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bl_info = {
    "name": "LoopTools",
    "author": "Bart Crouch",
    "version": (4, 5, 2),
    "blender": (2, 69, 3),
    "location": "View3D > Toolbar and View3D > Specials (W-key)",
    "warning": "",
    "description": "Mesh modelling toolkit. Several tools to aid modelling",
    "wiki_url": "http://wiki.blender.org/index.php/Extensions:2.6/Py/"
        "Scripts/Modeling/LoopTools",
    "tracker_url": "https://developer.blender.org/T26189",
    "category": "Mesh"}


import bmesh
import bpy
import collections
import mathutils
import math
from bpy_extras import view3d_utils


##########################################
####### General functions ################
##########################################


# used by all tools to improve speed on reruns
looptools_cache = {}


# force a full recalculation next time
def cache_delete(tool):
    if tool in looptools_cache:
        del looptools_cache[tool]


# check cache for stored information
def cache_read(tool, object, bm, input_method, boundaries):
    # current tool not cached yet
    if tool not in looptools_cache:
        return(False, False, False, False, False)
    # check if selected object didn't change
    if object.name != looptools_cache[tool]["object"]:
        return(False, False, False, False, False)
    # check if input didn't change
    if input_method != looptools_cache[tool]["input_method"]:
        return(False, False, False, False, False)
    if boundaries != looptools_cache[tool]["boundaries"]:
        return(False, False, False, False, False)
    modifiers = [mod.name for mod in object.modifiers if mod.show_viewport \
        and mod.type == 'MIRROR']
    if modifiers != looptools_cache[tool]["modifiers"]:
        return(False, False, False, False, False)
    input = [v.index for v in bm.verts if v.select and not v.hide]
    if input != looptools_cache[tool]["input"]:
        return(False, False, False, False, False)
    # reading values
    single_loops = looptools_cache[tool]["single_loops"]
    loops = looptools_cache[tool]["loops"]
    derived = looptools_cache[tool]["derived"]
    mapping = looptools_cache[tool]["mapping"]

    return(True, single_loops, loops, derived, mapping)


# store information in the cache
def cache_write(tool, object, bm, input_method, boundaries, single_loops,
loops, derived, mapping):
    # clear cache of current tool
    if tool in looptools_cache:
        del looptools_cache[tool]
    # prepare values to be saved to cache
    input = [v.index for v in bm.verts if v.select and not v.hide]
    modifiers = [mod.name for mod in object.modifiers if mod.show_viewport \
        and mod.type == 'MIRROR']
    # update cache
    looptools_cache[tool] = {"input": input, "object": object.name,
        "input_method": input_method, "boundaries": boundaries,
        "single_loops": single_loops, "loops": loops,
        "derived": derived, "mapping": mapping, "modifiers": modifiers}


# calculates natural cubic splines through all given knots
def calculate_cubic_splines(bm_mod, tknots, knots):
    # hack for circular loops
    if knots[0] == knots[-1] and len(knots) > 1:
        circular = True
        k_new1 = []
        for k in range(-1, -5, -1):
            if k - 1 < -len(knots):
                k += len(knots)
            k_new1.append(knots[k-1])
        k_new2 = []
        for k in range(4):
            if k + 1 > len(knots) - 1:
                k -= len(knots)
            k_new2.append(knots[k+1])
        for k in k_new1:
            knots.insert(0, k)
        for k in k_new2:
            knots.append(k)
        t_new1 = []
        total1 = 0
        for t in range(-1, -5, -1):
            if t - 1 < -len(tknots):
                t += len(tknots)
            total1 += tknots[t] - tknots[t-1]
            t_new1.append(tknots[0] - total1)
        t_new2 = []
        total2 = 0
        for t in range(4):
            if t + 1 > len(tknots) - 1:
                t -= len(tknots)
            total2 += tknots[t+1] - tknots[t]
            t_new2.append(tknots[-1] + total2)
        for t in t_new1:
            tknots.insert(0, t)
        for t in t_new2:
            tknots.append(t)
    else:
        circular = False
    # end of hack

    n = len(knots)
    if n < 2:
        return False
    x = tknots[:]
    locs = [bm_mod.verts[k].co[:] for k in knots]
    result = []
    for j in range(3):
        a = []
        for i in locs:
            a.append(i[j])
        h = []
        for i in range(n-1):
            if x[i+1] - x[i] == 0:
                h.append(1e-8)
            else:
                h.append(x[i+1] - x[i])
        q = [False]
        for i in range(1, n-1):
            q.append(3/h[i]*(a[i+1]-a[i]) - 3/h[i-1]*(a[i]-a[i-1]))
        l = [1.0]
        u = [0.0]
        z = [0.0]
        for i in range(1, n-1):
            l.append(2*(x[i+1]-x[i-1]) - h[i-1]*u[i-1])
            if l[i] == 0:
                l[i] = 1e-8
            u.append(h[i] / l[i])
            z.append((q[i] - h[i-1] * z[i-1]) / l[i])
        l.append(1.0)
        z.append(0.0)
        b = [False for i in range(n-1)]
        c = [False for i in range(n)]
        d = [False for i in range(n-1)]
        c[n-1] = 0.0
        for i in range(n-2, -1, -1):
            c[i] = z[i] - u[i]*c[i+1]
            b[i] = (a[i+1]-a[i])/h[i] - h[i]*(c[i+1]+2*c[i])/3
            d[i] = (c[i+1]-c[i]) / (3*h[i])
        for i in range(n-1):
            result.append([a[i], b[i], c[i], d[i], x[i]])
    splines = []
    for i in range(len(knots)-1):
        splines.append([result[i], result[i+n-1], result[i+(n-1)*2]])
    if circular: # cleaning up after hack
        knots = knots[4:-4]
        tknots = tknots[4:-4]

    return(splines)


# calculates linear splines through all given knots
def calculate_linear_splines(bm_mod, tknots, knots):
    splines = []
    for i in range(len(knots)-1):
        a = bm_mod.verts[knots[i]].co
        b = bm_mod.verts[knots[i+1]].co
        d = b-a
        t = tknots[i]
        u = tknots[i+1]-t
        splines.append([a, d, t, u]) # [locStart, locDif, tStart, tDif]

    return(splines)


# calculate a best-fit plane to the given vertices
def calculate_plane(bm_mod, loop, method="best_fit", object=False):
    # getting the vertex locations
    locs = [bm_mod.verts[v].co.copy() for v in loop[0]]

    # calculating the center of masss
    com = mathutils.Vector()
    for loc in locs:
        com += loc
    com /= len(locs)
    x, y, z = com

    if method == 'best_fit':
        # creating the covariance matrix
        mat = mathutils.Matrix(((0.0, 0.0, 0.0),
                                (0.0, 0.0, 0.0),
                                (0.0, 0.0, 0.0),
                                ))
        for loc in locs:
            mat[0][0] += (loc[0]-x)**2
            mat[1][0] += (loc[0]-x)*(loc[1]-y)
            mat[2][0] += (loc[0]-x)*(loc[2]-z)
            mat[0][1] += (loc[1]-y)*(loc[0]-x)
            mat[1][1] += (loc[1]-y)**2
            mat[2][1] += (loc[1]-y)*(loc[2]-z)
            mat[0][2] += (loc[2]-z)*(loc[0]-x)
            mat[1][2] += (loc[2]-z)*(loc[1]-y)
            mat[2][2] += (loc[2]-z)**2

        # calculating the normal to the plane
        normal = False
        try:
            mat = matrix_invert(mat)
        except:
            ax = 2
            if math.fabs(sum(mat[0])) < math.fabs(sum(mat[1])):
                if math.fabs(sum(mat[0])) < math.fabs(sum(mat[2])):
                    ax = 0
            elif math.fabs(sum(mat[1])) < math.fabs(sum(mat[2])):
                ax = 1
            if ax == 0:
                normal = mathutils.Vector((1.0, 0.0, 0.0))
            elif ax == 1:
                normal = mathutils.Vector((0.0, 1.0, 0.0))
            else:
                normal = mathutils.Vector((0.0, 0.0, 1.0))
        if not normal:
            # warning! this is different from .normalize()
            itermax = 500
            iter = 0
            vec = mathutils.Vector((1.0, 1.0, 1.0))
            vec2 = (mat * vec)/(mat * vec).length
            while vec != vec2 and iter<itermax:
                iter+=1
                vec = vec2
                vec2 = mat * vec
                if vec2.length != 0:
                    vec2 /= vec2.length
            if vec2.length == 0:
                vec2 = mathutils.Vector((1.0, 1.0, 1.0))
            normal = vec2

    elif method == 'normal':
        # averaging the vertex normals
        v_normals = [bm_mod.verts[v].normal for v in loop[0]]
        normal = mathutils.Vector()
        for v_normal in v_normals:
            normal += v_normal
        normal /= len(v_normals)
        normal.normalize()

    elif method == 'view':
        # calculate view normal
        rotation = bpy.context.space_data.region_3d.view_matrix.to_3x3().\
            inverted()
        normal = rotation * mathutils.Vector((0.0, 0.0, 1.0))
        if object:
            normal = object.matrix_world.inverted().to_euler().to_matrix() * \
                     normal

    return(com, normal)


# calculate splines based on given interpolation method (controller function)
def calculate_splines(interpolation, bm_mod, tknots, knots):
    if interpolation == 'cubic':
        splines = calculate_cubic_splines(bm_mod, tknots, knots[:])
    else: # interpolations == 'linear'
        splines = calculate_linear_splines(bm_mod, tknots, knots[:])

    return(splines)


# check loops and only return valid ones
def check_loops(loops, mapping, bm_mod):
    valid_loops = []
    for loop, circular in loops:
        # loop needs to have at least 3 vertices
        if len(loop) < 3:
            continue
        # loop needs at least 1 vertex in the original, non-mirrored mesh
        if mapping:
            all_virtual = True
            for vert in loop:
                if mapping[vert] > -1:
                    all_virtual = False
                    break
            if all_virtual:
                continue
        # vertices can not all be at the same location
        stacked = True
        for i in range(len(loop) - 1):
            if (bm_mod.verts[loop[i]].co - \
            bm_mod.verts[loop[i+1]].co).length > 1e-6:
                stacked = False
                break
        if stacked:
            continue
        # passed all tests, loop is valid
        valid_loops.append([loop, circular])

    return(valid_loops)


# input: bmesh, output: dict with the edge-key as key and face-index as value
def dict_edge_faces(bm):
    edge_faces = dict([[edgekey(edge), []] for edge in bm.edges if \
        not edge.hide])
    for face in bm.faces:
        if face.hide:
            continue
        for key in face_edgekeys(face):
            edge_faces[key].append(face.index)

    return(edge_faces)


# input: bmesh (edge-faces optional), output: dict with face-face connections
def dict_face_faces(bm, edge_faces=False):
    if not edge_faces:
        edge_faces = dict_edge_faces(bm)

    connected_faces = dict([[face.index, []] for face in bm.faces if \
        not face.hide])
    for face in bm.faces:
        if face.hide:
            continue
        for edge_key in face_edgekeys(face):
            for connected_face in edge_faces[edge_key]:
                if connected_face == face.index:
                    continue
                connected_faces[face.index].append(connected_face)

    return(connected_faces)


# input: bmesh, output: dict with the vert index as key and edge-keys as value
def dict_vert_edges(bm):
    vert_edges = dict([[v.index, []] for v in bm.verts if not v.hide])
    for edge in bm.edges:
        if edge.hide:
            continue
        ek = edgekey(edge)
        for vert in ek:
            vert_edges[vert].append(ek)

    return(vert_edges)


# input: bmesh, output: dict with the vert index as key and face index as value
def dict_vert_faces(bm):
    vert_faces = dict([[v.index, []] for v in bm.verts if not v.hide])
    for face in bm.faces:
        if not face.hide:
            for vert in face.verts:
                vert_faces[vert.index].append(face.index)

    return(vert_faces)


# input: list of edge-keys, output: dictionary with vertex-vertex connections
def dict_vert_verts(edge_keys):
    # create connection data
    vert_verts = {}
    for ek in edge_keys:
        for i in range(2):
            if ek[i] in vert_verts:
                vert_verts[ek[i]].append(ek[1-i])
            else:
                vert_verts[ek[i]] = [ek[1-i]]

    return(vert_verts)


# return the edgekey ([v1.index, v2.index]) of a bmesh edge
def edgekey(edge):
    return(tuple(sorted([edge.verts[0].index, edge.verts[1].index])))


# returns the edgekeys of a bmesh face
def face_edgekeys(face):
    return([tuple(sorted([edge.verts[0].index, edge.verts[1].index])) for \
        edge in face.edges])


# calculate input loops
def get_connected_input(object, bm, scene, input):
    # get mesh with modifiers applied
    derived, bm_mod = get_derived_bmesh(object, bm, scene)

    # calculate selected loops
    edge_keys = [edgekey(edge) for edge in bm_mod.edges if \
        edge.select and not edge.hide]
    loops = get_connected_selections(edge_keys)

    # if only selected loops are needed, we're done
    if input == 'selected':
        return(derived, bm_mod, loops)
    # elif input == 'all':
    loops = get_parallel_loops(bm_mod, loops)

    return(derived, bm_mod, loops)


# sorts all edge-keys into a list of loops
def get_connected_selections(edge_keys):
    # create connection data
    vert_verts = dict_vert_verts(edge_keys)

    # find loops consisting of connected selected edges
    loops = []
    while len(vert_verts) > 0:
        loop = [iter(vert_verts.keys()).__next__()]
        growing = True
        flipped = False

        # extend loop
        while growing:
            # no more connection data for current vertex
            if loop[-1] not in vert_verts:
                if not flipped:
                    loop.reverse()
                    flipped = True
                else:
                    growing = False
            else:
                extended = False
                for i, next_vert in enumerate(vert_verts[loop[-1]]):
                    if next_vert not in loop:
                        vert_verts[loop[-1]].pop(i)
                        if len(vert_verts[loop[-1]]) == 0:
                            del vert_verts[loop[-1]]
                        # remove connection both ways
                        if next_vert in vert_verts:
                            if len(vert_verts[next_vert]) == 1:
                                del vert_verts[next_vert]
                            else:
                                vert_verts[next_vert].remove(loop[-1])
                        loop.append(next_vert)
                        extended = True
                        break
                if not extended:
                    # found one end of the loop, continue with next
                    if not flipped:
                        loop.reverse()
                        flipped = True
                    # found both ends of the loop, stop growing
                    else:
                        growing = False

        # check if loop is circular
        if loop[0] in vert_verts:
            if loop[-1] in vert_verts[loop[0]]:
                # is circular
                if len(vert_verts[loop[0]]) == 1:
                    del vert_verts[loop[0]]
                else:
                    vert_verts[loop[0]].remove(loop[-1])
                if len(vert_verts[loop[-1]]) == 1:
                    del vert_verts[loop[-1]]
                else:
                    vert_verts[loop[-1]].remove(loop[0])
                loop = [loop, True]
            else:
                # not circular
                loop = [loop, False]
        else:
            # not circular
            loop = [loop, False]

        loops.append(loop)

    return(loops)


# get the derived mesh data, if there is a mirror modifier
def get_derived_bmesh(object, bm, scene):
    # check for mirror modifiers
    if 'MIRROR' in [mod.type for mod in object.modifiers if mod.show_viewport]:
        derived = True
        # disable other modifiers
        show_viewport = [mod.name for mod in object.modifiers if \
            mod.show_viewport]
        for mod in object.modifiers:
            if mod.type != 'MIRROR':
                mod.show_viewport = False
        # get derived mesh
        bm_mod = bmesh.new()
        mesh_mod = object.to_mesh(scene, True, 'PREVIEW')
        bm_mod.from_mesh(mesh_mod)
        bpy.context.blend_data.meshes.remove(mesh_mod)
        # re-enable other modifiers
        for mod_name in show_viewport:
            object.modifiers[mod_name].show_viewport = True
    # no mirror modifiers, so no derived mesh necessary
    else:
        derived = False
        bm_mod = bm

    return(derived, bm_mod)


# return a mapping of derived indices to indices
def get_mapping(derived, bm, bm_mod, single_vertices, full_search, loops):
    if not derived:
        return(False)

    if full_search:
        verts = [v for v in bm.verts if not v.hide]
    else:
        verts = [v for v in bm.verts if v.select and not v.hide]

    # non-selected vertices around single vertices also need to be mapped
    if single_vertices:
        mapping = dict([[vert, -1] for vert in single_vertices])
        verts_mod = [bm_mod.verts[vert] for vert in single_vertices]
        for v in verts:
            for v_mod in verts_mod:
                if (v.co - v_mod.co).length < 1e-6:
                    mapping[v_mod.index] = v.index
                    break
        real_singles = [v_real for v_real in mapping.values() if v_real>-1]

        verts_indices = [vert.index for vert in verts]
        for face in [face for face in bm.faces if not face.select \
        and not face.hide]:
            for vert in face.verts:
                if vert.index in real_singles:
                    for v in face.verts:
                        if not v.index in verts_indices:
                            if v not in verts:
                                verts.append(v)
                    break

    # create mapping of derived indices to indices
    mapping = dict([[vert, -1] for loop in loops for vert in loop[0]])
    if single_vertices:
        for single in single_vertices:
            mapping[single] = -1
    verts_mod = [bm_mod.verts[i] for i in mapping.keys()]
    for v in verts:
        for v_mod in verts_mod:
            if (v.co - v_mod.co).length < 1e-6:
                mapping[v_mod.index] = v.index
                verts_mod.remove(v_mod)
                break

    return(mapping)


# calculate the determinant of a matrix
def matrix_determinant(m):
    determinant = m[0][0] * m[1][1] * m[2][2] + m[0][1] * m[1][2] * m[2][0] \
        + m[0][2] * m[1][0] * m[2][1] - m[0][2] * m[1][1] * m[2][0] \
        - m[0][1] * m[1][0] * m[2][2] - m[0][0] * m[1][2] * m[2][1]

    return(determinant)


# custom matrix inversion, to provide higher precision than the built-in one
def matrix_invert(m):
    r = mathutils.Matrix((
        (m[1][1]*m[2][2] - m[1][2]*m[2][1], m[0][2]*m[2][1] - m[0][1]*m[2][2],
        m[0][1]*m[1][2] - m[0][2]*m[1][1]),
        (m[1][2]*m[2][0] - m[1][0]*m[2][2], m[0][0]*m[2][2] - m[0][2]*m[2][0],
        m[0][2]*m[1][0] - m[0][0]*m[1][2]),
        (m[1][0]*m[2][1] - m[1][1]*m[2][0], m[0][1]*m[2][0] - m[0][0]*m[2][1],
        m[0][0]*m[1][1] - m[0][1]*m[1][0])))

    return (r * (1 / matrix_determinant(m)))


