createMesh.py

# ##### BEGIN GPL LICENSE BLOCK #####
#
#  This program is free software; you can redistribute it and/or
#  modify it under the terms of the GNU General Public License
#  as published by the Free Software Foundation; either version 2
#  of the License, or (at your option) any later version.
#
#  This program is distributed in the hope that it will be useful,
#  but WITHOUT ANY WARRANTY; without even the implied warranty of
#  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
#  GNU General Public License for more details.
#
#  You should have received a copy of the GNU General Public License
#  along with this program; if not, write to the Free Software Foundation,
#  Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
#
# ##### END GPL LICENSE BLOCK #####

import bpy
from mathutils import (
        Matrix,
        Vector,
        )
from math import (
        sin, cos,
        tan, radians,
        )
from random import triangular
from bpy_extras.object_utils import AddObjectHelper, object_data_add

NARROW_UI = 180
MAX_INPUT_NUMBER = 50

GLOBAL_SCALE = 1       # 1 blender unit = X mm


# next two utility functions are stolen from import_obj.py

def unpack_list(list_of_tuples):
    l = []
    for t in list_of_tuples:
        l.extend(t)
    return l


def unpack_face_list(list_of_tuples):
    l = []
    for t in list_of_tuples:
        face = [i for i in t]

        if len(face) != 3 and len(face) != 4:
            raise RuntimeError("{0} vertices in face".format(len(face)))

        # rotate indices if the 4th is 0
        if len(face) == 4 and face[3] == 0:
            face = [face[3], face[0], face[1], face[2]]

        if len(face) == 3:
            face.append(0)

        l.extend(face)

    return l


"""
Remove Doubles takes a list on Verts and a list of Faces and
removes the doubles, much like Blender does in edit mode.
It doesn’t have the range function  but it will round the corrdinates
and remove verts that are very close together.  The function
is useful because you can perform a "Remove Doubles" with out
having to enter Edit Mode. Having to enter edit mode has the
disadvantage of not being able to interactively change the properties.
"""


def RemoveDoubles(verts, faces, Decimal_Places=4):

    new_verts = []
    new_faces = []
    dict_verts = {}
    Rounded_Verts = []

    for v in verts:
        Rounded_Verts.append([round(v[0], Decimal_Places),
                              round(v[1], Decimal_Places),
                              round(v[2], Decimal_Places)])

    for face in faces:
        new_face = []
        for vert_index in face:
            Real_co = tuple(verts[vert_index])
            Rounded_co = tuple(Rounded_Verts[vert_index])

            if Rounded_co not in dict_verts:
                dict_verts[Rounded_co] = len(dict_verts)
                new_verts.append(Real_co)
            if dict_verts[Rounded_co] not in new_face:
                new_face.append(dict_verts[Rounded_co])
        if len(new_face) == 3 or len(new_face) == 4:
            new_faces.append(new_face)

    return new_verts, new_faces


def Scale_Mesh_Verts(verts, scale_factor):
    Ret_verts = []
    for v in verts:
        Ret_verts.append([v[0] * scale_factor, v[1] * scale_factor, v[2] * scale_factor])
    return Ret_verts


# Create a matrix representing a rotation.
#
# Parameters:
#
#        * angle (float) - The angle of rotation desired.
#        * matSize (int) - The size of the rotation matrix to construct. Can be 2d, 3d, or 4d.
#        * axisFlag (string (optional)) - Possible values:
#              o "x - x-axis rotation"
#              o "y - y-axis rotation"
#              o "z - z-axis rotation"
#              o "r - arbitrary rotation around vector"
#        * axis (Vector object. (optional)) - The arbitrary axis of rotation used with "R"
#
# Returns: Matrix object.
#    A new rotation matrix.

def Simple_RotationMatrix(angle, matSize, axisFlag):
    if matSize != 4:
        print("Simple_RotationMatrix can only do 4x4")

    q = radians(angle)  # make the rotation go clockwise

    if axisFlag == 'x':
        matrix = Matrix.Rotation(q, 4, 'X')
    elif axisFlag == 'y':
        matrix = Matrix.Rotation(q, 4, 'Y')
    elif axisFlag == 'z':
        matrix = Matrix.Rotation(q, 4, 'Z')
    else:
        print("Simple_RotationMatrix can only do x y z axis")
    return matrix


# ####################################################################
#              Converter Functions For Bolt Factory
# ####################################################################

def Flat_To_Radius(FLAT):
    h = (float(FLAT) / 2) / cos(radians(30))
    return h


def Get_Phillips_Bit_Height(Bit_Dia):
    Flat_Width_half = (Bit_Dia * (0.5 / 1.82)) / 2.0
    Bit_Rad = Bit_Dia / 2.0
    x = Bit_Rad - Flat_Width_half
    y = tan(radians(60)) * x
    return float(y)


