FemMeshTools.py

# ***************************************************************************
# *                                                                         *
# *   Copyright (c) 2016 - Bernd Hahnebach <bernd@bimstatik.org>            *
# *                                                                         *
# *   This program is free software; you can redistribute it and/or modify  *
# *   it under the terms of the GNU Lesser General Public License (LGPL)    *
# *   as published by the Free Software Foundation; either version 2 of     *
# *   the License, or (at your option) any later version.                   *
# *   for detail see the LICENCE text file.                                 *
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# *   but WITHOUT ANY WARRANTY; without even the implied warranty of        *
# *   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the         *
# *   GNU Library General Public License for more details.                  *
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# *   License along with this program; if not, write to the Free Software   *
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__title__ = "Tools for the work with FEM meshes"
__author__ = "Bernd Hahnebach"
__url__ = "http://www.freecadweb.org"


import FreeCAD


def get_femnodes_by_femobj_with_references(femmesh, femobj):
    node_set = []
    if femmesh.GroupCount:
        node_set = get_femnode_set_from_group_data(femmesh, femobj)
        # print 'node_set_group: ', node_set
    if not node_set:
        node_set = get_femnodes_by_references(femmesh, femobj['Object'].References)
        # print 'node_set_nogroup: ', node_set
    return node_set


def get_femelements_by_references(femmesh, femelement_table, references):
    '''get the femelements for a list of references
    '''
    references_femelements = []
    for ref in references:
        ref_femnodes = get_femnodes_by_refshape(femmesh, ref)  # femnodes for the current ref
        references_femelements += get_femelements_by_femnodes(femelement_table, ref_femnodes)  # femelements for all references
    return references_femelements


def get_femnodes_by_references(femmesh, references):
    '''get the femnodes for a list of references
    '''
    references_femnodes = []
    for ref in references:
        references_femnodes += get_femnodes_by_refshape(femmesh, ref)

    # return references_femnodes  # keeps duplicate nodes, keeps node order

    # if nodes are used for nodesets, duplicats should be removed
    return list(set(references_femnodes))  # removes duplicate nodes, sortes node order


def get_femnodes_by_refshape(femmesh, ref):
    nodes = []
    for refelement in ref[1]:
        if refelement:
            r = ref[0].Shape.getElement(refelement)  # Vertex, Edge, Face
        else:
            r = ref[0].Shape  # solid
        print('  ReferenceShape : ', r.ShapeType, ', ', ref[0].Name, ', ', ref[0].Label, ' --> ', refelement)
        if r.ShapeType == 'Vertex':
            nodes += femmesh.getNodesByVertex(r)
        elif r.ShapeType == 'Edge':
            nodes += femmesh.getNodesByEdge(r)
        elif r.ShapeType == 'Face':
            nodes += femmesh.getNodesByFace(r)
        elif r.ShapeType == 'Solid':
            nodes += femmesh.getNodesBySolid(r)
        else:
            print('  No Vertice, Edge, Face or Solid as reference shapes!')
    return nodes


def get_femelement_table(femmesh):
    """ get_femelement_table(femmesh): { elementid : [ nodeid, nodeid, ... , nodeid ] }"""
    femelement_table = {}
    if is_solid_femmesh(femmesh):
        for i in femmesh.Volumes:
            femelement_table[i] = femmesh.getElementNodes(i)
    elif is_face_femmesh(femmesh):
        for i in femmesh.Faces:
            femelement_table[i] = femmesh.getElementNodes(i)
    elif is_edge_femmesh(femmesh):
        for i in femmesh.Edges:
            femelement_table[i] = femmesh.getElementNodes(i)
    else:
        FreeCAD.Console.PrintError('Neither solid nor face nor edge femmesh!\n')
    return femelement_table


def get_femelements_by_femnodes(femelement_table, node_list):
    '''for every femelement of femelement_table
    if all nodes of the femelement are in node_list,
    the femelement is added to the list which is returned
    e: elementlist
    nodes: nodelist '''
    e = []  # elementlist
    for elementID in sorted(femelement_table):
        nodecount = 0
        for nodeID in femelement_table[elementID]:
            if nodeID in node_list:
                nodecount = nodecount + 1
        if nodecount == len(femelement_table[elementID]):   # all nodes of the element are in the node_list!
            e.append(elementID)
    return e


def get_femvolumeelements_by_femfacenodes(femelement_table, node_list):
    '''assume femelement_table only has volume elements
    for every femvolumeelement of femelement_table
    for tetra4 and tetra10 the C++ methods could be used --> test again to be sure
    if hexa8 volume element --> if exact 4 element nodes are in node_list --> add femelement
    if hexa20 volume element --> if exact 8 element nodes are in node_list --> add femelement
    if penta6 volume element --> if exact 3 or 6 element nodes are in node_list --> add femelement
    if penta15 volume element --> if exact 6 or 8 element nodes are in node_list --> add femelement
    e: elementlist
    nodes: nodelist '''
    e = []  # elementlist
    for elementID in sorted(femelement_table):
        nodecount = 0
        el_nd_ct = len(femelement_table[elementID])
        if el_nd_ct == 4:  # tetra4
            for nodeID in femelement_table[elementID]:
                if nodeID in node_list:
                    nodecount = nodecount + 1
            if nodecount == 3:
                e.append(elementID)
        elif el_nd_ct == 10:  # tetra10
            for nodeID in femelement_table[elementID]:
                if nodeID in node_list:
                    nodecount = nodecount + 1
            if nodecount == 4:
                e.append(elementID)
        elif el_nd_ct == 8:  # hexa8
            for nodeID in femelement_table[elementID]:
                if nodeID in node_list:
                    nodecount = nodecount + 1
            if nodecount == 4:
                e.append(elementID)
        elif el_nd_ct == 20:  # hexa20
            for nodeID in femelement_table[elementID]:
                if nodeID in node_list:
                    nodecount = nodecount + 1
            if nodecount == 8:
                e.append(elementID)
        elif el_nd_ct == 6:  # penta6
            for nodeID in femelement_table[elementID]:
                if nodeID in node_list:
                    nodecount = nodecount + 1
            if nodecount == 3 or nodecount == 4:
                e.append(elementID)
        elif el_nd_ct == 15:  # penta15
            for nodeID in femelement_table[elementID]:
                if nodeID in node_list:
                    nodecount = nodecount + 1
            if nodecount == 6 or nodecount == 8:
                e.append(elementID)
        else:
            FreeCAD.Console.PrintError('Error in get_femvolumeelements_by_femfacenodes(): not known volume element: ' + el_nd_ct + '\n')
    # print sorted(e)
    return e


def get_femelement_sets(femmesh, femelement_table, fem_objects):  # fem_objects = FreeCAD FEM document objects
    # get femelements for reference shapes of each obj.References
    count_femelements = 0
    referenced_femelements = []
    has_remaining_femelements = None
    for fem_object_i, fem_object in enumerate(fem_objects):
        obj = fem_object['Object']
        fem_object['ShortName'] = get_elset_short_name(obj, fem_object_i)  # unique short identifier
        if obj.References:
            ref_shape_femelements = []
            ref_shape_femelements = get_femelements_by_references(femmesh, femelement_table, obj.References)
            referenced_femelements += ref_shape_femelements
            count_femelements += len(ref_shape_femelements)
            fem_object['FEMElements'] = ref_shape_femelements
        else:
            has_remaining_femelements = obj.Name
    # get remaining femelements for the fem_objects
    if has_remaining_femelements:
        remaining_femelements = []
        for elemid in femelement_table:
            if elemid not in referenced_femelements:
                remaining_femelements.append(elemid)
        count_femelements += len(remaining_femelements)
        for fem_object in fem_objects:
            obj = fem_object['Object']
            if obj.Name == has_remaining_femelements:
                fem_object['FEMElements'] = sorted(remaining_femelements)
    # check if all worked out well
    if not femelements_count_ok(len(femelement_table), count_femelements):
        FreeCAD.Console.PrintError('Error in get_femelement_sets -- > femelements_count_ok() failed!\n')


