force_list[name]->set_property(parameters);
+        }
+        else if (name.compare("Mesh>HarmonicDye") == 0)
+        {
+            mesh_force_list[name] = std::make_unique<ComputeVertexHarmonicSpinEnergy>(_system);
+            mesh_force_list[name]->set_property(parameters);
+        }
+        else if (name.compare("Mesh>SurfaceTension") == 0)
+        {
+            mesh_force_list[name] = std::make_unique<ComputeVertexSurfaceTension>(_system);
+            mesh_force_list[name]->set_property(parameters);
+        }
+        else if (name.compare("Mesh>SubstrateCylinder") == 0)
+        {
+            mesh_force_list[name] = std::make_unique<ComputeVertexSubstrateCylinderEnergy>(_system);
+            mesh_force_list[name]->set_property(parameters);
+        }
         else
             py::print(name, " potential not found");
 
@@ -206,8 +231,11 @@ class EvolverClass
     std::map<std::string, std::map<std::string, std::string>> get_integrator_info(void)
     {
         std::map<std::string, std::map<std::string, std::string>> integrators_info;
-        //for (const auto &integrator : mesh_integrator_list)
-        //   integrators_info[integrator.first] = integrator.second->get_info();
+        for (const auto &integrator : mesh_integrator_list)
+           integrators_info[integrator.first] = integrator.second->get_info();
+
+        for (const auto &integrator : mesh_integrator_montecarlo_list)
+           integrators_info[integrator.first] = integrator.second->get_info();
 
         return integrators_info;
     }
diff --git a/pymembrane/cppmodule/src/evolver/pybind_export_evolver.hpp b/pymembrane/cppmodule/src/evolver/pybind_export_evolver.hpp
index 2b0fc945..660470f4 100644
--- a/pymembrane/cppmodule/src/evolver/pybind_export_evolver.hpp
+++ b/pymembrane/cppmodule/src/evolver/pybind_export_evolver.hpp
@@ -68,6 +68,7 @@ void export_EvolverClass(py::module &m)
         .def("set", &EvolverClass::set_property<std::map<std::string, std::string>>, "set/modify properties for integrartors/forces/minimizers/contraints")
         //common
         .def("get_force_info", &EvolverClass::get_force_info, "get information about potentials and integrators")
+        .def("get_integrator_info", &EvolverClass::get_integrator_info, "get information about integrators and integrators")
         .def("get_minimizer_info", &EvolverClass::get_minimizer_info, "get information about minimizer")
         ;
 }
diff --git a/pymembrane/cppmodule/src/integrators/integrator_brownian_vertex.hpp b/pymembrane/cppmodule/src/integrators/integrator_brownian_vertex.hpp
index d704ccaa..c8a9c7b8 100755
--- a/pymembrane/cppmodule/src/integrators/integrator_brownian_vertex.hpp
+++ b/pymembrane/cppmodule/src/integrators/integrator_brownian_vertex.hpp
@@ -1,30 +1,29 @@
 /************************************************************************************
-* MIT License                                                                       *
-*                                                                                   *
-* Copyright (c) 2023 Dr. Daniel Alejandro Matoz Fernandez                           *
-*               fdamatoz@gmail.com                                                  *
-* Permission is hereby granted, free of charge, to any person obtaining a copy      *
-* of this software and associated documentation files (the "Software"), to deal     *
-* in the Software without restriction, including without limitation the rights      *
-* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell         *
-* copies of the Software, and to permit persons to whom the Software is             *
-* furnished to do so, subject to the following conditions:                          *
-*                                                                                   *
-* The above copyright notice and this permission notice shall be included in all    *
-* copies or substantial portions of the Software.                                   *
-*                                                                                   *
-* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR        *
-* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,          *
-* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE       *
-* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER            *
-* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,     *
-* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE     *
-* SOFTWARE.                                                                         *
-*************************************************************************************/
+ * MIT License                                                                       *
+ *                                                                                   *
+ * Copyright (c) 2023 Dr. Daniel Alejandro Matoz Fernandez                           *
+ *               fdamatoz@gmail.com                                                  *
+ * Permission is hereby granted, free of charge, to any person obtaining a copy      *
+ * of this software and associated documentation files (the "Software"), to deal     *
+ * in the Software without restriction, including without limitation the rights      *
+ * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell         *
+ * copies of the Software, and to permit persons to whom the Software is             *
+ * furnished to do so, subject to the following conditions:                          *
+ *                                                                                   *
+ * The above copyright notice and this permission notice shall be included in all    *
+ * copies or substantial portions of the Software.                                   *
+ *                                                                                   *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR        *
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,          *
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE       *
+ * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER            *
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,     *
+ * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE     *
+ * SOFTWARE.                                                                         *
+ *************************************************************************************/
 #ifndef __integrator_brownian_vertex__hpp__
 #define __integrator_brownian_vertex__hpp__
 
-
 #include <iostream>
 
 #include "integratorclass.hpp"
@@ -32,7 +31,7 @@
 
 /**
  * @class IntegratorBrownianMeshVertex
- * @brief Integrator Brownian class implements Brownian dynamics for the vertices position. 
+ * @brief Integrator Brownian class implements Brownian dynamics for the vertices position.
  */
 class IntegratorBrownianMeshVertex : public IntegratorClass
 {
@@ -40,8 +39,8 @@ class IntegratorBrownianMeshVertex : public IntegratorClass
   /** @brief VertexIntegrator Constructor */
   IntegratorBrownianMeshVertex(SystemClass &system) : IntegratorClass(system)
   {
-    name = "brownian";
-    type = "vertex";
+    m_name = "brownian";
+    m_type = "vertex";
     this->set_default_properties();
   }
   /** @brief destructor */
@@ -53,7 +52,7 @@ class IntegratorBrownianMeshVertex : public IntegratorClass
     m_mu = 1.0 / m_gamma;
     this->set_temperature(0.0);
     this->set_time_step(5e-3);
-    m_seed = 123456; ///default value
+    m_seed = 123456; /// default value
     m_rng = std::make_unique<RNG>(m_seed);
     this->update_temperature_parameters();
     this->update_time_step_parameters();
@@ -95,7 +94,16 @@ class IntegratorBrownianMeshVertex : public IntegratorClass
         print_warning_property_name(item.first);
     }
   }
-
+  std::map<std::string, std::string> get_info(void) override
+  {
+    std::map<std::string, std::string> value;
+    value["name"] = m_name;
+    value["type"] = m_type;
+    value["T"] = util::to_string(this->get_temperature());
+    value["dt"] = util::to_string(this->get_time_step());
+    value["m_gamma"] = util::to_string(this->m_gamma);
+    return value;
+  }
   /**  @brief Propagate system for a time step */
   void prestep(void) override {}
 
@@ -104,10 +112,9 @@ class IntegratorBrownianMeshVertex : public IntegratorClass
 private:
   real m_gamma;        //!< Friction coefficient
   real m_mu;           //!< Mobility (1/gamma)
-  real m_B, m_sqrt_dt;   //!< useful quantities
+  real m_B, m_sqrt_dt; //!< useful quantities
   unsigned int m_seed; //!< random number seed;
-  RNG_ptr m_rng;           //!< Random number generator
+  RNG_ptr m_rng;       //!< Random number generator
 };
 
 #endif
-
diff --git a/pymembrane/cppmodule/src/integrators/integrator_verlet_vertex.hpp b/pymembrane/cppmodule/src/integrators/integrator_verlet_vertex.hpp
index f660197f..897277f9 100644
--- a/pymembrane/cppmodule/src/integrators/integrator_verlet_vertex.hpp
+++ b/pymembrane/cppmodule/src/integrators/integrator_verlet_vertex.hpp
@@ -30,8 +30,8 @@
 
 /**
  * @class IntegratorVelocityVerletMeshVertex
- * @brief Integrator IntegratorVelocityVerletMeshVertex class implements 
- * the Velocity Verlet dynamics for the vertices position. 
+ * @brief Integrator IntegratorVelocityVerletMeshVertex class implements
+ * the Velocity Verlet dynamics for the vertices position.
  */
 class IntegratorVelocityVerletMeshVertex : public IntegratorClass
 {
@@ -39,8 +39,8 @@ class IntegratorVelocityVerletMeshVertex : public IntegratorClass
     /** @brief VertexIntegrator Constructor */
     IntegratorVelocityVerletMeshVertex(SystemClass &system) : IntegratorClass(system)
     {
-        name = "brownian";
-        type = "vertex";
+        m_name = "brownian";
+        m_type = "vertex";
         this->set_default_properties();
     }
     /** @brief destructor */
@@ -84,15 +84,25 @@ class IntegratorVelocityVerletMeshVertex : public IntegratorClass
                 print_warning_property_name(item.first);
         }
     }
-
+    std::map<std::string, std::string> get_info(void) override
+    {
+        std::map<std::string, std::string> value;
+        value["name"] = m_name;
+        value["type"] = m_type;
+        value["T"] = util::to_string(this->get_temperature());
+        value["dt"] = util::to_string(this->get_time_step());
+        value["m_has_limit"] = util::to_string(this->m_has_limit);
+        value["m_limit_val"] = util::to_string(this->m_limit_val);
+        return value;
+    }
     /**  @brief Propagate system for a time step */
     void prestep(void) override;
 
     void poststep(void) override;
 
 private:
-    real m_limit_val;    //!< Maximum vertex mobility (1/gamma)
-    bool m_has_limit;    //!< set the limit on/off
+    real m_limit_val; //!< Maximum vertex mobility (1/gamma)
+    bool m_has_limit; //!< set the limit on/off
 };
 
 #endif
diff --git a/pymembrane/cppmodule/src/integrators/integratorclass.hpp b/pymembrane/cppmodule/src/integrators/integratorclass.hpp
index b6f69f4c..5252369e 100755
--- a/pymembrane/cppmodule/src/integrators/integratorclass.hpp
+++ b/pymembrane/cppmodule/src/integrators/integratorclass.hpp
@@ -1,26 +1,26 @@
 /************************************************************************************
-* MIT License                                                                       *
-*                                                                                   *
-* Copyright (c) 2023 Dr. Daniel Alejandro Matoz Fernandez                           *
-*               fdamatoz@gmail.com                                                  *
-* Permission is hereby granted, free of charge, to any person obtaining a copy      *
-* of this software and associated documentation files (the "Software"), to deal     *
-* in the Software without restriction, including without limitation the rights      *
-* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell         *
-* copies of the Software, and to permit persons to whom the Software is             *
-* furnished to do so, subject to the following conditions:                          *
-*                                                                                   *
-* The above copyright notice and this permission notice shall be included in all    *
-* copies or substantial portions of the Software.                                   *
-*                                                                                   *
-* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR        *
-* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,          *
-* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE       *
-* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER            *
-* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,     *
-* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE     *
-* SOFTWARE.                                                                         *
-*************************************************************************************/
+ * MIT License                                                                       *
+ *                                                                                   *
+ * Copyright (c) 2023 Dr. Daniel Alejandro Matoz Fernandez                           *
+ *               fdamatoz@gmail.com                                                  *
+ * Permission is hereby granted, free of charge, to any person obtaining a copy      *
+ * of this software and associated documentation files (the "Software"), to deal     *
+ * in the Software without restriction, including without limitation the rights      *
+ * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell         *
+ * copies of the Software, and to permit persons to whom the Software is             *
+ * furnished to do so, subject to the following conditions:                          *
+ *                                                                                   *
+ * The above copyright notice and this permission notice shall be included in all    *
+ * copies or substantial portions of the Software.                                   *
+ *                                                                                   *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR        *
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,          *
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE       *
+ * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER            *
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,     *
+ * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE     *
+ * SOFTWARE.                                                                         *
+ *************************************************************************************/
 #ifndef __integratorclass__hpp__
 #define __integratorclass__hpp__
 
@@ -34,107 +34,110 @@
 #include <pybind11/pybind11.h>
 namespace py = pybind11;
 
-
 /**
  * @class IntegratorClass
  * @brief Abstract class for is the base class for all integrators
- * 
+ *
  */
 class IntegratorClass
 {
 public:
-  /**
-   * @brief IntegratorClass Constructor
-   * 
-   * @param potentials pointer to the loaded potentials
-   * @param param pointer to the integrator parameters
-   */
-  IntegratorClass(SystemClass &system) : _system(system)
-  {
-  }
-  /**
-     * @brief IntegratorClass Destructor
-     */
-  virtual ~IntegratorClass()
-  {
-  }
-  /**
-     * @brief abstract pre step integrator function
-     * @param void 
-     */
-  virtual void prestep(void) = 0;
-  /**
-     * @brief abstract pre step integrator function
-     * @param void 
-     */
-  virtual void poststep(void) = 0;
-  /**
-     * @brief set the integration temperature
-     * @param temperature
-     */
-  void set_temperature(const real &_T)
-  {
-    T = fabs(_T);
-    update_temperature_parameters();
-  }
-  /**
-   * @brief update the parameters that depend on the temperature
-   * @return void 
-   */
-  virtual void update_temperature_parameters() {}
+   /**
+    * @brief IntegratorClass Constructor
+    *
+    * @param potentials pointer to the loaded potentials
+    * @param param pointer to the integrator parameters
+    */
+   IntegratorClass(SystemClass &system) : _system(system)
+   {
+   }
+   /**
+    * @brief IntegratorClass Destructor
+    */
+   virtual ~IntegratorClass()
+   {
+   }
+   /**
+    * @brief abstract pre step integrator function
+    * @param void
+    */
+   virtual void prestep(void) = 0;
+   /**
+    * @brief abstract pre step integrator function
+    * @param void
+    */
+   virtual void poststep(void) = 0;
+   /**
+    * @brief set the integration temperature
+    * @param temperature
+    */
+   void set_temperature(const real &_T)
+   {
+      T = fabs(_T);
+      update_temperature_parameters();
+   }
+   /**
+    * @brief update the parameters that depend on the temperature
+    * @return void
+    */
+   virtual void update_temperature_parameters() {}
+
+   /**
+    * @brief Get the temperature for the integrator object
+    * @return real
+    */
+   real get_temperature(void) const { return T; }
+   /**
+    * @brief set the integration temperature
+    * @param temperature
+    */
+   virtual void set_time_step(const real &_dt)
+   {
+      dt = fabs(_dt);
+      update_time_step_parameters();
+   }
+   /**
+    * @brief update the parameters that depend on the time step
+    * @return void
+    */
+   virtual void update_time_step_parameters() {}
+   /**
+    * @brief Get the time step for the integrator object
+    * @return real
+    */
+   real get_time_step(void) const { return dt; }
+   /**
+    * @brief Get the name object
+    * @return std::string
+    */
+   std::string get_name(void) { return m_name; }
+   /**
+    * @brief Get the type object
+    * @return std::string
+    */
+   std::string get_type(void) { return m_type; }
 
-  /**
-     * @brief Get the temperature for the integrator object
-     * @return real 
-     */
-  real get_temperature(void) const { return T; }
-  /**
-     * @brief set the integration temperature
-     * @param temperature
-     */
-  virtual void set_time_step(const real &_dt)
-  {
-    dt = fabs(_dt);
-    update_time_step_parameters();
-  }
-  /**
-   * @brief update the parameters that depend on the time step
-   * @return void 
-   */
-  virtual void update_time_step_parameters() {}
-  /**
-     * @brief Get the time step for the integrator object
-     * @return real 
-     */
-  real get_time_step(void) const { return dt; }
-  /**
-     * @brief Get the name object
-     * @return std::string 
-     */
-  std::string get_name(void) { return name; }
-  /**
-     * @brief Get the type object
-     * @return std::string 
-     */
-  std::string get_type(void) { return type; }
+   /**
+    * @brief Get the type object
+    * @return std::string
+    */
+   virtual std::map<std::string, std::string> get_info(void) = 0;
 
-  virtual void set_default_properties(void) = 0;
-  virtual void set_property(std::map<std::string, std::map<std::pair<std::string, std::string>, std::string>> &value_map) { this->print_warning_calling("map<string, map<pair<string, string>, string>> "); };
-  virtual void set_property(std::map<std::string, std::map<std::string, std::string>> &value_map) { this->print_warning_calling("map<string, map<string, string>>"); };
-  virtual void set_property(std::map<std::string, std::string> &value_map) { this->print_warning_calling("std::map<std::string, std::string>"); }
-  void print_warning_calling(const std::string &message) { py::print("integrator ", name, " cannot be called with ", message); }
-  void print_warning_property_name(const std::string &message) { py::print("parameter ", message, " is not part of ", name, "-", type, " integrator"); }
+   virtual void set_default_properties(void) = 0;
+   virtual void set_property(std::map<std::string, std::map<std::pair<std::string, std::string>, std::string>> &value_map) { this->print_warning_calling("map<string, map<pair<string, string>, string>> "); };
+   virtual void set_property(std::map<std::string, std::map<std::string, std::string>> &value_map) { this->print_warning_calling("map<string, map<string, string>>"); };
+   virtual void set_property(std::map<std::string, std::string> &value_map) { this->print_warning_calling("std::map<std::string, std::string>"); }
+   void print_warning_calling(const std::string &message) { py::print("integrator ", m_name, " cannot be called with ", message); }
+   void print_warning_property_name(const std::string &message) { py::print("parameter ", message, " is not part of ", m_name, "-", m_type, " integrator"); }
 
 protected:
-  SystemClass &_system; //!< reference to system class where the box and particles are stored
-  std::string name;     //!< Integrator name
-  std::string type;     //!< integrator type, active, torque, etc
-  real T;               //!< Temperature of the system
-  real dt;              //!< Time Step
+   SystemClass &_system; //!< reference to system class where the box and particles are stored
+   std::string m_name;   //!< Integrator name
+   std::string m_type;   //!< integrator type, active, torque, etc
+   real T;               //!< Temperature of the system
+   real dt;              //!< Time Step
 };
 
 typedef std::shared_ptr<IntegratorClass> IntegratorClass_ptr;
 