# ####################################################################
#                    Miscellaneous Utilities
# ####################################################################

# Returns a list of verts rotated by the given matrix. Used by SpinDup
def Rot_Mesh(verts, matrix):
    from mathutils import Vector
    return [(matrix @ Vector(v))[:] for v in verts]


# Returns a list of faces that has there index incremented by offset
def Copy_Faces(faces, offset):
    return [[(i + offset) for i in f] for f in faces]


# Much like Blenders built in SpinDup
def SpinDup(VERTS, FACES, DEGREE, DIVISIONS, AXIS):
    verts = []
    faces = []

    if DIVISIONS == 0:
        DIVISIONS = 1

    step = DEGREE / DIVISIONS  # set step so pieces * step = degrees in arc

    for i in range(int(DIVISIONS)):
        rotmat = Simple_RotationMatrix(step * i, 4, AXIS)  # 4x4 rotation matrix, 30d about the x axis.
        Rot = Rot_Mesh(VERTS, rotmat)
        faces.extend(Copy_Faces(FACES, len(verts)))
        verts.extend(Rot)
    return verts, faces


# Returns a list of verts that have been moved up the z axis by DISTANCE
def Move_Verts_Up_Z(VERTS, DISTANCE):
    ret = []
    for v in VERTS:
        ret.append([v[0], v[1], v[2] + DISTANCE])
    return ret


# Returns a list of verts and faces that has been mirrored in the AXIS
def Mirror_Verts_Faces(VERTS, FACES, AXIS, FLIP_POINT=0):
    ret_vert = []
    ret_face = []
    offset = len(VERTS)
    if AXIS == 'y':
        for v in VERTS:
            Delta = v[0] - FLIP_POINT
            ret_vert.append([FLIP_POINT - Delta, v[1], v[2]])
    if AXIS == 'x':
        for v in VERTS:
            Delta = v[1] - FLIP_POINT
            ret_vert.append([v[0], FLIP_POINT - Delta, v[2]])
    if AXIS == 'z':
        for v in VERTS:
            Delta = v[2] - FLIP_POINT
            ret_vert.append([v[0], v[1], FLIP_POINT - Delta])

    for f in FACES:
        fsub = []
        for i in range(len(f)):
            fsub.append(f[i] + offset)
        fsub.reverse()  # flip the order to make norm point out
        ret_face.append(fsub)

    return ret_vert, ret_face


# Returns a list of faces that
# make up an array of 4 point polygon.
def Build_Face_List_Quads(OFFSET, COLUMN, ROW, FLIP=0):
    Ret = []
    RowStart = 0
    for j in range(ROW):
        for i in range(COLUMN):
            Res1 = RowStart + i
            Res2 = RowStart + i + (COLUMN + 1)
            Res3 = RowStart + i + (COLUMN + 1) + 1
            Res4 = RowStart + i + 1
            if FLIP:
                Ret.append([OFFSET + Res1, OFFSET + Res2, OFFSET + Res3, OFFSET + Res4])
            else:
                Ret.append([OFFSET + Res4, OFFSET + Res3, OFFSET + Res2, OFFSET + Res1])
        RowStart += COLUMN + 1
    return Ret


# Returns a list of faces that makes up a fill pattern for a
# circle
def Fill_Ring_Face(OFFSET, NUM, FACE_DOWN=0):
    Ret = []
    Face = [1, 2, 0]
    TempFace = [0, 0, 0]
    # A = 0  # UNUSED
    B = 1
    C = 2
    if NUM < 3:
        return None
    for i in range(NUM - 2):
        if (i % 2):
            TempFace[0] = Face[C]
            TempFace[1] = Face[C] + 1
            TempFace[2] = Face[B]
            if FACE_DOWN:
                Ret.append([OFFSET + Face[2], OFFSET + Face[1], OFFSET + Face[0]])
            else:
                Ret.append([OFFSET + Face[0], OFFSET + Face[1], OFFSET + Face[2]])
        else:
            TempFace[0] = Face[C]
            if Face[C] == 0:
                TempFace[1] = NUM - 1
            else:
                TempFace[1] = Face[C] - 1
            TempFace[2] = Face[B]
            if FACE_DOWN:
                Ret.append([OFFSET + Face[0], OFFSET + Face[1], OFFSET + Face[2]])
            else:
                Ret.append([OFFSET + Face[2], OFFSET + Face[1], OFFSET + Face[0]])

        Face[0] = TempFace[0]
        Face[1] = TempFace[1]
        Face[2] = TempFace[2]
    return Ret