def get_femnode_set_from_group_data(femmesh, fem_object):
    # get femnodes from femmesh groupdata for reference shapes of each obj.References
    # we assume the mesh group data fits with the reference shapes, no check is done in this regard !!!
    # what happens if a reference shape was changed, but the mesh and the mesh groups were not created new !?!
    obj = fem_object['Object']
    if femmesh.GroupCount:
        for g in femmesh.Groups:
            grp_name = femmesh.getGroupName(g)
            if grp_name.startswith(obj.Name + '_'):
                if femmesh.getGroupElementType(g) == "Node":
                    print("Constraint: " + obj.Name + " --> " + "mesh group: " + grp_name)
                    group_nodes = femmesh.getGroupElements(g)  # == ref_shape_femelements
    return group_nodes


def get_femelement_sets_from_group_data(femmesh, fem_objects):
    # get femelements from femmesh groupdata for reference shapes of each obj.References
    count_femelements = 0
    sum_group_elements = []
    # we assume the mesh group data fits with the reference shapes, no check is done in this regard !!!
    # what happens if a reference shape was changed, but the mesh and the mesh groups were not created new !?!
    for fem_object_i, fem_object in enumerate(fem_objects):
        obj = fem_object['Object']
        fem_object['ShortName'] = get_elset_short_name(obj, fem_object_i)  # unique short identifier
        if femmesh.GroupCount:
            for g in femmesh.Groups:
                grp_name = femmesh.getGroupName(g)
                if grp_name.startswith(obj.Name + '_'):
                    if femmesh.getGroupElementType(g) == "Volume":
                        print("Constraint: " + obj.Name + " --> " + "mesh group: " + grp_name)
                        group_elements = femmesh.getGroupElements(g)  # == ref_shape_femelements
                        sum_group_elements += group_elements
                        count_femelements += len(group_elements)
                        fem_object['FEMElements'] = group_elements
    # check if all worked out well
    if not femelements_count_ok(femmesh.VolumeCount, count_femelements):
        FreeCAD.Console.PrintError('Error in get_femelement_sets_from_group_data -- > femelements_count_ok() failed!\n')
        return False
    else:
        return True
    print("")


def get_elset_short_name(obj, i):
    if hasattr(obj, "Proxy") and obj.Proxy.Type == 'MechanicalMaterial':
        return 'Mat' + str(i)
    elif hasattr(obj, "Proxy") and obj.Proxy.Type == 'FemBeamSection':
        return 'Beam' + str(i)
    elif hasattr(obj, "Proxy") and obj.Proxy.Type == 'FemShellThickness':
        return 'Shell' + str(i)
    else:
        print('Error: ', obj.Name, ' --> ', obj.Proxy.Type)


def get_force_obj_vertex_nodeload_table(femmesh, frc_obj):
    # force_obj_node_load_table = [('refshape_name.elemname',node_load_table), ..., ('refshape_name.elemname',node_load_table)]
    force_obj_node_load_table = []
    node_load = frc_obj.Force / len(frc_obj.References)
    for o, elem_tup in frc_obj.References:
        node_count = len(elem_tup)
        for elem in elem_tup:
            ref_node = o.Shape.getElement(elem)
            node = femmesh.getNodesByVertex(ref_node)
            elem_info_string = 'node load on shape: ' + o.Name + ':' + elem
            force_obj_node_load_table.append((elem_info_string, {node[0]: node_load / node_count}))

    return force_obj_node_load_table


def get_force_obj_edge_nodeload_table(femmesh, femelement_table, femnodes_mesh, frc_obj):
    # force_obj_node_load_table = [('refshape_name.elemname',node_load_table), ..., ('refshape_name.elemname',node_load_table)]
    force_obj_node_load_table = []
    sum_ref_edge_length = 0
    sum_ref_edge_node_length = 0  # for debugging
    sum_node_load = 0  # for debugging
    for o, elem_tup in frc_obj.References:
        for elem in elem_tup:
            sum_ref_edge_length += o.Shape.getElement(elem).Length
    if sum_ref_edge_length != 0:
        force_per_sum_ref_edge_length = frc_obj.Force / sum_ref_edge_length
    for o, elem_tup in frc_obj.References:
        for elem in elem_tup:
            ref_edge = o.Shape.getElement(elem)

            # edge_table = { meshedgeID : ( nodeID, ... , nodeID ) }
            edge_table = get_ref_edgenodes_table(femmesh, femelement_table, ref_edge)

            # node_length_table = [ (nodeID, length), ... , (nodeID, length) ]  some nodes will have more than one entry
            node_length_table = get_ref_edgenodes_lengths(femnodes_mesh, edge_table)

            # node_sum_length_table = { nodeID : Length, ... , nodeID : Length }  LengthSum for each node, one entry for each node
            node_sum_length_table = get_ref_shape_node_sum_geom_table(node_length_table)

            # node_load_table = { nodeID : NodeLoad, ... , nodeID : NodeLoad }  NodeLoad for each node, one entry for each node
            node_load_table = {}
            sum_node_lengths = 0  # for debugging
            for node in node_sum_length_table:
                sum_node_lengths += node_sum_length_table[node]  # for debugging
                node_load_table[node] = node_sum_length_table[node] * force_per_sum_ref_edge_length
            ratio_refedge_lengths = sum_node_lengths / ref_edge.Length
            if ratio_refedge_lengths < 0.99 or ratio_refedge_lengths > 1.01:
                FreeCAD.Console.PrintError('Error on: ' + frc_obj.Name + ' --> ' + o.Name + '.' + elem + '\n')
                print('  sum_node_lengths:', sum_node_lengths)
                print('  refedge_length:  ', ref_edge.Length)
                bad_refedge = ref_edge
            sum_ref_edge_node_length += sum_node_lengths

            elem_info_string = 'node loads on shape: ' + o.Name + ':' + elem
            force_obj_node_load_table.append((elem_info_string, node_load_table))

    for ref_shape in force_obj_node_load_table:
        for node in ref_shape[1]:
            sum_node_load += ref_shape[1][node]  # for debugging

    ratio = sum_node_load / frc_obj.Force
    if ratio < 0.99 or ratio > 1.01:
        print('Deviation  sum_node_load to frc_obj.Force is more than 1% :  ', ratio)
        print('  sum_ref_edge_node_length: ', sum_ref_edge_node_length)
        print('  sum_ref_edge_length:      ', sum_ref_edge_length)
        print('  sum_node_load:          ', sum_node_load)
        print('  frc_obj.Force:          ', frc_obj.Force)
        print('  the reason could be simply a circle length --> see method get_ref_edge_node_lengths')
        print('  the reason could also be an problem in retrieving the ref_edge_node_length')