# returns a list of all loops parallel to the input, input included
def get_parallel_loops(bm_mod, loops):
    # get required dictionaries
    edge_faces = dict_edge_faces(bm_mod)
    connected_faces = dict_face_faces(bm_mod, edge_faces)
    # turn vertex loops into edge loops
    edgeloops = []
    for loop in loops:
        edgeloop = [[sorted([loop[0][i], loop[0][i+1]]) for i in \
            range(len(loop[0])-1)], loop[1]]
        if loop[1]: # circular
            edgeloop[0].append(sorted([loop[0][-1], loop[0][0]]))
        edgeloops.append(edgeloop[:])
    # variables to keep track while iterating
    all_edgeloops = []
    has_branches = False

    for loop in edgeloops:
        # initialise with original loop
        all_edgeloops.append(loop[0])
        newloops = [loop[0]]
        verts_used = []
        for edge in loop[0]:
            if edge[0] not in verts_used:
                verts_used.append(edge[0])
            if edge[1] not in verts_used:
                verts_used.append(edge[1])

        # find parallel loops
        while len(newloops) > 0:
            side_a = []
            side_b = []
            for i in newloops[-1]:
                i = tuple(i)
                forbidden_side = False
                if not i in edge_faces:
                    # weird input with branches
                    has_branches = True
                    break
                for face in edge_faces[i]:
                    if len(side_a) == 0 and forbidden_side != "a":
                        side_a.append(face)
                        if forbidden_side:
                            break
                        forbidden_side = "a"
                        continue
                    elif side_a[-1] in connected_faces[face] and \
                    forbidden_side != "a":
                        side_a.append(face)
                        if forbidden_side:
                            break
                        forbidden_side = "a"
                        continue
                    if len(side_b) == 0 and forbidden_side != "b":
                        side_b.append(face)
                        if forbidden_side:
                            break
                        forbidden_side = "b"
                        continue
                    elif side_b[-1] in connected_faces[face] and \
                    forbidden_side != "b":
                        side_b.append(face)
                        if forbidden_side:
                            break
                        forbidden_side = "b"
                        continue

            if has_branches:
                # weird input with branches
                break

            newloops.pop(-1)
            sides = []
            if side_a:
                sides.append(side_a)
            if side_b:
                sides.append(side_b)

            for side in sides:
                extraloop = []
                for fi in side:
                    for key in face_edgekeys(bm_mod.faces[fi]):
                        if key[0] not in verts_used and key[1] not in \
                        verts_used:
                            extraloop.append(key)
                            break
                if extraloop:
                    for key in extraloop:
                        for new_vert in key:
                            if new_vert not in verts_used:
                                verts_used.append(new_vert)
                    newloops.append(extraloop)
                    all_edgeloops.append(extraloop)

    # input contains branches, only return selected loop
    if has_branches:
        return(loops)

    # change edgeloops into normal loops
    loops = []
    for edgeloop in all_edgeloops:
        loop = []
        # grow loop by comparing vertices between consecutive edge-keys
        for i in range(len(edgeloop)-1):
            for vert in range(2):
                if edgeloop[i][vert] in edgeloop[i+1]:
                    loop.append(edgeloop[i][vert])
                    break
        if loop:
            # add starting vertex
            for vert in range(2):
                if edgeloop[0][vert] != loop[0]:
                    loop = [edgeloop[0][vert]] + loop
                    break
            # add ending vertex
            for vert in range(2):
                if edgeloop[-1][vert] != loop[-1]:
                    loop.append(edgeloop[-1][vert])
                    break
            # check if loop is circular
            if loop[0] == loop[-1]:
                circular = True
                loop = loop[:-1]
            else:
                circular = False
        loops.append([loop, circular])

    return(loops)


# gather initial data
def initialise():
    global_undo = bpy.context.user_preferences.edit.use_global_undo
    bpy.context.user_preferences.edit.use_global_undo = False
    object = bpy.context.active_object
    if 'MIRROR' in [mod.type for mod in object.modifiers if mod.show_viewport]:
        # ensure that selection is synced for the derived mesh
        bpy.ops.object.mode_set(mode='OBJECT')
        bpy.ops.object.mode_set(mode='EDIT')
    bm = bmesh.from_edit_mesh(object.data)

    return(global_undo, object, bm)


# move the vertices to their new locations
def move_verts(object, bm, mapping, move, influence):
    for loop in move:
        for index, loc in loop:
            if mapping:
                if mapping[index] == -1:
                    continue
                else:
                    index = mapping[index]
            if influence >= 0:
                bm.verts[index].co = loc*(influence/100) + \
                    bm.verts[index].co*((100-influence)/100)
            else:
                bm.verts[index].co = loc
    bm.normal_update()
    object.data.update()


# load custom tool settings
def settings_load(self):
    lt = bpy.context.window_manager.looptools
    tool = self.name.split()[0].lower()
    keys = self.as_keywords().keys()
    for key in keys:
        setattr(self, key, getattr(lt, tool + "_" + key))


# store custom tool settings
def settings_write(self):
    lt = bpy.context.window_manager.looptools
    tool = self.name.split()[0].lower()
    keys = self.as_keywords().keys()
    for key in keys:
        setattr(lt, tool + "_" + key, getattr(self, key))


# clean up and set settings back to original state
def terminate(global_undo):
    # update editmesh cached data
    obj = bpy.context.active_object
    if obj.mode == 'EDIT':
        bmesh.update_edit_mesh(obj.data, tessface=True, destructive=True)

    bpy.context.user_preferences.edit.use_global_undo = global_undo


##########################################
####### Bridge functions #################
##########################################

# calculate a cubic spline through the middle section of 4 given coordinates
def bridge_calculate_cubic_spline(bm, coordinates):
    result = []
    x = [0, 1, 2, 3]

    for j in range(3):
        a = []
        for i in coordinates:
            a.append(float(i[j]))
        h = []
        for i in range(3):
            h.append(x[i+1]-x[i])
        q = [False]
        for i in range(1,3):
            q.append(3.0/h[i]*(a[i+1]-a[i])-3.0/h[i-1]*(a[i]-a[i-1]))
        l = [1.0]
        u = [0.0]
        z = [0.0]
        for i in range(1,3):
            l.append(2.0*(x[i+1]-x[i-1])-h[i-1]*u[i-1])
            u.append(h[i]/l[i])
            z.append((q[i]-h[i-1]*z[i-1])/l[i])
        l.append(1.0)
        z.append(0.0)
        b = [False for i in range(3)]
        c = [False for i in range(4)]
        d = [False for i in range(3)]
        c[3] = 0.0
        for i in range(2,-1,-1):
            c[i] = z[i]-u[i]*c[i+1]
            b[i] = (a[i+1]-a[i])/h[i]-h[i]*(c[i+1]+2.0*c[i])/3.0
            d[i] = (c[i+1]-c[i])/(3.0*h[i])
        for i in range(3):
            result.append([a[i], b[i], c[i], d[i], x[i]])
    spline = [result[1], result[4], result[7]]

    return(spline)


# return a list with new vertex location vectors, a list with face vertex
# integers, and the highest vertex integer in the virtual mesh
def bridge_calculate_geometry(bm, lines, vertex_normals, segments,
interpolation, cubic_strength, min_width, max_vert_index):
    new_verts = []
    faces = []

    # calculate location based on interpolation method
    def get_location(line, segment, splines):
        v1 = bm.verts[lines[line][0]].co
        v2 = bm.verts[lines[line][1]].co
        if interpolation == 'linear':
            return v1 + (segment/segments) * (v2-v1)
        else: # interpolation == 'cubic'
            m = (segment/segments)
            ax,bx,cx,dx,tx = splines[line][0]
            x = ax+bx*m+cx*m**2+dx*m**3
            ay,by,cy,dy,ty = splines[line][1]
            y = ay+by*m+cy*m**2+dy*m**3
            az,bz,cz,dz,tz = splines[line][2]
            z = az+bz*m+cz*m**2+dz*m**3
            return mathutils.Vector((x, y, z))

    # no interpolation needed
    if segments == 1:
        for i, line in enumerate(lines):
            if i < len(lines)-1:
                faces.append([line[0], lines[i+1][0], lines[i+1][1], line[1]])
    # more than 1 segment, interpolate
    else:
        # calculate splines (if necessary) once, so no recalculations needed
        if interpolation == 'cubic':
            splines = []
            for line in lines:
                v1 = bm.verts[line[0]].co
                v2 = bm.verts[line[1]].co
                size = (v2-v1).length * cubic_strength
                splines.append(bridge_calculate_cubic_spline(bm,
                    [v1+size*vertex_normals[line[0]], v1, v2,
                    v2+size*vertex_normals[line[1]]]))
        else:
            splines = False

        # create starting situation
        virtual_width = [(bm.verts[lines[i][0]].co -
                          bm.verts[lines[i+1][0]].co).length for i
                          in range(len(lines)-1)]
        new_verts = [get_location(0, seg, splines) for seg in range(1,
            segments)]
        first_line_indices = [i for i in range(max_vert_index+1,
            max_vert_index+segments)]

        prev_verts = new_verts[:] # vertex locations of verts on previous line
        prev_vert_indices = first_line_indices[:]
        max_vert_index += segments - 1 # highest vertex index in virtual mesh
        next_verts = [] # vertex locations of verts on current line
        next_vert_indices = []

        for i, line in enumerate(lines):
            if i < len(lines)-1:
                v1 = line[0]
                v2 = lines[i+1][0]
                end_face = True
                for seg in range(1, segments):
                    loc1 = prev_verts[seg-1]
                    loc2 = get_location(i+1, seg, splines)
                    if (loc1-loc2).length < (min_width/100)*virtual_width[i] \
                    and line[1]==lines[i+1][1]:
                        # triangle, no new vertex
                        faces.append([v1, v2, prev_vert_indices[seg-1],
                            prev_vert_indices[seg-1]])
                        next_verts += prev_verts[seg-1:]
                        next_vert_indices += prev_vert_indices[seg-1:]
                        end_face = False
                        break
                    else:
                        if i == len(lines)-2 and lines[0] == lines[-1]:
                            # quad with first line, no new vertex
                            faces.append([v1, v2, first_line_indices[seg-1],
                                prev_vert_indices[seg-1]])
                            v2 = first_line_indices[seg-1]
                            v1 = prev_vert_indices[seg-1]
                        else:
                            # quad, add new vertex
                            max_vert_index += 1
                            faces.append([v1, v2, max_vert_index,
                                prev_vert_indices[seg-1]])
                            v2 = max_vert_index
                            v1 = prev_vert_indices[seg-1]
                            new_verts.append(loc2)
                            next_verts.append(loc2)
                            next_vert_indices.append(max_vert_index)
                if end_face:
                    faces.append([v1, v2, lines[i+1][1], line[1]])

                prev_verts = next_verts[:]
                prev_vert_indices = next_vert_indices[:]
                next_verts = []
                next_vert_indices = []

    return(new_verts, faces, max_vert_index)


# calculate lines (list of lists, vertex indices) that are used for bridging
def bridge_calculate_lines(bm, loops, mode, twist, reverse):
    lines = []
    loop1, loop2 = [i[0] for i in loops]
    loop1_circular, loop2_circular = [i[1] for i in loops]
    circular = loop1_circular or loop2_circular
    circle_full = False

    # calculate loop centers
    centers = []
    for loop in [loop1, loop2]:
        center = mathutils.Vector()
        for vertex in loop:
            center += bm.verts[vertex].co
        center /= len(loop)
        centers.append(center)
    for i, loop in enumerate([loop1, loop2]):
        for vertex in loop:
            if bm.verts[vertex].co == centers[i]:
                # prevent zero-length vectors in angle comparisons
                centers[i] += mathutils.Vector((0.01, 0, 0))
                break
    center1, center2 = centers

    # calculate the normals of the virtual planes that the loops are on
    normals = []
    normal_plurity = False
    for i, loop in enumerate([loop1, loop2]):
        # covariance matrix
        mat = mathutils.Matrix(((0.0, 0.0, 0.0),
                                (0.0, 0.0, 0.0),
                                (0.0, 0.0, 0.0)))
        x, y, z = centers[i]
        for loc in [bm.verts[vertex].co for vertex in loop]:
            mat[0][0] += (loc[0]-x)**2
            mat[1][0] += (loc[0]-x)*(loc[1]-y)
            mat[2][0] += (loc[0]-x)*(loc[2]-z)
            mat[0][1] += (loc[1]-y)*(loc[0]-x)
            mat[1][1] += (loc[1]-y)**2
            mat[2][1] += (loc[1]-y)*(loc[2]-z)
            mat[0][2] += (loc[2]-z)*(loc[0]-x)
            mat[1][2] += (loc[2]-z)*(loc[1]-y)
            mat[2][2] += (loc[2]-z)**2
        # plane normal
        normal = False
        if sum(mat[0]) < 1e-6 or sum(mat[1]) < 1e-6 or sum(mat[2]) < 1e-6:
            normal_plurity = True
        try:
            mat.invert()
        except:
            if sum(mat[0]) == 0:
                normal = mathutils.Vector((1.0, 0.0, 0.0))
            elif sum(mat[1]) == 0:
                normal = mathutils.Vector((0.0, 1.0, 0.0))
            elif sum(mat[2]) == 0:
                normal = mathutils.Vector((0.0, 0.0, 1.0))
        if not normal:
            # warning! this is different from .normalize()
            itermax = 500
            iter = 0
            vec = mathutils.Vector((1.0, 1.0, 1.0))
            vec2 = (mat * vec)/(mat * vec).length
            while vec != vec2 and iter<itermax:
                iter+=1
                vec = vec2
                vec2 = mat * vec
                if vec2.length != 0:
                    vec2 /= vec2.length
            if vec2.length == 0:
                vec2 = mathutils.Vector((1.0, 1.0, 1.0))
            normal = vec2
        normals.append(normal)
    # have plane normals face in the same direction (maximum angle: 90 degrees)
    if ((center1 + normals[0]) - center2).length < \
    ((center1 - normals[0]) - center2).length:
        normals[0].negate()
    if ((center2 + normals[1]) - center1).length > \
    ((center2 - normals[1]) - center1).length:
        normals[1].negate()

    # rotation matrix, representing the difference between the plane normals
    axis = normals[0].cross(normals[1])
    axis = mathutils.Vector([loc if abs(loc) > 1e-8 else 0 for loc in axis])
    if axis.angle(mathutils.Vector((0, 0, 1)), 0) > 1.5707964:
        axis.negate()
    angle = normals[0].dot(normals[1])
    rotation_matrix = mathutils.Matrix.Rotation(angle, 4, axis)

    # if circular, rotate loops so they are aligned
    if circular:
        # make sure loop1 is the circular one (or both are circular)
        if loop2_circular and not loop1_circular:
            loop1_circular, loop2_circular = True, False
            loop1, loop2 = loop2, loop1

        # match start vertex of loop1 with loop2
        target_vector = bm.verts[loop2[0]].co - center2
        dif_angles = [[(rotation_matrix * (bm.verts[vertex].co - center1)
                       ).angle(target_vector, 0), False, i] for
                       i, vertex in enumerate(loop1)]
        dif_angles.sort()
        if len(loop1) != len(loop2):
            angle_limit = dif_angles[0][0] * 1.2 # 20% margin
            dif_angles = [[(bm.verts[loop2[0]].co - \
                bm.verts[loop1[index]].co).length, angle, index] for \
                angle, distance, index in dif_angles if angle <= angle_limit]
            dif_angles.sort()
        loop1 = loop1[dif_angles[0][2]:] + loop1[:dif_angles[0][2]]

    # have both loops face the same way
    if normal_plurity and not circular:
        second_to_first, second_to_second, second_to_last = \
            [(bm.verts[loop1[1]].co - center1).\
            angle(bm.verts[loop2[i]].co - center2) for i in [0, 1, -1]]
        last_to_first, last_to_second = [(bm.verts[loop1[-1]].co - \
            center1).angle(bm.verts[loop2[i]].co - center2) for \
            i in [0, 1]]
        if (min(last_to_first, last_to_second)*1.1 < min(second_to_first, \
        second_to_second)) or (loop2_circular and second_to_last*1.1 < \
        min(second_to_first, second_to_second)):
            loop1.reverse()
            if circular:
                loop1 = [loop1[-1]] + loop1[:-1]
    else:
        angle = (bm.verts[loop1[0]].co - center1).\
            cross(bm.verts[loop1[1]].co - center1).angle(normals[0], 0)
        target_angle = (bm.verts[loop2[0]].co - center2).\
            cross(bm.verts[loop2[1]].co - center2).angle(normals[1], 0)
        limit = 1.5707964 # 0.5*pi, 90 degrees
        if not ((angle > limit and target_angle > limit) or \
        (angle < limit and target_angle < limit)):
            loop1.reverse()
            if circular:
                loop1 = [loop1[-1]] + loop1[:-1]
        elif normals[0].angle(normals[1]) > limit:
            loop1.reverse()
            if circular:
                loop1 = [loop1[-1]] + loop1[:-1]

    # both loops have the same length
    if len(loop1) == len(loop2):
        # manual override
        if twist:
            if abs(twist) < len(loop1):
                loop1 = loop1[twist:]+loop1[:twist]
        if reverse:
            loop1.reverse()

        lines.append([loop1[0], loop2[0]])
        for i in range(1, len(loop1)):
            lines.append([loop1[i], loop2[i]])

    # loops of different lengths
    else:
        # make loop1 longest loop
        if len(loop2) > len(loop1):
            loop1, loop2 = loop2, loop1
            loop1_circular, loop2_circular = loop2_circular, loop1_circular

        # manual override
        if twist:
            if abs(twist) < len(loop1):
                loop1 = loop1[twist:]+loop1[:twist]
        if reverse:
            loop1.reverse()

        # shortest angle difference doesn't always give correct start vertex
        if loop1_circular and not loop2_circular:
            shifting = 1
            while shifting:
                if len(loop1) - shifting < len(loop2):
                    shifting = False
                    break
                to_last, to_first = [(rotation_matrix *
                    (bm.verts[loop1[-1]].co - center1)).angle((bm.\
                    verts[loop2[i]].co - center2), 0) for i in [-1, 0]]
                if to_first < to_last:
                    loop1 = [loop1[-1]] + loop1[:-1]
                    shifting += 1
                else:
                    shifting = False
                    break

        # basic shortest side first
        if mode == 'basic':
            lines.append([loop1[0], loop2[0]])
            for i in range(1, len(loop1)):
                if i >= len(loop2) - 1:
                    # triangles
                    lines.append([loop1[i], loop2[-1]])
                else:
                    # quads
                    lines.append([loop1[i], loop2[i]])

        # shortest edge algorithm
        else: # mode == 'shortest'
            lines.append([loop1[0], loop2[0]])
            prev_vert2 = 0
            for i in range(len(loop1) -1):
                if prev_vert2 == len(loop2) - 1 and not loop2_circular:
                    # force triangles, reached end of loop2
                    tri, quad = 0, 1
                elif prev_vert2 == len(loop2) - 1 and loop2_circular:
                    # at end of loop2, but circular, so check with first vert
                    tri, quad = [(bm.verts[loop1[i+1]].co -
                                  bm.verts[loop2[j]].co).length
                                 for j in [prev_vert2, 0]]

                    circle_full = 2
                elif len(loop1) - 1 - i == len(loop2) - 1 - prev_vert2 and \
                not circle_full:
                    # force quads, otherwise won't make it to end of loop2
                    tri, quad = 1, 0
                else:
                    # calculate if tri or quad gives shortest edge
                    tri, quad = [(bm.verts[loop1[i+1]].co -
                                  bm.verts[loop2[j]].co).length
                                 for j in range(prev_vert2, prev_vert2+2)]