# ####################################################################
#                    Create Allen Bit
# ####################################################################

def Allen_Fill(OFFSET, FLIP=0):
    faces = []
    Lookup = [[19, 1, 0],
              [19, 2, 1],
              [19, 3, 2],
              [19, 20, 3],
              [20, 4, 3],
              [20, 5, 4],
              [20, 6, 5],
              [20, 7, 6],
              [20, 8, 7],
              [20, 9, 8],

              [20, 21, 9],

              [21, 10, 9],
              [21, 11, 10],
              [21, 12, 11],
              [21, 13, 12],
              [21, 14, 13],
              [21, 15, 14],

              [21, 22, 15],
              [22, 16, 15],
              [22, 17, 16],
              [22, 18, 17]
              ]
    for i in Lookup:
        if FLIP:
            faces.append([OFFSET + i[2], OFFSET + i[1], OFFSET + i[0]])
        else:
            faces.append([OFFSET + i[0], OFFSET + i[1], OFFSET + i[2]])

    return faces


def Allen_Bit_Dia(FLAT_DISTANCE):
    Flat_Radius = (float(FLAT_DISTANCE) / 2.0) / cos(radians(30))
    return (Flat_Radius * 1.05) * 2.0


def Allen_Bit_Dia_To_Flat(DIA):
    Flat_Radius = (DIA / 2.0) / 1.05
    return (Flat_Radius * cos(radians(30))) * 2.0


def Create_Allen_Bit(FLAT_DISTANCE, HEIGHT):
    verts = []
    faces = []
    DIV_COUNT = 36

    Flat_Radius = (float(FLAT_DISTANCE) / 2.0) / cos(radians(30))
    OUTTER_RADIUS = Flat_Radius * 1.05
    Outter_Radius_Height = Flat_Radius * (0.1 / 5.77)
    FaceStart_Outside = len(verts)
    Deg_Step = 360.0 / float(DIV_COUNT)

    for i in range(int(DIV_COUNT / 2) + 1):  # only do half and mirror later
        x = sin(radians(i * Deg_Step)) * OUTTER_RADIUS
        y = cos(radians(i * Deg_Step)) * OUTTER_RADIUS
        verts.append([x, y, 0])

    FaceStart_Inside = len(verts)

    Deg_Step = 360.0 / float(6)
    for i in range(int(6 / 2) + 1):
        x = sin(radians(i * Deg_Step)) * Flat_Radius
        y = cos(radians(i * Deg_Step)) * Flat_Radius
        verts.append([x, y, 0 - Outter_Radius_Height])

    faces.extend(Allen_Fill(FaceStart_Outside, 0))

    FaceStart_Bottom = len(verts)

    Deg_Step = 360.0 / float(6)
    for i in range(int(6 / 2) + 1):
        x = sin(radians(i * Deg_Step)) * Flat_Radius
        y = cos(radians(i * Deg_Step)) * Flat_Radius
        verts.append([x, y, 0 - HEIGHT])

    faces.extend(Build_Face_List_Quads(FaceStart_Inside, 3, 1, True))
    faces.extend(Fill_Ring_Face(FaceStart_Bottom, 4))

    M_Verts, M_Faces = Mirror_Verts_Faces(verts, faces, 'y')
    verts.extend(M_Verts)
    faces.extend(M_Faces)

    return verts, faces, OUTTER_RADIUS * 2.0


# ####################################################################
#                    Create Phillips Bit
# ####################################################################

def Phillips_Fill(OFFSET, FLIP=0):
    faces = []
    Lookup = [[0, 1, 10],
              [1, 11, 10],
              [1, 2, 11],
              [2, 12, 11],

              [2, 3, 12],
              [3, 4, 12],
              [4, 5, 12],
              [5, 6, 12],
              [6, 7, 12],

              [7, 13, 12],
              [7, 8, 13],
              [8, 14, 13],
              [8, 9, 14],

              [10, 11, 16, 15],
              [11, 12, 16],
              [12, 13, 16],
              [13, 14, 17, 16],
              [15, 16, 17, 18]
              ]
    for i in Lookup:
        if FLIP:
            if len(i) == 3:
                faces.append([OFFSET + i[2], OFFSET + i[1], OFFSET + i[0]])
            else:
                faces.append([OFFSET + i[3], OFFSET + i[2], OFFSET + i[1], OFFSET + i[0]])
        else:
            if len(i) == 3:
                faces.append([OFFSET + i[0], OFFSET + i[1], OFFSET + i[2]])
            else:
                faces.append([OFFSET + i[0], OFFSET + i[1], OFFSET + i[2], OFFSET + i[3]])
    return faces


def Create_Phillips_Bit(FLAT_DIA, FLAT_WIDTH, HEIGHT):
    verts = []
    faces = []