        # try debugging of the last bad refedge
        print('DEBUGGING')
        print(bad_refedge)

        print('bad_refedge_nodes')
        bad_refedge_nodes = femmesh.getNodesByEdge(bad_refedge)
        print(len(bad_refedge_nodes))
        print(bad_refedge_nodes)
        # import FreeCADGui
        # FreeCADGui.ActiveDocument.Compound_Mesh.HighlightedNodes = bad_refedge_nodes

        print('bad_edge_table')
        # bad_edge_table = { meshedgeID : ( nodeID, ... , nodeID ) }
        bad_edge_table = get_ref_edgenodes_table(femmesh, femelement_table, bad_refedge)
        print(len(bad_edge_table))
        bad_edge_table_nodes = []
        for elem in bad_edge_table:
            print(elem, ' --> ', bad_edge_table[elem])
            for node in bad_edge_table[elem]:
                if node not in bad_edge_table_nodes:
                    bad_edge_table_nodes.append(node)
        print('sorted(bad_edge_table_nodes)')
        print(sorted(bad_edge_table_nodes))   # should be == bad_refedge_nodes
        # import FreeCADGui
        # FreeCADGui.ActiveDocument.Compound_Mesh.HighlightedNodes = bad_edge_table_nodes
        # bad_node_length_table = [ (nodeID, length), ... , (nodeID, length) ]  some nodes will have more than one entry

        print('good_edge_table')
        good_edge_table = delete_duplicate_mesh_elements(bad_edge_table)
        for elem in good_edge_table:
            print(elem, ' --> ', bad_edge_table[elem])

        print('bad_node_length_table')
        bad_node_length_table = get_ref_edgenodes_lengths(femnodes_mesh, bad_edge_table)
        for n, l in bad_node_length_table:
            print(n, ' --> ', l)

    return force_obj_node_load_table


def get_pressure_obj_faces(femmesh, femobj):
    pressure_faces = []
    for o, elem_tup in femobj['Object'].References:
        for elem in elem_tup:
            ref_shape = o.Shape.getElement(elem)
            elem_info_string = 'face load on shape: ' + o.Name + ':' + elem
            print(elem_info_string)
            if ref_shape.ShapeType == 'Face':
                pressure_faces.append((elem_info_string, femmesh.getccxVolumesByFace(ref_shape)))
    return pressure_faces


def get_force_obj_face_nodeload_table(femmesh, femelement_table, femnodes_mesh, frc_obj):
    # force_obj_node_load_table = [('refshape_name.elemname',node_load_table), ..., ('refshape_name.elemname',node_load_table)]
    force_obj_node_load_table = []
    sum_ref_face_area = 0
    sum_ref_face_node_area = 0  # for debugging
    sum_node_load = 0  # for debugging
    for o, elem_tup in frc_obj.References:
        for elem in elem_tup:
            sum_ref_face_area += o.Shape.getElement(elem).Area
    if sum_ref_face_area != 0:
        force_per_sum_ref_face_area = frc_obj.Force / sum_ref_face_area
    for o, elem_tup in frc_obj.References:
        for elem in elem_tup:
            ref_face = o.Shape.getElement(elem)

            # face_table = { meshfaceID : ( nodeID, ... , nodeID ) }
            face_table = get_ref_facenodes_table(femmesh, femelement_table, ref_face)

            # node_area_table = [ (nodeID, Area), ... , (nodeID, Area) ]  some nodes will have more than one entry
            node_area_table = get_ref_facenodes_areas(femnodes_mesh, face_table)

            # node_sum_area_table = { nodeID : Area, ... , nodeID : Area }  AreaSum for each node, one entry for each node
            node_sum_area_table = get_ref_shape_node_sum_geom_table(node_area_table)

            # node_load_table = { nodeID : NodeLoad, ... , nodeID : NodeLoad }  NodeLoad for each node, one entry for each node
            node_load_table = {}
            sum_node_areas = 0  # for debugging
            for node in node_sum_area_table:
                sum_node_areas += node_sum_area_table[node]  # for debugging
                node_load_table[node] = node_sum_area_table[node] * force_per_sum_ref_face_area
            ratio_refface_areas = sum_node_areas / ref_face.Area
            if ratio_refface_areas < 0.99 or ratio_refface_areas > 1.01:
                FreeCAD.Console.PrintError('Error on: ' + frc_obj.Name + ' --> ' + o.Name + '.' + elem + '\n')
                print('  sum_node_areas:', sum_node_areas)
                print('  ref_face_area:  ', ref_face.Area)
            sum_ref_face_node_area += sum_node_areas

            elem_info_string = 'node loads on shape: ' + o.Name + ':' + elem
            force_obj_node_load_table.append((elem_info_string, node_load_table))

    for ref_shape in force_obj_node_load_table:
        for node in ref_shape[1]:
            sum_node_load += ref_shape[1][node]  # for debugging

    ratio = sum_node_load / frc_obj.Force
    if ratio < 0.99 or ratio > 1.01:
        print('Deviation  sum_node_load to frc_obj.Force is more than 1% :  ', ratio)
        print('  sum_ref_face_node_area: ', sum_ref_face_node_area)
        print('  sum_ref_face_area:      ', sum_ref_face_area)
        print('  sum_node_load:          ', sum_node_load)
        print('  frc_obj.Force:          ', frc_obj.Force)
        print('  the reason could be simply a circle area --> see method get_ref_face_node_areas')
        print('  the reason could also be an problem in retrieving the ref_face_node_area')

    return force_obj_node_load_table


def get_ref_edgenodes_table(femmesh, femelement_table, refedge):
    edge_table = {}  # { meshedgeID : ( nodeID, ... , nodeID ) }
    refedge_nodes = femmesh.getNodesByEdge(refedge)
    if is_solid_femmesh(femmesh):
        refedge_fem_volumeelements = []
        # if at least two nodes of a femvolumeelement are in refedge_nodes the volume is added to refedge_fem_volumeelements
        for elem in femelement_table:
            nodecount = 0
            for node in femelement_table[elem]:
                if node in refedge_nodes:
                    nodecount += 1
            if nodecount > 1:
                refedge_fem_volumeelements.append(elem)
        # for every refedge_fem_volumeelement look which of his nodes is in refedge_nodes --> add all these nodes to edge_table
        for elem in refedge_fem_volumeelements:
            fe_refedge_nodes = []
            for node in femelement_table[elem]:
                if node in refedge_nodes:
                    fe_refedge_nodes.append(node)
                edge_table[elem] = fe_refedge_nodes  # { volumeID : ( edgenodeID, ... , edgenodeID  )} # only the refedge nodes
        #  FIXME duplicate_mesh_elements: as soon as contact ans springs are supported the user should decide on which edge the load is applied
        edge_table = delete_duplicate_mesh_elements(edge_table)
    elif is_face_femmesh(femmesh):
        refedge_fem_faceelements = []
        # if at least two nodes of a femfaceelement are in refedge_nodes the volume is added to refedge_fem_volumeelements
        for elem in femelement_table:
            nodecount = 0
            for node in femelement_table[elem]:
                if node in refedge_nodes:
                    nodecount += 1
            if nodecount > 1:
                refedge_fem_faceelements.append(elem)
        # for every refedge_fem_faceelement look which of his nodes is in refedge_nodes --> add all these nodes to edge_table
        for elem in refedge_fem_faceelements:
            fe_refedge_nodes = []
            for node in femelement_table[elem]:
                if node in refedge_nodes:
                    fe_refedge_nodes.append(node)
                edge_table[elem] = fe_refedge_nodes  # { faceID : ( edgenodeID, ... , edgenodeID  )} # only the refedge nodes
        #  FIXME duplicate_mesh_elements: as soon as contact ans springs are supported the user should decide on which edge the load is applied
        edge_table = delete_duplicate_mesh_elements(edge_table)
    elif is_edge_femmesh(femmesh):
        refedge_fem_edgeelements = get_femelements_by_femnodes(femelement_table, refedge_nodes)
        for elem in refedge_fem_edgeelements:
            edge_table[elem] = femelement_table[elem]  # { edgeID : ( nodeID, ... , nodeID  )} # all nodes off this femedgeelement
    return edge_table


def get_ref_edgenodes_lengths(femnodes_mesh, edge_table):
    # calulate the appropriate node_length for every node of every mesh edge (me)
    # G. Lakshmi Narasaiah, Finite Element Analysis, p206ff