 #endif
-
-
diff --git a/pymembrane/cppmodule/src/integrators/montecarlointegrator.hpp b/pymembrane/cppmodule/src/integrators/montecarlointegrator.hpp
index d1c36601..59e97700 100755
--- a/pymembrane/cppmodule/src/integrators/montecarlointegrator.hpp
+++ b/pymembrane/cppmodule/src/integrators/montecarlointegrator.hpp
@@ -83,12 +83,16 @@ class MonteCarloIntegrator
      * @brief Get the name object
      * @return std::string 
      */
-  std::string get_name(void) { return name; }
+  std::string get_name(void) { return m_name; }
   /**
      * @brief Get the type object
      * @return std::string 
      */
-  std::string get_type(void) { return type; }
+  std::string get_type(void) { return m_type; }
+
+
+  virtual std::map<std::string, std::string> get_info(void) = 0;
+
   /**
      * @brief get name
      * @param temperature
@@ -106,14 +110,14 @@ class MonteCarloIntegrator
   virtual void set_property(std::map<std::string, std::map<std::pair<std::string, std::string>, std::string>> &value_map) { this->print_warning_calling("map<string, map<pair<string, string>, string>> "); };
   virtual void set_property(std::map<std::string, std::map<std::string, std::string>> &value_map) { this->print_warning_calling("map<string, map<string, string>>"); };
   virtual void set_property(std::map<std::string, std::string> &value_map) { this->print_warning_calling("std::map<std::string, std::string>"); }
-  void print_warning_calling(const std::string &message) { py::print("integrator ", name, " cannot be called with ", message); }
-  void print_warning_property_name(const std::string &message) { py::print("parameter ", message, " is not part of ", name, "-", type, " integrator"); }
+  void print_warning_calling(const std::string &message) { py::print("integrator ", m_name, " cannot be called with ", message); }
+  void print_warning_property_name(const std::string &message) { py::print("parameter ", message, " is not part of ", m_name, "-", m_type, " integrator"); }
 
 protected:
   SystemClass &_system;       //!< reference to system class where the box and particles are stored
   VertexCompute &_potentials; //!< Compute potential pointer
-  std::string name;           //!< Integrator name
-  std::string type;           //!< integrator type, active, torque, etc
+  std::string m_name;           //!< Integrator name
+  std::string m_type;           //!< integrator type, active, torque, etc
   real T;                     //!< Temperature of the system
   int integrate_every;
   double minimum_energy;    
diff --git a/pymembrane/cppmodule/src/integrators/montercarlo_flip_edge.cpp b/pymembrane/cppmodule/src/integrators/montercarlo_flip_edge.cpp
index 1c2fa29a..03f8d5f4 100644
--- a/pymembrane/cppmodule/src/integrators/montercarlo_flip_edge.cpp
+++ b/pymembrane/cppmodule/src/integrators/montercarlo_flip_edge.cpp
@@ -1,27 +1,205 @@
 #include "montercarlo_flip_edge.hpp"
-#include "../mesh/edge_flip.hpp"
 
 bool MonteCarloIntegratorFlipEdge::edge_flip(int flip_edge_index, bool flip_face_up)
 {
-    auto can_flip = pymemb::EdgeFlip_lambda(flip_edge_index,
-                               flip_face_up,
-                               &_system.faces[0],
-                              &_system.vertices[0],
-                               &_system.edges[0],
-                               &_system.halfedges[0],
-                               _system.get_box());
-    return can_flip;
+    int v0 = _system.edges[flip_edge_index].v0;
+    int v1 = _system.edges[flip_edge_index].v1;
+    int v2 = _system.edges[flip_edge_index].v2;
+    int v3 = _system.edges[flip_edge_index].v3;
+
+    int face_k = _system.edges[flip_edge_index].face_k;
+    int face_l = _system.edges[flip_edge_index].face_l;
+
+    //(0) Check that the edge is not a boundary edge
+    if (_system.edges[flip_edge_index].boundary == true)
+        return false;
+
+    //(1) first we need to check if we don't destroy the triangulation by flipping the edge.
+    // This can be done by checking that the connectivity of the edges v0, v2 of the involve edge is
+    // strictly larger than 3.
+    int he, first, he_pair, he_pair_next;
+    int n_neighbors_v0 = 0, n_neighbors_v2 = 0;
+
+    //check v0
+    he = _system.vertices[v0]._hedge;
+    first = he;
+
+    do
+    {
+        n_neighbors_v0++;
+        // MOVE TO THE NEXT FACE
+        he_pair = _system.halfedges[he].pair;
+        he_pair_next = _system.halfedges[he_pair].next;
+        he = he_pair_next;
+    } while ((he != first));
+
+    //check v2
+    he = _system.vertices[v2]._hedge;
+    first = he;
+
+    do
+    {
+        n_neighbors_v2++;
+        // MOVE TO THE NEXT FACE
+        he_pair = _system.halfedges[he].pair;
+        he_pair_next = _system.halfedges[he_pair].next;
+        he = he_pair_next;
+    } while ((he != first));
+
+    if (n_neighbors_v0 <= 4 || n_neighbors_v2 <= 4)
+        return false;
+
+    ///(2) Check that the vertices v0 and v2 do not take part of an obtuse triangles.
+    // If that happens then an edge flip might destroy the triangulation.
+    // If the sum of angles next to each of the two sides of the edge is >= PI
+    // the flip would break triangulation. We disallow such a move.
+    // For example, in this case edge cannot be flipped
+    //          1:X
+    //          * *
+    //        *  *
+    //      *   * 
+    //   0:X---X:2 <-- This angle is < PI and the edge cannot be flipped! 
+    //      *   *
+    //       *  *
+    //         * *
+    //          3:X
+    real3 r02, r01, r03;
+    vsub(r02, _system.vertices[v2].r, _system.vertices[v0].r);
+    vsub(r03, _system.vertices[v3].r, _system.vertices[v0].r);
+    vsub(r01, _system.vertices[v1].r, _system.vertices[v0].r);
+    real r02_norm = sqrt(vdot(r02, r02));
+    real r03_norm = sqrt(vdot(r03, r03));
+    real r01_norm = sqrt(vdot(r01, r01));
+    real angle_r01_r02 = acos(vdot(r01, r02) / (r01_norm * r02_norm));
+    real angle_r03_r02 = acos(vdot(r03, r02) / (r03_norm * r02_norm));
+    if ((angle_r01_r02 + angle_r03_r02) >= defPI)
+        return false;
+
+    real3 r20, r21, r23;
+    vsub(r20, _system.vertices[v0].r, _system.vertices[v2].r);
+    vsub(r23, _system.vertices[v3].r, _system.vertices[v2].r);
+    vsub(r21, _system.vertices[v1].r, _system.vertices[v2].r);
+    real r23_norm = sqrt(vdot(r23, r23));
+    real r21_norm = sqrt(vdot(r21, r21));
+    real angle_r21_r20 = acos(vdot(r21, r20) / (r21_norm * r02_norm));
+    real angle_r23_r20 = acos(vdot(r23, r20) / (r23_norm * r02_norm));
+    if ((angle_r21_r20 + angle_r23_r20) >= defPI)
+        return false;
+
+    //update the halfedges
+    int he_vec[6]; //he01, he12, he20, he02, he23, he30;
+    int he_edge = _system.edges[flip_edge_index]._hedge;
+    if (_system.halfedges[he_edge].vert_from == v0)
+    {
+        he_vec[3] = he_edge;                           //he02
+        he_vec[2] = _system.halfedges[he_vec[3]].pair; //he20
+    }
+    else
+    {
+        he_vec[2] = he_edge;                           //he20
+        he_vec[3] = _system.halfedges[he_vec[2]].pair; //he02
+    }
+    he_vec[0] = _system.halfedges[he_vec[2]].next; //he01
+    he_vec[1] = _system.halfedges[he_vec[2]].prev; //he12
+    he_vec[4] = _system.halfedges[he_vec[3]].next; //he23
+    he_vec[5] = _system.halfedges[he_vec[3]].prev; //he30
+
+    //deal with the from, to vertices in the "new" flip edge
+    _system.halfedges[he_vec[2]].vert_from = v3;
+    _system.halfedges[he_vec[2]].vert_to = v1;
+    _system.halfedges[he_vec[3]].vert_from = v1;
+    _system.halfedges[he_vec[3]].vert_to = v3;
+
+    //flip face: this stage is crucial if we want to make the faces diffuse
+    int new_face_k = face_k;
+    int new_face_l = face_l;
+    if (flip_face_up == false) //counter-clock wise
+    {
+        new_face_k = face_l;
+        new_face_l = face_k;
+    }
+    //deal with the references inside of the halfedges
+    //he12 > h23 > h20
+    _system.halfedges[he_vec[1]].next = he_vec[4];
+    _system.halfedges[he_vec[1]].prev = he_vec[2];
+    _system.halfedges[he_vec[4]].next = he_vec[2];
+    _system.halfedges[he_vec[4]].prev = he_vec[1];
+    _system.halfedges[he_vec[2]].next = he_vec[1];
+    _system.halfedges[he_vec[2]].prev = he_vec[4];
+    //faces
+    _system.halfedges[he_vec[1]].face = new_face_k;
+    _system.halfedges[he_vec[4]].face = new_face_k;
+    _system.halfedges[he_vec[2]].face = new_face_k;
+
+    //he01 > h02 > h30
+    _system.halfedges[he_vec[0]].next = he_vec[3];
+    _system.halfedges[he_vec[0]].prev = he_vec[5];
+    _system.halfedges[he_vec[3]].next = he_vec[5];
+    _system.halfedges[he_vec[3]].prev = he_vec[0];
+    _system.halfedges[he_vec[5]].next = he_vec[0];
+    _system.halfedges[he_vec[5]].prev = he_vec[3];
+    //faces
+    _system.halfedges[he_vec[5]].face = new_face_l;
+    _system.halfedges[he_vec[0]].face = new_face_l;
+    _system.halfedges[he_vec[3]].face = new_face_l;
+
+    //deal with the faces and references to the halfedges
+    //face_k
+    _system.faces[new_face_k].v1 = v1;
+    _system.faces[new_face_k].v2 = v2;
+    _system.faces[new_face_k].v3 = v3;
+    _system.faces[new_face_k]._hedge = he_vec[2];
+    //face_l
+    _system.faces[new_face_l].v1 = v3;
+    _system.faces[new_face_l].v2 = v0;
+    _system.faces[new_face_l].v3 = v1;
+    _system.faces[new_face_l]._hedge = he_vec[3];
+
+    //deal with the halfedge references to the vertices
+    if (_system.vertices[v0]._hedge == he_vec[3] /*he02*/)
+        _system.vertices[v0]._hedge = he_vec[0]; /*h01*/
+    if (_system.vertices[v2]._hedge == he_vec[2] /*he20*/)
+        _system.vertices[v2]._hedge = he_vec[4]; /*h23*/
+
+    //deal with the i,j,v0,v1,v2,v3 in the edge list
+    for (auto he_index : he_vec)
+    {
+        HE_HalfEdgeProp he = _system.halfedges[he_index];
+        HE_HalfEdgeProp he_pair = _system.halfedges[_system.halfedges[he_index].pair];
+        int edge_index = he.edge;
+        _system.edges[edge_index].face_k = he.face;      //!< index to one of the faces shared by this edge -1 if is outer face
+        _system.edges[edge_index].face_l = he_pair.face; //!< index to one of the faces shared by this edge -1 if is outer face
+        _system.edges[edge_index].v0 = he.vert_to;
+        _system.edges[edge_index].v2 = he.vert_from;
+        _system.edges[edge_index].j = he.vert_to;
+        _system.edges[edge_index].i = he.vert_from;
+        int he_next = he.next;
+        _system.edges[edge_index].v1 = _system.halfedges[he_next].vert_to;
+        int he_index_pair_next = he_pair.next;
+        _system.edges[edge_index].v3 = _system.halfedges[he_index_pair_next].vert_to;
+    }
+    return true;
 }
 
 int MonteCarloIntegratorFlipEdge::integrate(void)
 {
     int accepted_moves = 0;
+    // std::copy(freezed_edge.begin(), freezed_edge.end(), std::ostream_iterator<bool>(std::cout, ","));
     for (int edge_index = 0; edge_index < _system.Numedges; edge_index++)
+    // for (int ii = 0; ii < 10; ii++)
     {
-        if (freezed_edge[_system.edges[edge_index].type] == false)
+        // int edge_index = _system.Numedges * m_rng->drnd();
+        // std::cout<<"flip "<<edge_index<<std::endl;
+
+		int v0t=_system.vertices[_system.edges[edge_index].v0].type;
+		int v1t=_system.vertices[_system.edges[edge_index].v1].type;
+		int v2t=_system.vertices[_system.edges[edge_index].v2].type;
+		int v3t=_system.vertices[_system.edges[edge_index].v3].type;
+		
+		//PARTICLE-OCCUPIED VERTICES DO NOT PARTICIPATE IN FLIPPING
+        if ((freezed_edge[_system.edges[edge_index].type] == false) && (v0t==-1) && (v1t==-1) && (v2t==-1) && (v3t==-1))
         {
             double delE = -this->ComputeEnergyFromEdge(edge_index);
-            //decide of the flip is possible
             if (this->edge_flip(edge_index, true) == true)
             {
                 delE+=this->ComputeEnergyFromEdge(edge_index);
@@ -32,10 +210,11 @@ int MonteCarloIntegratorFlipEdge::integrate(void)
                     {
                         this->edge_flip(edge_index, true);
                         accepted_moves--;
-                    }
+                    } 
                 }
             }
          }
+
     }
     return (accepted_moves);
 }
diff --git a/pymembrane/cppmodule/src/integrators/montercarlo_flip_edge.hpp b/pymembrane/cppmodule/src/integrators/montercarlo_flip_edge.hpp
index 9a720624..f9993de6 100644
--- a/pymembrane/cppmodule/src/integrators/montercarlo_flip_edge.hpp
+++ b/pymembrane/cppmodule/src/integrators/montercarlo_flip_edge.hpp
@@ -29,8 +29,8 @@ class MonteCarloIntegratorFlipEdge : public MonteCarloIntegrator
 public:
     MonteCarloIntegratorFlipEdge(SystemClass &system, VertexCompute &potentials) : MonteCarloIntegrator(system, potentials)
     {
-        name = "edge flip";
-        type = "monte carlo";
+        m_name = "edge flip";
+        m_type = "monte carlo";
         this->set_default_properties();
     }
     ~MonteCarloIntegratorFlipEdge() {}
@@ -80,12 +80,18 @@ class MonteCarloIntegratorFlipEdge : public MonteCarloIntegrator
             this->print_warning_property_name(item.first);
         }
     }
-
+    std::map<std::string, std::string> get_info(void) override
+    {
+        std::map<std::string, std::string> value;
+        value["name"] = m_name;
+        value["type"] = m_type;
+        value["T"] = util::to_string(this->get_temperature());
+        return value;
+    }
     bool edge_flip(int, bool);
     int integrate(void) override;
 
 private:
-    double m_dx, m_dy, m_dz;
     unsigned int m_seed;
     RNG_ptr m_rng;
     pymemb::vector<bool> freezed_edge;
diff --git a/pymembrane/cppmodule/src/integrators/montercarlo_spin_vertex.cpp b/pymembrane/cppmodule/src/integrators/montercarlo_spin_vertex.cpp
new file mode 100644
index 00000000..e68dfb11
--- /dev/null
+++ b/pymembrane/cppmodule/src/integrators/montercarlo_spin_vertex.cpp
@@ -0,0 +1,33 @@
+#include "montercarlo_spin_vertex.hpp"
+
+
+int MonteCarloIntegratorSpinVertex::integrate(void)
+{
+    int accepted_moves = 0;
+	int sum_mag=0;
+	int vertex_index;
+    for(int vertex_step = 0; vertex_step<_system.Numvertices; vertex_step++)
+    {
+        vertex_index=_system.Numvertices*(m_rng->drnd());
+		//  attempt to move the vertex
+        double energy_i = this->ComputeEnergyFromVertex(vertex_index);
+        _system.vertices[vertex_index].spin *= -1;
+        double energy_f = this->ComputeEnergyFromVertex(vertex_index);
+        double delE = energy_f - energy_i;
+        accepted_moves++;
+		
+        if (!(delE<0.0))
+        {
+			double rnd_numEli=m_rng->drnd();
+            if(!( rnd_numEli < exp(-delE/get_temperature())))
+            {
+                _system.vertices[vertex_index].spin *= -1;
+                accepted_moves--;
+            } 
+        }	
+		sum_mag+= _system.vertices[vertex_index].spin;
+    }
+	
+
+    return(accepted_moves);
+}
diff --git a/pymembrane/cppmodule/src/integrators/montercarlo_spin_vertex.hpp b/pymembrane/cppmodule/src/integrators/montercarlo_spin_vertex.hpp
new file mode 100644
index 00000000..fda996c2
--- /dev/null
+++ b/pymembrane/cppmodule/src/integrators/montercarlo_spin_vertex.hpp
@@ -0,0 +1,98 @@
+/*!
+ * \file montercarlo_vertex.hpp
+ * \author Daniel Matoz , fdamatoz@gmail.com
+ * \date 29-Dec-2018
+ * \brief Declaration of IntegratorBrownianVertex class
+ */
+
+#ifndef __montercarlo_spin_vertex_HPP__
+#define __montercarlo_spin_vertex_HPP__
+
+
+#include <iostream>
+#include "montecarlointegrator.hpp"
+#include "../rng/rng.hpp"
+#include "../types/globaltypes.hpp"
+#include "../utils/fromstring.hpp"
+#include "../system/systemclass.hpp"
+/**
+ * @class MonteCarloIntegratorSpinVertex
+ * @brief Integrator Brownian class implements Brownian dynamics for the vertex position. 
+ */
+class MonteCarloIntegratorSpinVertex : public MonteCarloIntegrator
+{
+public:
+  /** @brief VertexIntegrator Constructor */
+  MonteCarloIntegratorSpinVertex(SystemClass &system, VertexCompute &potentials) : MonteCarloIntegrator(system, potentials)
+  {
+    m_type = "monte carlo";
+    m_name = "vertex move";
+    this->set_default_properties();
+  }
+  /** @brief destructor */
+  ~MonteCarloIntegratorSpinVertex() {}
+
+  void set_default_properties(void) override
+  { 
+    pymemb::vector<bool> _freezed_vertex(NUM_TYPES_ALLOWED, false);
+    freezed_vertex = _freezed_vertex;
+    this->set_temperature(0.0);
+    m_seed = 123456; ///default value
+    m_rng = std::make_unique<RNG>(m_seed);
+  }
+
+  using MonteCarloIntegrator::set_property;
+  void set_property(std::map<std::string, std::string> &value_map) override
+  {
+    for (const auto &item : value_map)
+    {
+      if (item.first.compare("T") == 0)
+      {
+        this->set_temperature(util::from_string_double(item.second));
+        this->update_temperature_parameters();
+      }
+      else if (item.first.compare("seed") == 0)
+      {
+        m_seed = uint(util::from_string_int(item.second));
+        m_rng = std::make_unique<RNG>(m_seed);
+      }
+      else
+        this->print_warning_property_name(item.first);
+    }
+  }
+
+  void set_property(std::map<std::string, std::map<std::string, std::string>> &value_map) override
+  {
+    for (const auto &item : value_map)
+    {
+      if (item.first.compare("freeze") == 0)
+      {
+        pymemb::vector<bool> _freezed_vertex = util::from_dict_to_vector_types(pymemb::copy(freezed_vertex), item.second);
+        freezed_vertex = _freezed_vertex;
+      }
+      else
+        this->print_warning_property_name(item.first);
+    }
+  }
+  std::map<std::string, std::string> get_info(void) override
+  {
+    std::map<std::string, std::string> value;
+    value["name"] = m_name;
+    value["type"] = m_type;
+    value["T"] = util::to_string(this->get_temperature());
+    return value;
+  }
+
+  int integrate(void) override;
+
+private:
+  unsigned int m_seed; //!< random number seed;
+  RNG_ptr m_rng;       //!< Random number generator
+  pymemb::vector<bool> freezed_vertex;
+};
+
+typedef std::shared_ptr<MonteCarloIntegratorSpinVertex> MonteCarloIntegratorSpinVertex_ptr;
+
+#endif
+
+
diff --git a/pymembrane/cppmodule/src/integrators/montercarlo_swap_edge.hpp b/pymembrane/cppmodule/src/integrators/montercarlo_swap_edge.hpp
index 168ec77a..9d83f40a 100755
--- a/pymembrane/cppmodule/src/integrators/montercarlo_swap_edge.hpp
+++ b/pymembrane/cppmodule/src/integrators/montercarlo_swap_edge.hpp
@@ -29,8 +29,8 @@ class MonteCarloIntegratorSwapEdge : public MonteCarloIntegrator
 public:
   MonteCarloIntegratorSwapEdge(SystemClass &system, VertexCompute &potentials) : MonteCarloIntegrator(system, potentials)
   {
-    name = "edge swap";
-    type = "monte carlo";
+    m_name = "edge swap";
+    m_type = "monte carlo";
     this->set_default_properties();
   }
   ~MonteCarloIntegratorSwapEdge() {}
@@ -92,11 +92,19 @@ class MonteCarloIntegratorSwapEdge : public MonteCarloIntegrator
         this->print_warning_property_name(item.first);
     }
   }
-
+  std::map<std::string, std::string> get_info(void) override
+  {
+    std::map<std::string, std::string> value;
+    value["name"] = m_name;
+    value["type"] = m_type;
+    value["T"] = util::to_string(this->get_temperature());
+    value["stochastic_tunnelling"] = util::to_string(stochastic_tunnelling);
+    value["stochastic_gamma"] = util::to_string(stochastic_gamma);
+    return value;
+  }
   int integrate(void) override;
 