    DIV_COUNT = 36
    FLAT_RADIUS = FLAT_DIA * 0.5
    OUTTER_RADIUS = FLAT_RADIUS * 1.05

    Flat_Half = float(FLAT_WIDTH) / 2.0

    FaceStart_Outside = len(verts)
    Deg_Step = 360.0 / float(DIV_COUNT)
    for i in range(int(DIV_COUNT / 4) + 1):  # only do half and mirror later
        x = sin(radians(i * Deg_Step)) * OUTTER_RADIUS
        y = cos(radians(i * Deg_Step)) * OUTTER_RADIUS
        verts.append([x, y, 0])

    # FaceStart_Inside = len(verts)               # UNUSED
    verts.append([0, FLAT_RADIUS, 0])             # 10
    verts.append([Flat_Half, FLAT_RADIUS, 0])     # 11
    verts.append([Flat_Half, Flat_Half, 0])       # 12
    verts.append([FLAT_RADIUS, Flat_Half, 0])     # 13
    verts.append([FLAT_RADIUS, 0, 0])             # 14

    verts.append([0, Flat_Half, 0 - HEIGHT])          # 15
    verts.append([Flat_Half, Flat_Half, 0 - HEIGHT])  # 16
    verts.append([Flat_Half, 0, 0 - HEIGHT])          # 17

    verts.append([0, 0, 0 - HEIGHT])            # 18

    faces.extend(Phillips_Fill(FaceStart_Outside, True))

    Spin_Verts, Spin_Face = SpinDup(verts, faces, 360, 4, 'z')

    return Spin_Verts, Spin_Face, OUTTER_RADIUS * 2


# ####################################################################
#                    Create Head Types
# ####################################################################

def Max_Pan_Bit_Dia(HEAD_DIA):
    HEAD_RADIUS = HEAD_DIA * 0.5
    XRad = HEAD_RADIUS * 1.976
    return (sin(radians(10)) * XRad) * 2.0


def Create_Pan_Head(HOLE_DIA, HEAD_DIA, SHANK_DIA, HEIGHT, RAD1, RAD2, FACE_OFFSET, DIV_COUNT):

    HOLE_RADIUS = HOLE_DIA * 0.5
    HEAD_RADIUS = HEAD_DIA * 0.5
    SHANK_RADIUS = SHANK_DIA * 0.5

    verts = []
    faces = []
    Row = 0

    XRad = HEAD_RADIUS * 1.976
    ZRad = HEAD_RADIUS * 1.768
    EndRad = HEAD_RADIUS * 0.284
    EndZOffset = HEAD_RADIUS * 0.432
    HEIGHT = HEAD_RADIUS * 0.59

    """
    Dome_Rad =  5.6
    RAD_Offset = 4.9
    OtherRad = 0.8
    OtherRad_X_Offset = 4.2
    OtherRad_Z_Offset = 2.52
    XRad = 9.88
    ZRad = 8.84
    EndRad = 1.42
    EndZOffset = 2.16
    HEIGHT = 2.95
    """
    FaceStart = FACE_OFFSET

    z = cos(radians(10)) * ZRad
    verts.append([HOLE_RADIUS, 0.0, (0.0 - ZRad) + z])
    Start_Height = 0 - ((0.0 - ZRad) + z)
    Row += 1

    # for i in range(0,30,10):  was 0 to 30 more work needed to make this look good.
    for i in range(10, 30, 10):
        x = sin(radians(i)) * XRad
        z = cos(radians(i)) * ZRad
        verts.append([x, 0.0, (0.0 - ZRad) + z])
        Row += 1

    for i in range(20, 140, 10):
        x = sin(radians(i)) * EndRad
        z = cos(radians(i)) * EndRad
        if ((0.0 - EndZOffset) + z) < (0.0 - HEIGHT):
            verts.append([(HEAD_RADIUS - EndRad) + x, 0.0, 0.0 - HEIGHT])
        else:
            verts.append([(HEAD_RADIUS - EndRad) + x, 0.0, (0.0 - EndZOffset) + z])
        Row += 1

    verts.append([SHANK_RADIUS, 0.0, (0.0 - HEIGHT)])
    Row += 1

    verts.append([SHANK_RADIUS, 0.0, (0.0 - HEIGHT) - Start_Height])
    Row += 1

    sVerts, sFaces = SpinDup(verts, faces, 360, DIV_COUNT, 'z')
    sVerts.extend(verts)  # add the start verts to the Spin verts to complete the loop

    faces.extend(Build_Face_List_Quads(FaceStart, Row - 1, DIV_COUNT))