    #  [ (nodeID, length), ... , (nodeID, length) ]  some nodes will have more than one entry
    if (not femnodes_mesh) or (not edge_table):
        FreeCAD.Console.PrintError("Error in get_ref_edgenodes_lengths(): Empty femnodes_mesh or edge_table!\n")
        return []
    node_length_table = []
    mesh_edge_length = 0
    # print(len(edge_table))
    for me in edge_table:
        femmesh_edgetype = len(edge_table[me])
        if femmesh_edgetype == 2:  # 2 node femmesh edge
            # end_node_length = mesh_edge_length / 2
            #    ______
            #  P1      P2
            P1 = femnodes_mesh[edge_table[me][0]]
            P2 = femnodes_mesh[edge_table[me][1]]
            edge_vec = P2 - P1
            mesh_edge_length = edge_vec.Length
            # print(mesh_edge_length)
            end_node_length = mesh_edge_length / 2.0
            node_length_table.append((edge_table[me][0], end_node_length))
            node_length_table.append((edge_table[me][1], end_node_length))

        elif femmesh_edgetype == 3:  # 3 node femmesh edge
            # end_node_length = mesh_edge_length / 6
            # middle_node_length = mesh_face_area * 2 / 3
            #   _______ _______
            # P1       P3      P2
            P1 = femnodes_mesh[edge_table[me][0]]
            P2 = femnodes_mesh[edge_table[me][1]]
            P3 = femnodes_mesh[edge_table[me][2]]
            edge_vec1 = P3 - P1
            edge_vec2 = P2 - P3
            mesh_edge_length = edge_vec1.Length + edge_vec2.Length
            # print(me, ' --> ', mesh_edge_length)
            end_node_length = mesh_edge_length / 6.0
            middle_node_length = mesh_edge_length * 2.0 / 3.0
            node_length_table.append((edge_table[me][0], end_node_length))
            node_length_table.append((edge_table[me][1], end_node_length))
            node_length_table.append((edge_table[me][2], middle_node_length))
    return node_length_table


def get_ref_facenodes_table(femmesh, femelement_table, ref_face):
    face_table = {}  # { meshfaceID : ( nodeID, ... , nodeID ) }
    if is_solid_femmesh(femmesh):
        if has_no_face_data(femmesh):
            print('No face date in volume mesh. We try to use getccxVolumesByFace() to retrive the volume elments of the ref_face!')
            # there is no face data
            # the problem if we retrive the nodes ourself is they are not sorted we just have the nodes. We need to sourt them according
            # the shell mesh notaion of tria3, tria6, quad4, quad8
            ref_face_nodes = femmesh.getNodesByFace(ref_face)
            # try to use getccxVolumesByFace() to get the volume ids of element with elementfaces on the ref_face --> should work for tetra4 and tetra10
            ref_face_volume_elements = femmesh.getccxVolumesByFace(ref_face)  # list of tupels (mv, ccx_face_nr)
            if ref_face_volume_elements:  # mesh with tetras
                print('Use of getccxVolumesByFace() has returned volume elements of the ref_face!')
                for ve in ref_face_volume_elements:
                    veID = ve[0]
                    ve_ref_face_nodes = []
                    for nodeID in femelement_table[veID]:
                        if nodeID in ref_face_nodes:
                            ve_ref_face_nodes.append(nodeID)
                    face_table[veID] = ve_ref_face_nodes  # { volumeID : ( facenodeID, ... , facenodeID ) } only the ref_face nodes
            else:  # mesh with hexa or penta
                print('Use of getccxVolumesByFace() has NOT returned volume elements of the ref_face! We try to use get_femvolumeelements_by_femfacenodes()!')
                ref_face_volume_elements = get_femvolumeelements_by_femfacenodes(femelement_table, ref_face_nodes)  # list of integer [mv]
                for veID in ref_face_volume_elements:
                    ve_ref_face_nodes = []
                    for nodeID in femelement_table[veID]:
                        if nodeID in ref_face_nodes:
                            ve_ref_face_nodes.append(nodeID)
                    face_table[veID] = ve_ref_face_nodes  # { volumeID : ( facenodeID, ... , facenodeID ) } only the ref_face nodes
                face_table = build_mesh_faces_of_volume_elements(face_table, femelement_table)  # we need to resort the nodes to make them build a element face
        else:  # the femmesh has face_data
            faces = femmesh.getFacesByFace(ref_face)   # (mv, mf)
            for mf in faces:
                face_table[mf] = femmesh.getElementNodes(mf)
    elif is_face_femmesh(femmesh):
        ref_face_nodes = femmesh.getNodesByFace(ref_face)
        ref_face_elements = get_femelements_by_femnodes(femelement_table, ref_face_nodes)
        for mf in ref_face_elements:
            face_table[mf] = femelement_table[mf]
    # print face_table
    return face_table