 private:
-  double m_dx, m_dy, m_dz;
   unsigned int m_seed;
   RNG_ptr m_rng;
   bool stochastic_tunnelling;
diff --git a/pymembrane/cppmodule/src/integrators/montercarlo_swap_vertex.hpp b/pymembrane/cppmodule/src/integrators/montercarlo_swap_vertex.hpp
index fe84bd6c..8da4eea8 100755
--- a/pymembrane/cppmodule/src/integrators/montercarlo_swap_vertex.hpp
+++ b/pymembrane/cppmodule/src/integrators/montercarlo_swap_vertex.hpp
@@ -29,8 +29,8 @@ class MonteCarloIntegratorSwapVertex : public MonteCarloIntegrator
 public:
   MonteCarloIntegratorSwapVertex(SystemClass &system, VertexCompute &potentials) : MonteCarloIntegrator(system, potentials)
   {
-    name = "vertex swap";
-    type = "monte carlo";
+    m_name = "vertex swap";
+    m_type = "monte carlo";
     this->set_default_properties();
   }
   ~MonteCarloIntegratorSwapVertex() {}
@@ -91,11 +91,18 @@ class MonteCarloIntegratorSwapVertex : public MonteCarloIntegrator
         this->print_warning_property_name(item.first);
     }
   }
-
+  std::map<std::string, std::string> get_info(void) override
+  {
+    std::map<std::string, std::string> value;
+    value["name"] = m_name;
+    value["type"] = m_type;
+    value["T"] = util::to_string(this->get_temperature());
+    value["integrate_every"] = util::to_string(this->integrate_every);
+    return value;
+  }
   int integrate(void) override;
 
 private:
-  double m_dx, m_dy, m_dz;
   unsigned int m_seed; //!< random number seed;
   RNG_ptr m_rng;       //!< Random number generator
   bool stochastic_tunnelling;
diff --git a/pymembrane/cppmodule/src/integrators/montercarlo_vertex.cpp b/pymembrane/cppmodule/src/integrators/montercarlo_vertex.cpp
index 92f823a0..5cb0f311 100755
--- a/pymembrane/cppmodule/src/integrators/montercarlo_vertex.cpp
+++ b/pymembrane/cppmodule/src/integrators/montercarlo_vertex.cpp
@@ -6,57 +6,109 @@ int MonteCarloIntegratorVertex::integrate(void)
     int accepted_moves = 0;
     for(int vertex_index = 0; vertex_index<_system.Numvertices; vertex_index++)
     {
+
+		// The following IF makes sure that we only move either particle-free vertices or the central vertex of a particle:	
+		if ((_system.vertices[vertex_index].type==-1) || (_system.vertices[vertex_index].type==vertex_index)) {
+		
+		
         //attempt to move the vertex
-        real dx, dy, dz;
-        auto r_old = _system.vertices[vertex_index].r;
+        double dx, dy, dz;
+		double orig_pos[_system.Numvertices][3]; 
+
         if (m_spherical_move)
-        {
-            auto len_r_old = sqrt(r_old.x * r_old.x + r_old.y * r_old.y + r_old.z * r_old.z);
-            auto sigma = sqrt(m_dx * m_dx + m_dy * m_dy + m_dz * m_dz);
-            dx = m_rng->gauss_rng(sigma);
-            dy = m_rng->gauss_rng(sigma);
-            dz = m_rng->gauss_rng(sigma);
-            auto x_new = r_old.x + dx;
-            auto y_new = r_old.y + dy;
-            auto z_new = r_old.z + dz;
-            auto len_r_new = sqrt(x_new * x_new + y_new * y_new + z_new * z_new);
-            auto scale = len_r_old / len_r_new;
-            dx = scale * x_new - r_old.x;
-            dy = scale * y_new - r_old.y;
-            dz = scale * z_new - r_old.z;
-        }
-        else
-        {
-            dx = m_dx * (m_rng->drnd() - 0.5);
-            dy = m_dy * (m_rng->drnd() - 0.5);
-            dz = m_dz * (m_rng->drnd() - 0.5);
-        }
-        //Compute the initial energy
-        auto energy_i = this->ComputeEnergyFromVertex(vertex_index);
-        //Move the vertex
-        _system.vertices[vertex_index].r.x+= dx;
-        _system.vertices[vertex_index].r.y+= dy;
-        _system.vertices[vertex_index].r.z+= dz;
-        //Enforce periodic boundary conditions
-        //particles may have been moved slightly outside the box by the above steps, wrap them back into place
-        pymemb::enforce_periodic(_system.vertices[vertex_index].r, _system.vertices[vertex_index].ip, _system.get_box());
-        //Compute the final energy
-        auto energy_f = this->ComputeEnergyFromVertex(vertex_index);
-        //Compute the energy difference
-        auto delE = energy_f - energy_i;
-        //Accept or reject the move
-        accepted_moves++;
-        // std::cout << "vertexmove:"<<vertex_index<<std::endl;
-        if (!(delE<0.0))
-        {
-            //reject the move
-            if(!(m_rng->drnd() < exp(-delE/get_temperature())))
-            {
-                _system.vertices[vertex_index].r = r_old;
-                accepted_moves--;
-                // std::cout<< "regret"<<std::endl;
-            }
-        }
+			{
+				double x = _system.vertices[vertex_index].r.x, y =_system.vertices[vertex_index].r.y, z= _system.vertices[vertex_index].r.z;
+				double r = sqrt(x * x + y * y + z * z);
+				double sigma = sqrt(m_dx * m_dx + m_dy * m_dy + m_dz * m_dz);
+				dx = m_rng->gauss_rng(sigma);
+				dy = m_rng->gauss_rng(sigma);
+				dz = m_rng->gauss_rng(sigma);
+				double x_new = x + dx, y_new = y + dy, z_new = z + dz;
+				double r_new = sqrt(x_new * x_new + y_new * y_new + z_new * z_new);
+				double scale = r / r_new;
+				dx = scale * x_new - x;
+				dy = scale * y_new - y;
+				dz = scale * z_new - z;
+			}
+			else
+			{
+				dx = m_dx * (m_rng->drnd() - 0.5);
+				dy = m_dy * (m_rng->drnd() - 0.5);
+				dz = m_dz * (m_rng->drnd() - 0.5);
+			}
+			
+
+			double energy_i = this->ComputeEnergyFromVertex(vertex_index);
+			
+			if (_system.vertices[vertex_index].type==-1) {    //Particle-free vertices move as usual.
+				_system.vertices[vertex_index].r.x+= dx;
+				_system.vertices[vertex_index].r.y+= dy;
+				_system.vertices[vertex_index].r.z+= dz;
+			} else if (_system.vertices[vertex_index].type==vertex_index) {  //Vertices located "inside a particle" move together with the particle center, as a solid body.
+					for(int vertex_index_ii = 0; vertex_index_ii<_system.Numvertices; vertex_index_ii++) {
+							if (_system.vertices[vertex_index_ii].type==vertex_index) {
+									//Keep the original positions, to be able to step back, if MC step is declined.
+								double x=_system.vertices[vertex_index_ii].r.x;
+								double y=_system.vertices[vertex_index_ii].r.y;
+								double z=_system.vertices[vertex_index_ii].r.z;
+								orig_pos[vertex_index_ii][0]=x;
+								orig_pos[vertex_index_ii][1]=y;
+								orig_pos[vertex_index_ii][2]=z;
+								double x_new=x + dx;
+								double y_new=y + dy;
+								double z_new=z + dz;
+								double dx1 = dx;
+								double dy1 = dy;
+								double dz1 = dz;
+
+								if (m_spherical_move) {
+									double r = sqrt(x * x + y * y + z * z);
+									double r_new = sqrt(x_new * x_new + y_new * y_new + z_new * z_new);
+									double scale = r / r_new;
+									double dx1 = scale * x_new - x;
+									double dy1 = scale * y_new - y;
+									double dz1 = scale * z_new - z;
+								}
+								_system.vertices[vertex_index_ii].r.x+=dx1;
+								_system.vertices[vertex_index_ii].r.y+=dy1;
+								_system.vertices[vertex_index_ii].r.z+=dz1;
+							}
+								
+					}
+			}
+			double energy_f = this->ComputeEnergyFromVertex(vertex_index);
+			double delE = energy_f - energy_i;
+		
+			accepted_moves++;
+
+			if (!(delE<0.0))
+			{
+				if (!(m_rng->drnd() < exp(-delE/get_temperature())))
+				{
+					if (_system.vertices[vertex_index].type==-1) { 
+						_system.vertices[vertex_index].r.x-= dx;
+						_system.vertices[vertex_index].r.y-= dy;
+						_system.vertices[vertex_index].r.z-= dz;
+					} else if (_system.vertices[vertex_index].type==vertex_index) {  //Vertices located "inside a particle" move together with the particle center, as a solid body.
+						for(int vertex_index_ii = 0; vertex_index_ii<_system.Numvertices; vertex_index_ii++) {
+							if (_system.vertices[vertex_index_ii].type==vertex_index) {
+								_system.vertices[vertex_index_ii].r.x=orig_pos[vertex_index_ii][0];
+								_system.vertices[vertex_index_ii].r.y=orig_pos[vertex_index_ii][1];
+								_system.vertices[vertex_index_ii].r.z=orig_pos[vertex_index_ii][2];
+							}
+						}
+					}
+				
+					accepted_moves--;
+				}
+			}
+		}
     }
-    return(accepted_moves);
+	
+ 	double totE=0;
+	for(int vertex_index = 0; vertex_index<_system.Numvertices; vertex_index++)
+    {
+		totE+=this->ComputeEnergyFromVertex(vertex_index);
+	}
+    return(accepted_moves); 
 }
diff --git a/pymembrane/cppmodule/src/integrators/montercarlo_vertex.hpp b/pymembrane/cppmodule/src/integrators/montercarlo_vertex.hpp
index fba42edb..5ee1ac59 100644
--- a/pymembrane/cppmodule/src/integrators/montercarlo_vertex.hpp
+++ b/pymembrane/cppmodule/src/integrators/montercarlo_vertex.hpp
@@ -28,8 +28,8 @@ class MonteCarloIntegratorVertex : public MonteCarloIntegrator
   /** @brief VertexIntegrator Constructor */
   MonteCarloIntegratorVertex(SystemClass &system, VertexCompute &potentials) : MonteCarloIntegrator(system, potentials)
   {
-    type = "monte carlo";
-    name = "vertex move";
+    m_type = "monte carlo";
+    m_name = "vertex move";
     this->set_default_properties();
   }
   /** @brief destructor */
@@ -90,7 +90,7 @@ class MonteCarloIntegratorVertex : public MonteCarloIntegrator
         m_spherical_move = util::from_string_bool(item.second);
       }
       else
-        this->print_warning_property_name(name);
+        this->print_warning_property_name(item.first);
     }
   }
 
@@ -107,6 +107,19 @@ class MonteCarloIntegratorVertex : public MonteCarloIntegrator
         this->print_warning_property_name(item.first);
     }
   }
+
+  std::map<std::string, std::string> get_info(void) override
+  {
+    std::map<std::string, std::string> value;
+    value["name"] = m_name;
+    value["type"] = m_type;
+    value["T"] = util::to_string(this->get_temperature());
+    value["spherical_move"] = util::to_string(m_spherical_move);
+    value["dx"] = util::to_string(m_dx);
+    value["dy"] = util::to_string(m_dy);
+    value["dz"] = util::to_string(m_dz);
+    return value;
+  }
   int integrate(void) override;
 
 private:
diff --git a/pymembrane/cppmodule/src/mesh/computegeometry.hpp b/pymembrane/cppmodule/src/mesh/computegeometry.hpp
index fd39a184..6a908c4c 100644
--- a/pymembrane/cppmodule/src/mesh/computegeometry.hpp
+++ b/pymembrane/cppmodule/src/mesh/computegeometry.hpp
@@ -12,6 +12,9 @@ namespace pymemb
     real3 unit_vector(const real3 &v)
     {
         real norm = sqrt(vdot(v,v));
+        if (norm == 0)
+            return v;
+        
         real3 v_unit = v;
         v_unit.x/=norm;
         v_unit.y/=norm;
@@ -19,6 +22,12 @@ namespace pymemb
         return(v_unit);
     }
   
+    inline
+    real vector_dot(const real3 &v1, const real3 &v2)
+    {
+        return vdot(v1, v2);
+    }
+
     inline 
     real3 vector_cross(const real3 &v1, const real3 &v2)
     {
@@ -53,6 +62,18 @@ namespace pymemb
         return (pymemb::minimum_image(v2, v1, box));
     }
 
+    inline
+    real vector_squared_length(const real3 &v)
+    {
+        return v.x*v.x + v.y*v.y + v.z*v.z;
+    }
+
+    inline
+    real vector_length(const real3 &v)
+    {
+        return sqrt(vector_squared_length(v));
+    }
+
     inline 
     void compute_form_factor_triangle(real *_metric, const real3 &r1, const real3 &r2, const real3 &r3, const BoxType &box)
     {
@@ -143,7 +164,7 @@ namespace pymemb
         real3 v12, v13;
         vsub(v12, r2, r1);
         vsub(v13, r3, r1);
-        real angle = acos(vdot(v12, v13) / sqrt(vdot(v12, v12) * vdot(v13, v13)));
+        real angle = acos(vdot(v12, v13) / (sqrt(vdot(v12, v12)) * sqrt(vdot(v13, v13))));
         return angle;
     }
 