    # Global_Head_Height = HEIGHT  # UNUSED

    return Move_Verts_Up_Z(sVerts, Start_Height), faces, HEIGHT


def Create_Dome_Head(HOLE_DIA, HEAD_DIA, SHANK_DIA, HEIGHT, RAD1, RAD2, FACE_OFFSET, DIV_COUNT):
    HOLE_RADIUS = HOLE_DIA * 0.5
    HEAD_RADIUS = HEAD_DIA * 0.5
    SHANK_RADIUS = SHANK_DIA * 0.5

    verts = []
    faces = []
    Row = 0
    # Dome_Rad =  HEAD_RADIUS * (1.0/1.75)

    Dome_Rad = HEAD_RADIUS * 1.12
    # Head_Height = HEAD_RADIUS * 0.78
    RAD_Offset = HEAD_RADIUS * 0.98
    Dome_Height = HEAD_RADIUS * 0.64
    OtherRad = HEAD_RADIUS * 0.16
    OtherRad_X_Offset = HEAD_RADIUS * 0.84
    OtherRad_Z_Offset = HEAD_RADIUS * 0.504

    """
    Dome_Rad =  5.6
    RAD_Offset = 4.9
    Dome_Height = 3.2
    OtherRad = 0.8
    OtherRad_X_Offset = 4.2
    OtherRad_Z_Offset = 2.52
   """

    FaceStart = FACE_OFFSET

    verts.append([HOLE_RADIUS, 0.0, 0.0])
    Row += 1

    for i in range(0, 60, 10):
        x = sin(radians(i)) * Dome_Rad
        z = cos(radians(i)) * Dome_Rad
        if ((0.0 - RAD_Offset) + z) <= 0:
            verts.append([x, 0.0, (0.0 - RAD_Offset) + z])
            Row += 1

    for i in range(60, 160, 10):
        x = sin(radians(i)) * OtherRad
        z = cos(radians(i)) * OtherRad
        z = (0.0 - OtherRad_Z_Offset) + z
        if z < (0.0 - Dome_Height):
            z = (0.0 - Dome_Height)
        verts.append([OtherRad_X_Offset + x, 0.0, z])
        Row += 1

    verts.append([SHANK_RADIUS, 0.0, (0.0 - Dome_Height)])
    Row += 1

    sVerts, sFaces = SpinDup(verts, faces, 360, DIV_COUNT, 'z')
    sVerts.extend(verts)   # add the start verts to the Spin verts to complete the loop

    faces.extend(Build_Face_List_Quads(FaceStart, Row - 1, DIV_COUNT))

    return sVerts, faces, Dome_Height


def Create_CounterSink_Head(HOLE_DIA, HEAD_DIA, SHANK_DIA, HEIGHT, RAD1, DIV_COUNT):

    HOLE_RADIUS = HOLE_DIA * 0.5
    HEAD_RADIUS = HEAD_DIA * 0.5
    SHANK_RADIUS = SHANK_DIA * 0.5

    verts = []
    faces = []
    Row = 0

    # HEAD_RADIUS = (HEIGHT/tan(radians(60))) + SHANK_RADIUS
    HEIGHT = tan(radians(60)) * (HEAD_RADIUS - SHANK_RADIUS)

    FaceStart = len(verts)

    verts.append([HOLE_RADIUS, 0.0, 0.0])
    Row += 1

    # rad
    for i in range(0, 100, 10):
        x = sin(radians(i)) * RAD1
        z = cos(radians(i)) * RAD1
        verts.append([(HEAD_RADIUS - RAD1) + x, 0.0, (0.0 - RAD1) + z])
        Row += 1

    verts.append([SHANK_RADIUS, 0.0, 0.0 - HEIGHT])
    Row += 1

    sVerts, sFaces = SpinDup(verts, faces, 360, DIV_COUNT, 'z')
    sVerts.extend(verts)    # add the start verts to the Spin verts to complete the loop

    faces.extend(Build_Face_List_Quads(FaceStart, Row - 1, DIV_COUNT))

    return sVerts, faces, HEIGHT


def Create_Cap_Head(HOLE_DIA, HEAD_DIA, SHANK_DIA, HEIGHT, RAD1, RAD2, DIV_COUNT):