def build_mesh_faces_of_volume_elements(face_table, femelement_table):
    # node index of facenodes in femelementtable volume element
    # if we know the position of the node we can build the element face out of the unsorted face nodes
    face_nodenumber_table = {}  # { volumeID : ( index, ... , index ) }
    for veID in face_table:
        face_nodenumber_table[veID] = []
        for n in face_table[veID]:
            index = femelement_table[veID].index(n)
            # print(index)
            face_nodenumber_table[veID].append(index + 1)  # lokale node number = index + 1
        # print 'VolElement:', veID
        # print '  --> ', femelement_table[veID]
        # print '  --> ', face_table[veID]
        # print '  --> ', face_nodenumber_table[veID]
    for veID in face_nodenumber_table:
        vol_node_ct = len(femelement_table[veID])
        face_node_indexs = sorted(face_nodenumber_table[veID])
        if vol_node_ct == 10:  # tetra10 --> tria6 face
            if face_node_indexs == [1, 2, 3, 5, 6, 7]:  # node order of face  in tetra10 volume element
                node_numbers = (1, 2, 3, 5, 6, 7)       # node order of a tria6 face of tetra10
            elif face_node_indexs == [1, 2, 4, 5, 8, 9]:
                node_numbers = (1, 4, 2, 8, 9, 5)
            elif face_node_indexs == [1, 3, 4, 7, 8, 10]:
                node_numbers = (1, 3, 4, 7, 10, 8)
            elif face_node_indexs == [2, 3, 4, 6, 9, 10]:
                node_numbers = (2, 4, 3, 9, 10, 6)
            else:
                FreeCAD.Console.PrintError("Error in build_mesh_faces_of_volume_elements(): hexa20: face not found!" + str(face_node_indexs) + "\n")
        elif vol_node_ct == 4:  # tetra4 --> tria3 face
            if face_node_indexs == [1, 2, 3]:  # node order of face  in tetra4 volume element
                node_numbers = (1, 2, 3)       # node order of a tria3 face of tetra4
            elif face_node_indexs == [1, 2, 4]:
                node_numbers = (1, 4, 2, 8)
            elif face_node_indexs == [1, 3, 4]:
                node_numbers = (1, 3, 4)
            elif face_node_indexs == [2, 3, 4]:
                node_numbers = (2, 4, 3)
            else:
                FreeCAD.Console.PrintError("Error in build_mesh_faces_of_volume_elements(): hexa20: face not found!" + str(face_node_indexs) + "\n")
        elif vol_node_ct == 20:  # hexa20 --> quad8 face
            if face_node_indexs == [1, 2, 3, 4, 9, 10, 11, 12]:  # node order of face  in hexa20 volume element
                node_numbers = (1, 2, 3, 4, 9, 10, 11, 12)       # node order of a quad8 face of hexa20
            elif face_node_indexs == [5, 6, 7, 8, 13, 14, 15, 16]:
                node_numbers = (5, 8, 7, 6, 16, 15, 14, 13)
            elif face_node_indexs == [1, 2, 5, 6, 9, 13, 17, 18]:
                node_numbers = (1, 5, 6, 2, 17, 13, 18, 9)
            elif face_node_indexs == [3, 4, 7, 8, 11, 15, 19, 20]:
                node_numbers = (3, 7, 8, 4, 19, 15, 20, 11)
            elif face_node_indexs == [1, 4, 5, 8, 12, 16, 17, 20]:
                node_numbers = (1, 4, 8, 5, 12, 20, 16, 17)
            elif face_node_indexs == [2, 3, 6, 7, 10, 14, 18, 19]:
                node_numbers = (2, 6, 7, 3, 18, 14, 19, 10)
            else:
                FreeCAD.Console.PrintError("Error in build_mesh_faces_of_volume_elements(): hexa20: face not found!" + str(face_node_indexs) + "\n")
        elif vol_node_ct == 8:  # hexa8 --> quad4 face
            face_node_indexs = sorted(face_nodenumber_table[veID])
            if face_node_indexs == [1, 2, 3, 4]:  # node order of face  in hexa8 volume element
                node_numbers = (1, 2, 3, 4)       # node order of a quad8 face of hexa8
            elif face_node_indexs == [5, 6, 7, 8]:
                node_numbers = (5, 8, 7, 6)
            elif face_node_indexs == [1, 2, 5, 6]:
                node_numbers = (1, 5, 6, 2)
            elif face_node_indexs == [3, 4, 7, 8]:
                node_numbers = (3, 7, 8, 4)
            elif face_node_indexs == [1, 4, 5, 8]:
                node_numbers = (1, 4, 8, 5)
            elif face_node_indexs == [2, 3, 6, 7]:
                node_numbers = (2, 6, 7, 3)
            else:
                FreeCAD.Console.PrintError("Error in build_mesh_faces_of_volume_elements(): hexa20: face not found!" + str(face_node_indexs) + "\n")
        elif vol_node_ct == 15:  # penta15 --> tria6 and quad8 faces
            if face_node_indexs == [1, 2, 3, 7, 8, 9]:  # node order of face  in penta15 volume element
                node_numbers = (1, 2, 3, 7, 8, 9)       # node order of a tria6 face of penta15
            elif face_node_indexs == [4, 5, 6, 10, 11, 12]:
                node_numbers = (4, 6, 5, 12, 11, 10)  # tria6
            elif face_node_indexs == [1, 2, 4, 5, 7, 10, 13, 14]:
                node_numbers = (1, 4, 5, 2, 13, 10, 14, 7)  # quad8
            elif face_node_indexs == [1, 3, 4, 6, 9, 12, 13, 15]:
                node_numbers = (1, 3, 6, 4, 9, 15, 12, 13)  # quad8
            elif face_node_indexs == [2, 3, 5, 6, 8, 11, 14, 15]:
                node_numbers = (2, 5, 6, 3, 14, 11, 15, 8)  # quad8
            else:
                FreeCAD.Console.PrintError("Error in build_mesh_faces_of_volume_elements(): penta15: face not found!" + str(face_node_indexs) + "\n")
        elif vol_node_ct == 6:  # penta6 --> tria3 and quad4 faces
            if face_node_indexs == [1, 2, 3]:  # node order of face  in penta6 volume element
                node_numbers = (1, 2, 3)       # node order of a tria3 face of penta6
            elif face_node_indexs == [4, 5, 6]:
                node_numbers = (4, 6, 5)  # tria3
            elif face_node_indexs == [1, 2, 4, 5]:
                node_numbers = (1, 4, 5, 2)  # quad4
            elif face_node_indexs == [1, 3, 4, 6]:
                node_numbers = (1, 3, 6, 4)  # quad4
            elif face_node_indexs == [2, 3, 5, 6]:
                node_numbers = (2, 5, 6, 3)  # quad4
            else:
                FreeCAD.Console.PrintError("Error in build_mesh_faces_of_volume_elements(): pent6: face not found!" + str(face_node_indexs) + "\n")
        else:
            FreeCAD.Console.PrintError("Error in build_mesh_faces_of_volume_elements(): Volume not implemented: volume node count" + str(vol_node_ct) + "\n")
        face_nodes = []
        for i in node_numbers:
            i -= 1  # node_number starts with 1, index starts with 0 --> index = node number - 1
            face_nodes.append(femelement_table[veID][i])
        face_table[veID] = face_nodes  # reset the entry in face_table
        # print '  --> ', face_table[veID]
    return face_table


def get_ref_facenodes_areas(femnodes_mesh, face_table):
    # calulate the appropriate node_areas for every node of every mesh face (mf)
    # G. Lakshmi Narasaiah, Finite Element Analysis, p206ff
    # FIXME only gives exact results in case of a real triangle. If for S6 or C3D10 elements
    # the midnodes are not on the line between the end nodes the area will not be a triangle
    # see http://forum.freecadweb.org/viewtopic.php?f=18&t=10939&start=40#p91355  and ff
    # same applies for the quads, results are exact only if mid nodes are on the line between corner nodes

    #  [ (nodeID,Area), ... , (nodeID,Area) ]  some nodes will have more than one entry
    if (not femnodes_mesh) or (not face_table):
        FreeCAD.Console.PrintError("Error: Empty femnodes_mesh or face_table!\n")
        return []
    node_area_table = []
    mesh_face_area = 0
    for mf in face_table:
        femmesh_facetype = len(face_table[mf])
        # nodes in face_table need to be in the right node order for the following calcualtions
        if femmesh_facetype == 3:  # 3 node femmesh face triangle
            # corner_node_area = mesh_face_area / 3.0
            #      P3
            #      /\
            #     /  \
            #    /____\
            #  P1      P2
            P1 = femnodes_mesh[face_table[mf][0]]
            P2 = femnodes_mesh[face_table[mf][1]]
            P3 = femnodes_mesh[face_table[mf][2]]

            mesh_face_area = get_triangle_area(P1, P2, P3)
            corner_node_area = mesh_face_area / 3.0

            node_area_table.append((face_table[mf][0], corner_node_area))
            node_area_table.append((face_table[mf][1], corner_node_area))
            node_area_table.append((face_table[mf][2], corner_node_area))

        elif femmesh_facetype == 4:  # 4 node femmesh face quad
            # corner_node_area = mesh_face_area / 4.0
            #  P4_______P3
            #    |     /|
            #    | t2 / |
            #    |   /  |
            #    |  /   |
            #    | / t1 |
            #    |/_____|
            #  P1       P2
            P1 = femnodes_mesh[face_table[mf][0]]
            P2 = femnodes_mesh[face_table[mf][1]]
            P3 = femnodes_mesh[face_table[mf][2]]
            P4 = femnodes_mesh[face_table[mf][3]]

            mesh_face_t1_area = get_triangle_area(P1, P2, P3)
            mesh_face_t2_area = get_triangle_area(P1, P3, P4)
            mesh_face_area = mesh_face_t1_area + mesh_face_t1_area
            corner_node_area = mesh_face_area / 4.0

            node_area_table.append((face_table[mf][0], corner_node_area))
            node_area_table.append((face_table[mf][1], corner_node_area))
            node_area_table.append((face_table[mf][2], corner_node_area))
            node_area_table.append((face_table[mf][3], corner_node_area))