                # triangle
                if tri < quad:
                    lines.append([loop1[i+1], loop2[prev_vert2]])
                    if circle_full == 2:
                        circle_full = False
                # quad
                elif not circle_full:
                    lines.append([loop1[i+1], loop2[prev_vert2+1]])
                    prev_vert2 += 1
                # quad to first vertex of loop2
                else:
                    lines.append([loop1[i+1], loop2[0]])
                    prev_vert2 = 0
                    circle_full = True

    # final face for circular loops
    if loop1_circular and loop2_circular:
        lines.append([loop1[0], loop2[0]])

    return(lines)


# calculate number of segments needed
def bridge_calculate_segments(bm, lines, loops, segments):
    # return if amount of segments is set by user
    if segments != 0:
        return segments

    # edge lengths
    average_edge_length = [(bm.verts[vertex].co - \
        bm.verts[loop[0][i+1]].co).length for loop in loops for \
        i, vertex in enumerate(loop[0][:-1])]
    # closing edges of circular loops
    average_edge_length += [(bm.verts[loop[0][-1]].co - \
        bm.verts[loop[0][0]].co).length for loop in loops if loop[1]]

    # average lengths
    average_edge_length = sum(average_edge_length) / len(average_edge_length)
    average_bridge_length = sum([(bm.verts[v1].co - \
        bm.verts[v2].co).length for v1, v2 in lines]) / len(lines)

    segments = max(1, round(average_bridge_length / average_edge_length))

    return(segments)


# return dictionary with vertex index as key, and the normal vector as value
def bridge_calculate_virtual_vertex_normals(bm, lines, loops, edge_faces,
edgekey_to_edge):
    if not edge_faces: # interpolation isn't set to cubic
        return False

    # pity reduce() isn't one of the basic functions in python anymore
    def average_vector_dictionary(dic):
        for key, vectors in dic.items():
            #if type(vectors) == type([]) and len(vectors) > 1:
            if len(vectors) > 1:
                average = mathutils.Vector()
                for vector in vectors:
                    average += vector
                average /= len(vectors)
                dic[key] = [average]
        return dic

    # get all edges of the loop
    edges = [[edgekey_to_edge[tuple(sorted([loops[j][0][i],
        loops[j][0][i+1]]))] for i in range(len(loops[j][0])-1)] for \
        j in [0,1]]
    edges = edges[0] + edges[1]
    for j in [0, 1]:
        if loops[j][1]: # circular
            edges.append(edgekey_to_edge[tuple(sorted([loops[j][0][0],
                loops[j][0][-1]]))])

    """
    calculation based on face topology (assign edge-normals to vertices)

    edge_normal = face_normal x edge_vector
    vertex_normal = average(edge_normals)
    """
    vertex_normals = dict([(vertex, []) for vertex in loops[0][0]+loops[1][0]])
    for edge in edges:
        faces = edge_faces[edgekey(edge)] # valid faces connected to edge

        if faces:
            # get edge coordinates
            v1, v2 = [bm.verts[edgekey(edge)[i]].co for i in [0,1]]
            edge_vector = v1 - v2
            if edge_vector.length < 1e-4:
                # zero-length edge, vertices at same location
                continue
            edge_center = (v1 + v2) / 2

            # average face coordinates, if connected to more than 1 valid face
            if len(faces) > 1:
                face_normal = mathutils.Vector()
                face_center = mathutils.Vector()
                for face in faces:
                    face_normal += face.normal
                    face_center += face.calc_center_median()
                face_normal /= len(faces)
                face_center /= len(faces)
            else:
                face_normal = faces[0].normal
                face_center = faces[0].calc_center_median()
            if face_normal.length < 1e-4:
                # faces with a surface of 0 have no face normal
                continue

            # calculate virtual edge normal
            edge_normal = edge_vector.cross(face_normal)
            edge_normal.length = 0.01
            if (face_center - (edge_center + edge_normal)).length > \
            (face_center - (edge_center - edge_normal)).length:
                # make normal face the correct way
                edge_normal.negate()
            edge_normal.normalize()
            # add virtual edge normal as entry for both vertices it connects
            for vertex in edgekey(edge):
                vertex_normals[vertex].append(edge_normal)

    """
    calculation based on connection with other loop (vertex focused method)
    - used for vertices that aren't connected to any valid faces

    plane_normal = edge_vector x connection_vector
    vertex_normal = plane_normal x edge_vector
    """
    vertices = [vertex for vertex, normal in vertex_normals.items() if not \
        normal]

    if vertices:
        # edge vectors connected to vertices
        edge_vectors = dict([[vertex, []] for vertex in vertices])
        for edge in edges:
            for v in edgekey(edge):
                if v in edge_vectors:
                    edge_vector = bm.verts[edgekey(edge)[0]].co - \
                        bm.verts[edgekey(edge)[1]].co
                    if edge_vector.length < 1e-4:
                        # zero-length edge, vertices at same location
                        continue
                    edge_vectors[v].append(edge_vector)

        # connection vectors between vertices of both loops
        connection_vectors = dict([[vertex, []] for vertex in vertices])
        connections = dict([[vertex, []] for vertex in vertices])
        for v1, v2 in lines:
            if v1 in connection_vectors or v2 in connection_vectors:
                new_vector = bm.verts[v1].co - bm.verts[v2].co
                if new_vector.length < 1e-4:
                    # zero-length connection vector,
                    # vertices in different loops at same location
                    continue
                if v1 in connection_vectors:
                    connection_vectors[v1].append(new_vector)
                    connections[v1].append(v2)
                if v2 in connection_vectors:
                    connection_vectors[v2].append(new_vector)
                    connections[v2].append(v1)
        connection_vectors = average_vector_dictionary(connection_vectors)
        connection_vectors = dict([[vertex, vector[0]] if vector else \
            [vertex, []] for vertex, vector in connection_vectors.items()])

        for vertex, values in edge_vectors.items():
            # vertex normal doesn't matter, just assign a random vector to it
            if not connection_vectors[vertex]:
                vertex_normals[vertex] = [mathutils.Vector((1, 0, 0))]
                continue

            # calculate to what location the vertex is connected,
            # used to determine what way to flip the normal
            connected_center = mathutils.Vector()
            for v in connections[vertex]:
                connected_center += bm.verts[v].co
            if len(connections[vertex]) > 1:
                connected_center /= len(connections[vertex])
            if len(connections[vertex]) == 0:
                # shouldn't be possible, but better safe than sorry
                vertex_normals[vertex] = [mathutils.Vector((1, 0, 0))]
                continue

            # can't do proper calculations, because of zero-length vector
            if not values:
                if (connected_center - (bm.verts[vertex].co + \
                connection_vectors[vertex])).length < (connected_center - \
                (bm.verts[vertex].co - connection_vectors[vertex])).\
                length:
                    connection_vectors[vertex].negate()
                vertex_normals[vertex] = [connection_vectors[vertex].\
                    normalized()]
                continue

            # calculate vertex normals using edge-vectors,
            # connection-vectors and the derived plane normal
            for edge_vector in values:
                plane_normal = edge_vector.cross(connection_vectors[vertex])
                vertex_normal = edge_vector.cross(plane_normal)
                vertex_normal.length = 0.1
                if (connected_center - (bm.verts[vertex].co + \
                vertex_normal)).length < (connected_center - \
                (bm.verts[vertex].co - vertex_normal)).length:
                # make normal face the correct way
                    vertex_normal.negate()
                vertex_normal.normalize()
                vertex_normals[vertex].append(vertex_normal)

    # average virtual vertex normals, based on all edges it's connected to
    vertex_normals = average_vector_dictionary(vertex_normals)
    vertex_normals = dict([[vertex, vector[0]] for vertex, vector in \
        vertex_normals.items()])

    return(vertex_normals)


# add vertices to mesh
def bridge_create_vertices(bm, vertices):
    for i in range(len(vertices)):
        bm.verts.new(vertices[i])


# add faces to mesh
def bridge_create_faces(object, bm, faces, twist):
    # have the normal point the correct way
    if twist < 0:
        [face.reverse() for face in faces]
        faces = [face[2:]+face[:2] if face[0]==face[1] else face for \
            face in faces]

    # eekadoodle prevention
    for i in range(len(faces)):
        if not faces[i][-1]:
            if faces[i][0] == faces[i][-1]:
                faces[i] = [faces[i][1], faces[i][2], faces[i][3], faces[i][1]]
            else:
                faces[i] = [faces[i][-1]] + faces[i][:-1]
        # result of converting from pre-bmesh period
        if faces[i][-1] == faces[i][-2]:
            faces[i] = faces[i][:-1]

    new_faces = []
    for i in range(len(faces)):
        new_faces.append(bm.faces.new([bm.verts[v] for v in faces[i]]))
    bm.normal_update()
    object.data.update(calc_edges=True) # calc_edges prevents memory-corruption

    return(new_faces)


# calculate input loops
def bridge_get_input(bm):
    # create list of internal edges, which should be skipped
    eks_of_selected_faces = [item for sublist in [face_edgekeys(face) for \
        face in bm.faces if face.select and not face.hide] for item in sublist]
    edge_count = {}
    for ek in eks_of_selected_faces:
        if ek in edge_count:
            edge_count[ek] += 1
        else:
            edge_count[ek] = 1
    internal_edges = [ek for ek in edge_count if edge_count[ek] > 1]

    # sort correct edges into loops
    selected_edges = [edgekey(edge) for edge in bm.edges if edge.select \
        and not edge.hide and edgekey(edge) not in internal_edges]
    loops = get_connected_selections(selected_edges)

    return(loops)


# return values needed by the bridge operator
def bridge_initialise(bm, interpolation):
    if interpolation == 'cubic':
        # dict with edge-key as key and list of connected valid faces as value
        face_blacklist = [face.index for face in bm.faces if face.select or \
            face.hide]
        edge_faces = dict([[edgekey(edge), []] for edge in bm.edges if not \
            edge.hide])
        for face in bm.faces:
            if face.index in face_blacklist:
                continue
            for key in face_edgekeys(face):
                edge_faces[key].append(face)
        # dictionary with the edge-key as key and edge as value
        edgekey_to_edge = dict([[edgekey(edge), edge] for edge in \
            bm.edges if edge.select and not edge.hide])
    else:
        edge_faces = False
        edgekey_to_edge = False

    # selected faces input
    old_selected_faces = [face.index for face in bm.faces if face.select \
        and not face.hide]

    # find out if faces created by bridging should be smoothed
    smooth = False
    if bm.faces:
        if sum([face.smooth for face in bm.faces])/len(bm.faces) \
        >= 0.5:
            smooth = True

    return(edge_faces, edgekey_to_edge, old_selected_faces, smooth)


# return a string with the input method
def bridge_input_method(loft, loft_loop):
    method = ""
    if loft:
        if loft_loop:
            method = "Loft loop"
        else:
            method = "Loft no-loop"
    else:
        method = "Bridge"

    return(method)


# match up loops in pairs, used for multi-input bridging
def bridge_match_loops(bm, loops):
    # calculate average loop normals and centers
    normals = []
    centers = []
    for vertices, circular in loops:
        normal = mathutils.Vector()
        center = mathutils.Vector()
        for vertex in vertices:
            normal += bm.verts[vertex].normal
            center += bm.verts[vertex].co
        normals.append(normal / len(vertices) / 10)
        centers.append(center / len(vertices))

    # possible matches if loop normals are faced towards the center
    # of the other loop
    matches = dict([[i, []] for i in range(len(loops))])
    matches_amount = 0
    for i in range(len(loops) + 1):
        for j in range(i+1, len(loops)):
            if (centers[i] - centers[j]).length > (centers[i] - (centers[j] \
            + normals[j])).length and (centers[j] - centers[i]).length > \
            (centers[j] - (centers[i] + normals[i])).length:
                matches_amount += 1
                matches[i].append([(centers[i] - centers[j]).length, i, j])
                matches[j].append([(centers[i] - centers[j]).length, j, i])
    # if no loops face each other, just make matches between all the loops
    if matches_amount == 0:
        for i in range(len(loops) + 1):
            for j in range(i+1, len(loops)):
                matches[i].append([(centers[i] - centers[j]).length, i, j])
                matches[j].append([(centers[i] - centers[j]).length, j, i])
    for key, value in matches.items():
        value.sort()

    # matches based on distance between centers and number of vertices in loops
    new_order = []
    for loop_index in range(len(loops)):
        if loop_index in new_order:
            continue
        loop_matches = matches[loop_index]
        if not loop_matches:
            continue
        shortest_distance = loop_matches[0][0]
        shortest_distance *= 1.1
        loop_matches = [[abs(len(loops[loop_index][0]) - \
            len(loops[loop[2]][0])), loop[0], loop[1], loop[2]] for loop in \
            loop_matches if loop[0] < shortest_distance]
        loop_matches.sort()
        for match in loop_matches:
            if match[3] not in new_order:
                new_order += [loop_index, match[3]]
                break

    # reorder loops based on matches
    if len(new_order) >= 2:
        loops = [loops[i] for i in new_order]

    return(loops)


# remove old_selected_faces
def bridge_remove_internal_faces(bm, old_selected_faces):
    # collect bmesh faces and internal bmesh edges
    remove_faces = [bm.faces[face] for face in old_selected_faces]
    edges = collections.Counter([edge.index for face in remove_faces for \
        edge in face.edges])
    remove_edges = [bm.edges[edge] for edge in edges if edges[edge] > 1]

    # remove internal faces and edges
    for face in remove_faces:
        bm.faces.remove(face)
    for edge in remove_edges:
        bm.edges.remove(edge)


# update list of internal faces that are flagged for removal
def bridge_save_unused_faces(bm, old_selected_faces, loops):
    # key: vertex index, value: lists of selected faces using it
    vertex_to_face = dict([[i, []] for i in range(len(bm.verts))])
    [[vertex_to_face[vertex.index].append(face) for vertex in \
        bm.faces[face].verts] for face in old_selected_faces]

    # group selected faces that are connected
    groups = []
    grouped_faces = []
    for face in old_selected_faces:
        if face in grouped_faces:
            continue
        grouped_faces.append(face)
        group = [face]
        new_faces = [face]
        while new_faces:
            grow_face = new_faces[0]
            for vertex in bm.faces[grow_face].verts:
                vertex_face_group = [face for face in vertex_to_face[\
                    vertex.index] if face not in grouped_faces]
                new_faces += vertex_face_group
                grouped_faces += vertex_face_group
                group += vertex_face_group
            new_faces.pop(0)
        groups.append(group)

    # key: vertex index, value: True/False (is it in a loop that is used)
    used_vertices = dict([[i, 0] for i in range(len(bm.verts))])
    for loop in loops:
        for vertex in loop[0]:
            used_vertices[vertex] = True

    # check if group is bridged, if not remove faces from internal faces list
    for group in groups:
        used = False
        for face in group:
            if used:
                break
            for vertex in bm.faces[face].verts:
                if used_vertices[vertex.index]:
                    used = True
                    break
        if not used:
            for face in group:
                old_selected_faces.remove(face)


# add the newly created faces to the selection
def bridge_select_new_faces(new_faces, smooth):
    for face in new_faces:
        face.select_set(True)
        face.smooth = smooth


# sort loops, so they are connected in the correct order when lofting
def bridge_sort_loops(bm, loops, loft_loop):
    # simplify loops to single points, and prepare for pathfinding
    x, y, z = [[sum([bm.verts[i].co[j] for i in loop[0]]) / \
        len(loop[0]) for loop in loops] for j in range(3)]
    nodes = [mathutils.Vector((x[i], y[i], z[i])) for i in range(len(loops))]

    active_node = 0
    open = [i for i in range(1, len(loops))]
    path = [[0,0]]
    # connect node to path, that is shortest to active_node
    while len(open) > 0:
        distances = [(nodes[active_node] - nodes[i]).length for i in open]
        active_node = open[distances.index(min(distances))]
        open.remove(active_node)
        path.append([active_node, min(distances)])
    # check if we didn't start in the middle of the path
    for i in range(2, len(path)):
        if (nodes[path[i][0]]-nodes[0]).length < path[i][1]:
            temp = path[:i]
            path.reverse()
            path = path[:-i] + temp
            break

    # reorder loops
    loops = [loops[i[0]] for i in path]
    # if requested, duplicate first loop at last position, so loft can loop
    if loft_loop:
        loops = loops + [loops[0]]

    return(loops)


# remapping old indices to new position in list
def bridge_update_old_selection(bm, old_selected_faces):
    #old_indices = old_selected_faces[:]
    #old_selected_faces = []
    #for i, face in enumerate(bm.faces):
    #    if face.index in old_indices:
    #        old_selected_faces.append(i)

    old_selected_faces = [i for i, face in enumerate(bm.faces) if face.index \
        in old_selected_faces]

    return(old_selected_faces)


##########################################
####### Circle functions #################
##########################################

# convert 3d coordinates to 2d coordinates on plane
def circle_3d_to_2d(bm_mod, loop, com, normal):
    # project vertices onto the plane
    verts = [bm_mod.verts[v] for v in loop[0]]
    verts_projected = [[v.co - (v.co - com).dot(normal) * normal, v.index]
                       for v in verts]

    # calculate two vectors (p and q) along the plane
    m = mathutils.Vector((normal[0] + 1.0, normal[1], normal[2]))
    p = m - (m.dot(normal) * normal)
    if p.dot(p) == 0.0:
        m = mathutils.Vector((normal[0], normal[1] + 1.0, normal[2]))
        p = m - (m.dot(normal) * normal)
    q = p.cross(normal)

    # change to 2d coordinates using perpendicular projection
    locs_2d = []
    for loc, vert in verts_projected:
        vloc = loc - com
        x = p.dot(vloc) / p.dot(p)
        y = q.dot(vloc) / q.dot(q)
        locs_2d.append([x, y, vert])

    return(locs_2d, p, q)


# calculate a best-fit circle to the 2d locations on the plane
def circle_calculate_best_fit(locs_2d):
    # initial guess
    x0 = 0.0
    y0 = 0.0
    r = 1.0