    HOLE_RADIUS = HOLE_DIA * 0.5
    HEAD_RADIUS = HEAD_DIA * 0.5
    SHANK_RADIUS = SHANK_DIA * 0.5

    verts = []
    faces = []
    Row = 0
    BEVEL = HEIGHT * 0.01

    FaceStart = len(verts)

    verts.append([HOLE_RADIUS, 0.0, 0.0])
    Row += 1

    # rad
    for i in range(0, 100, 10):
        x = sin(radians(i)) * RAD1
        z = cos(radians(i)) * RAD1
        verts.append([(HEAD_RADIUS - RAD1) + x, 0.0, (0.0 - RAD1) + z])
        Row += 1

    verts.append([HEAD_RADIUS, 0.0, 0.0 - HEIGHT + BEVEL])
    Row += 1

    verts.append([HEAD_RADIUS - BEVEL, 0.0, 0.0 - HEIGHT])
    Row += 1

    # rad2
    for i in range(0, 100, 10):
        x = sin(radians(i)) * RAD2
        z = cos(radians(i)) * RAD2
        verts.append([(SHANK_RADIUS + RAD2) - x, 0.0, (0.0 - HEIGHT - RAD2) + z])
        Row += 1

    sVerts, sFaces = SpinDup(verts, faces, 360, DIV_COUNT, 'z')
    sVerts.extend(verts)    # add the start verts to the Spin verts to complete the loop

    faces.extend(Build_Face_List_Quads(FaceStart, Row - 1, DIV_COUNT))

    return sVerts, faces, HEIGHT + RAD2


def Create_Hex_Head(FLAT, HOLE_DIA, SHANK_DIA, HEIGHT):

    verts = []
    faces = []
    HOLE_RADIUS = HOLE_DIA * 0.5
    Half_Flat = FLAT / 2
    TopBevelRadius = Half_Flat - (Half_Flat * (0.05 / 8))
    Undercut_Height = (Half_Flat * (0.05 / 8))
    Shank_Bevel = (Half_Flat * (0.05 / 8))
    Flat_Height = HEIGHT - Undercut_Height - Shank_Bevel
    # Undercut_Height = 5
    SHANK_RADIUS = SHANK_DIA / 2
    Row = 0

    verts.append([0.0, 0.0, 0.0])

    FaceStart = len(verts)

    # inner hole
    x = sin(radians(0)) * HOLE_RADIUS
    y = cos(radians(0)) * HOLE_RADIUS
    verts.append([x, y, 0.0])

    x = sin(radians(60 / 6)) * HOLE_RADIUS
    y = cos(radians(60 / 6)) * HOLE_RADIUS
    verts.append([x, y, 0.0])

    x = sin(radians(60 / 3)) * HOLE_RADIUS
    y = cos(radians(60 / 3)) * HOLE_RADIUS
    verts.append([x, y, 0.0])

    x = sin(radians(60 / 2)) * HOLE_RADIUS
    y = cos(radians(60 / 2)) * HOLE_RADIUS
    verts.append([x, y, 0.0])
    Row += 1

    # bevel
    x = sin(radians(0)) * TopBevelRadius
    y = cos(radians(0)) * TopBevelRadius
    vec1 = Vector([x, y, 0.0])
    verts.append([x, y, 0.0])

    x = sin(radians(60 / 6)) * TopBevelRadius
    y = cos(radians(60 / 6)) * TopBevelRadius
    vec2 = Vector([x, y, 0.0])
    verts.append([x, y, 0.0])

    x = sin(radians(60 / 3)) * TopBevelRadius
    y = cos(radians(60 / 3)) * TopBevelRadius
    vec3 = Vector([x, y, 0.0])
    verts.append([x, y, 0.0])

    x = sin(radians(60 / 2)) * TopBevelRadius
    y = cos(radians(60 / 2)) * TopBevelRadius
    vec4 = Vector([x, y, 0.0])
    verts.append([x, y, 0.0])
    Row += 1

    # Flats
    x = tan(radians(0)) * Half_Flat
    dvec = vec1 - Vector([x, Half_Flat, 0.0])
    verts.append([x, Half_Flat, -dvec.length])

    x = tan(radians(60 / 6)) * Half_Flat
    dvec = vec2 - Vector([x, Half_Flat, 0.0])
    verts.append([x, Half_Flat, -dvec.length])

    x = tan(radians(60 / 3)) * Half_Flat
    dvec = vec3 - Vector([x, Half_Flat, 0.0])
    Lowest_Point = -dvec.length
    verts.append([x, Half_Flat, -dvec.length])

    x = tan(radians(60 / 2)) * Half_Flat
    dvec = vec4 - Vector([x, Half_Flat, 0.0])
    Lowest_Point = -dvec.length
    verts.append([x, Half_Flat, -dvec.length])
    Row += 1

    # down Bits Tri
    x = tan(radians(0)) * Half_Flat
    verts.append([x, Half_Flat, Lowest_Point])

    x = tan(radians(60 / 6)) * Half_Flat
    verts.append([x, Half_Flat, Lowest_Point])

    x = tan(radians(60 / 3)) * Half_Flat
    verts.append([x, Half_Flat, Lowest_Point])

    x = tan(radians(60 / 2)) * Half_Flat
    verts.append([x, Half_Flat, Lowest_Point])
    Row += 1