        elif femmesh_facetype == 6:  # 6 node femmesh face triangle
            # corner_node_area = 0
            # middle_node_area = mesh_face_area / 3.0
            #         P3
            #         /\
            #        /t3\
            #       /    \
            #     P6------P5
            #     / \ t4 / \
            #    /t1 \  /t2 \
            #   /_____\/_____\
            # P1      P4      P2
            P1 = femnodes_mesh[face_table[mf][0]]
            P2 = femnodes_mesh[face_table[mf][1]]
            P3 = femnodes_mesh[face_table[mf][2]]
            P4 = femnodes_mesh[face_table[mf][3]]
            P5 = femnodes_mesh[face_table[mf][4]]
            P6 = femnodes_mesh[face_table[mf][5]]

            mesh_face_t1_area = get_triangle_area(P1, P4, P6)
            mesh_face_t2_area = get_triangle_area(P2, P5, P4)
            mesh_face_t3_area = get_triangle_area(P3, P6, P5)
            mesh_face_t4_area = get_triangle_area(P4, P5, P6)
            mesh_face_area = mesh_face_t1_area + mesh_face_t2_area + mesh_face_t3_area + mesh_face_t4_area
            middle_node_area = mesh_face_area / 3.0

            node_area_table.append((face_table[mf][0], 0))
            node_area_table.append((face_table[mf][1], 0))
            node_area_table.append((face_table[mf][2], 0))
            node_area_table.append((face_table[mf][3], middle_node_area))
            node_area_table.append((face_table[mf][4], middle_node_area))
            node_area_table.append((face_table[mf][5], middle_node_area))

        elif femmesh_facetype == 8:  # 8 node femmesh face quad
            # corner_node_area = -mesh_face_area / 12.0  (negativ!)
            # mid-side nodes = mesh_face_area / 3.0
            #  P4_________P7________P3
            #    |      / |  \      |
            #    | t4 /   |    \ t3 |
            #    |  /     |      \  |
            #    |/       |        \|
            #  P8|    t5  |   t6    |P6
            #    |\       |       / |
            #    |  \     |     /   |
            #    | t1 \   |   /  t2 |
            #    |______\_|_/_______|
            #  P1         P5        P2
            P1 = femnodes_mesh[face_table[mf][0]]
            P2 = femnodes_mesh[face_table[mf][1]]
            P3 = femnodes_mesh[face_table[mf][2]]
            P4 = femnodes_mesh[face_table[mf][3]]
            P5 = femnodes_mesh[face_table[mf][4]]
            P6 = femnodes_mesh[face_table[mf][5]]
            P7 = femnodes_mesh[face_table[mf][6]]
            P8 = femnodes_mesh[face_table[mf][7]]

            mesh_face_t1_area = get_triangle_area(P1, P5, P8)
            mesh_face_t2_area = get_triangle_area(P5, P2, P6)
            mesh_face_t3_area = get_triangle_area(P6, P3, P7)
            mesh_face_t4_area = get_triangle_area(P7, P4, P8)
            mesh_face_t5_area = get_triangle_area(P5, P7, P8)
            mesh_face_t6_area = get_triangle_area(P5, P6, P7)
            mesh_face_area = mesh_face_t1_area + mesh_face_t2_area + mesh_face_t3_area + mesh_face_t4_area + mesh_face_t5_area + mesh_face_t6_area
            corner_node_area = -mesh_face_area / 12.0
            middle_node_area = mesh_face_area / 3.0

            node_area_table.append((face_table[mf][0], corner_node_area))
            node_area_table.append((face_table[mf][1], corner_node_area))
            node_area_table.append((face_table[mf][2], corner_node_area))
            node_area_table.append((face_table[mf][3], corner_node_area))
            node_area_table.append((face_table[mf][4], middle_node_area))
            node_area_table.append((face_table[mf][5], middle_node_area))
            node_area_table.append((face_table[mf][6], middle_node_area))
            node_area_table.append((face_table[mf][7], middle_node_area))
    return node_area_table


def get_ref_shape_node_sum_geom_table(node_geom_table):
    # shape could be Edge or Face, geom could be lenght or area
    # summ of legth or area for each node of the ref_shape
    node_sum_geom_table = {}
    for n, A in node_geom_table:
        # print(n, ' --> ', A)
        if n in node_sum_geom_table:
            node_sum_geom_table[n] = node_sum_geom_table[n] + A
        else:
            node_sum_geom_table[n] = A
    return node_sum_geom_table


def get_analysis_group_elements(aAnalysis, aPart):
    ''' all Reference shapes of all Analysis member are searched in the Shape of aPart. If found in shape they are added to a dict
    {ConstraintName : ['ShapeType of the Elements'], [ElementID, ElementID, ...], ...}
    '''
    aShape = aPart.Shape
    group_elements = {}
    empty_references = []
    for m in aAnalysis.Member:
        if hasattr(m, "References"):
            # print(m.Name)
            key = m.Name
            indexes = []
            stype = None
            if m.References:
                for r in m.References:
                    parent = r[0]
                    childs = r[1]
                    # print(parent)
                    # print(childs)
                    for child in childs:
                        if child:
                            # Face, Edge, Vertex
                            ref_shape = parent.Shape.getElement(child)
                        else:
                            # Solid
                            ref_shape = parent.Shape
                        if not stype:
                            stype = ref_shape.ShapeType
                        elif stype != ref_shape.ShapeType:
                            FreeCAD.Console.PrintError('Error, two refschapes in References with different ShapeTypes.\n')
                        # print(ref_shape)
                        found_element = find_element_in_shape(aShape, ref_shape)
                        if found_element is not None:
                            indexes.append(found_element)
                        else:
                            FreeCAD.Console.PrintError('Problem: No element found for: ' + str(ref_shape) + '\n')
                            print('    ' + m.Name)
                            print('    ' + str(m.References))
                            print('    ' + r[0].Name)
                group_elements[key] = [stype, sorted(indexes)]
            else:
                print('Empty reference: ' + m.Name)
                empty_references.append(m)
    if empty_references:
        if len(empty_references) == 1:
            group_elements = get_anlysis_empty_references_group_elements(group_elements, aAnalysis, aShape)
        else:
            FreeCAD.Console.PrintError('Error: more than one object with empty references!\n')
            print(empty_references)
    # check if all groups have elements:
    for g in group_elements:
        # print group_elements[g][1]
        if len(group_elements[g][1]) == 0:
            FreeCAD.Console.PrintError('Error: shapes for: ' + g + 'not found!\n')
    return group_elements


def get_anlysis_empty_references_group_elements(group_elements, aAnalysis, aShape):
    '''get the elementIDs if the Reference shape is empty
    see get_analysis_group_elements()
    '''
    material_ref_shapes = []
    material_shape_type = ''
    missed_material_refshapes = []
    empty_reference_material = None
    for m in aAnalysis.Member:
        # only materials could have an empty reference without beeing something wrong!
        if m.isDerivedFrom("App::MaterialObjectPython"):
            if hasattr(m, "References") and m.References:
                if not material_shape_type:
                    material_shape_type = group_elements[m.Name][0]
                elif material_shape_type != group_elements[m.Name][0]:
                    print('Problem, material shape type does not match get_anlysis_empty_references_group_elements')
                for i in group_elements[m.Name][1]:
                    material_ref_shapes.append(i)
            elif hasattr(m, "References") and not m.References:
                if not empty_reference_material:
                    empty_reference_material = m.Name
                else:
                    print('Problem in get_anlysis_empty_references_group_elements, we seams to have two materials with empty referneces')
                    return {}
    if material_shape_type == 'Solid':
        # print(len(aShape.Solids))
        for i in range(len(aShape.Solids)):
            if i not in material_ref_shapes:
                missed_material_refshapes.append(i)
    elif material_shape_type == 'Face':
        # print(len(aShape.Faces))
        for i in range(len(aShape.Faces)):
            if i not in material_ref_shapes:
                missed_material_refshapes.append(i)
    elif material_shape_type == 'Edge':
        # print(len(aShape.Edges))
        for i in range(len(aShape.Edges)):
            if i not in material_ref_shapes:
                missed_material_refshapes.append(i)
    else:
        print('It seams we only have one material with no reference shapes. Means the whole solid is one material. Since we only support material groups for Solids at the moment this should be Solid')
        material_shape_type = 'Solid'
        missed_material_refshapes.append(0)
    # print(sorted(material_ref_shapes))
    # print(sorted(missed_material_refshapes))
    # print(group_elements)
    group_elements[empty_reference_material] = [material_shape_type, sorted(missed_material_refshapes)]
    # print(group_elements)
    return group_elements