    # calculate center and radius (non-linear least squares solution)
    for iter in range(500):
        jmat = []
        k = []
        for v in locs_2d:
            d = (v[0]**2-2.0*x0*v[0]+v[1]**2-2.0*y0*v[1]+x0**2+y0**2)**0.5
            jmat.append([(x0-v[0])/d, (y0-v[1])/d, -1.0])
            k.append(-(((v[0]-x0)**2+(v[1]-y0)**2)**0.5-r))
        jmat2 = mathutils.Matrix(((0.0, 0.0, 0.0),
                                  (0.0, 0.0, 0.0),
                                  (0.0, 0.0, 0.0),
                                  ))
        k2 = mathutils.Vector((0.0, 0.0, 0.0))
        for i in range(len(jmat)):
            k2 += mathutils.Vector(jmat[i])*k[i]
            jmat2[0][0] += jmat[i][0]**2
            jmat2[1][0] += jmat[i][0]*jmat[i][1]
            jmat2[2][0] += jmat[i][0]*jmat[i][2]
            jmat2[1][1] += jmat[i][1]**2
            jmat2[2][1] += jmat[i][1]*jmat[i][2]
            jmat2[2][2] += jmat[i][2]**2
        jmat2[0][1] = jmat2[1][0]
        jmat2[0][2] = jmat2[2][0]
        jmat2[1][2] = jmat2[2][1]
        try:
            jmat2.invert()
        except:
            pass
        dx0, dy0, dr = jmat2 * k2
        x0 += dx0
        y0 += dy0
        r += dr
        # stop iterating if we're close enough to optimal solution
        if abs(dx0)<1e-6 and abs(dy0)<1e-6 and abs(dr)<1e-6:
            break

    # return center of circle and radius
    return(x0, y0, r)


# calculate circle so no vertices have to be moved away from the center
def circle_calculate_min_fit(locs_2d):
    # center of circle
    x0 = (min([i[0] for i in locs_2d])+max([i[0] for i in locs_2d]))/2.0
    y0 = (min([i[1] for i in locs_2d])+max([i[1] for i in locs_2d]))/2.0
    center = mathutils.Vector([x0, y0])
    # radius of circle
    r = min([(mathutils.Vector([i[0], i[1]])-center).length for i in locs_2d])

    # return center of circle and radius
    return(x0, y0, r)


# calculate the new locations of the vertices that need to be moved
def circle_calculate_verts(flatten, bm_mod, locs_2d, com, p, q, normal):
    # changing 2d coordinates back to 3d coordinates
    locs_3d = []
    for loc in locs_2d:
        locs_3d.append([loc[2], loc[0]*p + loc[1]*q + com])

    if flatten: # flat circle
        return(locs_3d)

    else: # project the locations on the existing mesh
        vert_edges = dict_vert_edges(bm_mod)
        vert_faces = dict_vert_faces(bm_mod)
        faces = [f for f in bm_mod.faces if not f.hide]
        rays = [normal, -normal]
        new_locs = []
        for loc in locs_3d:
            projection = False
            if bm_mod.verts[loc[0]].co == loc[1]: # vertex hasn't moved
                projection = loc[1]
            else:
                dif = normal.angle(loc[1]-bm_mod.verts[loc[0]].co)
                if -1e-6 < dif < 1e-6 or math.pi-1e-6 < dif < math.pi+1e-6:
                    # original location is already along projection normal
                    projection = bm_mod.verts[loc[0]].co
                else:
                    # quick search through adjacent faces
                    for face in vert_faces[loc[0]]:
                        verts = [v.co for v in bm_mod.faces[face].verts]
                        if len(verts) == 3: # triangle
                            v1, v2, v3 = verts
                            v4 = False
                        else: # assume quad
                            v1, v2, v3, v4 = verts[:4]
                        for ray in rays:
                            intersect = mathutils.geometry.\
                            intersect_ray_tri(v1, v2, v3, ray, loc[1])
                            if intersect:
                                projection = intersect
                                break
                            elif v4:
                                intersect = mathutils.geometry.\
                                intersect_ray_tri(v1, v3, v4, ray, loc[1])
                                if intersect:
                                    projection = intersect
                                    break
                        if projection:
                            break
            if not projection:
                # check if projection is on adjacent edges
                for edgekey in vert_edges[loc[0]]:
                    line1 = bm_mod.verts[edgekey[0]].co
                    line2 = bm_mod.verts[edgekey[1]].co
                    intersect, dist = mathutils.geometry.intersect_point_line(\
                        loc[1], line1, line2)
                    if 1e-6 < dist < 1 - 1e-6:
                        projection = intersect
                        break
            if not projection:
                # full search through the entire mesh
                hits = []
                for face in faces:
                    verts = [v.co for v in face.verts]
                    if len(verts) == 3: # triangle
                        v1, v2, v3 = verts
                        v4 = False
                    else: # assume quad
                        v1, v2, v3, v4 = verts[:4]
                    for ray in rays:
                        intersect = mathutils.geometry.intersect_ray_tri(\
                            v1, v2, v3, ray, loc[1])
                        if intersect:
                            hits.append([(loc[1] - intersect).length,
                                intersect])
                            break
                        elif v4:
                            intersect = mathutils.geometry.intersect_ray_tri(\
                                v1, v3, v4, ray, loc[1])
                            if intersect:
                                hits.append([(loc[1] - intersect).length,
                                    intersect])
                                break
                if len(hits) >= 1:
                    # if more than 1 hit with mesh, closest hit is new loc
                    hits.sort()
                    projection = hits[0][1]
            if not projection:
                # nothing to project on, remain at flat location
                projection = loc[1]
            new_locs.append([loc[0], projection])

        # return new positions of projected circle
        return(new_locs)


# check loops and only return valid ones
def circle_check_loops(single_loops, loops, mapping, bm_mod):
    valid_single_loops = {}
    valid_loops = []
    for i, [loop, circular] in enumerate(loops):
        # loop needs to have at least 3 vertices
        if len(loop) < 3:
            continue
        # loop needs at least 1 vertex in the original, non-mirrored mesh
        if mapping:
            all_virtual = True
            for vert in loop:
                if mapping[vert] > -1:
                    all_virtual = False
                    break
            if all_virtual:
                continue
        # loop has to be non-collinear
        collinear = True
        loc0 = mathutils.Vector(bm_mod.verts[loop[0]].co[:])
        loc1 = mathutils.Vector(bm_mod.verts[loop[1]].co[:])
        for v in loop[2:]:
            locn = mathutils.Vector(bm_mod.verts[v].co[:])
            if loc0 == loc1 or loc1 == locn:
                loc0 = loc1
                loc1 = locn
                continue
            d1 = loc1-loc0
            d2 = locn-loc1
            if -1e-6 < d1.angle(d2, 0) < 1e-6:
                loc0 = loc1
                loc1 = locn
                continue
            collinear = False
            break
        if collinear:
            continue
        # passed all tests, loop is valid
        valid_loops.append([loop, circular])
        valid_single_loops[len(valid_loops)-1] = single_loops[i]

    return(valid_single_loops, valid_loops)


# calculate the location of single input vertices that need to be flattened
def circle_flatten_singles(bm_mod, com, p, q, normal, single_loop):
    new_locs = []
    for vert in single_loop:
        loc = mathutils.Vector(bm_mod.verts[vert].co[:])
        new_locs.append([vert,  loc - (loc-com).dot(normal)*normal])

    return(new_locs)


# calculate input loops
def circle_get_input(object, bm, scene):
    # get mesh with modifiers applied
    derived, bm_mod = get_derived_bmesh(object, bm, scene)

    # create list of edge-keys based on selection state
    faces = False
    for face in bm.faces:
        if face.select and not face.hide:
            faces = True
            break
    if faces:
        # get selected, non-hidden , non-internal edge-keys
        eks_selected = [key for keys in [face_edgekeys(face) for face in \
            bm_mod.faces if face.select and not face.hide] for key in keys]
        edge_count = {}
        for ek in eks_selected:
            if ek in edge_count:
                edge_count[ek] += 1
            else:
                edge_count[ek] = 1
        edge_keys = [edgekey(edge) for edge in bm_mod.edges if edge.select \
            and not edge.hide and edge_count.get(edgekey(edge), 1)==1]
    else:
        # no faces, so no internal edges either
        edge_keys = [edgekey(edge) for edge in bm_mod.edges if edge.select \
            and not edge.hide]

    # add edge-keys around single vertices
    verts_connected = dict([[vert, 1] for edge in [edge for edge in \
        bm_mod.edges if edge.select and not edge.hide] for vert in \
        edgekey(edge)])
    single_vertices = [vert.index for vert in bm_mod.verts if \
        vert.select and not vert.hide and not \
        verts_connected.get(vert.index, False)]

    if single_vertices and len(bm.faces)>0:
        vert_to_single = dict([[v.index, []] for v in bm_mod.verts \
            if not v.hide])
        for face in [face for face in bm_mod.faces if not face.select \
        and not face.hide]:
            for vert in face.verts:
                vert = vert.index
                if vert in single_vertices:
                    for ek in face_edgekeys(face):
                        if not vert in ek:
                            edge_keys.append(ek)
                            if vert not in vert_to_single[ek[0]]:
                                vert_to_single[ek[0]].append(vert)
                            if vert not in vert_to_single[ek[1]]:
                                vert_to_single[ek[1]].append(vert)
                    break

    # sort edge-keys into loops
    loops = get_connected_selections(edge_keys)

    # find out to which loops the single vertices belong
    single_loops = dict([[i, []] for i in range(len(loops))])
    if single_vertices and len(bm.faces)>0:
        for i, [loop, circular] in enumerate(loops):
            for vert in loop:
                if vert_to_single[vert]:
                    for single in vert_to_single[vert]:
                        if single not in single_loops[i]:
                            single_loops[i].append(single)

    return(derived, bm_mod, single_vertices, single_loops, loops)


# recalculate positions based on the influence of the circle shape
def circle_influence_locs(locs_2d, new_locs_2d, influence):
    for i in range(len(locs_2d)):
        oldx, oldy, j = locs_2d[i]
        newx, newy, k = new_locs_2d[i]
        altx = newx*(influence/100)+ oldx*((100-influence)/100)
        alty = newy*(influence/100)+ oldy*((100-influence)/100)
        locs_2d[i] = [altx, alty, j]

    return(locs_2d)


# project 2d locations on circle, respecting distance relations between verts
def circle_project_non_regular(locs_2d, x0, y0, r):
    for i in range(len(locs_2d)):
        x, y, j = locs_2d[i]
        loc = mathutils.Vector([x-x0, y-y0])
        loc.length = r
        locs_2d[i] = [loc[0], loc[1], j]

    return(locs_2d)


# project 2d locations on circle, with equal distance between all vertices
def circle_project_regular(locs_2d, x0, y0, r):
    # find offset angle and circling direction
    x, y, i = locs_2d[0]
    loc = mathutils.Vector([x-x0, y-y0])
    loc.length = r
    offset_angle = loc.angle(mathutils.Vector([1.0, 0.0]), 0.0)
    loca = mathutils.Vector([x-x0, y-y0, 0.0])
    if loc[1] < -1e-6:
        offset_angle *= -1
    x, y, j = locs_2d[1]
    locb = mathutils.Vector([x-x0, y-y0, 0.0])
    if loca.cross(locb)[2] >= 0:
        ccw = 1
    else:
        ccw = -1
    # distribute vertices along the circle
    for i in range(len(locs_2d)):
        t = offset_angle + ccw * (i / len(locs_2d) * 2 * math.pi)
        x = math.cos(t) * r
        y = math.sin(t) * r
        locs_2d[i] = [x, y, locs_2d[i][2]]

    return(locs_2d)


# shift loop, so the first vertex is closest to the center
def circle_shift_loop(bm_mod, loop, com):
    verts, circular = loop
    distances = [[(bm_mod.verts[vert].co - com).length, i] \
        for i, vert in enumerate(verts)]
    distances.sort()
    shift = distances[0][1]
    loop = [verts[shift:] + verts[:shift], circular]

    return(loop)


##########################################
####### Curve functions ##################
##########################################

# create lists with knots and points, all correctly sorted
def curve_calculate_knots(loop, verts_selected):
    knots = [v for v in loop[0] if v in verts_selected]
    points = loop[0][:]
    # circular loop, potential for weird splines
    if loop[1]:
        offset = int(len(loop[0]) / 4)
        kpos = []
        for k in knots:
            kpos.append(loop[0].index(k))
        kdif = []
        for i in range(len(kpos) - 1):
            kdif.append(kpos[i+1] - kpos[i])
        kdif.append(len(loop[0]) - kpos[-1] + kpos[0])
        kadd = []
        for k in kdif:
            if k > 2 * offset:
                kadd.append([kdif.index(k), True])
            # next 2 lines are optional, they insert
            # an extra control point in small gaps
            #elif k > offset:
            #   kadd.append([kdif.index(k), False])
        kins = []
        krot = False
        for k in kadd: # extra knots to be added
            if k[1]: # big gap (break circular spline)
                kpos = loop[0].index(knots[k[0]]) + offset
                if kpos > len(loop[0]) - 1:
                    kpos -= len(loop[0])
                kins.append([knots[k[0]], loop[0][kpos]])
                kpos2 = k[0] + 1
                if kpos2 > len(knots)-1:
                    kpos2 -= len(knots)
                kpos2 = loop[0].index(knots[kpos2]) - offset
                if kpos2 < 0:
                    kpos2 += len(loop[0])
                kins.append([loop[0][kpos], loop[0][kpos2]])
                krot = loop[0][kpos2]
            else: # small gap (keep circular spline)
                k1 = loop[0].index(knots[k[0]])
                k2 = k[0] + 1
                if k2 > len(knots)-1:
                    k2 -= len(knots)
                k2 = loop[0].index(knots[k2])
                if k2 < k1:
                    dif = len(loop[0]) - 1 - k1 + k2
                else:
                    dif = k2 - k1
                kn = k1 + int(dif/2)
                if kn > len(loop[0]) - 1:
                    kn -= len(loop[0])
                kins.append([loop[0][k1], loop[0][kn]])
        for j in kins: # insert new knots
            knots.insert(knots.index(j[0]) + 1, j[1])
        if not krot: # circular loop
            knots.append(knots[0])
            points = loop[0][loop[0].index(knots[0]):]
            points += loop[0][0:loop[0].index(knots[0]) + 1]
        else: # non-circular loop (broken by script)
            krot = knots.index(krot)
            knots = knots[krot:] + knots[0:krot]
            if loop[0].index(knots[0]) > loop[0].index(knots[-1]):
                points = loop[0][loop[0].index(knots[0]):]
                points += loop[0][0:loop[0].index(knots[-1])+1]
            else:
                points = loop[0][loop[0].index(knots[0]):\
                    loop[0].index(knots[-1]) + 1]
    # non-circular loop, add first and last point as knots
    else:
        if loop[0][0] not in knots:
            knots.insert(0, loop[0][0])
        if loop[0][-1] not in knots:
            knots.append(loop[0][-1])

    return(knots, points)


# calculate relative positions compared to first knot
def curve_calculate_t(bm_mod, knots, points, pknots, regular, circular):
    tpoints = []
    loc_prev = False
    len_total = 0

    for p in points:
        if p in knots:
            loc = pknots[knots.index(p)] # use projected knot location
        else:
            loc = mathutils.Vector(bm_mod.verts[p].co[:])
        if not loc_prev:
            loc_prev = loc
        len_total += (loc-loc_prev).length
        tpoints.append(len_total)
        loc_prev = loc
    tknots = []
    for p in points:
        if p in knots:
            tknots.append(tpoints[points.index(p)])
    if circular:
        tknots[-1] = tpoints[-1]

    # regular option
    if regular:
        tpoints_average = tpoints[-1] / (len(tpoints) - 1)
        for i in range(1, len(tpoints) - 1):
            tpoints[i] = i * tpoints_average
        for i in range(len(knots)):
            tknots[i] = tpoints[points.index(knots[i])]
        if circular:
            tknots[-1] = tpoints[-1]


    return(tknots, tpoints)


# change the location of non-selected points to their place on the spline
def curve_calculate_vertices(bm_mod, knots, tknots, points, tpoints, splines,
interpolation, restriction):
    newlocs = {}
    move = []

    for p in points:
        if p in knots:
            continue
        m = tpoints[points.index(p)]
        if m in tknots:
            n = tknots.index(m)
        else:
            t = tknots[:]
            t.append(m)
            t.sort()
            n = t.index(m) - 1
        if n > len(splines) - 1:
            n = len(splines) - 1
        elif n < 0:
            n = 0

        if interpolation == 'cubic':
            ax, bx, cx, dx, tx = splines[n][0]
            x = ax + bx*(m-tx) + cx*(m-tx)**2 + dx*(m-tx)**3
            ay, by, cy, dy, ty = splines[n][1]
            y = ay + by*(m-ty) + cy*(m-ty)**2 + dy*(m-ty)**3
            az, bz, cz, dz, tz = splines[n][2]
            z = az + bz*(m-tz) + cz*(m-tz)**2 + dz*(m-tz)**3
            newloc = mathutils.Vector([x,y,z])
        else: # interpolation == 'linear'
            a, d, t, u = splines[n]
            newloc = ((m-t)/u)*d + a

        if restriction != 'none': # vertex movement is restricted
            newlocs[p] = newloc
        else: # set the vertex to its new location
            move.append([p, newloc])

    if restriction != 'none': # vertex movement is restricted
        for p in points:
            if p in newlocs:
                newloc = newlocs[p]
            else:
                move.append([p, bm_mod.verts[p].co])
                continue
            oldloc = bm_mod.verts[p].co
            normal = bm_mod.verts[p].normal
            dloc = newloc - oldloc
            if dloc.length < 1e-6:
                move.append([p, newloc])
            elif restriction == 'extrude': # only extrusions
                if dloc.angle(normal, 0) < 0.5 * math.pi + 1e-6:
                    move.append([p, newloc])
            else: # restriction == 'indent' only indentations
                if dloc.angle(normal) > 0.5 * math.pi - 1e-6:
                    move.append([p, newloc])

    return(move)


# trim loops to part between first and last selected vertices (including)
def curve_cut_boundaries(bm_mod, loops):
    cut_loops = []
    for loop, circular in loops:
        if circular:
            # don't cut
            cut_loops.append([loop, circular])
            continue
        selected = [bm_mod.verts[v].select for v in loop]
        first = selected.index(True)
        selected.reverse()
        last = -selected.index(True)
        if last == 0:
            cut_loops.append([loop[first:], circular])
        else:
            cut_loops.append([loop[first:last], circular])

    return(cut_loops)


# calculate input loops
def curve_get_input(object, bm, boundaries, scene):
    # get mesh with modifiers applied
    derived, bm_mod = get_derived_bmesh(object, bm, scene)

    # vertices that still need a loop to run through it
    verts_unsorted = [v.index for v in bm_mod.verts if \
        v.select and not v.hide]
    # necessary dictionaries
    vert_edges = dict_vert_edges(bm_mod)
    edge_faces = dict_edge_faces(bm_mod)
    correct_loops = []

    # find loops through each selected vertex
    while len(verts_unsorted) > 0:
        loops = curve_vertex_loops(bm_mod, verts_unsorted[0], vert_edges,
            edge_faces)
        verts_unsorted.pop(0)

        # check if loop is fully selected
        search_perpendicular = False
        i = -1
        for loop, circular in loops:
            i += 1
            selected = [v for v in loop if bm_mod.verts[v].select]
            if len(selected) < 2:
                # only one selected vertex on loop, don't use
                loops.pop(i)
                continue
            elif len(selected) == len(loop):
                search_perpendicular = loop
                break
        # entire loop is selected, find perpendicular loops
        if search_perpendicular:
            for vert in loop:
                if vert in verts_unsorted:
                    verts_unsorted.remove(vert)
            perp_loops = curve_perpendicular_loops(bm_mod, loop,
                vert_edges, edge_faces)
            for perp_loop in perp_loops:
                correct_loops.append(perp_loop)
        # normal input
        else:
            for loop, circular in loops:
                correct_loops.append([loop, circular])