    # down Bits

    x = tan(radians(0)) * Half_Flat
    verts.append([x, Half_Flat, -Flat_Height])

    x = tan(radians(60 / 6)) * Half_Flat
    verts.append([x, Half_Flat, -Flat_Height])

    x = tan(radians(60 / 3)) * Half_Flat
    verts.append([x, Half_Flat, -Flat_Height])

    x = tan(radians(60 / 2)) * Half_Flat
    verts.append([x, Half_Flat, -Flat_Height])
    Row += 1

    # Under cut
    x = sin(radians(0)) * Half_Flat
    y = cos(radians(0)) * Half_Flat
    vec1 = Vector([x, y, 0.0])
    verts.append([x, y, -Flat_Height])

    x = sin(radians(60 / 6)) * Half_Flat
    y = cos(radians(60 / 6)) * Half_Flat
    vec2 = Vector([x, y, 0.0])
    verts.append([x, y, -Flat_Height])

    x = sin(radians(60 / 3)) * Half_Flat
    y = cos(radians(60 / 3)) * Half_Flat
    vec3 = Vector([x, y, 0.0])
    verts.append([x, y, -Flat_Height])

    x = sin(radians(60 / 2)) * Half_Flat
    y = cos(radians(60 / 2)) * Half_Flat
    vec3 = Vector([x, y, 0.0])
    verts.append([x, y, -Flat_Height])
    Row += 1

    # Under cut down bit
    x = sin(radians(0)) * Half_Flat
    y = cos(radians(0)) * Half_Flat
    vec1 = Vector([x, y, 0.0])
    verts.append([x, y, -Flat_Height - Undercut_Height])

    x = sin(radians(60 / 6)) * Half_Flat
    y = cos(radians(60 / 6)) * Half_Flat
    vec2 = Vector([x, y, 0.0])
    verts.append([x, y, -Flat_Height - Undercut_Height])

    x = sin(radians(60 / 3)) * Half_Flat
    y = cos(radians(60 / 3)) * Half_Flat
    vec3 = Vector([x, y, 0.0])
    verts.append([x, y, -Flat_Height - Undercut_Height])

    x = sin(radians(60 / 2)) * Half_Flat
    y = cos(radians(60 / 2)) * Half_Flat
    vec3 = Vector([x, y, 0.0])
    verts.append([x, y, -Flat_Height - Undercut_Height])
    Row += 1

    # Under cut to Shank BEVEL
    x = sin(radians(0)) * (SHANK_RADIUS + Shank_Bevel)
    y = cos(radians(0)) * (SHANK_RADIUS + Shank_Bevel)
    vec1 = Vector([x, y, 0.0])
    verts.append([x, y, -Flat_Height - Undercut_Height])

    x = sin(radians(60 / 6)) * (SHANK_RADIUS + Shank_Bevel)
    y = cos(radians(60 / 6)) * (SHANK_RADIUS + Shank_Bevel)
    vec2 = Vector([x, y, 0.0])
    verts.append([x, y, -Flat_Height - Undercut_Height])

    x = sin(radians(60 / 3)) * (SHANK_RADIUS + Shank_Bevel)
    y = cos(radians(60 / 3)) * (SHANK_RADIUS + Shank_Bevel)
    vec3 = Vector([x, y, 0.0])
    verts.append([x, y, -Flat_Height - Undercut_Height])

    x = sin(radians(60 / 2)) * (SHANK_RADIUS + Shank_Bevel)
    y = cos(radians(60 / 2)) * (SHANK_RADIUS + Shank_Bevel)
    vec3 = Vector([x, y, 0.0])
    verts.append([x, y, -Flat_Height - Undercut_Height])
    Row += 1

    # Under cut to Shank BEVEL
    x = sin(radians(0)) * SHANK_RADIUS
    y = cos(radians(0)) * SHANK_RADIUS
    vec1 = Vector([x, y, 0.0])
    verts.append([x, y, -Flat_Height - Undercut_Height - Shank_Bevel])

    x = sin(radians(60 / 6)) * SHANK_RADIUS
    y = cos(radians(60 / 6)) * SHANK_RADIUS
    vec2 = Vector([x, y, 0.0])
    verts.append([x, y, -Flat_Height - Undercut_Height - Shank_Bevel])

    x = sin(radians(60 / 3)) * SHANK_RADIUS
    y = cos(radians(60 / 3)) * SHANK_RADIUS
    vec3 = Vector([x, y, 0.0])
    verts.append([x, y, -Flat_Height - Undercut_Height - Shank_Bevel])

    x = sin(radians(60 / 2)) * SHANK_RADIUS
    y = cos(radians(60 / 2)) * SHANK_RADIUS
    vec3 = Vector([x, y, 0.0])
    verts.append([x, y, -Flat_Height - Undercut_Height - Shank_Bevel])
    Row += 1

    faces.extend(Build_Face_List_Quads(FaceStart, 3, Row - 1))