@@ -280,5 +301,8 @@ namespace pymemb
         }
         return _need_wrapping;
     }
-} 
+
+}
+
+
 #endif
diff --git a/pymembrane/cppmodule/src/mesh/edge_flip.hpp b/pymembrane/cppmodule/src/mesh/edge_flip.hpp
index 8dfc1f8e..37130b48 100644
--- a/pymembrane/cppmodule/src/mesh/edge_flip.hpp
+++ b/pymembrane/cppmodule/src/mesh/edge_flip.hpp
@@ -6,6 +6,22 @@
 
 namespace pymemb
 {
+    inline bool edge_need_flip(const int flip_edge_index,
+                                HE_VertexProp *vertices,
+                                HE_EdgeProp *edges)
+    {
+        int v0 = edges[flip_edge_index].v0;
+        int v1 = edges[flip_edge_index].v1;
+        int v2 = edges[flip_edge_index].v2;
+        int v3 = edges[flip_edge_index].v3;
+
+
+        double angle012 = pymemb::compute_angle_vertex(vertices[v1].r, vertices[v0].r, vertices[v2].r);
+        double angle210 =  pymemb::compute_angle_vertex(vertices[v3].r, vertices[v0].r, vertices[v2].r);
+
+        return angle012 + angle210 > M_PI;
+    }
+
     inline bool CheckEdgeFlip_lambda(const int flip_edge_index,
                                      HE_FaceProp *faces,
                                      HE_VertexProp *vertices,
@@ -93,6 +109,8 @@ namespace pymemb
         real r02_norm_sq = (vdot(r02, r02));
         real r03_norm_sq = (vdot(r03, r03));
         real r01_norm_sq = (vdot(r01, r01));
+        if (r02_norm_sq == 0 || r02_norm_sq == 0 || r03_norm_sq == 0)
+            std::cout << "division by 0" << std::endl;
         real angle_r01_r02 = acos(vdot(r01, r02) / sqrt(r01_norm_sq * r02_norm_sq));
         real angle_r03_r02 = acos(vdot(r03, r02) / sqrt(r03_norm_sq * r02_norm_sq));
         if ((angle_r01_r02 + angle_r03_r02) >= defPI)
@@ -107,6 +125,8 @@ namespace pymemb
         r21 = pymemb::minimum_image(vertices[v2].r, vertices[v1].r, _box);
         real r23_norm_sq = (vdot(r23, r23));
         real r21_norm_sq = (vdot(r21, r21));
+        if (r23_norm_sq == 0 || r21_norm_sq == 0)
+            std::cout << "division by 0" << std::endl;
         real angle_r21_r20 = acos(vdot(r21, r20) / sqrt(r21_norm_sq * r02_norm_sq));
         real angle_r23_r20 = acos(vdot(r23, r20) / sqrt(r23_norm_sq * r02_norm_sq));
         if ((angle_r21_r20 + angle_r23_r20) >= defPI)
@@ -154,7 +174,6 @@ namespace pymemb
         // check v0
         he = vertices[v0]._hedge;
         first = he;
-
         do
         {
             n_neighbors_v0++;
@@ -176,7 +195,7 @@ namespace pymemb
             he_pair_next = halfedges[he_pair].next;
             he = he_pair_next;
         } while ((he != first));
-
+        
         // if (n_neighbors_v0 <= 4 || n_neighbors_v2 <= 4)
         if (n_neighbors_v0 < 3 || n_neighbors_v2 < 3)
         {
@@ -205,6 +224,8 @@ namespace pymemb
         real r02_norm_sq = (vdot(r02, r02));
         real r03_norm_sq = (vdot(r03, r03));
         real r01_norm_sq = (vdot(r01, r01));
+        if (r02_norm_sq == 0 || r01_norm_sq == 0 || r03_norm_sq == 0)
+            std::cout << "division by 0" << std::endl;
         real angle_r01_r02 = acos(vdot(r01, r02) / sqrt(r01_norm_sq * r02_norm_sq));
         real angle_r03_r02 = acos(vdot(r03, r02) / sqrt(r03_norm_sq * r02_norm_sq));
         if ((angle_r01_r02 + angle_r03_r02) >= defPI)
@@ -219,6 +240,8 @@ namespace pymemb
         r21 = pymemb::minimum_image(vertices[v2].r, vertices[v1].r, _box);
         real r23_norm_sq = (vdot(r23, r23));
         real r21_norm_sq = (vdot(r21, r21));
+        if (r23_norm_sq == 0 || r21_norm_sq == 0)
+            std::cout << "division by 0" << std::endl;
         real angle_r21_r20 = acos(vdot(r21, r20) / sqrt(r21_norm_sq * r02_norm_sq));
         real angle_r23_r20 = acos(vdot(r23, r20) / sqrt(r23_norm_sq * r02_norm_sq));
         if ((angle_r21_r20 + angle_r23_r20) >= defPI)
diff --git a/pymembrane/cppmodule/src/mesh/halfedges.hpp b/pymembrane/cppmodule/src/mesh/halfedges.hpp
index b0c6efc5..f90e190d 100644
--- a/pymembrane/cppmodule/src/mesh/halfedges.hpp
+++ b/pymembrane/cppmodule/src/mesh/halfedges.hpp
@@ -37,6 +37,7 @@ struct HE_Vertex
     real energy;  //!< Vertex energy
     real mass;    //!< Vertex mass
     inth3 ip;     //!< Periodic box image flags (to enable unwrapping of particle coordinates)
+    real spin; //!< ferromagnetic spin +1.0, -1.0
     PropertyVertices _property;
 };
 using HE_VertexProp = HE_Vertex<PropertyVertices>;
diff --git a/pymembrane/cppmodule/src/mesh/meshoperations.cpp b/pymembrane/cppmodule/src/mesh/meshoperations.cpp
index 5da7f34b..260af018 100644
--- a/pymembrane/cppmodule/src/mesh/meshoperations.cpp
+++ b/pymembrane/cppmodule/src/mesh/meshoperations.cpp
@@ -3,8 +3,21 @@
 #include "computegeometry.hpp"
 #include "../system/systemclass.hpp"
 #include "../box/pbc.hpp"
+#include <set>
 
-bool MeshOperations::check_if_edge_can_flip(int flip_edge_index)
+real MeshOperations::compute_average_edge_length()
+{
+    real avg_edge_length = 0.0;
+    for (int edge_id=0; edge_id<_system.Numedges; edge_id++)
+    {
+        int v0 = _system.edges[edge_id].i;
+        int v1 = _system.edges[edge_id].j;
+        avg_edge_length += pymemb::vector_length(pymemb::vector_subtract(_system.vertices[v0].r, _system.vertices[v1].r));
+    }
+    return avg_edge_length/_system.Numedges;
+}
+
+bool MeshOperations::check_if_edge_can_flip(const int& flip_edge_index)
 {
     auto can_flip = pymemb::CheckEdgeFlip_lambda(flip_edge_index,
                                                (&_system.faces[0]),
@@ -15,19 +28,176 @@ bool MeshOperations::check_if_edge_can_flip(int flip_edge_index)
     return can_flip;
 }
 
-void MeshOperations::edge_flip(const int& flip_edge_index, const bool& flip_face_up)
+bool MeshOperations::edge_need_flip(int flip_edge_index)
 {
+    int v0 = _system.edges[flip_edge_index].v0;
+    int v1 = _system.edges[flip_edge_index].v1;
+    int v2 = _system.edges[flip_edge_index].v2;
+    int v3 = _system.edges[flip_edge_index].v3;
+
+    real3 r0 = _system.vertices[v0].r;
+    real3 r1 = _system.vertices[v1].r;
+    real3 r2 = _system.vertices[v2].r;
+    real3 r3 = _system.vertices[v3].r;
+
+    // first check if edge can flip
+    real angle_0102 = pymemb::compute_angle_vertex(r0, r1, r2);
+    real angle_0203 = pymemb::compute_angle_vertex(r0, r2, r3);
+    if (angle_0102 + angle_0203 >= M_PI)
+        return false;
+
+    real angle_2120 = pymemb::compute_angle_vertex(r2, r1, r0);
+    real angle_2023 = pymemb::compute_angle_vertex(r2, r0, r3);
+    if (angle_2120 + angle_2023 >= M_PI)
+        return false;
+
+    int f0 = _system.edges[flip_edge_index].face_k;
+    int f1 = _system.edges[flip_edge_index].face_l;
+
+    real3 ra = _system.vertices[_system.faces[f0].v1].r;
+    real3 rb = _system.vertices[_system.faces[f0].v2].r;
+    real3 rc = _system.vertices[_system.faces[f0].v3].r;
+    real3 n_f0 = pymemb::compute_normal_triangle_unit(ra, rb, rc);
+
+    ra = _system.vertices[_system.faces[f1].v1].r;
+    rb = _system.vertices[_system.faces[f1].v2].r;
+    rc = _system.vertices[_system.faces[f1].v3].r;
+    real3 n_f1 = pymemb::compute_normal_triangle_unit(ra, rb, rc);
+
+    if (pymemb::vector_dot(n_f0, n_f1) < 0)
+        return false;
+    
+    // this condition is relevant when using surface tension and substrate
+    // to avoid flip on triple line
+    // comment or delete for other use
+    int t0 = _system.vertices[v0].type;
+    int t1 = _system.vertices[v1].type;
+    int t2 = _system.vertices[v2].type;
+    int t3 = _system.vertices[v3].type;
+    if (t0 == t2 && (t0 > t1 || t0 > t3))
+        return false;
+    
+
+    // then check if angles can be improved by flip
+    real angle012 = pymemb::compute_angle_vertex(r1, r0, r2);
+    real angle210 =  pymemb::compute_angle_vertex(r3, r0, r2);
+
+    return angle012 + angle210 > M_PI;
+}
+
+/*
+                 v0                          v0         
+               / | \                       /   \
+              /  |  \                     /     \
+             v3  |   v1      -->         v3------v1
+              \  |  /                     \     /
+               \ | /                       \   /
+                 v2                          v2
+*/
+
+
+void MeshOperations::edge_flip(int edge_index)
+{
+    int he02 = _system.edges[edge_index]._hedge;
+    int he20 = _system.halfedges[he02].pair;
+    int he21 = _system.halfedges[he02].next;
+    int he10 = _system.halfedges[he21].next;
+    int he03 = _system.halfedges[he20].next;
+    int he32 = _system.halfedges[he03].next;
+
+    int v0 = _system.halfedges[he02].vert_from;
+    int v1 = _system.halfedges[he21].vert_to;
+    int v2 = _system.halfedges[he02].vert_to;
+    int v3 = _system.halfedges[he03].vert_to;
+
+    int f021 = _system.halfedges[he02].face;
+    int f203 = _system.halfedges[he20].face;
+
+    //repurposed halfedges
+    int he13 = he02;
+    _system.halfedges[he13].vert_from = v1;
+    _system.halfedges[he13].vert_to = v3;
+    int he31 = he20;
+    _system.halfedges[he31].vert_from = v3;
+    _system.halfedges[he31].vert_to = v1;
+
+    //repurposed faces
+    int f132 = f021;
+    _system.faces[f132]._hedge = he13;
+    _system.faces[f132].v1 = v1;
+    _system.faces[f132].v2 = v3;
+    _system.faces[f132].v3 = v2;
+    int f310 = f203;
+    _system.faces[f310]._hedge = he31;
+    _system.faces[f310].v1 = v3;
+    _system.faces[f310].v2 = v1;
+    _system.faces[f310].v3 = v0;
+
+    //repurposed edge
+    _system.edges[edge_index].i = v1;
+    _system.edges[edge_index].j = v3;
+    _system.edges[edge_index].v0 = v1;
+    _system.edges[edge_index].v1 = v2;
+    _system.edges[edge_index].v2 = v3;
+    _system.edges[edge_index].v3 = v0;
+
+    //updating halfedges
+    _system.halfedges[he13].next = he32;
+    _system.halfedges[he32].prev = he13;
+    _system.halfedges[he32].next = he21;
+    _system.halfedges[he21].prev = he32;
+    _system.halfedges[he21].next = he13;
+    _system.halfedges[he13].prev = he21;
+    _system.halfedges[he31].next = he10;
+    _system.halfedges[he10].prev = he31;
+    _system.halfedges[he10].next = he03;
+    _system.halfedges[he03].prev = he10;
+    _system.halfedges[he03].next = he31;
+    _system.halfedges[he31].prev = he03;
+
+    _system.halfedges[he32].face = f132;
+    _system.halfedges[he10].face = f310;
+
+    //updating vertices
+    _system.vertices[v0]._hedge = he03;
+    _system.vertices[v2]._hedge = he21;
+
+    //updating edge
+    int edge = _system.halfedges[he10].edge;
+    if (_system.edges[edge].v1 == v2)
+        _system.edges[edge].v1 = v3;
+    if (_system.edges[edge].v3 == v2)
+        _system.edges[edge].v3 = v3;
+
+    edge = _system.halfedges[he03].edge;
+    if (_system.edges[edge].v1 == v2)
+        _system.edges[edge].v1 = v1;
+    if (_system.edges[edge].v3 == v2)
+        _system.edges[edge].v3 = v1;
 
-    pymemb::EdgeFlip_lambda(flip_edge_index,
-                               flip_face_up,
-                               &_system.faces[0],
-                              &_system.vertices[0],
-                               &_system.edges[0],
-                               &_system.halfedges[0],
-                               _system.get_box());
+    edge = _system.halfedges[he32].edge;
+    if (_system.edges[edge].v1 == v0)
+        _system.edges[edge].v1 = v1;
+    if (_system.edges[edge].v3 == v0)
+        _system.edges[edge].v3 = v1;
 
+    edge = _system.halfedges[he21].edge;
+    if (_system.edges[edge].v1 == v0)
+        _system.edges[edge].v1 = v3;
+    if (_system.edges[edge].v3 == v0)
+        _system.edges[edge].v3 = v3;
 }
 