    # boundaries option
    if boundaries:
        correct_loops = curve_cut_boundaries(bm_mod, correct_loops)

    return(derived, bm_mod, correct_loops)


# return all loops that are perpendicular to the given one
def curve_perpendicular_loops(bm_mod, start_loop, vert_edges, edge_faces):
    # find perpendicular loops
    perp_loops = []
    for start_vert in start_loop:
        loops = curve_vertex_loops(bm_mod, start_vert, vert_edges,
            edge_faces)
        for loop, circular in loops:
            selected = [v for v in loop if bm_mod.verts[v].select]
            if len(selected) == len(loop):
                continue
            else:
                perp_loops.append([loop, circular, loop.index(start_vert)])

    # trim loops to same lengths
    shortest = [[len(loop[0]), i] for i, loop in enumerate(perp_loops)\
        if not loop[1]]
    if not shortest:
        # all loops are circular, not trimming
        return([[loop[0], loop[1]] for loop in perp_loops])
    else:
        shortest = min(shortest)
    shortest_start = perp_loops[shortest[1]][2]
    before_start = shortest_start
    after_start = shortest[0] - shortest_start - 1
    bigger_before = before_start > after_start
    trimmed_loops = []
    for loop in perp_loops:
        # have the loop face the same direction as the shortest one
        if bigger_before:
            if loop[2] < len(loop[0]) / 2:
                loop[0].reverse()
                loop[2] = len(loop[0]) - loop[2] - 1
        else:
            if loop[2] > len(loop[0]) / 2:
                loop[0].reverse()
                loop[2] = len(loop[0]) - loop[2] - 1
        # circular loops can shift, to prevent wrong trimming
        if loop[1]:
            shift = shortest_start - loop[2]
            if loop[2] + shift > 0 and loop[2] + shift < len(loop[0]):
                loop[0] = loop[0][-shift:] + loop[0][:-shift]
            loop[2] += shift
            if loop[2] < 0:
                loop[2] += len(loop[0])
            elif loop[2] > len(loop[0]) -1:
                loop[2] -= len(loop[0])
        # trim
        start = max(0, loop[2] - before_start)
        end = min(len(loop[0]), loop[2] + after_start + 1)
        trimmed_loops.append([loop[0][start:end], False])

    return(trimmed_loops)


# project knots on non-selected geometry
def curve_project_knots(bm_mod, verts_selected, knots, points, circular):
    # function to project vertex on edge
    def project(v1, v2, v3):
        # v1 and v2 are part of a line
        # v3 is projected onto it
        v2 -= v1
        v3 -= v1
        p = v3.project(v2)
        return(p + v1)

    if circular: # project all knots
        start = 0
        end = len(knots)
        pknots = []
    else: # first and last knot shouldn't be projected
        start = 1
        end = -1
        pknots = [mathutils.Vector(bm_mod.verts[knots[0]].co[:])]
    for knot in knots[start:end]:
        if knot in verts_selected:
            knot_left = knot_right = False
            for i in range(points.index(knot)-1, -1*len(points), -1):
                if points[i] not in knots:
                    knot_left = points[i]
                    break
            for i in range(points.index(knot)+1, 2*len(points)):
                if i > len(points) - 1:
                    i -= len(points)
                if points[i] not in knots:
                    knot_right = points[i]
                    break
            if knot_left and knot_right and knot_left != knot_right:
                knot_left = mathutils.Vector(\
                    bm_mod.verts[knot_left].co[:])
                knot_right = mathutils.Vector(\
                    bm_mod.verts[knot_right].co[:])
                knot = mathutils.Vector(bm_mod.verts[knot].co[:])
                pknots.append(project(knot_left, knot_right, knot))
            else:
                pknots.append(mathutils.Vector(bm_mod.verts[knot].co[:]))
        else: # knot isn't selected, so shouldn't be changed
            pknots.append(mathutils.Vector(bm_mod.verts[knot].co[:]))
    if not circular:
        pknots.append(mathutils.Vector(bm_mod.verts[knots[-1]].co[:]))

    return(pknots)


# find all loops through a given vertex
def curve_vertex_loops(bm_mod, start_vert, vert_edges, edge_faces):
    edges_used = []
    loops = []

    for edge in vert_edges[start_vert]:
        if edge in edges_used:
            continue
        loop = []
        circular = False
        for vert in edge:
            active_faces = edge_faces[edge]
            new_vert = vert
            growing = True
            while growing:
                growing = False
                new_edges = vert_edges[new_vert]
                loop.append(new_vert)
                if len(loop) > 1:
                    edges_used.append(tuple(sorted([loop[-1], loop[-2]])))
                if len(new_edges) < 3 or len(new_edges) > 4:
                    # pole
                    break
                else:
                    # find next edge
                    for new_edge in new_edges:
                        if new_edge in edges_used:
                            continue
                        eliminate = False
                        for new_face in edge_faces[new_edge]:
                            if new_face in active_faces:
                                eliminate = True
                                break
                        if eliminate:
                            continue
                        # found correct new edge
                        active_faces = edge_faces[new_edge]
                        v1, v2 = new_edge
                        if v1 != new_vert:
                            new_vert = v1
                        else:
                            new_vert = v2
                        if new_vert == loop[0]:
                            circular = True
                        else:
                            growing = True
                        break
            if circular:
                break
            loop.reverse()
        loops.append([loop, circular])

    return(loops)


##########################################
####### Flatten functions ################
##########################################

# sort input into loops
def flatten_get_input(bm):
    vert_verts = dict_vert_verts([edgekey(edge) for edge in bm.edges \
        if edge.select and not edge.hide])
    verts = [v.index for v in bm.verts if v.select and not v.hide]

    # no connected verts, consider all selected verts as a single input
    if not vert_verts:
        return([[verts, False]])

    loops = []
    while len(verts) > 0:
        # start of loop
        loop = [verts[0]]
        verts.pop(0)
        if loop[-1] in vert_verts:
            to_grow = vert_verts[loop[-1]]
        else:
            to_grow = []
        # grow loop
        while len(to_grow) > 0:
            new_vert = to_grow[0]
            to_grow.pop(0)
            if new_vert in loop:
                continue
            loop.append(new_vert)
            verts.remove(new_vert)
            to_grow += vert_verts[new_vert]
        # add loop to loops
        loops.append([loop, False])

    return(loops)


# calculate position of vertex projections on plane
def flatten_project(bm, loop, com, normal):
    verts = [bm.verts[v] for v in loop[0]]
    verts_projected = [[v.index, mathutils.Vector(v.co[:]) - \
        (mathutils.Vector(v.co[:])-com).dot(normal)*normal] for v in verts]

    return(verts_projected)


##########################################
####### Gstretch functions ###############
##########################################

# fake stroke class, used to create custom strokes if no GP data is found
class gstretch_fake_stroke():
    def __init__(self, points):
        self.points = [gstretch_fake_stroke_point(p) for p in points]


# fake stroke point class, used in fake strokes
class gstretch_fake_stroke_point():
    def __init__(self, loc):
        self.co = loc


# flips loops, if necessary, to obtain maximum alignment to stroke
def gstretch_align_pairs(ls_pairs, object, bm_mod, method):
    # returns total distance between all verts in loop and corresponding stroke
    def distance_loop_stroke(loop, stroke, object, bm_mod, method):
        stroke_lengths_cache = False
        loop_length = len(loop[0])
        total_distance = 0

        if method != 'regular':
            relative_lengths = gstretch_relative_lengths(loop, bm_mod)

        for i, v_index in enumerate(loop[0]):
            if method == 'regular':
                relative_distance = i / (loop_length - 1)
            else:
                relative_distance = relative_lengths[i]

            loc1 = object.matrix_world * bm_mod.verts[v_index].co
            loc2, stroke_lengths_cache = gstretch_eval_stroke(stroke,
                relative_distance, stroke_lengths_cache)
            total_distance += (loc2 - loc1).length

        return(total_distance)

    if ls_pairs:
        for (loop, stroke) in ls_pairs:
            distance_loop_stroke
            total_dist = distance_loop_stroke(loop, stroke, object, bm_mod,
                method)
            loop[0].reverse()
            total_dist_rev = distance_loop_stroke(loop, stroke, object, bm_mod,
                method)
            if total_dist_rev > total_dist:
                loop[0].reverse()

    return(ls_pairs)


# calculate vertex positions on stroke
def gstretch_calculate_verts(loop, stroke, object, bm_mod, method):
    move = []
    stroke_lengths_cache = False
    loop_length = len(loop[0])
    matrix_inverse = object.matrix_world.inverted()

    # return intersection of line with stroke, or None
    def intersect_line_stroke(vec1, vec2, stroke):
        for i, p in enumerate(stroke.points[1:]):
            intersections = mathutils.geometry.intersect_line_line(vec1, vec2,
                p.co, stroke.points[i].co)
            if intersections and \
            (intersections[0] - intersections[1]).length < 1e-2:
                x, dist = mathutils.geometry.intersect_point_line(
                    intersections[0], p.co, stroke.points[i].co)
                if -1 < dist < 1:
                    return(intersections[0])
        return(None)

    if method == 'project':
        projection_vectors = []
        vert_edges = dict_vert_edges(bm_mod)

        for v_index in loop[0]:
            for ek in vert_edges[v_index]:
                v1, v2 = ek
                v1 = bm_mod.verts[v1]
                v2 = bm_mod.verts[v2]
                if v1.select + v2.select == 1 and not v1.hide and not v2.hide:
                    vec1 = object.matrix_world * v1.co
                    vec2 = object.matrix_world * v2.co
                    intersection = intersect_line_stroke(vec1, vec2, stroke)
                    if intersection:
                        break
            if not intersection:
                v = bm_mod.verts[v_index]
                intersection = intersect_line_stroke(v.co, v.co + v.normal,
                    stroke)
            if intersection:
                move.append([v_index, matrix_inverse * intersection])

    else:
        if method == 'irregular':
            relative_lengths = gstretch_relative_lengths(loop, bm_mod)

        for i, v_index in enumerate(loop[0]):
            if method == 'regular':
                relative_distance = i / (loop_length - 1)
            else: # method == 'irregular'
                relative_distance = relative_lengths[i]
            loc, stroke_lengths_cache = gstretch_eval_stroke(stroke,
                relative_distance, stroke_lengths_cache)
            loc = matrix_inverse * loc
            move.append([v_index, loc])

    return(move)


# create new vertices, based on GP strokes
def gstretch_create_verts(object, bm_mod, strokes, method, conversion,
conversion_distance, conversion_max, conversion_min, conversion_vertices):
    move = []
    stroke_verts = []
    mat_world = object.matrix_world.inverted()
    singles = gstretch_match_single_verts(bm_mod, strokes, mat_world)

    for stroke in strokes:
        stroke_verts.append([stroke, []])
        min_end_point = 0
        if conversion == 'vertices':
            min_end_point = conversion_vertices
            end_point = conversion_vertices
        elif conversion == 'limit_vertices':
            min_end_point = conversion_min
            end_point = conversion_max
        else:
            end_point = len(stroke.points)
        # creation of new vertices at fixed user-defined distances
        if conversion == 'distance':
            method = 'project'
            prev_point = stroke.points[0]
            stroke_verts[-1][1].append(bm_mod.verts.new(mat_world * \
                prev_point.co))
            distance = 0
            limit = conversion_distance
            for point in stroke.points:
                new_distance = distance + (point.co - prev_point.co).length
                iteration = 0
                while new_distance > limit:
                    to_cover = limit - distance + (limit * iteration)
                    new_loc = prev_point.co + to_cover * \
                        (point.co - prev_point.co).normalized()
                    stroke_verts[-1][1].append(bm_mod.verts.new(mat_world * \
                        new_loc))
                    new_distance -= limit
                    iteration += 1
                distance = new_distance
                prev_point = point
        # creation of new vertices for other methods
        else:
            # add vertices at stroke points
            for point in stroke.points[:end_point]:
                stroke_verts[-1][1].append(bm_mod.verts.new(\
                    mat_world * point.co))
            # add more vertices, beyond the points that are available
            if min_end_point > min(len(stroke.points), end_point):
                for i in range(min_end_point -
                (min(len(stroke.points), end_point))):
                    stroke_verts[-1][1].append(bm_mod.verts.new(\
                        mat_world * point.co))
                # force even spreading of points, so they are placed on stroke
                method = 'regular'
    bm_mod.verts.index_update()
    for stroke, verts_seq in stroke_verts:
        if len(verts_seq) < 2:
            continue
        # spread vertices evenly over the stroke
        if method == 'regular':
            loop = [[vert.index for vert in verts_seq], False]
            move += gstretch_calculate_verts(loop, stroke, object, bm_mod,
                method)
        # create edges
        for i, vert in enumerate(verts_seq):
            if i > 0:
                bm_mod.edges.new((verts_seq[i-1], verts_seq[i]))
            vert.select = True
        # connect single vertices to the closest stroke
        if singles:
            for vert, m_stroke, point in singles:
                if m_stroke != stroke:
                    continue
                bm_mod.edges.new((vert, verts_seq[point]))

    bmesh.update_edit_mesh(object.data)

    return(move)


# erases the grease pencil stroke
def gstretch_erase_stroke(stroke, context):
    # change 3d coordinate into a stroke-point
    def sp(loc, context):
        lib = {'name': "",
            'pen_flip': False,
            'is_start': False,
            'location': (0, 0, 0),
            'mouse': (view3d_utils.location_3d_to_region_2d(\
                context.region, context.space_data.region_3d, loc)),
            'pressure': 1,
            'time': 0}
        return(lib)

    if type(stroke) != bpy.types.GPencilStroke:
        # fake stroke, there is nothing to delete
        return

    erase_stroke = [sp(p.co, context) for p in stroke.points]
    if erase_stroke:
        erase_stroke[0]['is_start'] = True
    bpy.ops.gpencil.draw(mode='ERASER', stroke=erase_stroke)


# get point on stroke, given by relative distance (0.0 - 1.0)
def gstretch_eval_stroke(stroke, distance, stroke_lengths_cache=False):
    # use cache if available
    if not stroke_lengths_cache:
        lengths = [0]
        for i, p in enumerate(stroke.points[1:]):
            lengths.append((p.co - stroke.points[i].co).length + \
                lengths[-1])
        total_length = max(lengths[-1], 1e-7)
        stroke_lengths_cache = [length / total_length for length in
            lengths]
    stroke_lengths = stroke_lengths_cache[:]

    if distance in stroke_lengths:
        loc = stroke.points[stroke_lengths.index(distance)].co
    elif distance > stroke_lengths[-1]:
        # should be impossible, but better safe than sorry
        loc = stroke.points[-1].co
    else:
        stroke_lengths.append(distance)
        stroke_lengths.sort()
        stroke_index = stroke_lengths.index(distance)
        interval_length = stroke_lengths[stroke_index+1] - \
            stroke_lengths[stroke_index-1]
        distance_relative = (distance - stroke_lengths[stroke_index-1]) / \
            interval_length
        interval_vector = stroke.points[stroke_index].co - \
            stroke.points[stroke_index-1].co
        loc = stroke.points[stroke_index-1].co + \
            distance_relative * interval_vector

    return(loc, stroke_lengths_cache)


# create fake grease pencil strokes for the active object
def gstretch_get_fake_strokes(object, bm_mod, loops):
    strokes = []
    for loop in loops:
        p1 = object.matrix_world * bm_mod.verts[loop[0][0]].co
        p2 = object.matrix_world * bm_mod.verts[loop[0][-1]].co
        strokes.append(gstretch_fake_stroke([p1, p2]))

    return(strokes)


# get grease pencil strokes for the active object
def gstretch_get_strokes(object):
    gp = object.grease_pencil
    if not gp:
        return(None)
    layer = gp.layers.active
    if not layer:
        return(None)
    frame = layer.active_frame
    if not frame:
        return(None)
    strokes = frame.strokes
    if len(strokes) < 1:
        return(None)

    return(strokes)


# returns a list with loop-stroke pairs
def gstretch_match_loops_strokes(loops, strokes, object, bm_mod):
    if not loops or not strokes:
        return(None)

    # calculate loop centers
    loop_centers = []
    for loop in loops:
        center = mathutils.Vector()
        for v_index in loop[0]:
            center += bm_mod.verts[v_index].co
        center /= len(loop[0])
        center = object.matrix_world * center
        loop_centers.append([center, loop])

    # calculate stroke centers
    stroke_centers = []
    for stroke in strokes:
        center = mathutils.Vector()
        for p in stroke.points:
            center += p.co
        center /= len(stroke.points)
        stroke_centers.append([center, stroke, 0])

    # match, first by stroke use count, then by distance
    ls_pairs = []
    for lc in loop_centers:
        distances = []
        for i, sc in enumerate(stroke_centers):
            distances.append([sc[2], (lc[0] - sc[0]).length, i])
        distances.sort()
        best_stroke = distances[0][2]
        ls_pairs.append([lc[1], stroke_centers[best_stroke][1]])
        stroke_centers[best_stroke][2] += 1 # increase stroke use count

    return(ls_pairs)


# match single selected vertices to the closest stroke endpoint
# returns a list of tuples, constructed as: (vertex, stroke, stroke point index)
def gstretch_match_single_verts(bm_mod, strokes, mat_world):
    # calculate stroke endpoints in object space
    endpoints = []
    for stroke in strokes:
        endpoints.append((mat_world * stroke.points[0].co, stroke, 0))
        endpoints.append((mat_world * stroke.points[-1].co, stroke, -1))

    distances = []
    # find single vertices (not connected to other selected verts)
    for vert in bm_mod.verts:
        if not vert.select:
            continue
        single = True
        for edge in vert.link_edges:
            if edge.other_vert(vert).select:
                single = False
                break
        if not single:
            continue
        # calculate distances from vertex to endpoints
        distance = [((vert.co - loc).length, vert, stroke, stroke_point,
            endpoint_index) for endpoint_index, (loc, stroke, stroke_point) in
            enumerate(endpoints)]
        distance.sort()
        distances.append(distance[0])

    # create matches, based on shortest distance first
    singles = []
    while distances:
        distances.sort()
        singles.append((distances[0][1], distances[0][2], distances[0][3]))
        endpoints.pop(distances[0][4])
        distances.pop(0)
        distances_new = []
        for (i, vert, j, k, l) in distances:
            distance_new = [((vert.co - loc).length, vert, stroke, stroke_point,
                endpoint_index) for endpoint_index, (loc, stroke,
                stroke_point) in enumerate(endpoints)]
            distance_new.sort()
            distances_new.append(distance_new[0])
        distances = distances_new

    return(singles)