def find_element_in_shape(aShape, anElement):
    # import Part
    if anElement.ShapeType == 'Solid' or anElement.ShapeType == 'CompSolid':
        for index, solid in enumerate(aShape.Solids):
            # print(is_same_geometry(solid, anElement))
            if is_same_geometry(solid, anElement):
                # print(index)
                # Part.show(aShape.Solids[index])
                return index
        FreeCAD.Console.PrintError('Solid ' + str(anElement) + ' not found in: ' + str(aShape) + '\n')
        if anElement.ShapeType == 'Solid' and aShape.ShapeType == 'Solid':
            print('We have been searching for a Solid in a Solid and we have not found it. In most cases this should be searching for a Solid inside a CompSolid. Check the ShapeType of your Part to mesh.')
        # Part.show(anElement)
        # Part.show(aShape)
    elif anElement.ShapeType == 'Face' or anElement.ShapeType == 'Shell':
        for index, face in enumerate(aShape.Faces):
            # print(is_same_geometry(face, anElement))
            if is_same_geometry(face, anElement):
                # print(index)
                # Part.show(aShape.Faces[index])
                return index
    elif anElement.ShapeType == 'Edge' or anElement.ShapeType == 'Wire':
        for index, face in enumerate(aShape.Edges):
            # print(is_same_geometry(face, anElement))
            if is_same_geometry(face, anElement):
                # print(index)
                # Part.show(aShape.Edges[index])
                return index
    elif anElement.ShapeType == 'Vertex':
        for index, face in enumerate(aShape.Vertexes):
            # print(is_same_geometry(face, anElement))
            if is_same_geometry(face, anElement):
                # print(index)
                # Part.show(aShape.Vertexes[index])
                return index
    elif anElement.ShapeType == 'Compound':
        FreeCAD.Console.PrintError('Compound is not supported.\n')


def is_same_geometry(shape1, shape2):
    # the vertexes and the CenterOfMass are compared
    # it is a hack, but I do not know any better !
    # check of Volume and Area before starting with the vertices could be added
    # BoundBox is possible too, but is BB calcualtions robust?!
    # print(shape1)
    # print(shape2)
    same_Vertexes = 0
    if len(shape1.Vertexes) == len(shape2.Vertexes) and len(shape1.Vertexes) > 1:
        # compare CenterOfMass
        if shape1.CenterOfMass != shape2.CenterOfMass:
            return False
        else:
            # compare the Vertexes
            for vs1 in shape1.Vertexes:
                for vs2 in shape2.Vertexes:
                    if vs1.X == vs2.X and vs1.Y == vs2.Y and vs1.Z == vs2.Z:
                        same_Vertexes += 1
                        continue
            # print(same_Vertexes)
            if same_Vertexes == len(shape1.Vertexes):
                return True
            else:
                return False
    if len(shape1.Vertexes) == len(shape2.Vertexes) and len(shape1.Vertexes) == 1:
        vs1 = shape1.Vertexes[0]
        vs2 = shape2.Vertexes[0]
        if vs1.X == vs2.X and vs1.Y == vs2.Y and vs1.Z == vs2.Z:
            return True
        else:
            return False
    else:
        return False


def femelements_count_ok(len_femelement_table, count_femelements):
    if count_femelements == len_femelement_table:
        print('Count FEM elements as sum of constraints: ', count_femelements)
        print('Count FEM elements of the FreeCAD FEM mesh:  ', len_femelement_table)
        return True
    else:
        print('ERROR: femelement_table != count_femelements')
        print('Count FEM elements as sum of constraints: ', count_femelements)
        print('Count FEM elements of the FreeCAD FEM Mesh:  ', len_femelement_table)
        return False


def delete_duplicate_mesh_elements(refelement_table):
    new_refelement_table = {}  # duplicates deleted
    for elem, nodes in refelement_table.items():
        if sorted(nodes) not in sortlistoflistvalues(new_refelement_table.values()):
            new_refelement_table[elem] = nodes
    return new_refelement_table


def get_triangle_area(P1, P2, P3):
    # import Part
    # W = Part.Wire([Part.makeLine(P1,P2), Part.makeLine(P2,P3), Part.makeLine(P3,P1)])
    # Part.show(Part.Face(W))
    vec1 = P2 - P1
    vec2 = P3 - P1
    vec3 = vec1.cross(vec2)
    return 0.5 * vec3.Length


def sortlistoflistvalues(listoflists):
    new_list = []
    for l in listoflists:
        new_list.append(sorted(l))
    return new_list


def is_solid_femmesh(femmesh):
    if femmesh.VolumeCount > 0:  # solid femmesh
        return True


def has_no_face_data(femmesh):
    if femmesh.FaceCount == 0:   # femmesh has no face data, could be a edge femmesh or a solid femmesh without face data
        return True


def is_face_femmesh(femmesh):
    if femmesh.VolumeCount == 0 and femmesh.FaceCount > 0:  # face femmesh
        return True


def is_edge_femmesh(femmesh):
    if femmesh.VolumeCount == 0 and femmesh.FaceCount == 0 and femmesh.EdgeCount > 0:  # edge femmesh
        return True


def get_three_non_colinear_nodes(nodes_coords):
    # Code to obtain three non-colinear nodes on the PlaneRotation support face
    # nodes_coords --> [(nodenumber, x, y, z), (nodenumber, x, y, z), ...]
    if not nodes_coords:
        print(len(nodes_coords))
        print('Error: No nodes in nodes_coords')
        return []
    dum_max = [1, 2, 3, 4, 5, 6, 7, 8, 0]
    for i in range(len(nodes_coords)):
        for j in range(len(nodes_coords) - 1 - i):
            x_1 = nodes_coords[j][1]
            x_2 = nodes_coords[j + 1][1]
            y_1 = nodes_coords[j][2]
            y_2 = nodes_coords[j + 1][2]
            z_1 = nodes_coords[j][3]
            z_2 = nodes_coords[j + 1][3]
            node_1 = nodes_coords[j][0]
            node_2 = nodes_coords[j + 1][0]
            distance = ((x_1 - x_2) ** 2 + (y_1 - y_2) ** 2 + (z_1 - z_2) ** 2) ** 0.5
            if distance > dum_max[8]:
                dum_max = [node_1, x_1, y_1, z_1, node_2, x_2, y_2, z_2, distance]
    node_dis = [1, 0]
    for i in range(len(nodes_coords)):
        x_1 = dum_max[1]
        x_2 = dum_max[5]
        x_3 = nodes_coords[i][1]
        y_1 = dum_max[2]
        y_2 = dum_max[6]
        y_3 = nodes_coords[i][2]
        z_1 = dum_max[3]
        z_2 = dum_max[7]
        z_3 = nodes_coords[i][3]
        node_3 = int(nodes_coords[j][0])
        distance_1 = ((x_1 - x_3) ** 2 + (y_1 - y_3) ** 2 + (z_1 - z_3) ** 2) ** 0.5
        distance_2 = ((x_3 - x_2) ** 2 + (y_3 - y_2) ** 2 + (z_3 - z_2) ** 2) ** 0.5
        tot = distance_1 + distance_2
        if tot > node_dis[1]:
            node_dis = [node_3, tot]
    node_1 = int(dum_max[0])
    node_2 = int(dum_max[4])
    print([node_1, node_2, node_3])
    return [node_1, node_2, node_3]