+void MeshOperations::refine_mesh_edge_flip()
+{
+    for(int edge_index=0; edge_index<_system.Numedges; edge_index++)
+    {
+        if (edge_need_flip(edge_index))
+            edge_flip(edge_index);
+    }
+}
+
+/*
 void MeshOperations::equiangulation(void)
 {
     Equiangulation_kernel(_system.Numedges,
@@ -35,10 +205,10 @@ void MeshOperations::equiangulation(void)
                           (&_system.vertices[0]),
                           (&_system.edges[0]),
                           (&_system.halfedges[0]),
-                          true,
+                          true
                           );
     for (int flip_edge_index = 0;
-         flip_edge_index < Numedges;
+         flip_edge_index < _system.Numedges;
          flip_edge_index += 1)
     {
         // retrieve the vertices around the edge
@@ -65,4 +235,792 @@ void MeshOperations::equiangulation(void)
             py::print("flipped edge =%i\n", flip_edge_index);
         }
     }
+}*/
+
+void MeshOperations::compute_vertex_connexity(int vertex_index)
+{
+    _system.vertices[vertex_index].coordination = 0;
+    int he = _system.vertices[vertex_index]._hedge;
+    int first = he;
+    do
+    {
+        _system.vertices[vertex_index].coordination++;
+        int he_pair = _system.halfedges[he].pair;
+        he = _system.halfedges[he_pair].next;
+    } while (he != first);
+}
+
+void MeshOperations::compute_vertices_connexities()
+{
+    for (int i=0; i<_system.Numvertices; i++)
+    {
+        compute_vertex_connexity(i);
+    }
+}
+
+
+
+int MeshOperations::create_vertex(real mass)
+{
+    HE_Vertex<PropertyVertices> vertex;
+    vertex.id = _system.Numvertices;
+    vertex.mass = mass;
+    vertex.type = 1;
+    _system.vertices.push_back(vertex);
+    _system.Numvertices++;
+    return vertex.id;
+}
+
+int MeshOperations::create_edge()
+{
+    HE_Edge<PropertyEdges> e;
+    HE_HalfEdge<PropertyEdges> he0;
+    HE_HalfEdge<PropertyEdges> he1;
+    he0.index = _system.Numhalfedges;
+    he1.index = _system.Numhalfedges+1;
+    e.id = _system.Numedges;
+    he0.pair = he1.index;
+    he0.edge = e.id;
+    he1.pair = he0.index;
+    he1.edge = e.id;
+    e._hedge = he0.index;
+    _system.edges.push_back(e);
+    _system.halfedges.push_back(he0);
+    _system.halfedges.push_back(he1);
+    _system.Numedges++;
+    _system.Numhalfedges += 2;
+    return e.id;
+}
+
+int MeshOperations::create_face()
+{
+    HE_Face<PropertyFaces> f;
+    f.id = _system.Numfaces;
+    _system.faces.push_back(f);
+    _system.Numfaces++;
+    return f.id;
+}
+
+void MeshOperations::delete_vertex(int vertex_index)
+{
+    // shift all vertices in the array > vertex_index
+    for (int vid=vertex_index; vid<_system.Numvertices-1; vid++)
+    {
+        _system.vertices[vid] = _system.vertices[vid+1];
+        _system.vertices[vid].id--;
+    }
+
+    // udpating vertices id in edge structure
+    for (int edge_id=0; edge_id<_system.Numedges; edge_id++)
+    {
+        if (_system.edges[edge_id].i > vertex_index)
+            _system.edges[edge_id].i--;
+        if (_system.edges[edge_id].j > vertex_index)
+            _system.edges[edge_id].j--;   
+        if (_system.edges[edge_id].v0 > vertex_index)
+            _system.edges[edge_id].v0--;
+        if (_system.edges[edge_id].v1 > vertex_index)
+            _system.edges[edge_id].v1--;
+        if (_system.edges[edge_id].v2 > vertex_index)
+            _system.edges[edge_id].v2--;
+        if (_system.edges[edge_id].v3 > vertex_index)
+            _system.edges[edge_id].v3--;
+    }
+
+    // udpating vertices id in halfedge structure
+    for (int hedge_id=0; hedge_id<_system.Numhalfedges; hedge_id++)
+    {
+        if (_system.halfedges[hedge_id].vert_from > vertex_index)
+            _system.halfedges[hedge_id].vert_from--;
+        if (_system.halfedges[hedge_id].vert_to > vertex_index)
+            _system.halfedges[hedge_id].vert_to--;
+    }
+
+    // updating vertices id in face structure
+    for (int face_id=0; face_id<_system.Numfaces; face_id++)
+    {
+        if (_system.faces[face_id].v1 > vertex_index)
+            _system.faces[face_id].v1--;
+        if (_system.faces[face_id].v2 > vertex_index)
+            _system.faces[face_id].v2--;
+        if (_system.faces[face_id].v3 > vertex_index)
+            _system.faces[face_id].v3--;
+    }
+
+    _system.Numvertices--;
+}
+
+void MeshOperations::delete_edge(int edge_index)
+{
+    int he = _system.edges[edge_index]._hedge;
+    int he_pair = _system.halfedges[he].pair;
+    if (he < he_pair)
+        he_pair--;
+    delete_hedge(he);
+    delete_hedge(he_pair);
+
+    // shift all edges in the array > edge_index
+    for (int edge_id=edge_index; edge_id<_system.Numedges-1; edge_id++)
+    {
+        _system.edges[edge_id] = _system.edges[edge_id+1];
+        _system.edges[edge_id].id--;
+    }
+
+    // udpating edges id in halfedge structure
+    for (int hedge_id=0; hedge_id<_system.Numhalfedges; hedge_id++)
+    {
+        if(_system.halfedges[hedge_id].edge > edge_index)
+            _system.halfedges[hedge_id].edge--;
+    }
+
+    _system.Numedges--;
+}
+
+void MeshOperations::delete_face(int face_index)
+{
+    // shift all faces in the array > face_index
+    for (int face_id=face_index; face_id<_system.Numfaces-1; face_id++)
+    {
+        _system.faces[face_id] = _system.faces[face_id+1];
+        _system.faces[face_id].id--;
+    }
+
+    // udpating faces id in edge structure
+    for (int edge_id=0; edge_id<_system.Numedges; edge_id++)
+    {
+        if (_system.edges[edge_id].face_k > face_index)
+            _system.edges[edge_id].face_k--;
+        if (_system.edges[edge_id].face_l > face_index)
+            _system.edges[edge_id].face_l--;
+    }
+
+    // udpating faces id in halfedge structure
+    for (int hedge_id=0; hedge_id<_system.Numhalfedges; hedge_id++)
+    {
+        if (_system.halfedges[hedge_id].face > face_index)
+            _system.halfedges[hedge_id].face--;
+    }
+
+    _system.Numfaces--;
+}
+
+void MeshOperations::delete_hedge(int hedge_index)
+{
+    // shift all halfedges in the array > hedge_index
+    for (int hedge_id=hedge_index; hedge_id<_system.Numhalfedges-1; hedge_id++)
+    {
+        _system.halfedges[hedge_id] = _system.halfedges[hedge_id+1];
+        _system.halfedges[hedge_id].index--;
+    }
+
+    // udpating halfedges id in vertex structure
+    for (int vertex_id=0; vertex_id<_system.Numvertices; vertex_id++)
+    {
+        if (_system.vertices[vertex_id]._hedge > hedge_index)
+            _system.vertices[vertex_id]._hedge--;
+    }
+
+    // updating halfedges id in edge structure
+    for (int edge_id=0; edge_id<_system.Numedges; edge_id++)
+    {
+        if (_system.edges[edge_id]._hedge > hedge_index)
+            _system.edges[edge_id]._hedge--;
+    }
+
+    // updating halfedges id in face structure
+    for (int face_id=0; face_id<_system.Numfaces; face_id++)
+    {
+        if (_system.faces[face_id]._hedge > hedge_index)
+            _system.faces[face_id]._hedge--;
+    }
+
+    _system.Numhalfedges--;
+
+    for (int hedge_id=0; hedge_id<_system.Numhalfedges; hedge_id++)
+    {
+        if (_system.halfedges[hedge_id].next > hedge_index)
+            _system.halfedges[hedge_id].next--;
+        if (_system.halfedges[hedge_id].pair > hedge_index)
+            _system.halfedges[hedge_id].pair--;
+        if (_system.halfedges[hedge_id].prev > hedge_index)
+            _system.halfedges[hedge_id].prev--;
+    }
+}
+
+
+
+bool MeshOperations::edge_can_collapse(int edge_index)
+{
+    int he01 = _system.edges[edge_index]._hedge;
+    int v0 = _system.halfedges[he01].vert_from;
+    int v1 = _system.halfedges[he01].vert_to;
+    // First we check which of the two points will be kept
+    // if one of them is higher type, we keep this one
+    if (_system.vertices[v0].type < _system.vertices[v1].type)
+    {
+        he01 = _system.halfedges[he01].pair;
+        v0 = _system.halfedges[he01].vert_from;
+        v1 = _system.halfedges[he01].vert_to;
+    }
+    real3 r0 = _system.vertices[v0].r;
+    real3 r1 = _system.vertices[v1].r;
+
+
+    int he = _system.vertices[v0]._hedge;
+    int first = he;
+    std::set<int> v0_neighbours;
+    do
+    {
+        v0_neighbours.insert(_system.halfedges[he].vert_to);
+        he = _system.halfedges[he].pair;
+        he = _system.halfedges[he].next;
+    } while (he != first);
+
+    int count = 0;
+    he = _system.vertices[v1]._hedge;
+    first = he;
+    do
+    {
+        if( v0_neighbours.find(_system.halfedges[he].vert_to) != v0_neighbours.end())
+            count++;
+        he = _system.halfedges[he].pair;
+        he = _system.halfedges[he].next;
+    } while (he != first);
+
+    if (count != 2)
+        return false;
+
+    int stop = _system.halfedges[he01].pair;
+
+    he = _system.halfedges[he01].next;
+    he = _system.halfedges[he].pair;
+    he = _system.halfedges[he].next;
+    do
+    {
+        int v2 = _system.halfedges[he].vert_to;
+        int he_next = _system.halfedges[he].next;
+        int v3 = _system.halfedges[he_next].vert_to;
+        real3 r2 = _system.vertices[v2].r;
+        real3 r3 = _system.vertices[v3].r;
+
+        real3 n123 = pymemb::compute_normal_triangle_unit(r1, r2, r3);
+        real3 n023 = pymemb::compute_normal_triangle_unit(r0, r2, r3);
+
+        // a triangle will flip, can't perform edge collapse
+        if (pymemb::vector_dot(n123, n023) <= 0)
+            return false;
+
+        he = _system.halfedges[he].pair;
+        he = _system.halfedges[he].next;
+    } while (he != stop);
+
+    return true;
+}
+
+
+/*      Collapsing edge v0v1
+
+*/          
+
+void MeshOperations::edge_case_collapse(int he01, int &del_e1, int &del_e2, int &del_f0, int &del_f1)
+{
+    int he12 = _system.halfedges[he01].next;
+    int he20 = _system.halfedges[he12].next;
+    int he10 = _system.halfedges[he01].pair;
+    int he03 = _system.halfedges[he10].next;
+    int he31 = _system.halfedges[he03].next;
+    int he = _system.halfedges[he31].pair;
+    int he32 = _system.halfedges[he].next;
+    int v0 = _system.halfedges[he01].vert_from;
+    int v1 = _system.halfedges[he01].vert_to;
+    int v2 = _system.halfedges[he20].vert_from;
+    int v3 = _system.halfedges[he03].vert_to;
+
+    del_e1 = _system.halfedges[he12].edge;
+    del_e2 = _system.halfedges[he31].edge;
+    del_f0 = _system.halfedges[he01].face;
+    del_f1 = _system.halfedges[he10].face;
+    int f132 = _system.halfedges[he32].face;
+
+    //updating halfedges
+    _system.halfedges[he20].next = he03;
+    _system.halfedges[he03].prev = he20;
+    _system.halfedges[he03].next = he32;
+    _system.halfedges[he32].prev = he03;
+    _system.halfedges[he32].next = he20;
+    _system.halfedges[he20].prev = he32;
+    _system.halfedges[he20].face = f132;
+    _system.halfedges[he03].face = f132;
+
+    //updating vertices
+    _system.vertices[v0]._hedge = he03;
+    _system.vertices[v2]._hedge = he20;
+    _system.vertices[v3]._hedge = he32;
+
+    //updating face
+    _system.faces[f132].v1 = v0;
+    _system.faces[f132].v2 = v3;
+    _system.faces[f132].v3 = v2;
+    _system.faces[f132]._hedge = he32;
+
+    //updating edges
+    int e02 = _system.halfedges[he20].edge;
+    if (_system.edges[e02].v1 == v1)
+        _system.edges[e02].v1 = v3;
+    if (_system.edges[e02].v3 == v1)
+        _system.edges[e02].v3 = v3;
+    int he_pair = _system.halfedges[he20].pair;
+    _system.edges[e02].face_k = f132;
+    _system.edges[e02].face_l = _system.halfedges[he_pair].face;
+
+    int e03 = _system.halfedges[he03].edge;
+    if (_system.edges[e03].v1 == v1)
+        _system.edges[e03].v1 = v2;
+    if (_system.edges[e03].v3 == v1)
+        _system.edges[e03].v3 = v2;
+    he_pair = _system.halfedges[he03].pair;
+    _system.edges[e03].face_k = f132;
+    _system.edges[e03].face_l = _system.halfedges[he_pair].face;
+
+    int e23 = _system.halfedges[he32].edge;
+    if (_system.edges[e23].v1 == v1)
+        _system.edges[e23].v1 = v0;
+    if (_system.edges[e23].v3 == v1)
+        _system.edges[e23].v3 = v0;
+}
+
+
+void MeshOperations::edge_collapse(int edge_index, int &del_vertex, int &del_e1,
+                                    int &del_e2, int &del_f0, int &del_f1)
+{
+    int he01 = _system.edges[edge_index]._hedge;
+    int v0 = _system.halfedges[he01].vert_from;
+    int v1 = _system.halfedges[he01].vert_to;
+
+    // First we check which of the two points will be kept
+    // if one of them is higher type, we keep this one
+    if (_system.vertices[v0].type < _system.vertices[v1].type)
+    {
+        he01 = _system.halfedges[he01].pair;
+        v0 = _system.halfedges[he01].vert_from;
+        v1 = _system.halfedges[he01].vert_to;
+    }
+    
+    del_vertex = v1;
+    
+    compute_vertex_connexity(v1);
+    // dealing with edge case
+    if (_system.vertices[v1].coordination == 3)
+    {
+        edge_case_collapse(he01, del_e1, del_e2, del_f0, del_f1);
+        return;
+    }
+
+    // Get all ids needed
+    del_f0 = _system.halfedges[he01].face;
+    int he10 = _system.halfedges[he01].pair;
+    del_f1 = _system.halfedges[he10].face;
+    int he03 = _system.halfedges[he10].next;
+    int he31 = _system.halfedges[he03].next;
+    int he12 = _system.halfedges[he01].next;
+    int he20 = _system.halfedges[he12].next;
+    int he = _system.halfedges[he31].pair;
+    int he35 = _system.halfedges[he].next;
+    int he51 = _system.halfedges[he35].next;
+    he = _system.halfedges[he12].pair;
+    int he14 = _system.halfedges[he].next;
+    int he42 = _system.halfedges[he14].next;
+
+    del_e1 = _system.halfedges[he31].edge;
+    del_e2 = _system.halfedges[he12].edge;
+
+    int v2 =_system.halfedges[he12].vert_to;
+    int v3 = _system.halfedges[he03].vert_to;
+    int v4 = _system.halfedges[he14].vert_to;
+    int v5 = _system.halfedges[he51].vert_from;
+
+    he = he14;
+    do
+    {
+        _system.halfedges[he].vert_from = v0;
+        int edge = _system.halfedges[he].edge;
+        _system.edges[edge].i = v0;
+        _system.edges[edge].j = _system.halfedges[he].vert_to;
+        _system.edges[edge].v0 = v0;
+        _system.edges[edge].v2 = _system.halfedges[he].vert_to;
+
+        int he_pair = _system.halfedges[he].pair;
+        int he_next = _system.halfedges[he].next;
+        _system.halfedges[he_pair].vert_to = v0;
+
+        //Updating face
+        int face = _system.halfedges[he].face;
+        _system.faces[face]._hedge = he_next;
+        _system.faces[face].v1 = v0;
+        _system.faces[face].v2 = _system.halfedges[he].vert_to;
+        _system.faces[face].v3 = _system.halfedges[he_next].vert_to;
+
+        int outer_edge = _system.halfedges[he_next].edge;
+        if (_system.edges[outer_edge].v1 == v1)
+            _system.edges[outer_edge].v1 = v0;
+        if (_system.edges[outer_edge].v3 == v1)
+            _system.edges[outer_edge].v3 = v0;
+
+        he = _system.halfedges[he_pair].next;
+    } while(he != he10);
+
+    // Updating vertices
+    _system.vertices[v2]._hedge = he20;
+    _system.vertices[v3]._hedge = he35;
+    _system.vertices[v0]._hedge = he03;
+
+
+    // Updating halfedges
+    _system.halfedges[he03].next = he35;
+    _system.halfedges[he35].prev = he03;
+    _system.halfedges[he51].next = he03;
+    _system.halfedges[he03].prev = he51;
+    _system.halfedges[he20].next = he14;
+    _system.halfedges[he14].prev = he20;
+
+    _system.halfedges[he03].face = _system.halfedges[he35].face;
+    _system.halfedges[he42].next = he20;
+    _system.halfedges[he20].prev = he42;
+    _system.halfedges[he20].face = _system.halfedges[he42].face;
+
+    // Updating outer edges
+
+    int outer_edge = _system.halfedges[he20].edge;
+    if (_system.edges[outer_edge].v1 == v1)
+        _system.edges[outer_edge].v1 = v4;
+    if (_system.edges[outer_edge].v3 == v1)
+        _system.edges[outer_edge].v3 = v4;
+    he = _system.halfedges[he20].pair;
+    _system.edges[outer_edge].face_k = _system.halfedges[he].face;
+    _system.edges[outer_edge].face_l = _system.halfedges[he14].face;
+
+    outer_edge = _system.halfedges[he03].edge;
+    if (_system.edges[outer_edge].v1 == v1)
+        _system.edges[outer_edge].v1 = v5;
+    if (_system.edges[outer_edge].v3 == v1)
+        _system.edges[outer_edge].v3 = v5;
+    he = _system.halfedges[he03].pair;
+    _system.edges[outer_edge].face_k = _system.halfedges[he].face;
+    _system.edges[outer_edge].face_l = _system.halfedges[he35].face;
+    
+}
+
+/*      Splitting edge v0v2
+         v0                                 v0
+       / | \                              / | \
+      /  |  \                            /  |  \
+    v3   |   v1          -->            v3--v4--v1
+      \  |  /                            \  |  /
+       \ | /                              \ | /
+         v2                                 v2
+
+    Repurpose face : f034 = f032 // f041 = f021
+    Repurpose edge : e04 = e02
+    Repurpose halfedge : he04 = he02 // he40 = he20
+*/
+
+void MeshOperations::edge_split(int edge_index, int v4, int e34, int e14, int e24,
+                                int f243, int f142)
+{
+    // First get all ids needed
+    int he02 = _system.edges[edge_index]._hedge;
+    int v0 = _system.halfedges[he02].vert_from;
+    int v2 = _system.halfedges[he02].vert_to;
+    int he21 = _system.halfedges[he02].next;
+    int v1 = _system.halfedges[he21].vert_to;
+    int he_pair = _system.halfedges[he02].pair;
+    int he03 = _system.halfedges[he_pair].next;
+    int v3 = _system.halfedges[he03].vert_to;
+    int he23 = _system.halfedges[he03].next;
+    he23 = _system.halfedges[he23].pair;
+    int he01 = _system.halfedges[he21].next;
+    he01 = _system.halfedges[he01].pair;
+
+    int he34 = _system.edges[e34]._hedge;
+    int he43 = _system.halfedges[he34].pair;
+    int he14 = _system.edges[e14]._hedge;
+    int he41 = _system.halfedges[he14].pair;
+    int he24 = _system.edges[e24]._hedge;
+    int he42 = _system.halfedges[he24].pair;
+    
+    int f021 = _system.halfedges[he02].face;
+    int f032 = _system.halfedges[he03].face;
+
+    _system.vertices[v4].r = pymemb::vector_sum(_system.vertices[v0].r, _system.vertices[v2].r);
+    aXvec(0.5, _system.vertices[v4].r);
+    _system.vertices[v4]._hedge = he43;
+    _system.vertices[v4].type = std::min(_system.vertices[v0].type, _system.vertices[v2].type);
+
+    // Setting up topology on new halfedges
+    _system.halfedges[he34].vert_from = v3;
+    _system.halfedges[he34].vert_to = v4;
+    _system.halfedges[he34].next = _system.halfedges[he02].pair;
+    _system.halfedges[he34].prev = he03;
+    _system.halfedges[he34].face = f032;
+
+    _system.halfedges[he43].vert_from = v4;
+    _system.halfedges[he43].vert_to = v3;
+    _system.halfedges[he43].next = _system.halfedges[he23].pair;
+    _system.halfedges[he43].prev = he24;
+    _system.halfedges[he43].face = f243;
+
+    _system.halfedges[he14].vert_from = v1;
+    _system.halfedges[he14].vert_to = v4;
+    _system.halfedges[he14].next = he42;
+    _system.halfedges[he14].prev = he21;
+    _system.halfedges[he14].face = f142;
+
+    _system.halfedges[he41].vert_from = v4;
+    _system.halfedges[he41].vert_to = v1;
+    _system.halfedges[he41].next = _system.halfedges[he01].pair;
+    _system.halfedges[he41].prev = he02;
+    _system.halfedges[he41].face = f021;
+
+    _system.halfedges[he24].vert_from = v2;
+    _system.halfedges[he24].vert_to = v4;
+    _system.halfedges[he24].next = he43;
+    _system.halfedges[he24].prev = _system.halfedges[he23].pair;
+    _system.halfedges[he24].face = f243;
+
+    _system.halfedges[he42].vert_from = v4;
+    _system.halfedges[he42].vert_to = v2;
+    _system.halfedges[he42].next = he21;
+    _system.halfedges[he42].prev = he14;
+    _system.halfedges[he42].face = f142;
+
+    // Setting up new edges
+    _system.edges[e34].i = v3;
+    _system.edges[e34].j = v4;
+    _system.edges[e34]._hedge = he34;
+    _system.edges[e34].face_k = _system.halfedges[he34].face;
+    _system.edges[e34].face_l = _system.halfedges[he43].face;
+    _system.edges[e34].v0 = v3;
+    _system.edges[e34].v1 = v0;
+    _system.edges[e34].v2 = v4;
+    _system.edges[e34].v3 = v2;
+
+    _system.edges[e14].i = v1;
+    _system.edges[e14].j = v4;
+    _system.edges[e14]._hedge = he14;
+    _system.edges[e14].face_k = _system.halfedges[he14].face;
+    _system.edges[e14].face_l = _system.halfedges[he41].face;
+    _system.edges[e14].v0 = v1;
+    _system.edges[e14].v1 = v2;
+    _system.edges[e14].v2 = v4;
+    _system.edges[e14].v3 = v0;
+
+    _system.edges[e24].i = v2;
+    _system.edges[e24].j = v4;
+    _system.edges[e24]._hedge = he24;
+    _system.edges[e24].face_k = _system.halfedges[he24].face;
+    _system.edges[e24].face_l = _system.halfedges[he42].face;
+    _system.edges[e24].v0 = v2;
+    _system.edges[e24].v1 = v3;
+    _system.edges[e24].v2 = v4;
+    _system.edges[e24].v3 = v1;
+
+    // Setting up new face
+    _system.faces[f243].v1 = v2;
+    _system.faces[f243].v2 = v4;
+    _system.faces[f243].v3 = v3;
+    _system.faces[f243]._hedge = he24;
+
+    _system.faces[f142].v1 = v1;
+    _system.faces[f142].v2 = v4;
+    _system.faces[f142].v3 = v2;
+    _system.faces[f142]._hedge = he14;
+
+    // Updating vertices
+    _system.vertices[v2]._hedge = he21;
+
+    // Updating repurposed halfedges
+    _system.halfedges[he02].vert_to = v4;
+    _system.halfedges[he02].next = he41;
+
+    int he = _system.halfedges[he02].pair;
+    _system.halfedges[he].vert_from = v4;
+    _system.halfedges[he].prev = he34;
+
+
+    // Updating repurposed edge
+    _system.edges[edge_index].i = v0;
+    _system.edges[edge_index].j = v4;
+    _system.edges[edge_index].v0 = v0;
+    _system.edges[edge_index].v1 = v1;
+    _system.edges[edge_index].v2 = v4;
+    _system.edges[edge_index].v3 = v3;
+
+    // Updating repurposed faces
+    _system.faces[f021].v1 = v0;
+    _system.faces[f021].v2 = v4;
+    _system.faces[f021].v3 = v1;
+    _system.faces[f021]._hedge = he02;
+
+    _system.faces[f032].v1 = v0;
+    _system.faces[f032].v2 = v3;
+    _system.faces[f032].v3 = v4;
+    _system.faces[f032]._hedge = he03;
+    
+    // Updating exterior halfedges
+    he = _system.halfedges[he23].pair;
+    _system.halfedges[he].face = f243;
+    _system.halfedges[he].next = he24;
+    _system.halfedges[he].prev = he43;
+
+    _system.halfedges[he21].face = f142;
+    _system.halfedges[he21].next = he14;
+    _system.halfedges[he21].prev = he42;
+
+    he = _system.halfedges[he01].pair;
+    _system.halfedges[he].prev = he41;
+
+    _system.halfedges[he03].next = he34;
+
+    // Updating exterior edges
+    int e = _system.halfedges[he23].edge;
+    _system.edges[e].face_k = _system.halfedges[he23].face;
+    _system.edges[e].face_l = _system.halfedges[he24].face;
+    _system.edges[e].v0 = v2;
+    he = _system.halfedges[he23].next;
+    _system.edges[e].v1 = _system.halfedges[he].vert_to;
+    _system.edges[e].v2 = v3;
+    _system.edges[e].v3 = v4;
+
+    e = _system.halfedges[he21].edge;
+    _system.edges[e].face_k = _system.halfedges[he21].face;
+    he = _system.halfedges[he21].pair;
+    _system.edges[e].face_l = _system.halfedges[he].face;
+    _system.edges[e].v0 = v2;
+    he = _system.halfedges[he].next;
+    _system.edges[e].v1 = _system.halfedges[he].vert_to;
+    _system.edges[e].v2 = v1;
+    _system.edges[e].v3 = v4;
+
+    e = _system.halfedges[he01].edge;
+    _system.edges[e].face_k = _system.halfedges[he01].face;
+    _system.edges[e].face_l = _system.halfedges[he02].face;
+    _system.edges[e].v0 = v0;
+    _system.edges[e].v1 = v4;
+    _system.edges[e].v2 = v1;
+    he = _system.halfedges[he01].next;
+    _system.edges[e].v3 = _system.halfedges[he].vert_to;
+
+    e = _system.halfedges[he03].edge;
+    _system.edges[e].face_k = _system.halfedges[he03].face;
+    he = _system.halfedges[he03].pair;
+    _system.edges[e].face_l = _system.halfedges[he].face;
+    _system.edges[e].v0 = v0;
+    _system.edges[e].v1 = v4;
+    _system.edges[e].v2 = v3;
+    he = _system.halfedges[he].next;
+    _system.edges[e].v3 = _system.halfedges[he].vert_to;
+}
+
+
+void MeshOperations::refine_mesh_edge_split(real threshold)
+{
+    real avg_edge_length = compute_average_edge_length();
+    for (int edge_id=0; edge_id<_system.Numedges; edge_id++)
+    {
+        int v0 = _system.edges[edge_id].i;
+        int v1 = _system.edges[edge_id].j;
+        real edge_length = pymemb::vector_length(pymemb::vector_subtract(_system.vertices[v0].r, _system.vertices[v1].r));
+        if (edge_length/avg_edge_length > threshold)
+        {
+            int v = create_vertex();
+            int e0 = create_edge();
+            int e1 = create_edge();
+            int e2 = create_edge();
+            int f0 = create_face();
+            int f1 = create_face();
+            edge_split(edge_id, v, e0, e1, e2, f0, f1);
+        }
+    }    
+}
+
+void MeshOperations::simplify_mesh(real threshold)
+{
+    real avg_edge_length = compute_average_edge_length();
+    for (int edge_id=0; edge_id<_system.Numedges; edge_id++)
+    {
+        int v0 = _system.edges[edge_id].i;
+        int v1 = _system.edges[edge_id].j;
+
+        real edge_length = pymemb::vector_length(pymemb::vector_subtract(_system.vertices[v0].r, _system.vertices[v1].r));
+        if (edge_length/avg_edge_length < threshold)
+        {
+            int del_v, del_e1, del_e2, del_f0, del_f1;
+            edge_collapse(edge_id, del_v, del_e1, del_e2, del_f0, del_f1);
+            delete_vertex(del_v);
+            _system.vertices.resize(_system.Numvertices);
+            delete_edge(del_e1);
+            if (del_e1 < del_e2)
+                del_e2--;
+            if (del_e1 < edge_id)
+                edge_id--;
+            delete_edge(del_e2);
+            if (del_e2 < edge_id)
+                edge_id--;
+            delete_edge(edge_id);
+            _system.halfedges.resize(_system.Numhalfedges);
+            _system.edges.resize(_system.Numedges);
+            delete_face(del_f0);
+            if (del_f0 < del_f1)
+                del_f1--;
+            delete_face(del_f1);
+            _system.faces.resize(_system.Numfaces);
+        }
+    }
+}
+
+void MeshOperations::adapt_mesh(real threshold)
+{
+    real avg_edge_length = compute_average_edge_length();
+
+    std::vector<std::pair<real, int>> sorted_edges;
+    for (int edge_id=0; edge_id<_system.Numedges; edge_id++)
+    {
+        real3 a = _system.vertices[_system.edges[edge_id].i].r;
+        real3 b = _system.vertices[_system.edges[edge_id].j].r;
+
+        std::pair<real, int> len_edge(pymemb::vector_length(pymemb::vector_subtract(a, b)), edge_id);
+        sorted_edges.push_back(len_edge);
+    }
+    std::sort(sorted_edges.begin(), sorted_edges.end());
+
+    
+    int i=0;
+    int j=sorted_edges.size()-1;
+    while (i < j)
+    {
+        real min_ratio = sorted_edges[i].first/avg_edge_length;
+        real max_ratio = sorted_edges[j].first/avg_edge_length;
+
+        if (min_ratio < threshold || max_ratio > (1/threshold))
+        {
+            if (edge_can_collapse(sorted_edges[i].second))
+            {
+                int del_e1, del_e2, del_v, del_f0, del_f1;
+                edge_collapse(sorted_edges[i].second, del_v, del_e1, del_e2, del_f0, del_f1);
+                
+                while (del_e1 == sorted_edges[j].second || del_e2 == sorted_edges[j].second)
+                    j--;
+
+                edge_split(sorted_edges[j].second, del_v, sorted_edges[i].second, del_e1, del_e2, del_f0, del_f1);
+            }
+            else
+                j++;       
+        }
+
+        else
+            break;
+        i++;
+        j--;
+    }
+
 }
diff --git a/pymembrane/cppmodule/src/mesh/meshoperations.hpp b/pymembrane/cppmodule/src/mesh/meshoperations.hpp
index 3ed537da..fae2d1ed 100644
--- a/pymembrane/cppmodule/src/mesh/meshoperations.hpp
+++ b/pymembrane/cppmodule/src/mesh/meshoperations.hpp
@@ -21,9 +21,34 @@ class MeshOperations
     ~MeshOperations(void) {}
 