# returns list with a relative distance (0.0 - 1.0) of each vertex on the loop
def gstretch_relative_lengths(loop, bm_mod):
    lengths = [0]
    for i, v_index in enumerate(loop[0][1:]):
        lengths.append((bm_mod.verts[v_index].co - \
            bm_mod.verts[loop[0][i]].co).length + lengths[-1])
        total_length = max(lengths[-1], 1e-7)
        relative_lengths = [length / total_length for length in
            lengths]

    return(relative_lengths)


# convert cache-stored strokes into usable (fake) GP strokes
def gstretch_safe_to_true_strokes(safe_strokes):
    strokes = []
    for safe_stroke in safe_strokes:
        strokes.append(gstretch_fake_stroke(safe_stroke))

    return(strokes)


# convert a GP stroke into a list of points which can be stored in cache
def gstretch_true_to_safe_strokes(strokes):
    safe_strokes = []
    for stroke in strokes:
        safe_strokes.append([p.co.copy() for p in stroke.points])

    return(safe_strokes)


# force consistency in GUI, max value can never be lower than min value
def gstretch_update_max(self, context):
    # called from operator settings (after execution)
    if 'conversion_min' in self.keys():
        if self.conversion_min > self.conversion_max:
            self.conversion_max = self.conversion_min
    # called from toolbar
    else:
        lt = context.window_manager.looptools
        if lt.gstretch_conversion_min > lt.gstretch_conversion_max:
            lt.gstretch_conversion_max = lt.gstretch_conversion_min


# force consistency in GUI, min value can never be higher than max value
def gstretch_update_min(self, context):
    # called from operator settings (after execution)
    if 'conversion_max' in self.keys():
        if self.conversion_max < self.conversion_min:
            self.conversion_min = self.conversion_max
    # called from toolbar
    else:
        lt = context.window_manager.looptools
        if lt.gstretch_conversion_max < lt.gstretch_conversion_min:
            lt.gstretch_conversion_min = lt.gstretch_conversion_max


##########################################
####### Relax functions ##################
##########################################

# create lists with knots and points, all correctly sorted
def relax_calculate_knots(loops):
    all_knots = []
    all_points = []
    for loop, circular in loops:
        knots = [[], []]
        points = [[], []]
        if circular:
            if len(loop)%2 == 1: # odd
                extend = [False, True, 0, 1, 0, 1]
            else: # even
                extend = [True, False, 0, 1, 1, 2]
        else:
            if len(loop)%2 == 1: # odd
                extend = [False, False, 0, 1, 1, 2]
            else: # even
                extend = [False, False, 0, 1, 1, 2]
        for j in range(2):
            if extend[j]:
                loop = [loop[-1]] + loop + [loop[0]]
            for i in range(extend[2+2*j], len(loop), 2):
                knots[j].append(loop[i])
            for i in range(extend[3+2*j], len(loop), 2):
                if loop[i] == loop[-1] and not circular:
                    continue
                if len(points[j]) == 0:
                    points[j].append(loop[i])
                elif loop[i] != points[j][0]:
                    points[j].append(loop[i])
            if circular:
                if knots[j][0] != knots[j][-1]:
                    knots[j].append(knots[j][0])
        if len(points[1]) == 0:
            knots.pop(1)
            points.pop(1)
        for k in knots:
            all_knots.append(k)
        for p in points:
            all_points.append(p)

    return(all_knots, all_points)


# calculate relative positions compared to first knot
def relax_calculate_t(bm_mod, knots, points, regular):
    all_tknots = []
    all_tpoints = []
    for i in range(len(knots)):
        amount = len(knots[i]) + len(points[i])
        mix  = []
        for j in range(amount):
            if j%2 == 0:
                mix.append([True, knots[i][round(j/2)]])
            elif j == amount-1:
                mix.append([True, knots[i][-1]])
            else:
                mix.append([False, points[i][int(j/2)]])
        len_total = 0
        loc_prev = False
        tknots = []
        tpoints = []
        for m in mix:
            loc = mathutils.Vector(bm_mod.verts[m[1]].co[:])
            if not loc_prev:
                loc_prev = loc
            len_total += (loc - loc_prev).length
            if m[0]:
                tknots.append(len_total)
            else:
                tpoints.append(len_total)
            loc_prev = loc
        if regular:
            tpoints = []
            for p in range(len(points[i])):
                tpoints.append((tknots[p] + tknots[p+1]) / 2)
        all_tknots.append(tknots)
        all_tpoints.append(tpoints)

    return(all_tknots, all_tpoints)


# change the location of the points to their place on the spline
def relax_calculate_verts(bm_mod, interpolation, tknots, knots, tpoints,
points, splines):
    change = []
    move = []
    for i in range(len(knots)):
        for p in points[i]:
            m = tpoints[i][points[i].index(p)]
            if m in tknots[i]:
                n = tknots[i].index(m)
            else:
                t = tknots[i][:]
                t.append(m)
                t.sort()
                n = t.index(m)-1
            if n > len(splines[i]) - 1:
                n = len(splines[i]) - 1
            elif n < 0:
                n = 0

            if interpolation == 'cubic':
                ax, bx, cx, dx, tx = splines[i][n][0]
                x = ax + bx*(m-tx) + cx*(m-tx)**2 + dx*(m-tx)**3
                ay, by, cy, dy, ty = splines[i][n][1]
                y = ay + by*(m-ty) + cy*(m-ty)**2 + dy*(m-ty)**3
                az, bz, cz, dz, tz = splines[i][n][2]
                z = az + bz*(m-tz) + cz*(m-tz)**2 + dz*(m-tz)**3
                change.append([p, mathutils.Vector([x,y,z])])
            else: # interpolation == 'linear'
                a, d, t, u = splines[i][n]
                if u == 0:
                    u = 1e-8
                change.append([p, ((m-t)/u)*d + a])
    for c in change:
        move.append([c[0], (bm_mod.verts[c[0]].co + c[1]) / 2])

    return(move)


##########################################
####### Space functions ##################
##########################################

# calculate relative positions compared to first knot
def space_calculate_t(bm_mod, knots):
    tknots = []
    loc_prev = False
    len_total = 0
    for k in knots:
        loc = mathutils.Vector(bm_mod.verts[k].co[:])
        if not loc_prev:
            loc_prev = loc
        len_total += (loc - loc_prev).length
        tknots.append(len_total)
        loc_prev = loc
    amount = len(knots)
    t_per_segment = len_total / (amount - 1)
    tpoints = [i * t_per_segment for i in range(amount)]

    return(tknots, tpoints)


# change the location of the points to their place on the spline
def space_calculate_verts(bm_mod, interpolation, tknots, tpoints, points,
splines):
    move = []
    for p in points:
        m = tpoints[points.index(p)]
        if m in tknots:
            n = tknots.index(m)
        else:
            t = tknots[:]
            t.append(m)
            t.sort()
            n = t.index(m) - 1
        if n > len(splines) - 1:
            n = len(splines) - 1
        elif n < 0:
            n = 0

        if interpolation == 'cubic':
            ax, bx, cx, dx, tx = splines[n][0]
            x = ax + bx*(m-tx) + cx*(m-tx)**2 + dx*(m-tx)**3
            ay, by, cy, dy, ty = splines[n][1]
            y = ay + by*(m-ty) + cy*(m-ty)**2 + dy*(m-ty)**3
            az, bz, cz, dz, tz = splines[n][2]
            z = az + bz*(m-tz) + cz*(m-tz)**2 + dz*(m-tz)**3
            move.append([p, mathutils.Vector([x,y,z])])
        else: # interpolation == 'linear'
            a, d, t, u = splines[n]
            move.append([p, ((m-t)/u)*d + a])

    return(move)


##########################################
####### Operators ########################
##########################################

# bridge operator
class Bridge(bpy.types.Operator):
    bl_idname = 'mesh.looptools_bridge'
    bl_label = "Bridge / Loft"
    bl_description = "Bridge two, or loft several, loops of vertices"
    bl_options = {'REGISTER', 'UNDO'}

    cubic_strength = bpy.props.FloatProperty(name = "Strength",
        description = "Higher strength results in more fluid curves",
        default = 1.0,
        soft_min = -3.0,
        soft_max = 3.0)
    interpolation = bpy.props.EnumProperty(name = "Interpolation mode",
        items = (('cubic', "Cubic", "Gives curved results"),
            ('linear', "Linear", "Basic, fast, straight interpolation")),
        description = "Interpolation mode: algorithm used when creating "\
            "segments",
        default = 'cubic')
    loft = bpy.props.BoolProperty(name = "Loft",
        description = "Loft multiple loops, instead of considering them as "\
            "a multi-input for bridging",
        default = False)
    loft_loop = bpy.props.BoolProperty(name = "Loop",
        description = "Connect the first and the last loop with each other",
        default = False)
    min_width = bpy.props.IntProperty(name = "Minimum width",
        description = "Segments with an edge smaller than this are merged "\
            "(compared to base edge)",
        default = 0,
        min = 0,
        max = 100,
        subtype = 'PERCENTAGE')
    mode = bpy.props.EnumProperty(name = "Mode",
        items = (('basic', "Basic", "Fast algorithm"), ('shortest',
            "Shortest edge", "Slower algorithm with better vertex matching")),
        description = "Algorithm used for bridging",
        default = 'shortest')
    remove_faces = bpy.props.BoolProperty(name = "Remove faces",
        description = "Remove faces that are internal after bridging",
        default = True)
    reverse = bpy.props.BoolProperty(name = "Reverse",
        description = "Manually override the direction in which the loops "\
                      "are bridged. Only use if the tool gives the wrong " \
                      "result",
        default = False)
    segments = bpy.props.IntProperty(name = "Segments",
        description = "Number of segments used to bridge the gap "\
            "(0 = automatic)",
        default = 1,
        min = 0,
        soft_max = 20)
    twist = bpy.props.IntProperty(name = "Twist",
        description = "Twist what vertices are connected to each other",
        default = 0)

    @classmethod
    def poll(cls, context):
        ob = context.active_object
        return (ob and ob.type == 'MESH' and context.mode == 'EDIT_MESH')

    def draw(self, context):
        layout = self.layout
        #layout.prop(self, "mode") # no cases yet where 'basic' mode is needed

        # top row
        col_top = layout.column(align=True)
        row = col_top.row(align=True)
        col_left = row.column(align=True)
        col_right = row.column(align=True)
        col_right.active = self.segments != 1
        col_left.prop(self, "segments")
        col_right.prop(self, "min_width", text="")
        # bottom row
        bottom_left = col_left.row()
        bottom_left.active = self.segments != 1
        bottom_left.prop(self, "interpolation", text="")
        bottom_right = col_right.row()
        bottom_right.active = self.interpolation == 'cubic'
        bottom_right.prop(self, "cubic_strength")
        # boolean properties
        col_top.prop(self, "remove_faces")
        if self.loft:
            col_top.prop(self, "loft_loop")

        # override properties
        col_top.separator()
        row = layout.row(align = True)
        row.prop(self, "twist")
        row.prop(self, "reverse")

    def invoke(self, context, event):
        # load custom settings
        context.window_manager.looptools.bridge_loft = self.loft
        settings_load(self)
        return self.execute(context)

    def execute(self, context):
        # initialise
        global_undo, object, bm = initialise()
        edge_faces, edgekey_to_edge, old_selected_faces, smooth = \
            bridge_initialise(bm, self.interpolation)
        settings_write(self)

        # check cache to see if we can save time
        input_method = bridge_input_method(self.loft, self.loft_loop)
        cached, single_loops, loops, derived, mapping = cache_read("Bridge",
            object, bm, input_method, False)
        if not cached:
            # get loops
            loops = bridge_get_input(bm)
            if loops:
                # reorder loops if there are more than 2
                if len(loops) > 2:
                    if self.loft:
                        loops = bridge_sort_loops(bm, loops, self.loft_loop)
                    else:
                        loops = bridge_match_loops(bm, loops)

        # saving cache for faster execution next time
        if not cached:
            cache_write("Bridge", object, bm, input_method, False, False,
                loops, False, False)

        if loops:
            # calculate new geometry
            vertices = []
            faces = []
            max_vert_index = len(bm.verts)-1
            for i in range(1, len(loops)):
                if not self.loft and i%2 == 0:
                    continue
                lines = bridge_calculate_lines(bm, loops[i-1:i+1],
                    self.mode, self.twist, self.reverse)
                vertex_normals = bridge_calculate_virtual_vertex_normals(bm,
                    lines, loops[i-1:i+1], edge_faces, edgekey_to_edge)
                segments = bridge_calculate_segments(bm, lines,
                    loops[i-1:i+1], self.segments)
                new_verts, new_faces, max_vert_index = \
                    bridge_calculate_geometry(bm, lines, vertex_normals,
                    segments, self.interpolation, self.cubic_strength,
                    self.min_width, max_vert_index)
                if new_verts:
                    vertices += new_verts
                if new_faces:
                    faces += new_faces
            # make sure faces in loops that aren't used, aren't removed
            if self.remove_faces and old_selected_faces:
                bridge_save_unused_faces(bm, old_selected_faces, loops)
            # create vertices
            if vertices:
                bridge_create_vertices(bm, vertices)
            # create faces
            if faces:
                new_faces = bridge_create_faces(object, bm, faces, self.twist)
                old_selected_faces = [i for i, face in enumerate(bm.faces) \
                    if face.index in old_selected_faces] # updating list
                bridge_select_new_faces(new_faces, smooth)
            # edge-data could have changed, can't use cache next run
            if faces and not vertices:
                cache_delete("Bridge")
            # delete internal faces
            if self.remove_faces and old_selected_faces:
                bridge_remove_internal_faces(bm, old_selected_faces)
            # make sure normals are facing outside
            bmesh.update_edit_mesh(object.data, tessface=False,
                destructive=True)
            bpy.ops.mesh.normals_make_consistent()

        # cleaning up
        terminate(global_undo)

        return{'FINISHED'}


# circle operator
class Circle(bpy.types.Operator):
    bl_idname = "mesh.looptools_circle"
    bl_label = "Circle"
    bl_description = "Move selected vertices into a circle shape"
    bl_options = {'REGISTER', 'UNDO'}

    custom_radius = bpy.props.BoolProperty(name = "Radius",
        description = "Force a custom radius",
        default = False)
    fit = bpy.props.EnumProperty(name = "Method",
        items = (("best", "Best fit", "Non-linear least squares"),
            ("inside", "Fit inside","Only move vertices towards the center")),
        description = "Method used for fitting a circle to the vertices",
        default = 'best')
    flatten = bpy.props.BoolProperty(name = "Flatten",
        description = "Flatten the circle, instead of projecting it on the " \
            "mesh",
        default = True)
    influence = bpy.props.FloatProperty(name = "Influence",
        description = "Force of the tool",
        default = 100.0,
        min = 0.0,
        max = 100.0,
        precision = 1,
        subtype = 'PERCENTAGE')
    radius = bpy.props.FloatProperty(name = "Radius",
        description = "Custom radius for circle",
        default = 1.0,
        min = 0.0,
        soft_max = 1000.0)
    regular = bpy.props.BoolProperty(name = "Regular",
        description = "Distribute vertices at constant distances along the " \
            "circle",
        default = True)

    @classmethod
    def poll(cls, context):
        ob = context.active_object
        return(ob and ob.type == 'MESH' and context.mode == 'EDIT_MESH')

    def draw(self, context):
        layout = self.layout
        col = layout.column()

        col.prop(self, "fit")
        col.separator()

        col.prop(self, "flatten")
        row = col.row(align=True)
        row.prop(self, "custom_radius")
        row_right = row.row(align=True)
        row_right.active = self.custom_radius
        row_right.prop(self, "radius", text="")
        col.prop(self, "regular")
        col.separator()

        col.prop(self, "influence")

    def invoke(self, context, event):
        # load custom settings
        settings_load(self)
        return self.execute(context)

    def execute(self, context):
        # initialise
        global_undo, object, bm = initialise()
        settings_write(self)
        # check cache to see if we can save time
        cached, single_loops, loops, derived, mapping = cache_read("Circle",
            object, bm, False, False)
        if cached:
            derived, bm_mod = get_derived_bmesh(object, bm, context.scene)
        else:
            # find loops
            derived, bm_mod, single_vertices, single_loops, loops = \
                circle_get_input(object, bm, context.scene)
            mapping = get_mapping(derived, bm, bm_mod, single_vertices,
                False, loops)
            single_loops, loops = circle_check_loops(single_loops, loops,
                mapping, bm_mod)

        # saving cache for faster execution next time
        if not cached:
            cache_write("Circle", object, bm, False, False, single_loops,
                loops, derived, mapping)

        move = []
        for i, loop in enumerate(loops):
            # best fitting flat plane
            com, normal = calculate_plane(bm_mod, loop)
            # if circular, shift loop so we get a good starting vertex
            if loop[1]:
                loop = circle_shift_loop(bm_mod, loop, com)
            # flatten vertices on plane
            locs_2d, p, q = circle_3d_to_2d(bm_mod, loop, com, normal)
            # calculate circle
            if self.fit == 'best':
                x0, y0, r = circle_calculate_best_fit(locs_2d)
            else: # self.fit == 'inside'
                x0, y0, r = circle_calculate_min_fit(locs_2d)
            # radius override
            if self.custom_radius:
                r = self.radius / p.length
            # calculate positions on circle
            if self.regular:
                new_locs_2d = circle_project_regular(locs_2d[:], x0, y0, r)
            else:
                new_locs_2d = circle_project_non_regular(locs_2d[:], x0, y0, r)
            # take influence into account
            locs_2d = circle_influence_locs(locs_2d, new_locs_2d,
                self.influence)
            # calculate 3d positions of the created 2d input
            move.append(circle_calculate_verts(self.flatten, bm_mod,
                locs_2d, com, p, q, normal))
            # flatten single input vertices on plane defined by loop
            if self.flatten and single_loops:
                move.append(circle_flatten_singles(bm_mod, com, p, q,
                    normal, single_loops[i]))

        # move vertices to new locations
        move_verts(object, bm, mapping, move, -1)

        # cleaning up
        if derived:
            bm_mod.free()
        terminate(global_undo)

        return{'FINISHED'}


# curve operator
class Curve(bpy.types.Operator):
    bl_idname = "mesh.looptools_curve"
    bl_label = "Curve"
    bl_description = "Turn a loop into a smooth curve"
    bl_options = {'REGISTER', 'UNDO'}

    boundaries = bpy.props.BoolProperty(name = "Boundaries",
        description = "Limit the tool to work within the boundaries of the "\
            "selected vertices",
        default = False)
    influence = bpy.props.FloatProperty(name = "Influence",
        description = "Force of the tool",
        default = 100.0,
        min = 0.0,
        max = 100.0,
        precision = 1,
        subtype = 'PERCENTAGE')
    interpolation = bpy.props.EnumProperty(name = "Interpolation",
        items = (("cubic", "Cubic", "Natural cubic spline, smooth results"),
            ("linear", "Linear", "Simple and fast linear algorithm")),
        description = "Algorithm used for interpolation",
        default = 'cubic')
    regular = bpy.props.BoolProperty(name = "Regular",
        description = "Distribute vertices at constant distances along the" \
            "curve",
        default = True)
    restriction = bpy.props.EnumProperty(name = "Restriction",
        items = (("none", "None", "No restrictions on vertex movement"),
            ("extrude", "Extrude only","Only allow extrusions (no "\
                "indentations)"),
            ("indent", "Indent only", "Only allow indentation (no "\
                "extrusions)")),
        description = "Restrictions on how the vertices can be moved",
        default = 'none')