def get_rectangular_coords(obj):
    from math import cos, sin, radians
    A = [1, 0, 0]
    B = [0, 1, 0]
    a_x = A[0]
    a_y = A[1]
    a_z = A[2]
    b_x = A[0]
    b_y = A[1]
    b_z = A[2]
    x_rot = radians(obj.X_rot)
    y_rot = radians(obj.Y_rot)
    z_rot = radians(obj.Z_rot)
    if obj.X_rot != 0:
        a_x = A[0]
        a_y = A[1] * cos(x_rot) + A[2] * sin(x_rot)
        a_z = A[2] * cos(x_rot) - A[1] * sin(x_rot)
        b_x = B[0]
        b_y = B[1] * cos(x_rot) + B[2] * sin(x_rot)
        b_z = B[2] * cos(x_rot) - B[1] * sin(x_rot)
        A = [a_x, a_y, a_z]
        B = [b_x, b_y, b_z]
    if obj.Y_rot != 0:
        a_x = A[0] * cos(y_rot) - A[2] * sin(y_rot)
        a_y = A[1]
        a_z = A[2] * cos(y_rot) + A[0] * sin(y_rot)
        b_x = B[0] * cos(y_rot) - B[2] * sin(y_rot)
        b_y = B[1]
        b_z = B[2] * cos(y_rot) + B[0] * sin(z_rot)
        A = [a_x, a_y, a_z]
        B = [b_x, b_y, b_z]
    if obj.Z_rot != 0:
        a_x = A[0] * cos(z_rot) + A[1] * sin(z_rot)
        a_y = A[1] * cos(z_rot) - A[0] * sin(z_rot)
        a_z = A[2]
        b_x = B[0] * cos(z_rot) + B[1] * sin(z_rot)
        b_y = B[1] * cos(z_rot) - B[0] * sin(z_rot)
        b_z = B[2]
        A = [a_x, a_y, a_z]
        B = [b_x, b_y, b_z]

    A_coords = str(round(A[0], 4)) + ',' + str(round(A[1], 4)) + ',' + str(round(A[2], 4))
    B_coords = str(round(B[0], 4)) + ',' + str(round(B[1], 4)) + ',' + str(round(B[2], 4))
    coords = A_coords + ',' + B_coords
    return coords


def get_cylindrical_coords(obj):
    vec = obj.Axis
    base = obj.BasePoint
    Ax = base[0] + 10 * vec[0]
    Ay = base[1] + 10 * vec[1]
    Az = base[2] + 10 * vec[2]
    Bx = base[0] - 10 * vec[0]
    By = base[1] - 10 * vec[1]
    Bz = base[2] - 10 * vec[2]
    A = [Ax, Ay, Az]
    B = [Bx, By, Bz]
    A_coords = str(A[0]) + ',' + str(A[1]) + ',' + str(A[2])
    B_coords = str(B[0]) + ',' + str(B[1]) + ',' + str(B[2])
    coords = A_coords + ',' + B_coords
    return coords


def make_femmesh(mesh_data):
    ''' makes an FreeCAD FEM Mesh object from FEM Mesh data
    '''
    import Fem
    mesh = Fem.FemMesh()
    m = mesh_data
    if ('Nodes' in m) and (len(m['Nodes']) > 0):
        print("Found: nodes")
        if (('Seg2Elem' in m) or
           ('Tria3Elem' in m) or
           ('Tria6Elem' in m) or
           ('Quad4Elem' in m) or
           ('Quad8Elem' in m) or
           ('Tetra4Elem' in m) or
           ('Tetra10Elem' in m) or
           ('Penta6Elem' in m) or
           ('Penta15Elem' in m) or
           ('Hexa8Elem' in m) or
           ('Hexa20Elem' in m)):

            nds = m['Nodes']
            print("Found: elements")
            for i in nds:
                n = nds[i]
                mesh.addNode(n[0], n[1], n[2], i)
            elms_hexa8 = m['Hexa8Elem']
            for i in elms_hexa8:
                e = elms_hexa8[i]
                mesh.addVolume([e[0], e[1], e[2], e[3], e[4], e[5], e[6], e[7]], i)
            elms_penta6 = m['Penta6Elem']
            for i in elms_penta6:
                e = elms_penta6[i]
                mesh.addVolume([e[0], e[1], e[2], e[3], e[4], e[5]], i)
            elms_tetra4 = m['Tetra4Elem']
            for i in elms_tetra4:
                e = elms_tetra4[i]
                mesh.addVolume([e[0], e[1], e[2], e[3]], i)
            elms_tetra10 = m['Tetra10Elem']
            for i in elms_tetra10:
                e = elms_tetra10[i]
                mesh.addVolume([e[0], e[1], e[2], e[3], e[4], e[5], e[6], e[7], e[8], e[9]], i)
            elms_penta15 = m['Penta15Elem']
            for i in elms_penta15:
                e = elms_penta15[i]
                mesh.addVolume([e[0], e[1], e[2], e[3], e[4], e[5], e[6], e[7], e[8], e[9],
                                e[10], e[11], e[12], e[13], e[14]], i)
            elms_hexa20 = m['Hexa20Elem']
            for i in elms_hexa20:
                e = elms_hexa20[i]
                mesh.addVolume([e[0], e[1], e[2], e[3], e[4], e[5], e[6], e[7], e[8], e[9],
                                e[10], e[11], e[12], e[13], e[14], e[15], e[16], e[17], e[18], e[19]], i)
            elms_tria3 = m['Tria3Elem']
            for i in elms_tria3:
                e = elms_tria3[i]
                mesh.addFace([e[0], e[1], e[2]], i)
            elms_tria6 = m['Tria6Elem']
            for i in elms_tria6:
                e = elms_tria6[i]
                mesh.addFace([e[0], e[1], e[2], e[3], e[4], e[5]], i)
            elms_quad4 = m['Quad4Elem']
            for i in elms_quad4:
                e = elms_quad4[i]
                mesh.addFace([e[0], e[1], e[2], e[3]], i)
            elms_quad8 = m['Quad8Elem']
            for i in elms_quad8:
                e = elms_quad8[i]
                mesh.addFace([e[0], e[1], e[2], e[3], e[4], e[5], e[6], e[7]], i)
            elms_seg2 = m['Seg2Elem']
            for i in elms_seg2:
                e = elms_seg2[i]
                mesh.addEdge(e[0], e[1])
            print("imported mesh: {} nodes, {} HEXA8, {} PENTA6, {} TETRA4, {} TETRA10, {} PENTA15".format(
                  len(nds), len(elms_hexa8), len(elms_penta6), len(elms_tetra4), len(elms_tetra10), len(elms_penta15)))
            print("imported mesh: {} HEXA20, {} TRIA3, {} TRIA6, {} QUAD4, {} QUAD8, {} SEG2".format(
                  len(elms_hexa20), len(elms_tria3), len(elms_tria6), len(elms_quad4), len(elms_quad8), len(elms_seg2)))
        else:
            FreeCAD.Console.PrintError("No Elements found!\n")
    else:
        FreeCAD.Console.PrintError("No Nodes found!\n")
    return mesh