     bool check_if_edge_can_flip(const int& flip_edge_index);
-    void edge_flip(const int& flip_edge_index, const bool& flip_face_up);
-    void equiangulation(void);
+    bool edge_need_flip(int flip_edge_index);
+    real compute_average_edge_length();
+    void edge_flip(int flip_edge_index);
+    void refine_mesh_edge_flip();
+    void simplify_mesh(real collapse_threshold=0.5);
+    void refine_mesh_edge_split(real split_threshhold=2.0);
+    void adapt_mesh(real threshold=0.5);
+    //void equiangulation(void);
+    void compute_vertices_connexities();
+
 private:
+    void compute_vertex_connexity(int vertex_index);
+    bool edge_need_collapse(int edge_index, real minimum);
+    bool edge_can_collapse(int edge_index);
+    void edge_case_collapse(int he01, int &del_e1, int &del_e2, int &del_f0, int &del_f1);
+    void edge_collapse(int edge_index);
+    void edge_collapse(int edge_index, int &del_vertex, int &del_e1, int &del_e2,
+                        int &del_f0, int &del_f1);
+    void edge_split(int edge_index, int new_vertex, int new_edge0, int new_edge1,
+                    int new_edge2, int new_f0, int new_f1);
+    int create_vertex(real mass=1.0);
+    int create_edge();
+    int create_face();
+    void delete_vertex(int vertex_index);
+    void delete_edge(int edge_index);
+    void delete_hedge(int hedge_index);
+    void delete_face(int face_index);
+
     SystemClass& _system;
 
 };
diff --git a/pymembrane/cppmodule/src/mesh/pybind_export_mesh.hpp b/pymembrane/cppmodule/src/mesh/pybind_export_mesh.hpp
index 2f7a5306..2f1865d6 100644
--- a/pymembrane/cppmodule/src/mesh/pybind_export_mesh.hpp
+++ b/pymembrane/cppmodule/src/mesh/pybind_export_mesh.hpp
@@ -86,7 +86,8 @@ void export_HE_Vertex(py::module &m)
         .def_readwrite("mass", &HE_VertexProp::mass, "mass")
         .def_readwrite("type", &HE_VertexProp::type, "type")
         .def_readonly("energy", &HE_VertexProp::energy, "Conservative Energy")
-        .def_readwrite("property", &HE_VertexProp::_property, "Properties");
+        .def_readwrite("property", &HE_VertexProp::_property, "Properties")
+        .def_readwrite("spin", &HE_VertexProp::spin, "Spin Value");
 }
 