    @classmethod
    def poll(cls, context):
        ob = context.active_object
        return(ob and ob.type == 'MESH' and context.mode == 'EDIT_MESH')

    def draw(self, context):
        layout = self.layout
        col = layout.column()

        col.prop(self, "interpolation")
        col.prop(self, "restriction")
        col.prop(self, "boundaries")
        col.prop(self, "regular")
        col.separator()

        col.prop(self, "influence")

    def invoke(self, context, event):
        # load custom settings
        settings_load(self)
        return self.execute(context)

    def execute(self, context):
        # initialise
        global_undo, object, bm = initialise()
        settings_write(self)
        # check cache to see if we can save time
        cached, single_loops, loops, derived, mapping = cache_read("Curve",
            object, bm, False, self.boundaries)
        if cached:
            derived, bm_mod = get_derived_bmesh(object, bm, context.scene)
        else:
            # find loops
            derived, bm_mod, loops = curve_get_input(object, bm,
                self.boundaries, context.scene)
            mapping = get_mapping(derived, bm, bm_mod, False, True, loops)
            loops = check_loops(loops, mapping, bm_mod)
        verts_selected = [v.index for v in bm_mod.verts if v.select \
            and not v.hide]

        # saving cache for faster execution next time
        if not cached:
            cache_write("Curve", object, bm, False, self.boundaries, False,
                loops, derived, mapping)

        move = []
        for loop in loops:
            knots, points = curve_calculate_knots(loop, verts_selected)
            pknots = curve_project_knots(bm_mod, verts_selected, knots,
                points, loop[1])
            tknots, tpoints = curve_calculate_t(bm_mod, knots, points,
                pknots, self.regular, loop[1])
            splines = calculate_splines(self.interpolation, bm_mod,
                tknots, knots)
            move.append(curve_calculate_vertices(bm_mod, knots, tknots,
                points, tpoints, splines, self.interpolation,
                self.restriction))

        # move vertices to new locations
        move_verts(object, bm, mapping, move, self.influence)

        # cleaning up
        if derived:
            bm_mod.free()
        terminate(global_undo)

        return{'FINISHED'}


# flatten operator
class Flatten(bpy.types.Operator):
    bl_idname = "mesh.looptools_flatten"
    bl_label = "Flatten"
    bl_description = "Flatten vertices on a best-fitting plane"
    bl_options = {'REGISTER', 'UNDO'}

    influence = bpy.props.FloatProperty(name = "Influence",
        description = "Force of the tool",
        default = 100.0,
        min = 0.0,
        max = 100.0,
        precision = 1,
        subtype = 'PERCENTAGE')
    plane = bpy.props.EnumProperty(name = "Plane",
        items = (("best_fit", "Best fit", "Calculate a best fitting plane"),
            ("normal", "Normal", "Derive plane from averaging vertex "\
            "normals"),
            ("view", "View", "Flatten on a plane perpendicular to the "\
            "viewing angle")),
        description = "Plane on which vertices are flattened",
        default = 'best_fit')
    restriction = bpy.props.EnumProperty(name = "Restriction",
        items = (("none", "None", "No restrictions on vertex movement"),
            ("bounding_box", "Bounding box", "Vertices are restricted to "\
            "movement inside the bounding box of the selection")),
        description = "Restrictions on how the vertices can be moved",
        default = 'none')

    @classmethod
    def poll(cls, context):
        ob = context.active_object
        return(ob and ob.type == 'MESH' and context.mode == 'EDIT_MESH')

    def draw(self, context):
        layout = self.layout
        col = layout.column()

        col.prop(self, "plane")
        #col.prop(self, "restriction")
        col.separator()

        col.prop(self, "influence")

    def invoke(self, context, event):
        # load custom settings
        settings_load(self)
        return self.execute(context)

    def execute(self, context):
        # initialise
        global_undo, object, bm = initialise()
        settings_write(self)
        # check cache to see if we can save time
        cached, single_loops, loops, derived, mapping = cache_read("Flatten",
            object, bm, False, False)
        if not cached:
            # order input into virtual loops
            loops = flatten_get_input(bm)
            loops = check_loops(loops, mapping, bm)

        # saving cache for faster execution next time
        if not cached:
            cache_write("Flatten", object, bm, False, False, False, loops,
                False, False)

        move = []
        for loop in loops:
            # calculate plane and position of vertices on them
            com, normal = calculate_plane(bm, loop, method=self.plane,
                object=object)
            to_move = flatten_project(bm, loop, com, normal)
            if self.restriction == 'none':
                move.append(to_move)
            else:
                move.append(to_move)
        move_verts(object, bm, False, move, self.influence)

        # cleaning up
        terminate(global_undo)

        return{'FINISHED'}


# gstretch operator
class GStretch(bpy.types.Operator):
    bl_idname = "mesh.looptools_gstretch"
    bl_label = "Gstretch"
    bl_description = "Stretch selected vertices to Grease Pencil stroke"
    bl_options = {'REGISTER', 'UNDO'}

    conversion = bpy.props.EnumProperty(name = "Conversion",
        items = (("distance", "Distance", "Set the distance between vertices "\
            "of the converted grease pencil stroke"),
            ("limit_vertices", "Limit vertices", "Set the minimum and maximum "\
            "number of vertices that converted GP strokes will have"),
            ("vertices", "Exact vertices", "Set the exact number of vertices "\
            "that converted grease pencil strokes will have. Short strokes "\
            "with few points may contain less vertices than this number."),
            ("none", "No simplification", "Convert each grease pencil point "\
            "to a vertex")),
        description = "If grease pencil strokes are converted to geometry, "\
            "use this simplification method",
        default = 'limit_vertices')
    conversion_distance = bpy.props.FloatProperty(name = "Distance",
        description = "Absolute distance between vertices along the converted "\
            "grease pencil stroke",
        default = 0.1,
        min = 0.000001,
        soft_min = 0.01,
        soft_max = 100)
    conversion_max = bpy.props.IntProperty(name = "Max Vertices",
        description = "Maximum number of vertices grease pencil strokes will "\
            "have, when they are converted to geomtery",
        default = 32,
        min = 3,
        soft_max = 500,
        update = gstretch_update_min)
    conversion_min = bpy.props.IntProperty(name = "Min Vertices",
        description = "Minimum number of vertices grease pencil strokes will "\
            "have, when they are converted to geomtery",
        default = 8,
        min = 3,
        soft_max = 500,
        update = gstretch_update_max)
    conversion_vertices = bpy.props.IntProperty(name = "Vertices",
        description = "Number of vertices grease pencil strokes will "\
            "have, when they are converted to geometry. If strokes have less "\
            "points than required, the 'Spread evenly' method is used.",
        default = 32,
        min = 3,
        soft_max = 500)
    delete_strokes = bpy.props.BoolProperty(name="Delete strokes",
        description = "Remove Grease Pencil strokes if they have been used "\
            "for Gstretch. WARNING: DOES NOT SUPPORT UNDO",
        default = False)
    influence = bpy.props.FloatProperty(name = "Influence",
        description = "Force of the tool",
        default = 100.0,
        min = 0.0,
        max = 100.0,
        precision = 1,
        subtype = 'PERCENTAGE')
    method = bpy.props.EnumProperty(name = "Method",
        items = (("project", "Project", "Project vertices onto the stroke, "\
            "using vertex normals and connected edges"),
            ("irregular", "Spread", "Distribute vertices along the full "\
            "stroke, retaining relative distances between the vertices"),
            ("regular", "Spread evenly", "Distribute vertices at regular "\
            "distances along the full stroke")),
        description = "Method of distributing the vertices over the Grease "\
            "Pencil stroke",
        default = 'regular')

    @classmethod
    def poll(cls, context):
        ob = context.active_object
        return(ob and ob.type == 'MESH' and context.mode == 'EDIT_MESH')

    def draw(self, context):
        layout = self.layout
        col = layout.column()

        col.prop(self, "method")
        col.prop(self, "delete_strokes")
        col.separator()

        col_conv = col.column(align=True)
        col_conv.prop(self, "conversion", text="")
        if self.conversion == 'distance':
            col_conv.prop(self, "conversion_distance")
        elif self.conversion == 'limit_vertices':
            row = col_conv.row(align=True)
            row.prop(self, "conversion_min", text="Min")
            row.prop(self, "conversion_max", text="Max")
        elif self.conversion == 'vertices':
            col_conv.prop(self, "conversion_vertices")
        col.separator()

        col.prop(self, "influence")

    def invoke(self, context, event):
        # flush cached strokes
        if 'Gstretch' in looptools_cache:
            looptools_cache['Gstretch']['single_loops'] = []
        # load custom settings
        settings_load(self)
        return self.execute(context)

    def execute(self, context):
        # initialise
        global_undo, object, bm = initialise()
        settings_write(self)

        # check cache to see if we can save time
        cached, safe_strokes, loops, derived, mapping = cache_read("Gstretch",
            object, bm, False, False)
        if cached:
            if safe_strokes:
                strokes = gstretch_safe_to_true_strokes(safe_strokes)
            # cached strokes were flushed (see operator's invoke function)
            elif object.grease_pencil:
                strokes = gstretch_get_strokes(object)
            else:
                derived, bm_mod = get_derived_bmesh(object, bm, context.scene)
                strokes = gstretch_get_fake_strokes(object, bm_mod, loops)
            derived, bm_mod = get_derived_bmesh(object, bm, context.scene)
        else:
            # find loops
            derived, bm_mod, loops = get_connected_input(object, bm,
                context.scene, input='selected')
            mapping = get_mapping(derived, bm, bm_mod, False, False, loops)
            loops = check_loops(loops, mapping, bm_mod)
            # get strokes
            if object.grease_pencil:
                strokes = gstretch_get_strokes(object)
            else:
                strokes = gstretch_get_fake_strokes(object, bm_mod, loops)

        # saving cache for faster execution next time
        if not cached:
            if strokes:
                safe_strokes = gstretch_true_to_safe_strokes(strokes)
            else:
                safe_strokes = []
            cache_write("Gstretch", object, bm, False, False,
                safe_strokes, loops, derived, mapping)

        # pair loops and strokes
        ls_pairs = gstretch_match_loops_strokes(loops, strokes, object, bm_mod)
        ls_pairs = gstretch_align_pairs(ls_pairs, object, bm_mod, self.method)

        move = []
        if not loops:
            # no selected geometry, convert GP to verts
            if strokes:
                move.append(gstretch_create_verts(object, bm, strokes,
                    self.method, self.conversion, self.conversion_distance,
                    self.conversion_max, self.conversion_min,
                    self.conversion_vertices))
                for stroke in strokes:
                    gstretch_erase_stroke(stroke, context)
        elif ls_pairs:
            for (loop, stroke) in ls_pairs:
                move.append(gstretch_calculate_verts(loop, stroke, object,
                    bm_mod, self.method))
                if self.delete_strokes:
                    if type(stroke) != bpy.types.GPencilStroke:
                        # in case of cached fake stroke, get the real one
                        if object.grease_pencil:
                            strokes = gstretch_get_strokes(object)
                            ls_pairs = gstretch_match_loops_strokes(loops,
                                strokes, object, bm_mod)
                            ls_pairs = gstretch_align_pairs(ls_pairs, object,
                                bm_mod, self.method)
                            for (l, s) in ls_pairs:
                                if l == loop:
                                    stroke = s
                                    break
                    gstretch_erase_stroke(stroke, context)

        # move vertices to new locations
        bmesh.update_edit_mesh(object.data, tessface=True,
                destructive=True)
        move_verts(object, bm, mapping, move, self.influence)

        # cleaning up
        if derived:
            bm_mod.free()
        terminate(global_undo)

        return{'FINISHED'}


# relax operator
class Relax(bpy.types.Operator):
    bl_idname = "mesh.looptools_relax"
    bl_label = "Relax"
    bl_description = "Relax the loop, so it is smoother"
    bl_options = {'REGISTER', 'UNDO'}

    input = bpy.props.EnumProperty(name = "Input",
        items = (("all", "Parallel (all)", "Also use non-selected "\
                "parallel loops as input"),
            ("selected", "Selection","Only use selected vertices as input")),
        description = "Loops that are relaxed",
        default = 'selected')
    interpolation = bpy.props.EnumProperty(name = "Interpolation",
        items = (("cubic", "Cubic", "Natural cubic spline, smooth results"),
            ("linear", "Linear", "Simple and fast linear algorithm")),
        description = "Algorithm used for interpolation",
        default = 'cubic')
    iterations = bpy.props.EnumProperty(name = "Iterations",
        items = (("1", "1", "One"),
            ("3", "3", "Three"),
            ("5", "5", "Five"),
            ("10", "10", "Ten"),
            ("25", "25", "Twenty-five")),
        description = "Number of times the loop is relaxed",
        default = "1")
    regular = bpy.props.BoolProperty(name = "Regular",
        description = "Distribute vertices at constant distances along the" \
            "loop",
        default = True)

    @classmethod
    def poll(cls, context):
        ob = context.active_object
        return(ob and ob.type == 'MESH' and context.mode == 'EDIT_MESH')

    def draw(self, context):
        layout = self.layout
        col = layout.column()

        col.prop(self, "interpolation")
        col.prop(self, "input")
        col.prop(self, "iterations")
        col.prop(self, "regular")

    def invoke(self, context, event):
        # load custom settings
        settings_load(self)
        return self.execute(context)

    def execute(self, context):
        # initialise
        global_undo, object, bm = initialise()
        settings_write(self)
        # check cache to see if we can save time
        cached, single_loops, loops, derived, mapping = cache_read("Relax",
            object, bm, self.input, False)
        if cached:
            derived, bm_mod = get_derived_bmesh(object, bm, context.scene)
        else:
            # find loops
            derived, bm_mod, loops = get_connected_input(object, bm,
                context.scene, self.input)
            mapping = get_mapping(derived, bm, bm_mod, False, False, loops)
            loops = check_loops(loops, mapping, bm_mod)
        knots, points = relax_calculate_knots(loops)

        # saving cache for faster execution next time
        if not cached:
            cache_write("Relax", object, bm, self.input, False, False, loops,
                derived, mapping)

        for iteration in range(int(self.iterations)):
            # calculate splines and new positions
            tknots, tpoints = relax_calculate_t(bm_mod, knots, points,
                self.regular)
            splines = []
            for i in range(len(knots)):
                splines.append(calculate_splines(self.interpolation, bm_mod,
                    tknots[i], knots[i]))
            move = [relax_calculate_verts(bm_mod, self.interpolation,
                tknots, knots, tpoints, points, splines)]
            move_verts(object, bm, mapping, move, -1)

        # cleaning up
        if derived:
            bm_mod.free()
        terminate(global_undo)

        return{'FINISHED'}


# space operator
class Space(bpy.types.Operator):
    bl_idname = "mesh.looptools_space"
    bl_label = "Space"
    bl_description = "Space the vertices in a regular distrubtion on the loop"
    bl_options = {'REGISTER', 'UNDO'}

    influence = bpy.props.FloatProperty(name = "Influence",
        description = "Force of the tool",
        default = 100.0,
        min = 0.0,
        max = 100.0,
        precision = 1,
        subtype = 'PERCENTAGE')
    input = bpy.props.EnumProperty(name = "Input",
        items = (("all", "Parallel (all)", "Also use non-selected "\
                "parallel loops as input"),
            ("selected", "Selection","Only use selected vertices as input")),
        description = "Loops that are spaced",
        default = 'selected')
    interpolation = bpy.props.EnumProperty(name = "Interpolation",
        items = (("cubic", "Cubic", "Natural cubic spline, smooth results"),
            ("linear", "Linear", "Vertices are projected on existing edges")),
        description = "Algorithm used for interpolation",
        default = 'cubic')

    @classmethod
    def poll(cls, context):
        ob = context.active_object
        return(ob and ob.type == 'MESH' and context.mode == 'EDIT_MESH')

    def draw(self, context):
        layout = self.layout
        col = layout.column()

        col.prop(self, "interpolation")
        col.prop(self, "input")
        col.separator()

        col.prop(self, "influence")

    def invoke(self, context, event):
        # load custom settings
        settings_load(self)
        return self.execute(context)

    def execute(self, context):
        # initialise
        global_undo, object, bm = initialise()
        settings_write(self)
        # check cache to see if we can save time
        cached, single_loops, loops, derived, mapping = cache_read("Space",
            object, bm, self.input, False)
        if cached:
            derived, bm_mod = get_derived_bmesh(object, bm, context.scene)
        else:
            # find loops
            derived, bm_mod, loops = get_connected_input(object, bm,
                context.scene, self.input)
            mapping = get_mapping(derived, bm, bm_mod, False, False, loops)
            loops = check_loops(loops, mapping, bm_mod)

        # saving cache for faster execution next time
        if not cached:
            cache_write("Space", object, bm, self.input, False, False, loops,
                derived, mapping)

        move = []
        for loop in loops:
            # calculate splines and new positions
            if loop[1]: # circular
                loop[0].append(loop[0][0])
            tknots, tpoints = space_calculate_t(bm_mod, loop[0][:])
            splines = calculate_splines(self.interpolation, bm_mod,
                tknots, loop[0][:])
            move.append(space_calculate_verts(bm_mod, self.interpolation,
                tknots, tpoints, loop[0][:-1], splines))
        # move vertices to new locations
        move_verts(object, bm, mapping, move, self.influence)

        # cleaning up
        if derived:
            bm_mod.free()
        terminate(global_undo)

        return{'FINISHED'}


##########################################
####### GUI and registration #############
##########################################

# menu containing all tools
class VIEW3D_MT_edit_mesh_looptools(bpy.types.Menu):
    bl_label = "LoopTools"

    def draw(self, context):
        layout = self.layout

        layout.operator("mesh.looptools_bridge", text="Bridge").loft = False
        layout.operator("mesh.looptools_circle")
        layout.operator("mesh.looptools_curve")
        layout.operator("mesh.looptools_flatten")
        layout.operator("mesh.looptools_gstretch")
        layout.operator("mesh.looptools_bridge", text="Loft").loft = True
        layout.operator("mesh.looptools_relax")
        layout.operator("mesh.looptools_space")


# panel containing all tools
class VIEW3D_PT_tools_looptools(bpy.types.Panel):
    bl_space_type = 'VIEW_3D'
    bl_region_type = 'TOOLS'
    bl_category = 'Tools'
    bl_context = "mesh_edit"
    bl_label = "LoopTools"
    bl_options = {'DEFAULT_CLOSED'}

    def draw(self, context):
        layout = self.layout
        col = layout.column(align=True)
        lt = context.window_manager.looptools

        # bridge - first line
        split = col.split(percentage=0.15, align=True)
        if lt.display_bridge:
            split.prop(lt, "display_bridge", text="", icon='DOWNARROW_HLT')
        else:
            split.prop(lt, "display_bridge", text="", icon='RIGHTARROW')
        split.operator("mesh.looptools_bridge", text="Bridge").loft = False
        # bridge - settings
        if lt.display_bridge:
            box = col.column(align=True).box().column()
            #box.prop(self, "mode")

            # top row
            col_top = box.column(align=True)
            row = col_top.row(align=True)
            col_left = row.column(align=True)
            col_right = row.column(align=True)
            col_right.active = lt.bridge_segments != 1
            col_left.prop(lt, "bridge_segments")
            col_right.prop(lt, "bridge_min_width", text="")
            # bottom row
            bottom_left = col_left.row()
            bottom_left.active = lt.bridge_segments != 1
            bottom_left.prop(lt, "bridge_interpolation", text="")
            bottom_right = col_right.row()
            bottom_right.active = lt.bridge_interpolation == 'cubic'
            bottom_right.prop(lt, "bridge_cubic_strength")
            # boolean properties
            col_top.prop(lt, "bridge_remove_faces")

            # override properties
            col_top.separator()
            row = box.row(align = True)
            row.prop(lt, "bridge_twist")
            row.prop(lt, "bridge_reverse")

        # circle - first line
        split = col.split(percentage=0.15, align=True)
        if lt.display_circle:
            split.prop(lt, "display_circle", text="", icon='DOWNARROW_HLT')
        else:
            split.prop(lt, "display_circle", text="", icon='RIGHTARROW')
        split.operator("mesh.looptools_circle")
        # circle - settings
        if lt.display_circle:
            box = col.column(align=True).box().column()
            box.prop(lt, "circle_fit")
            box.separator()

            box.prop(lt, "circle_flatten")
            row = box.row(align=True)
            row.prop(lt, "circle_custom_radius")
            row_right = row.row(align=True)
            row_right.active = lt.circle_custom_radius
            row_right.prop(lt, "circle_radius", text="")
            box.prop(lt, "circle_regular")
            box.separator()

            box.prop(lt, "circle_influence")

        # curve - first line
        split = col.split(percentage=0.15, align=True)
        if lt.display_curve:
            split.prop(lt, "display_curve", text="", icon='DOWNARROW_HLT')
        else:
            split.prop(lt, "display_curve", text="", icon='RIGHTARROW')
        split.operator("mesh.looptools_curve")
        # curve - settings
        if lt.display_curve:
            box = col.column(align=True).box().column()
            box.prop(lt, "curve_interpolation")
            box.prop(lt, "curve_restriction")
            box.prop(lt, "curve_boundaries")
            box.prop(lt, "curve_regular")
            box.separator()

            box.prop(lt, "curve_influence")

        # flatten - first line
        split = col.split(percentage=0.15, align=True)
        if lt.display_flatten:
            split.prop(lt, "display_flatten", text="", icon='DOWNARROW_HLT')
        else:
            split.prop(lt, "display_flatten", text="", icon='RIGHTARROW')
        split.operator("mesh.looptools_flatten")
        # flatten - settings
        if lt.display_flatten:
            box = col.column(align=True).box().column()
            box.prop(lt, "flatten_plane")
            #box.prop(lt, "flatten_restriction")
            box.separator()

            box.prop(lt, "flatten_influence")

        # gstretch - first line
        split = col.split(percentage=0.15, align=True)
        if lt.display_gstretch:
            split.prop(lt, "display_gstretch", text="", icon='DOWNARROW_HLT')
        else:
            split.prop(lt, "display_gstretch", text="", icon='RIGHTARROW')
        split.operator("mesh.looptools_gstretch")
        # gstretch settings
        if lt.display_gstretch:
            box = col.column(align=True).box().column()
            box.prop(lt, "gstretch_method")
            box.prop(lt, "gstretch_delete_strokes")
            box.separator()

            col_conv = box.column(align=True)
            col_conv.prop(lt, "gstretch_conversion", text="")
            if lt.gstretch_conversion == 'distance':
                col_conv.prop(lt, "gstretch_conversion_distance")
            elif lt.gstretch_conversion == 'limit_vertices':
                row = col_conv.row(align=True)
                row.prop(lt, "gstretch_conversion_min", text="Min")
                row.prop(lt, "gstretch_conversion_max", text="Max")
            elif lt.gstretch_conversion == 'vertices':
                col_conv.prop(lt, "gstretch_conversion_vertices")
            box.separator()

            box.prop(lt, "gstretch_influence")

        # loft - first line
        split = col.split(percentage=0.15, align=True)
        if lt.display_loft:
            split.prop(lt, "display_loft", text="", icon='DOWNARROW_HLT')
        else:
            split.prop(lt, "display_loft", text="", icon='RIGHTARROW')
        split.operator("mesh.looptools_bridge", text="Loft").loft = True
        # loft - settings
        if lt.display_loft:
            box = col.column(align=True).box().column()
            #box.prop(self, "mode")

            # top row
            col_top = box.column(align=True)
            row = col_top.row(align=True)
            col_left = row.column(align=True)
            col_right = row.column(align=True)
            col_right.active = lt.bridge_segments != 1
            col_left.prop(lt, "bridge_segments")
            col_right.prop(lt, "bridge_min_width", text="")
            # bottom row
            bottom_left = col_left.row()
            bottom_left.active = lt.bridge_segments != 1
            bottom_left.prop(lt, "bridge_interpolation", text="")
            bottom_right = col_right.row()
            bottom_right.active = lt.bridge_interpolation == 'cubic'
            bottom_right.prop(lt, "bridge_cubic_strength")
            # boolean properties
            col_top.prop(lt, "bridge_remove_faces")
            col_top.prop(lt, "bridge_loft_loop")

            # override properties
            col_top.separator()
            row = box.row(align = True)
            row.prop(lt, "bridge_twist")
            row.prop(lt, "bridge_reverse")

        # relax - first line
        split = col.split(percentage=0.15, align=True)
        if lt.display_relax:
            split.prop(lt, "display_relax", text="", icon='DOWNARROW_HLT')
        else:
            split.prop(lt, "display_relax", text="", icon='RIGHTARROW')
        split.operator("mesh.looptools_relax")
        # relax - settings
        if lt.display_relax:
            box = col.column(align=True).box().column()
            box.prop(lt, "relax_interpolation")
            box.prop(lt, "relax_input")
            box.prop(lt, "relax_iterations")
            box.prop(lt, "relax_regular")

        # space - first line
        split = col.split(percentage=0.15, align=True)
        if lt.display_space:
            split.prop(lt, "display_space", text="", icon='DOWNARROW_HLT')
        else:
            split.prop(lt, "display_space", text="", icon='RIGHTARROW')
        split.operator("mesh.looptools_space")
        # space - settings
        if lt.display_space:
            box = col.column(align=True).box().column()
            box.prop(lt, "space_interpolation")
            box.prop(lt, "space_input")
            box.separator()

            box.prop(lt, "space_influence")


# property group containing all properties for the gui in the panel
class LoopToolsProps(bpy.types.PropertyGroup):
    """
    Fake module like class
    bpy.context.window_manager.looptools
    """

    # general display properties
    display_bridge = bpy.props.BoolProperty(name = "Bridge settings",
        description = "Display settings of the Bridge tool",
        default = False)
    display_circle = bpy.props.BoolProperty(name = "Circle settings",
        description = "Display settings of the Circle tool",
        default = False)
    display_curve = bpy.props.BoolProperty(name = "Curve settings",
        description = "Display settings of the Curve tool",
        default = False)
    display_flatten = bpy.props.BoolProperty(name = "Flatten settings",
        description = "Display settings of the Flatten tool",
        default = False)
    display_gstretch = bpy.props.BoolProperty(name = "Gstretch settings",
        description = "Display settings of the Gstretch tool",
        default = False)
    display_loft = bpy.props.BoolProperty(name = "Loft settings",
        description = "Display settings of the Loft tool",
        default = False)
    display_relax = bpy.props.BoolProperty(name = "Relax settings",
        description = "Display settings of the Relax tool",
        default = False)
    display_space = bpy.props.BoolProperty(name = "Space settings",
        description = "Display settings of the Space tool",
        default = False)

    # bridge properties
    bridge_cubic_strength = bpy.props.FloatProperty(name = "Strength",
        description = "Higher strength results in more fluid curves",
        default = 1.0,
        soft_min = -3.0,
        soft_max = 3.0)
    bridge_interpolation = bpy.props.EnumProperty(name = "Interpolation mode",
        items = (('cubic', "Cubic", "Gives curved results"),
            ('linear', "Linear", "Basic, fast, straight interpolation")),
        description = "Interpolation mode: algorithm used when creating "\
            "segments",
        default = 'cubic')
    bridge_loft = bpy.props.BoolProperty(name = "Loft",
        description = "Loft multiple loops, instead of considering them as "\
            "a multi-input for bridging",
        default = False)
    bridge_loft_loop = bpy.props.BoolProperty(name = "Loop",
        description = "Connect the first and the last loop with each other",
        default = False)
    bridge_min_width = bpy.props.IntProperty(name = "Minimum width",
        description = "Segments with an edge smaller than this are merged "\
            "(compared to base edge)",
        default = 0,
        min = 0,
        max = 100,
        subtype = 'PERCENTAGE')
    bridge_mode = bpy.props.EnumProperty(name = "Mode",
        items = (('basic', "Basic", "Fast algorithm"),
                 ('shortest', "Shortest edge", "Slower algorithm with " \
                                               "better vertex matching")),
        description = "Algorithm used for bridging",
        default = 'shortest')
    bridge_remove_faces = bpy.props.BoolProperty(name = "Remove faces",
        description = "Remove faces that are internal after bridging",
        default = True)
    bridge_reverse = bpy.props.BoolProperty(name = "Reverse",
        description = "Manually override the direction in which the loops "\
                      "are bridged. Only use if the tool gives the wrong " \
                      "result",
        default = False)
    bridge_segments = bpy.props.IntProperty(name = "Segments",
        description = "Number of segments used to bridge the gap "\
            "(0 = automatic)",
        default = 1,
        min = 0,
        soft_max = 20)
    bridge_twist = bpy.props.IntProperty(name = "Twist",
        description = "Twist what vertices are connected to each other",
        default = 0)

    # circle properties
    circle_custom_radius = bpy.props.BoolProperty(name = "Radius",
        description = "Force a custom radius",
        default = False)
    circle_fit = bpy.props.EnumProperty(name = "Method",
        items = (("best", "Best fit", "Non-linear least squares"),
            ("inside", "Fit inside","Only move vertices towards the center")),
        description = "Method used for fitting a circle to the vertices",
        default = 'best')
    circle_flatten = bpy.props.BoolProperty(name = "Flatten",
        description = "Flatten the circle, instead of projecting it on the " \
            "mesh",
        default = True)
    circle_influence = bpy.props.FloatProperty(name = "Influence",
        description = "Force of the tool",
        default = 100.0,
        min = 0.0,
        max = 100.0,
        precision = 1,
        subtype = 'PERCENTAGE')
    circle_radius = bpy.props.FloatProperty(name = "Radius",
        description = "Custom radius for circle",
        default = 1.0,
        min = 0.0,
        soft_max = 1000.0)
    circle_regular = bpy.props.BoolProperty(name = "Regular",
        description = "Distribute vertices at constant distances along the " \
            "circle",
        default = True)

    # curve properties
    curve_boundaries = bpy.props.BoolProperty(name = "Boundaries",
        description = "Limit the tool to work within the boundaries of the "\
            "selected vertices",
        default = False)
    curve_influence = bpy.props.FloatProperty(name = "Influence",
        description = "Force of the tool",
        default = 100.0,
        min = 0.0,
        max = 100.0,
        precision = 1,
        subtype = 'PERCENTAGE')
    curve_interpolation = bpy.props.EnumProperty(name = "Interpolation",
        items = (("cubic", "Cubic", "Natural cubic spline, smooth results"),
            ("linear", "Linear", "Simple and fast linear algorithm")),
        description = "Algorithm used for interpolation",
        default = 'cubic')
    curve_regular = bpy.props.BoolProperty(name = "Regular",
        description = "Distribute vertices at constant distances along the " \
            "curve",
        default = True)
    curve_restriction = bpy.props.EnumProperty(name = "Restriction",
        items = (("none", "None", "No restrictions on vertex movement"),
            ("extrude", "Extrude only","Only allow extrusions (no "\
                "indentations)"),
            ("indent", "Indent only", "Only allow indentation (no "\
                "extrusions)")),
        description = "Restrictions on how the vertices can be moved",
        default = 'none')

    # flatten properties
    flatten_influence = bpy.props.FloatProperty(name = "Influence",
        description = "Force of the tool",
        default = 100.0,
        min = 0.0,
        max = 100.0,
        precision = 1,
        subtype = 'PERCENTAGE')
    flatten_plane = bpy.props.EnumProperty(name = "Plane",
        items = (("best_fit", "Best fit", "Calculate a best fitting plane"),
            ("normal", "Normal", "Derive plane from averaging vertex "\
            "normals"),
            ("view", "View", "Flatten on a plane perpendicular to the "\
            "viewing angle")),
        description = "Plane on which vertices are flattened",
        default = 'best_fit')
    flatten_restriction = bpy.props.EnumProperty(name = "Restriction",
        items = (("none", "None", "No restrictions on vertex movement"),
            ("bounding_box", "Bounding box", "Vertices are restricted to "\
            "movement inside the bounding box of the selection")),
        description = "Restrictions on how the vertices can be moved",
        default = 'none')

    # gstretch properties
    gstretch_conversion = bpy.props.EnumProperty(name = "Conversion",
        items = (("distance", "Distance", "Set the distance between vertices "\
            "of the converted grease pencil stroke"),
            ("limit_vertices", "Limit vertices", "Set the minimum and maximum "\
            "number of vertices that converted GP strokes will have"),
            ("vertices", "Exact vertices", "Set the exact number of vertices "\
            "that converted grease pencil strokes will have. Short strokes "\
            "with few points may contain less vertices than this number."),
            ("none", "No simplification", "Convert each grease pencil point "\
            "to a vertex")),
        description = "If grease pencil strokes are converted to geometry, "\
            "use this simplification method",
        default = 'limit_vertices')
    gstretch_conversion_distance = bpy.props.FloatProperty(name = "Distance",
        description = "Absolute distance between vertices along the converted "\
            "grease pencil stroke",
        default = 0.1,
        min = 0.000001,
        soft_min = 0.01,
        soft_max = 100)
    gstretch_conversion_max = bpy.props.IntProperty(name = "Max Vertices",
        description = "Maximum number of vertices grease pencil strokes will "\
            "have, when they are converted to geomtery",
        default = 32,
        min = 3,
        soft_max = 500,
        update = gstretch_update_min)
    gstretch_conversion_min = bpy.props.IntProperty(name = "Min Vertices",
        description = "Minimum number of vertices grease pencil strokes will "\
            "have, when they are converted to geomtery",
        default = 8,
        min = 3,
        soft_max = 500,
        update = gstretch_update_max)
    gstretch_conversion_vertices = bpy.props.IntProperty(name = "Vertices",
        description = "Number of vertices grease pencil strokes will "\
            "have, when they are converted to geometry. If strokes have less "\
            "points than required, the 'Spread evenly' method is used.",
        default = 32,
        min = 3,
        soft_max = 500)
    gstretch_delete_strokes = bpy.props.BoolProperty(name="Delete strokes",
        description = "Remove Grease Pencil strokes if they have been used "\
            "for Gstretch. WARNING: DOES NOT SUPPORT UNDO",
        default = False)
    gstretch_influence = bpy.props.FloatProperty(name = "Influence",
        description = "Force of the tool",
        default = 100.0,
        min = 0.0,
        max = 100.0,
        precision = 1,
        subtype = 'PERCENTAGE')
    gstretch_method = bpy.props.EnumProperty(name = "Method",
        items = (("project", "Project", "Project vertices onto the stroke, "\
            "using vertex normals and connected edges"),
            ("irregular", "Spread", "Distribute vertices along the full "\
            "stroke, retaining relative distances between the vertices"),
            ("regular", "Spread evenly", "Distribute vertices at regular "\
            "distances along the full stroke")),
        description = "Method of distributing the vertices over the Grease "\
            "Pencil stroke",
        default = 'regular')

    # relax properties
    relax_input = bpy.props.EnumProperty(name = "Input",
        items = (("all", "Parallel (all)", "Also use non-selected "\
                "parallel loops as input"),
            ("selected", "Selection","Only use selected vertices as input")),
        description = "Loops that are relaxed",
        default = 'selected')
    relax_interpolation = bpy.props.EnumProperty(name = "Interpolation",
        items = (("cubic", "Cubic", "Natural cubic spline, smooth results"),
            ("linear", "Linear", "Simple and fast linear algorithm")),
        description = "Algorithm used for interpolation",
        default = 'cubic')
    relax_iterations = bpy.props.EnumProperty(name = "Iterations",
        items = (("1", "1", "One"),
            ("3", "3", "Three"),
            ("5", "5", "Five"),
            ("10", "10", "Ten"),
            ("25", "25", "Twenty-five")),
        description = "Number of times the loop is relaxed",
        default = "1")
    relax_regular = bpy.props.BoolProperty(name = "Regular",
        description = "Distribute vertices at constant distances along the" \
            "loop",
        default = True)

    # space properties
    space_influence = bpy.props.FloatProperty(name = "Influence",
        description = "Force of the tool",
        default = 100.0,
        min = 0.0,
        max = 100.0,
        precision = 1,
        subtype = 'PERCENTAGE')
    space_input = bpy.props.EnumProperty(name = "Input",
        items = (("all", "Parallel (all)", "Also use non-selected "\
                "parallel loops as input"),
            ("selected", "Selection","Only use selected vertices as input")),
        description = "Loops that are spaced",
        default = 'selected')
    space_interpolation = bpy.props.EnumProperty(name = "Interpolation",
        items = (("cubic", "Cubic", "Natural cubic spline, smooth results"),
            ("linear", "Linear", "Vertices are projected on existing edges")),
        description = "Algorithm used for interpolation",
        default = 'cubic')


# draw function for integration in menus
def menu_func(self, context):
    self.layout.menu("VIEW3D_MT_edit_mesh_looptools")
    self.layout.separator()


# define classes for registration
classes = [VIEW3D_MT_edit_mesh_looptools,
    VIEW3D_PT_tools_looptools,
    LoopToolsProps,
    Bridge,
    Circle,
    Curve,
    Flatten,
    GStretch,
    Relax,
    Space]


# registering and menu integration
def register():
    for c in classes:
        bpy.utils.register_class(c)
    bpy.types.VIEW3D_MT_edit_mesh_specials.prepend(menu_func)
    bpy.types.WindowManager.looptools = bpy.props.PointerProperty(\
        type = LoopToolsProps)


# unregistering and removing menus
def unregister():
    for c in classes:
        bpy.utils.unregister_class(c)
    bpy.types.VIEW3D_MT_edit_mesh_specials.remove(menu_func)
    try:
        del bpy.types.WindowManager.looptools
    except:
        pass


if __name__ == "__main__":
    register()