 void export_HE_Vertex_Vector(py::module &m)
diff --git a/pymembrane/cppmodule/src/potentials/potentialBending.cpp b/pymembrane/cppmodule/src/potentials/potentialBending.cpp
index efb92c3b..3e003c61 100755
--- a/pymembrane/cppmodule/src/potentials/potentialBending.cpp
+++ b/pymembrane/cppmodule/src/potentials/potentialBending.cpp
@@ -158,7 +158,11 @@ real ComputeVertexBendingEnergy::compute_vertex_energy(int query_vertex_index)
                 real3 nk_ref, nl_ref;
                 nk_ref = _system.faces[_system.edges[edge_index].face_k].normal_reference;
                 nl_ref = _system.faces[_system.edges[edge_index].face_l].normal_reference;
-                energy += ComputeVertexBendingEnergy_lambda(nk, nl, nk_ref, nl_ref, kappa_tilde);
+					// Do not take into account the bending energy for vertices which are covered by a particle. 
+					// Therefore, an if statement was added. type==-1 is a free vertex.
+				if (_system.vertices[v0].type==-1) {
+					energy += ComputeVertexBendingEnergy_lambda(nk, nl, nk_ref, nl_ref, kappa_tilde);
+				}
             }
         }
         int he_prev = _system.halfedges[he].prev;
diff --git a/pymembrane/cppmodule/src/potentials/potentialHarmonicDye.cpp b/pymembrane/cppmodule/src/potentials/potentialHarmonicDye.cpp
new file mode 100644
index 00000000..de931b23
--- /dev/null
+++ b/pymembrane/cppmodule/src/potentials/potentialHarmonicDye.cpp
@@ -0,0 +1,247 @@
+#include "potentialHarmonicDye.hpp"
+
+
+
+double ComputeEdgeHarmonicSpinEnergy(const real3 r1,
+                                 const real3 r2,
+                                 const double k,
+                                 const double l0)
+{
+    real3 rij;
+    vsub(rij, r2, r1);
+
+    double dr = sqrt(vdot(rij, rij));
+
+    double energy = 0.5 * k * (dr - l0) * (dr - l0);
+
+    return energy;
+}
+
+double ComputeEdgeHarmonicSpinEnergy_ferro(const real s1,
+                                  const real s2,
+                                  const double J)
+{
+    auto H = -J*s1*s2;
+    return H;
+}
+
+void ComputeVertexHarmonicSpinEnergy_kernel(const int Numedges,
+                                        HE_EdgeProp *edges,
+                                        const HE_VertexProp *vertices,
+                                        const double *__restrict__ _k,
+                                        const double *__restrict__ _l0,
+                                        const double *__restrict__ _J)
+{
+    for (int edge_index = 0; edge_index < Numedges; edge_index++)
+    {
+        int type = edges[edge_index].type;
+
+        int v1 = edges[edge_index].i;
+        real3 _r1 = vertices[v1].r;
+        auto _s1 = vertices[v1].spin;
+
+        int v2 = edges[edge_index].j;
+        real3 _r2 = vertices[v2].r;
+        auto _s2 = vertices[v2].spin;
+		
+		auto _vtype1 = vertices[v1].type;
+		auto _vtype2 = vertices[v2].type;
+
+        //Harmonic Energy
+		//Free vertices have the full interaction. Vertices at the edge of a particle-covered
+		//surface area exhibit only half the interaction with their NN free vertices.
+		//Vertices covered by a particle do not interact between themselves.
+		double energy;
+		if ((_vtype1==-1) && (_vtype2==-1))
+			energy = ComputeEdgeHarmonicSpinEnergy(_r1, _r2, _k[type], _l0[type]); 
+		if (((_vtype1==-1) && (_vtype2>=0)) || ((_vtype1>=0) && (_vtype2==-1)))
+			energy = 0.5*ComputeEdgeHarmonicSpinEnergy(_r1, _r2, _k[type], _l0[type]); 
+
+
+		//COMMENTED FERRO ENERGY (no spins in particle-on-drop systems)
+        //Ferromagnetic Energy
+        //energy+=ComputeEdgeHarmonicSpinEnergy_ferro(_s1, _s2, _J[type]);
+
+        ///ADD ENERGY TO THAT EDGE
+        edges[edge_index].energy += energy;
+    }
+	
+/* 	double ener_tot;
+	for (int edge_index = 0; edge_index < Numedges; edge_index++) {
+		ener_tot+=edges[edge_index].energy;
+	}
+	std::cout << "Total: " << ener_tot << std::endl; */
+	
+}
+
+double ComputeVertexHarmonicSpinEnergy::compute_edge_energy(int query_edge_index)
+{
+    int type = _system.edges[query_edge_index].type;
+    int v1 = _system.edges[query_edge_index].i;
+    real3 _r1 = _system.vertices[v1].r;
+    auto _s1 = _system.vertices[v1].spin;
+
+    int v2 = _system.edges[query_edge_index].j;
+    real3 _r2 = _system.vertices[v2].r;
+    auto _s2 = _system.vertices[v2].spin;
+
+    //Harmonic Energy
+    double edge_energy = ComputeEdgeHarmonicSpinEnergy(_r1, _r2, k[type], l0[type]);
+    
+    //Ferromagnetic Energy
+    edge_energy+=ComputeEdgeHarmonicSpinEnergy_ferro(_s1, _s2, J[type]);
+    return edge_energy;
+}
+
+double ComputeVertexHarmonicSpinEnergy::compute_vertex_energy(int query_vertex_index)
+{
+
+    double harmonic_energy = 0.0;
+    //double ferro_energy = 0.0;  
+    ///< get the triangle that this vertex is part of
+    int he = _system.vertices[query_vertex_index]._hedge;
+    int first = he;
+	
+	if (_system.vertices[query_vertex_index].type==-1) {    //ELI: If we deal here with the energy of a particle-free vertex, do the usual calculation.
+		do
+		{
+			// DO SOMETHING WITH THAT FACE
+			int edge_index = _system.halfedges[he].edge;
+			int type = _system.edges[edge_index].type;
+			int v1 = _system.edges[edge_index].i;
+			int v2 = _system.edges[edge_index].j;
+
+			real3 _r1 = _system.vertices[v1].r;
+			real3 _r2 = _system.vertices[v2].r;
+			
+			//Vertices covered by a particle do not exhibit harmonic energy.
+			//Vertices at the edge of a particle-covered area have 1/2 interaction with their 
+			//free NN vertices.
+			auto _vtype1 = _system.vertices[v1].type;
+			auto _vtype2 = _system.vertices[v2].type;
+
+			if ((_vtype1==-1) && (_vtype2==-1))
+				harmonic_energy += ComputeEdgeHarmonicSpinEnergy(_r1, _r2, k[type], l0[type]); //ELI: Originally, there was a 0.5 factor here. I removed it.
+			if (((_vtype1==-1) && (_vtype2>=0)) || ((_vtype1>=0) && (_vtype2==-1)))
+				harmonic_energy += 0.5*ComputeEdgeHarmonicSpinEnergy(_r1, _r2, k[type], l0[type]); 
+			// Note: if ((_vtype1>=0) && (_vtype2>=0)) do nothing, as this is a spring "covered by a colloidal particle".
+		
+				
+
+			//ferro_energy += 0.5*ComputeEdgeHarmonicSpinEnergy_ferro(_s1, _s2, J[type]);
+			
+			// MOVE TO THE NEXT FACE
+			int he_pair = _system.halfedges[he].pair;
+			he = _system.halfedges[he_pair].next;
+		} while ((he != first));
+	} else if (_system.vertices[query_vertex_index].type==query_vertex_index) {   //ELI: if we deal with a vertex at the center of a particle. Check the energy of this particle's edge.
+		int edge_vert_ii;
+		edge_vert_ii=_system.vertices[query_vertex_index].mass;
+		do
+		{	
+			he = _system.vertices[edge_vert_ii]._hedge;
+			first = he;
+			do
+			{
+				// DO SOMETHING WITH THAT FACE
+				int edge_index = _system.halfedges[he].edge;
+				int type = _system.edges[edge_index].type;
+				int v1 = _system.edges[edge_index].i;
+				int v2 = _system.edges[edge_index].j;
+
+				real3 _r1 = _system.vertices[v1].r;
+				real3 _r2 = _system.vertices[v2].r;
+				
+				auto _vtype1 = _system.vertices[v1].type;
+				auto _vtype2 = _system.vertices[v2].type;
+
+				if ((_vtype1==-1) && (_vtype2==-1))
+					harmonic_energy += ComputeEdgeHarmonicSpinEnergy(_r1, _r2, k[type], l0[type]); 
+				if (((_vtype1==-1) && (_vtype2>=0)) || ((_vtype1>=0) && (_vtype2==-1)))
+					harmonic_energy += 0.5*ComputeEdgeHarmonicSpinEnergy(_r1, _r2, k[type], l0[type]); 
+			
+				// MOVE TO THE NEXT FACE
+				int he_pair = _system.halfedges[he].pair;
+				he = _system.halfedges[he_pair].next;
+			} while ((he != first));
+			edge_vert_ii=_system.vertices[edge_vert_ii].mass;
+		} while (edge_vert_ii!=-1);
+	
+	}
+	
+	
+// This block is for 
+/*     if(_system.vertices[query_vertex_index].spin>0.0)
+    {
+        auto vertex_type = _system.vertices[query_vertex_index].type;
+        harmonic_energy = Ea[vertex_type];
+    } */
+	
+    auto energy = harmonic_energy; // COMMENTED HERE: + ferro_energy;
+    return energy;
+}
+
+void ComputeVertexHarmonicSpinEnergy::compute_energy(void)
+{
+
+    ComputeVertexHarmonicSpinEnergy_kernel(_system.Numedges,
+                                       &_system.edges[0],
+                                       &_system.vertices[0],
+                                       &k[0],
+                                       &l0[0],
+                                       &J[0]);
+}
+
+double ComputeVertexHarmonicSpinForce(const real3 rij,
+                                  const double k,
+                                  const double l0)
+{
+    double dr = sqrt(vdot(rij, rij));
+    double fval = k * (dr - l0) / dr;
+    return fval;
+}
+
+void ComputeVertexHarmonicSpinForce_kernel(const int Numedges,
+                                       HE_VertexProp *vertices,
+                                       const HE_EdgeProp *__restrict__ edges,
+                                       const double *__restrict__ _k,
+                                       const double *__restrict__ _l0)
+{
+    //int i = blockIdx.x*blockDim.x + threadIdx.x;
+    //if(  i < Numvertices )
+    for (int edge_index = 0; edge_index < Numedges; edge_index++)
+    {
+
+        int v1 = edges[edge_index].i;
+        real3 _r1 = vertices[v1].r;
+
+        int v2 = edges[edge_index].j;
+        real3 _r2 = vertices[v2].r;
+
+        real3 _rij;
+        vsub(_rij, _r2, _r1);
+
+        int type = edges[edge_index].type;
+
+        double fval = ComputeVertexHarmonicSpinForce(_rij, _k[type], _l0[type]);
+
+        vertices[v1].forceC.x += fval * _rij.x;
+        vertices[v1].forceC.y += fval * _rij.y;
+        vertices[v1].forceC.z += fval * _rij.z;
+
+        vertices[v2].forceC.x += -1.0 * fval * _rij.x;
+        vertices[v2].forceC.y += -1.0 * fval * _rij.y;
+        vertices[v2].forceC.z += -1.0 * fval * _rij.z;
+    }
+}
+
+void ComputeVertexHarmonicSpinEnergy::compute(void)
+{
+
+    ComputeVertexHarmonicSpinForce_kernel(_system.Numedges,
+                                      &_system.vertices[0],
+                                      &_system.edges[0],
+                                      &k[0],
+                                      &l0[0]);
+}
+
diff --git a/pymembrane/cppmodule/src/potentials/potentialHarmonicDye.hpp b/pymembrane/cppmodule/src/potentials/potentialHarmonicDye.hpp
new file mode 100644
index 00000000..16822ddf
--- /dev/null
+++ b/pymembrane/cppmodule/src/potentials/potentialHarmonicDye.hpp
@@ -0,0 +1,107 @@
+/*!
+* @file potentialharmonic.hpp
+* @brief ComputeVertexHarmonicSpinEnergy class
+* @author Daniel Matoz, fdamatoz@gmail.com
+* @date 20-Sept-2017
+*/
+
+#ifndef __potentialHarmonicDye_HPP__
+#define __potentialHarmonicDye_HPP__
+
+/** @addtogroup computeenergy Compute Harmonic Edge Energy
+ *  @brief ComputeVertexHarmonicSpinEnergy definitions
+ *  @{
+ */
+//host
+#include "computeforceclass.hpp"
+
+//
+
+#include "../system/systemclass.hpp"
+#include "../mesh/computegeometry.hpp"
+
+/**
+ * @class ComputeVertexHarmonicSpinEnergy
+ * @brief ComputeVertexHarmonicSpinEnergy compute Vertex Harmonic (edge) Energy
+ */
+class ComputeVertexHarmonicSpinEnergy : public ComputeForceClass
+{
+public:
+  ComputeVertexHarmonicSpinEnergy(SystemClass &system) : ComputeForceClass(system)
+  {
+    m_name = "Harmonic"; //!< potential name
+    m_type = "edge";     //!< potential type
+    this->set_default_properties();
+  }
+
+  ~ComputeVertexHarmonicSpinEnergy() {}
+
+  void set_default_properties(void) override
+  {
+    pymemb::vector<real> _k(NUM_TYPES_ALLOWED, 0.0);
+    k = _k;
+    pymemb::vector<real> _l0(NUM_TYPES_ALLOWED, 1.0);
+    l0 = _l0;
+    pymemb::vector<real> _Ea(NUM_TYPES_ALLOWED, 1.0);
+    Ea = _Ea;
+  }
+
+  using ComputeForceClass::set_property;
+  void set_property(std::map<std::string, std::map<std::string, std::string>> &region_map) override
+  {
+    for (const auto &item : region_map)
+    {
+      if (item.first.compare("k") == 0)
+      {
+        pymemb::vector<real> _k = util::from_dict_to_vector_types(pymemb::copy(k), item.second);
+        k = _k;
+      }
+      else if (item.first.compare("l0") == 0)
+      {
+        pymemb::vector<real> _l0 = util::from_dict_to_vector_types(pymemb::copy(l0), item.second);
+        l0 = _l0;
+      }
+      else if (item.first.compare("J") == 0)
+      {
+        pymemb::vector<real> _J = util::from_dict_to_vector_types(pymemb::copy(l0), item.second);
+        J = _J;
+      }
+      else if (item.first.compare("Ea") == 0)
+      {
+        pymemb::vector<real> _Ea = util::from_dict_to_vector_types(pymemb::copy(l0), item.second);
+        Ea = _Ea;
+      }
+      else
+        this->print_warning_property_name(item.first);
+    }
+  }
+  
+  std::map<std::string, std::string> get_info(void) override
+  {
+    std::map<std::string, std::string> value;
+    value["name"] = m_name;
+    value["type"] = m_type;
+    value["k"] = util::to_string_vec(k);
+    value["l0"] = util::to_string_vec(l0);
+    value["J"] = util::to_string_vec(J);
+    value["Ea"] = util::to_string_vec(Ea);
+    return value;
+  }
+
+  void compute_energy(void) override;
+  void compute(void) override;
+  real compute_edge_energy(int) override;
+  real compute_vertex_energy(int) override;
+  void compute_stress(void) override {}
+  void compute_atomic_stress(void)override {}
+
+private:
+  pymemb::vector<real> k;  //!< spring constant
+  pymemb::vector<real> l0; //!< rest length
+  pymemb::vector<real> J; //!< rest length
+  pymemb::vector<real> Ea; //!< rest length
+
+};
+
+#endif
+
diff --git a/pymembrane/cppmodule/src/potentials/potentialIsing.cpp b/pymembrane/cppmodule/src/potentials/potentialIsing.cpp
new file mode 100644
index 00000000..2ee664ff
--- /dev/null
+++ b/pymembrane/cppmodule/src/potentials/potentialIsing.cpp
@@ -0,0 +1,91 @@
+#include "potentialIsing.hpp"
+
+/*! Iterate over all edges that origiante in the given vertex. If the
+    edge is shorter than \a m_min or longer than \a m_max infinity (actually
+    a very large number, \f$ 10^{15} \f$ is returned. Otherwise, this method
+    returns zero.
+
+    \f$ E_{limit} = \infty \f$ if \f$ r < l_{min} \f$ or \f$ r > l_{max} \f$ and
+    \f$ E_{limit} = 0 \f$ otherwise
+    \param v Pointer to the vertex
+*/
+
+real ComputeEdgeFerroEnergy_lambda(const real& s1,
+                                const real& s2,
+                                const real& J)
+{
+    auto H = -J * s1 * s2;
+    return H;
+}
+
+void ComputeVertexFerroEnergy_fn(int Numedges,
+                                 HE_EdgeProp *edges,
+                                 HE_VertexProp *vertices,
+                                 real *_J,
+                                 real *_h)
+{
+    for (int edge_index = 0; edge_index < Numedges; edge_index++)
+    {
+        int type = edges[edge_index].type;
+
+        int v1 = edges[edge_index].i;
+        auto _s1 = vertices[v1].spin;
+
+        int v2 = edges[edge_index].j;
+        auto _s2 = vertices[v2].spin;
+
+        edges[edge_index].energy += ComputeEdgeFerroEnergy_lambda(_s1, _s2, _J[type]);
+    }
+}
+
+void ComputeVertexFerromagneticEnergy::compute_energy(void)
+{
+
+    ComputeVertexFerroEnergy_fn(_system.Numedges,
+                                &_system.edges[0],
+                                &_system.vertices[0],
+                                &J[0],
+                                &h[0]);
+}
+
+real ComputeVertexFerromagneticEnergy::compute_edge_energy(int query_edge_index)
+{
+    int type = _system.edges[query_edge_index].type;
+
+    int v1 = _system.edges[query_edge_index].i;
+    auto _s1 = _system.vertices[v1].spin;
+
+    int v2 = _system.edges[query_edge_index].j;
+    auto _s2 = _system.vertices[v2].spin;
+
+    real edge_energy = ComputeEdgeFerroEnergy_lambda(_s1, _s2, J[type]);
+
+    return edge_energy;
+}
+
+real ComputeVertexFerromagneticEnergy::compute_vertex_energy(int query_vertex_index)
+{
+
+    real energy = 0.0;
+    ///< get the triangle that this vertex is part of
+    int he = _system.vertices[query_vertex_index]._hedge;
+    int first = he;
+    do
+    {
+        int edge_index = _system.halfedges[he].edge;
+        int type = _system.edges[edge_index].type;
+        int v1 = _system.edges[edge_index].i;
+        auto _s1 = _system.vertices[v1].spin;
+        int v2 = _system.edges[edge_index].j;
+        auto _s2 = _system.vertices[v2].spin;
+        energy += 0.5 * ComputeEdgeFerroEnergy_lambda(_s1, _s2, J[type]);
+        // MOVE TO THE NEXT edge
+        int he_pair = _system.halfedges[he].pair;
+        he = _system.halfedges[he_pair].next;
+    } while ((he != first));
+    return energy;
+}
+
+void ComputeVertexFerromagneticEnergy::compute(void)
+{
+}
diff --git a/pymembrane/cppmodule/src/potentials/potentialIsing.hpp b/pymembrane/cppmodule/src/potentials/potentialIsing.hpp
new file mode 100644
index 00000000..ea355343
--- /dev/null
+++ b/pymembrane/cppmodule/src/potentials/potentialIsing.hpp
@@ -0,0 +1,94 @@
+/*!
+* @file potentiallimit.hpp
+* @brief ComputeVertexFerromagneticEnergy class
+* @author Daniel Matoz, fdamatoz@gmail.com
+* @date 20-Sept-2017
+*/
+
+#ifndef __POTENTIALISING_HPP__
+#define __POTENTIALISING_HPP__
+
+/** @addtogroup computeenergy Compute tethering potential Energy
+ *  @brief ComputeVertexFerromagneticEnergy definitions
+ *  @{
+ */
+#include <math.h>
+//host
+#include "computeforceclass.hpp"
+
+//
+
+#include "../system/systemclass.hpp"
+#include "../mesh/computegeometry.hpp"
+
+/**
+ * @class ComputeVertexFerromagneticEnergy
+ * @brief ComputeVertexFerromagneticEnergy the tethering potential, if the edge length is larger than lmax then the energy is equal to inf
+ */
+ 
+/**
+ * @brief Example class that acts on the edges 
+ * 
+ */
+class ComputeVertexFerromagneticEnergy : public ComputeForceClass
+{
+public:
+  ComputeVertexFerromagneticEnergy(SystemClass &system) : ComputeForceClass(system)
+  {
+    m_name = "Limit"; //!< potential name
+    m_type = "edge";  //!< potential type
+    this->set_default_properties();
+  }
+  ~ComputeVertexFerromagneticEnergy() {}
+
+  void set_default_properties(void) override
+  {
+    pymemb::vector<real> _J(NUM_TYPES_ALLOWED, 1.0);
+    J = _J;
+    pymemb::vector<real> _h(NUM_TYPES_ALLOWED, 0.0);
+    h = _h;
+  }
+
+  using ComputeForceClass::set_property;
+  void set_property(std::map<std::string, std::map<std::string, std::string>> &region_map) override
+  {
+    for (const auto &item : region_map)
+    {
+      if (item.first.compare("J") == 0)
+      {
+        pymemb::vector<real> _J = util::from_dict_to_vector_types(pymemb::copy(J), item.second);
+        J = _J;
+      }
+      else if (item.first.compare("h") == 0)
+      {
+        pymemb::vector<real> _h = util::from_dict_to_vector_types(pymemb::copy(h), item.second);
+        h = _h;
+      }
+      else
+        this->print_warning_property_name(item.first);
+    }
+  }
+  
+  std::map<std::string, std::string> get_info(void) override
+  {
+    std::map<std::string, std::string> value;
+    value["name"] = m_name;
+    value["type"] = m_type;
+    value["J"] = util::to_string_vec(J);
+    value["h"] = util::to_string_vec(h);
+    return value;
+  }
+
+  void compute_energy(void) override;
+  void compute(void) override;
+  real compute_edge_energy(int) override;
+  real compute_vertex_energy(int) override;
+
+private:
+  pymemb::vector<real> J; //!< maximum edge allowed
+  pymemb::vector<real> h; //!< maximum edge allowed
+
+};
+
+#endif
+
diff --git a/pymembrane/cppmodule/src/potentials/potentialSubstrate.cpp b/pymembrane/cppmodule/src/potentials/potentialSubstrate.cpp
index d42d58f3..255c2566 100644
--- a/pymembrane/cppmodule/src/potentials/potentialSubstrate.cpp
+++ b/pymembrane/cppmodule/src/potentials/potentialSubstrate.cpp
@@ -12,12 +12,20 @@ void ComputeVertexLimitForce_fn(int Numvertices,
 
         auto fval = 0.0;
 
-        if (r.z >= 0.0)
-            fval = -_kz1[type] * r.z;
+        if (r.z >= 0.5)
+        {
+            //fval = -_kz1[type] * r.z;
+            vertices[vertex_index].r.z = 0.5;
+            vertices[vertex_index].type = 2;
+        }
         else
-            fval = -_kz2[type] * r.z;
+        {
+            //fval = -_kz2[type] * r.z;
+            if (r.z < 0.45)
+                vertices[vertex_index].type = 1;
 
-        vertices[vertex_index].forceC.z += fval;
+        }
+        //vertices[vertex_index].forceC.z += fval;
     }
 }
 void ComputeVertexSubstrateEnergy::compute(void)
diff --git a/pymembrane/cppmodule/src/potentials/potentialSubstrateCylinder.cpp b/pymembrane/cppmodule/src/potentials/potentialSubstrateCylinder.cpp
new file mode 100644
index 00000000..a6b8e24a
--- /dev/null
+++ b/pymembrane/cppmodule/src/potentials/potentialSubstrateCylinder.cpp
@@ -0,0 +1,117 @@
+#include "potentialSubstrateCylinder.hpp"
+
+bool isOutsideCylinder(real3 vertex_position,
+    real3 axis,
+    real3 cylinder_position,
+    real radius)
+{
+    real3 cv = pymemb::vector_subtract(vertex_position, cylinder_position);
+    real x = pymemb::vector_dot(cv, axis);
+    real3 proj;
+    Xvec1(proj, x, axis);
+    proj = pymemb::vector_sum(cylinder_position, proj);
+    real value = pymemb::vector_squared_length(cv) - pymemb::vector_squared_length(proj) - radius*radius;
+    return value >= 0;
+}
+
+void ProjectOnCylinderSurface(HE_VertexProp *vertices, int vertex_index, real radius, real3 proj)
+{
+    real3 fpush = pymemb::vector_subtract(vertices[vertex_index].r, proj);
+    fpush = pymemb::unit_vector(fpush);
+    Xvec1(fpush, radius, fpush);
+    vertices[vertex_index].r = pymemb::vector_sum(proj, fpush);
+    vertices[vertex_index].type = 2;
+}
+
+void ComputeVertexLimitForce_fn(int Numvertices,
+                                HE_VertexProp *vertices,                
+                                real3 axis,
+                                real3 cylinder_position,
+                                real radius,
+                                int* outside_cyl_count)
+{
+    for (int vertex_index=0; vertex_index < Numvertices; vertex_index++)
+    {
+        real3 vertex_position = vertices[vertex_index].r;
+
+        real3 cv = pymemb::vector_subtract(vertex_position, cylinder_position);
+        real x = pymemb::vector_dot(cv, axis);
+        real3 proj;
+        Xvec1(proj, x, axis);
+        proj = pymemb::vector_sum(cylinder_position, proj);
+        real value = pymemb::vector_length(pymemb::vector_subtract(proj, vertex_position)) - (radius);
+
+        if (value < 0 )
+        {
+            ProjectOnCylinderSurface(vertices, vertex_index, radius, proj);
+        }
+        else
+        {   
+            outside_cyl_count[vertex_index]++;
+        }
+    }
+}
+
+void ComputeVertexSubstrateCylinderEnergy::compute(void)
+{
+    real3 axis, position;
+    std::vector<int> outside_cyl_count = std::vector<int>(_system.Numvertices, 0);
+    for (int i=0; i<m_nbcyl[0]; i++)
+    {
+        axis.x = m_axis[i*3];
+        axis.y = m_axis[i*3+1];
+        axis.z = m_axis[i*3+2];
+        position.x = m_position[i*3];
+        position.y = m_position[i*3+1];
+        position.z = m_position[i*3+2];
+
+        ComputeVertexLimitForce_fn(_system.Numvertices,
+                                    &_system.vertices[0],
+                                    axis,
+                                    position,
+                                    m_radius[i],
+                                    &outside_cyl_count[0]);
+    }
+
+    for (int vertex_index=0; vertex_index<_system.Numvertices; vertex_index++)
+    {
+        if (outside_cyl_count[vertex_index] == m_nbcyl[0])
+        {
+            if (_system.vertices[vertex_index].type == 2)
+            {
+                
+                real dist_min = 10000;
+                int closest_cyl = 0;
+                real3 closest_proj;
+                for (int i=0; i<m_nbcyl[0]; i++)
+                {
+                    axis.x = m_axis[i*3];
+                    axis.y = m_axis[i*3+1];
+                    axis.z = m_axis[i*3+2];
+                    position.x = m_position[i*3];
+                    position.y = m_position[i*3+1];
+                    position.z = m_position[i*3+2];
+                    real3 vertex_position = _system.vertices[vertex_index].r;
+
+                    real3 cv = pymemb::vector_subtract(vertex_position, position);
+                    real x = pymemb::vector_dot(cv, axis);
+                    real3 proj;
+                    Xvec1(proj, x, axis);
+                    proj = pymemb::vector_sum(position, proj);
+                    real dist = pymemb::vector_length(pymemb::vector_subtract(proj, vertex_position));
+                    if (dist < dist_min)
+                    {
+                        dist_min = dist;
+                        closest_cyl = i;
+                        closest_proj = proj;
+                    }
+                }
+                ProjectOnCylinderSurface(&_system.vertices[0], vertex_index, m_radius[closest_cyl], closest_proj);
+            }
+            else
+                _system.vertices[vertex_index].type = 1;
+        }
+        else
+            _system.vertices[vertex_index].type = 2;
+    }
+}
\ No newline at end of file
diff --git a/pymembrane/cppmodule/src/potentials/potentialSubstrateCylinder.hpp b/pymembrane/cppmodule/src/potentials/potentialSubstrateCylinder.hpp
new file mode 100644
index 00000000..293f8fed
--- /dev/null
+++ b/pymembrane/cppmodule/src/potentials/potentialSubstrateCylinder.hpp
@@ -0,0 +1,103 @@
+/*!
+* @file potentialSubstrateCylinder.hpp
+* @brief ComputeVertexSubstrateCylinderEnergy class
+* @author Martin Leocmach, martin.leocmach@gmail.com
+* @date 01-April-2025
+*/
+
+#ifndef __potentialsubstratecylinder_HPP__
+#define __potentialsubstratecylinder_HPP__
+
+#include <math.h>
+//host
+#include "computeforceclass.hpp"
+
+//
+
+#include "../system/systemclass.hpp"
+#include "../mesh/computegeometry.hpp"
+
+/**
+ * @class ComputeVertexSubstrateCylinderEnergy
+ * @brief If a point is inside the cylinder, push it out
+ */
+class ComputeVertexSubstrateCylinderEnergy : public ComputeForceClass
+{
+public:
+    ComputeVertexSubstrateCylinderEnergy(SystemClass &system) : ComputeForceClass(system)
+    {
+    m_name = "Substrate-Cylinder"; //!< potential name
+    m_type = "vertex";  //!< potential type
+    this->set_default_properties();
+    }
+    ~ComputeVertexSubstrateCylinderEnergy() {}
+
+    void set_default_properties(void) override
+    {
+        pymemb::vector<real> n(NUM_TYPES_ALLOWED, 0.);
+        m_nbcyl = n;
+        m_nbcyl[0] = 1.0;
+        pymemb::vector<real> a(NUM_TYPES_ALLOWED, 0.);
+        m_axis = a;
+        m_axis[1] = 1.0;
+        pymemb::vector<real> p(NUM_TYPES_ALLOWED, 0.);
+        m_position = a;
+        pymemb::vector<real> r(NUM_TYPES_ALLOWED, 1.0);
+        m_radius = r;
+    }
+
+
+  using ComputeForceClass::set_property;
+  void set_property(std::map<std::string, std::map<std::string, std::string>> &region_map) override
+  {
+    for (const auto &item : region_map)
+    {
+      if (item.first.compare("nb_cylinder") == 0)
+      {
+        pymemb::vector<real> _n = util::from_dict_to_vector_types(pymemb::copy(m_axis), item.second);
+        m_nbcyl = _n;
+      }
+      if (item.first.compare("axis") == 0)
+      {
+        pymemb::vector<real> _a = util::from_dict_to_vector_types(pymemb::copy(m_axis), item.second);
+        m_axis = _a;
+      }
+      else if (item.first.compare("position") == 0)
+      {
+        pymemb::vector<real> _p = util::from_dict_to_vector_types(pymemb::copy(m_position), item.second);
+        m_position = _p;
+      }
+      else if (item.first.compare("radius") == 0)
+      {
+        pymemb::vector<real> _r = util::from_dict_to_vector_types(pymemb::copy(m_radius), item.second);
+        m_radius = _r;
+      }
+      else
+        this->print_warning_property_name(item.first);
+    }
+  }
+
+  std::map<std::string, std::string> get_info(void) override
+  {
+    std::map<std::string, std::string> value;
+    value["nb_cyl"] = m_nbcyl[0];
+    value["name"] = m_name;
+    value["type"] = m_type;
+    value["axis"] = util::to_string_vec(pymemb::vector<real>(m_axis.begin(), m_axis.begin()+2));
+    value["position"] = util::to_string_vec(pymemb::vector<real>(m_position.begin(), m_position.begin()+2));
+    value["radius"] = util::to_string_vec(m_radius);
+    return value;
+  }
+
+  void compute_energy(void) override {}
+  void compute(void) override;
+  double compute_edge_energy(int) override {return 0.0;}
+  double compute_vertex_energy(int) override {return 0.0;}
+
+private:
+    pymemb::vector<real> m_nbcyl;
+    pymemb::vector<real> m_axis;    //using types 0, 1, 2 for x, y, z coordinates of the axis
+    pymemb::vector<real> m_position;     //using types 0, 1, 2 for x, y, z coordinates of the position
+    pymemb::vector<real> m_radius;
+};
+#endif
\ No newline at end of file
diff --git a/pymembrane/cppmodule/src/potentials/potentialSurfaceTension.cpp b/pymembrane/cppmodule/src/potentials/potentialSurfaceTension.cpp
new file mode 100644
index 00000000..f959f95a
--- /dev/null
+++ b/pymembrane/cppmodule/src/potentials/potentialSurfaceTension.cpp
@@ -0,0 +1,190 @@
+#include "potentialSurfaceTension.hpp"
+
+bool is_triple_line_vertex(const int vid,
+                            HE_VertexProp *vertices,
+                            HE_HalfEdgeProp *halfedges)
+{
+    if (vertices[vid].type != 2)
+        return false;
+    
+    int he = vertices[vid]._hedge;
+    int first = he;
+
+    do
+    {
+        int v = halfedges[he].vert_to;
+        if (vertices[v].type == 1)
+            return true;
+        he = halfedges[he].pair;
+        he = halfedges[he].next;
+    } while (he != first);
+
+    return false;
+}
+
+void ComputeVertexSurfaceTensionForce_fn(const int vid,
+                                        HE_VertexProp *vertices,
+                                        HE_HalfEdgeProp *halfedges,
+                                        real *m_gamma,
+                                        real *curvature)
+{  
+    int he = vertices[vid]._hedge;
+    int first = he;
+    int type_0 = vertices[vid].type;
+    real3 a = vertices[vid].r;
+    real3 tension_force;
+    tension_force.x = 0;
+    tension_force.y = 0;
+    tension_force.z = 0;
+
+    real gamma_type = m_gamma[type_0];
+    if (type_0 == 1)
+    {
+        do
+        {
+            int v1 = halfedges[he].vert_to;
+            int he_next = halfedges[he].next;
+            int v2 = halfedges[he_next].vert_to;
+            real3 b = vertices[v1].r;
+            real3 c = vertices[v2].r;
+
+            real3 normal = pymemb::compute_normal_triangle_unit(a, b, c);
+            real area = pymemb::compute_area_triangle_from_vertex(a, b, c);
+            real angle = pymemb::compute_angle_vertex(a, b, c);
+            angle = angle/M_PI;
+            Xvec1(normal, angle*area, normal);
+
+            tension_force = pymemb::vector_sum(tension_force, normal);
+
+            he = halfedges[he].pair;
+            he = halfedges[he].next;
+        } while (he != first);
+
+        vertices[vid].forceC.x += tension_force.x*(-curvature[vid])*gamma_type;
+        vertices[vid].forceC.y += tension_force.y*(-curvature[vid])*gamma_type;
+        vertices[vid].forceC.z += tension_force.z*(-curvature[vid])*gamma_type;
+    }
+
+    else if (is_triple_line_vertex(vid, vertices, halfedges))
+    {
+        real3 triple_line_force;
+        triple_line_force.x = 0;
+        triple_line_force.y = 0;
+        triple_line_force.z = 0;
+        real triple_line_length = 0.0;
+        real3 line_normal, plane_normal;
+        line_normal.x = 0;
+        line_normal.y = 0;
+        line_normal.z = 0;
+        plane_normal.x = 0;
+        plane_normal.y = 0;
+        plane_normal.z = 0;
+        real3 tangent;
+        tangent.x = 0;
+        tangent.y = 0;
+        tangent.z = 0;
+        do
+        {
+            int v1 = halfedges[he].vert_to;
+            int he_next = halfedges[he].next;
+            int v2 = halfedges[he_next].vert_to;
+            real3 b = vertices[v1].r;
+            real3 c = vertices[v2].r;
+
+            if (is_triple_line_vertex(v1, vertices, halfedges))
+            {
+                real length = pymemb::vector_length(pymemb::vector_subtract(a, b))/2;
+                triple_line_length += length;
+                real3 p;
+                p.x = (a.x + b.x)/2;
+                p.y = (a.y + b.y)/2;
+                p.z = (a.z + b.z)/2;
+                real3 normal;
+                if (vertices[v2].type == 2)
+                    normal = pymemb::unit_vector(pymemb::vector_subtract(p, c));
+                else
+                {
+                    int he_pair = halfedges[he].pair;
+                    he_pair = halfedges[he_pair].next;
+                    real3 d = vertices[halfedges[he_pair].vert_to].r;
+                    normal = pymemb::unit_vector(pymemb::vector_subtract(p, d));
+                }
+                Xvec1(normal, length, normal);
+                line_normal = pymemb::vector_sum(line_normal, normal);
+            }
+
+            if (vertices[v1].type == 1 || vertices[v2].type == 1)
+            {
+                real area = pymemb::compute_area_triangle_from_vertex(a, b, c);
+                real3 p = pymemb::vector_sum(b, c);
+                Xvec1(p, 0.5, p);
+                real3 ap = pymemb::vector_subtract(p, a);
+                Xvec1(ap, area, ap);    //mesh_op.refine_mesh_edge_flip();
+                //mesh_op.adapt_mesh();
+                tangent = pymemb::vector_sum(tangent, ap);
+            }
+            else
+            {
+                real3 ab = pymemb::vector_subtract(b, a);
+                real3 ac = pymemb::vector_subtract(c, a);
+                real3 triangle_normal = pymemb::vector_cross(ab, ac);
+                plane_normal = pymemb::vector_sum(plane_normal, triangle_normal);
+            }
+
+            he = halfedges[he].pair;
+            he = halfedges[he].next;
+        } while (he != first);
+
+        tangent = pymemb::unit_vector(tangent);
+        Xvec1(tangent, triple_line_length, tangent);
+        plane_normal = pymemb::unit_vector(plane_normal);
+        real tproj = pymemb::vector_dot(tangent, plane_normal);
+        real3 tminus;
+        Xvec1(tminus, tproj, plane_normal);
+        tangent = pymemb::vector_subtract(tangent, tminus);
+        
+        line_normal = pymemb::unit_vector(line_normal);  
+        Xvec1(line_normal, triple_line_length, line_normal);
+
+        vertices[vid].forceC.x += tangent.x*m_gamma[1] + line_normal.x*m_gamma[2];
+        vertices[vid].forceC.y += tangent.y*m_gamma[1] + line_normal.y*m_gamma[2];
+        vertices[vid].forceC.z += tangent.z*m_gamma[1] + line_normal.z*m_gamma[2];
+    }
+}
+
+real ComputeVertexSurfaceTension::compute_face_energy(int face_id)
+{
+    int v1 = _system.faces[face_id].v1;
+    int v2 = _system.faces[face_id].v2;
+    int v3 = _system.faces[face_id].v3;
+
+    real area = pymemb::compute_area_triangle_from_vertex(_system.vertices[v1].r, _system.vertices[v2].r, _system.vertices[v3].r);
+
+    if (_system.vertices[v1].type == 1 || _system.vertices[v2].type == 1 || _system.vertices[v3].type == 1 )
+    {
+        return area * m_gamma[1];
+    }
+
+    return -m_gamma[2] * area;
+}
+
+void ComputeVertexSurfaceTension::compute_energy(void)
+{
+    for (int face_id=0; face_id <_system.Numfaces; face_id++)
+    {
+        _system.faces[face_id].energy = compute_face_energy(face_id);
+    }
+}
+
+void ComputeVertexSurfaceTension::compute(void)
+{
+    pymemb::vector<real> curvature = _system.compute_mesh.meancurvature();
+    //pymemb::vector<real> curvature = _system.compute_mesh.gaussiancurvature();
+
+    for(int i=0; i<_system.Numvertices; i++) {
+        ComputeVertexSurfaceTensionForce_fn(i, &_system.vertices[0],
+                                            &_system.halfedges[0],
+                                            &m_gamma[0],
+                                        &curvature[0]);
+    }
+}
\ No newline at end of file
diff --git a/pymembrane/cppmodule/src/potentials/potentialSurfaceTension.hpp b/pymembrane/cppmodule/src/potentials/potentialSurfaceTension.hpp
new file mode 100644
index 00000000..ed5ef962
--- /dev/null
+++ b/pymembrane/cppmodule/src/potentials/potentialSurfaceTension.hpp
@@ -0,0 +1,82 @@
+/*!
+* @file potentialSurfaceTension.hpp
+* @brief ComputeVertexSurfaceTension class
+* @author Martin Leocmach, martin.leocmach@gmail.com
+* @date 11-March-2025
+*/
+
+#ifndef __POTENTIALSURFACETENSION
+#define __POTENTIALSURFACETENSION
+
+/** @addtogroup computeenergy Compute surface tension energy
+ *  @brief ComputeVertexSurfaceTension definitions 
+ */
+
+#include "computeforceclass.hpp"
+
+#include "../system/systemclass.hpp"
+#include "../mesh/computegeometry.hpp"
+
+/**
+ * @class ComputeVertexSurfaceTension
+ * @brief Implements the surface tension to add to vertex energy
+ *
+ *
+ */
+
+class ComputeVertexSurfaceTension : public ComputeForceClass
+{
+public:
+    ComputeVertexSurfaceTension(SystemClass &system) : ComputeForceClass(system)
+    {
+        m_name = "Surface Tension";
+        m_type = "vertex";
+        this->set_default_properties();
+    }
+
+    ~ComputeVertexSurfaceTension() {}
+
+    void set_default_properties(void)override
+    {
+        std::vector<double> _gamma(NUM_TYPES_ALLOWED, 0.0);
+        m_gamma = _gamma;
+    }
+
+    using ComputeForceClass::set_property;
+    void set_property(std::map<std::string, std::map<std::string, std::string>> &region_map) override
+    {
+        for(const auto &item : region_map)
+        {
+            if (item.first.compare("gamma") == 0)
+            {
+                pymemb::vector<real> _gamma = util::from_dict_to_vector_types(pymemb::copy(m_gamma), item.second);
+                m_gamma = _gamma;
+            }
+            else
+                this->print_warning_property_name(item.first);
+        }
+    }
+
+    // Is second set_property overload necessary here?
+    // if yes TODO
+
+    std::map<std::string, std::string> get_info(void) override
+    {
+        std::map<std::string, std::string> value;
+        value["name"] = m_name;
+        value["type"] = m_type;
+        value["gamma"] = util::to_string_vec(m_gamma);
+        return value;
+    }
+
+    void compute_energy(void) override;
+    // if necessary TODO : add compute_edge_energy
+    real compute_face_energy(int) override;
+    void compute(void) override;
+
+private:
+    pymemb::vector<real> m_gamma; //!< list of tension coefficient, one per type
+};
+
+
+#endif
\ No newline at end of file
diff --git a/pymembrane/cppmodule/src/read_mesh.cpp b/pymembrane/cppmodule/src/read_mesh.cpp
index b360dc24..5294064c 100644
--- a/pymembrane/cppmodule/src/read_mesh.cpp
+++ b/pymembrane/cppmodule/src/read_mesh.cpp
@@ -25,6 +25,7 @@ void ReadMesh::__add_vertex(int id, real x, real y, real z, int type)
     vertex.normal.x = 0.;
     vertex.normal.y = 0.;
     vertex.normal.z = 0.;
+    vertex.spin = 1.0;
     vertices.push_back(vertex);
 }
 void ReadMesh::__add_face(int id, std::vector<int> verts, int orientation, int type)
diff --git a/pymembrane/cppmodule/src/system/pybind_export_system.hpp b/pymembrane/cppmodule/src/system/pybind_export_system.hpp
index 71677d92..837df3d8 100644
--- a/pymembrane/cppmodule/src/system/pybind_export_system.hpp
+++ b/pymembrane/cppmodule/src/system/pybind_export_system.hpp
@@ -34,9 +34,8 @@ void export_SystemClass(pybind11::module &m)
         .def("read_mesh_from_files", &SystemClass::read_mesh_from_files, pybind11::arg("files"), "read the mesh from a file, needs file route <faces, vertices>")
         .def("read_mesh_from_json", &SystemClass::read_mesh_from_json, pybind11::arg("file"), "read the mesh from a json file lists")
         .def_readonly("mesh_is_close", &SystemClass::close_surface, "return true if is close false otherwise")
-        
-
-        /*.def("getVertices", &SystemClass::get_vertices, "get the vertices in memb format")
+      
+        .def("getVertices", &SystemClass::get_vertices, "get the vertices in memb format")
         .def("getEdges", &SystemClass::get_edges, "get the edges in memb format")
         .def("getFaces", &SystemClass::get_faces, "get the faces in memb format")
         .def("getHalfedges", &SystemClass::get_halfedges, "return the halfedges in memb format")
@@ -55,7 +54,7 @@ void export_SystemClass(pybind11::module &m)
         .def("getStressEdges", &SystemClass::get_stress_edges)
         .def("getStressFaces", &SystemClass::get_stress_faces)
         .def("getStressVirial", &SystemClass::get_stress_virial)
-        .def("getStressKinetic", &SystemClass::get_stress_kinetic)*/
+        .def("getStressKinetic", &SystemClass::get_stress_kinetic)
 
         .def_readonly("Numfaces", &SystemClass::Numfaces)
         .def_readonly("Numedges", &SystemClass::Numedges)
@@ -74,7 +73,7 @@ void export_SystemClass(pybind11::module &m)
         .def_property("compute", &SystemClass::get_compute_mesh,  [] (SystemClass& self,ComputeMesh & _computer ){})
         .def_property("vertices", &SystemClass::get_vertices, &SystemClass::set_vertices)
         .def_property("edges", &SystemClass::get_edges, &SystemClass::set_edges)
-        .def_property("faces", &SystemClass::get_faces, &SystemClass::set_vertices)
+        .def_property("faces", &SystemClass::get_faces, &SystemClass::set_faces)
         .def_property("halfedges", &SystemClass::get_halfedges, &SystemClass::set_halfedges)