    Mirror_Verts, Mirror_Faces = Mirror_Verts_Faces(verts, faces, 'y')
    verts.extend(Mirror_Verts)
    faces.extend(Mirror_Faces)

    Spin_Verts, Spin_Faces = SpinDup(verts, faces, 360, 6, 'z')

    return Spin_Verts, Spin_Faces, 0 - (-HEIGHT)


# ####################################################################
#                    Create External Thread
# ####################################################################


def Thread_Start3(verts, INNER_RADIUS, OUTTER_RADIUS, PITCH, DIV_COUNT,
                  CREST_PERCENT, ROOT_PERCENT, Height_Offset):

    Ret_Row = 0

    Height_Start = Height_Offset - PITCH
    Height_Step = float(PITCH) / float(DIV_COUNT)
    Deg_Step = 360.0 / float(DIV_COUNT)

    Crest_Height = float(PITCH) * float(CREST_PERCENT) / float(100)
    Root_Height = float(PITCH) * float(ROOT_PERCENT) / float(100)
    Root_to_Crest_Height = Crest_to_Root_Height = \
                        (float(PITCH) - (Crest_Height + Root_Height)) / 2.0

    # thread start
    Rank = float(OUTTER_RADIUS - INNER_RADIUS) / float(DIV_COUNT)
    for j in range(4):

        for i in range(DIV_COUNT + 1):
            z = Height_Offset - (Height_Step * i)
            if z > Height_Start:
                z = Height_Start
            x = sin(radians(i * Deg_Step)) * OUTTER_RADIUS
            y = cos(radians(i * Deg_Step)) * OUTTER_RADIUS
            verts.append([x, y, z])
        Height_Offset -= Crest_Height
        Ret_Row += 1

        for i in range(DIV_COUNT + 1):
            z = Height_Offset - (Height_Step * i)
            if z > Height_Start:
                z = Height_Start

            x = sin(radians(i * Deg_Step)) * OUTTER_RADIUS
            y = cos(radians(i * Deg_Step)) * OUTTER_RADIUS
            verts.append([x, y, z])
        Height_Offset -= Crest_to_Root_Height
        Ret_Row += 1

        for i in range(DIV_COUNT + 1):
            z = Height_Offset - (Height_Step * i)
            if z > Height_Start:
                z = Height_Start

            x = sin(radians(i * Deg_Step)) * INNER_RADIUS
            y = cos(radians(i * Deg_Step)) * INNER_RADIUS
            if j == 0:
                x = sin(radians(i * Deg_Step)) * (OUTTER_RADIUS - (i * Rank))
                y = cos(radians(i * Deg_Step)) * (OUTTER_RADIUS - (i * Rank))
            verts.append([x, y, z])
        Height_Offset -= Root_Height
        Ret_Row += 1

        for i in range(DIV_COUNT + 1):
            z = Height_Offset - (Height_Step * i)
            if z > Height_Start:
                z = Height_Start

            x = sin(radians(i * Deg_Step)) * INNER_RADIUS
            y = cos(radians(i * Deg_Step)) * INNER_RADIUS

            if j == 0:
                x = sin(radians(i * Deg_Step)) * (OUTTER_RADIUS - (i * Rank))
                y = cos(radians(i * Deg_Step)) * (OUTTER_RADIUS - (i * Rank))
            verts.append([x, y, z])
        Height_Offset -= Root_to_Crest_Height
        Ret_Row += 1

    return Ret_Row, Height_Offset


def Create_Shank_Verts(START_DIA, OUTTER_DIA, LENGTH, Z_LOCATION, DIV_COUNT):

    verts = []

    START_RADIUS = START_DIA / 2
    OUTTER_RADIUS = OUTTER_DIA / 2

    Opp = abs(START_RADIUS - OUTTER_RADIUS)
    Taper_Lentgh = Opp / tan(radians(31))

    if Taper_Lentgh > LENGTH:
        Taper_Lentgh = 0

    Stright_Length = LENGTH - Taper_Lentgh

    Deg_Step = 360.0 / float(DIV_COUNT)

    Row = 0

    Lowest_Z_Vert = 0

    Height_Offset = Z_LOCATION

    # Ring
    for i in range(DIV_COUNT + 1):
        x = sin(radians(i * Deg_Step)) * START_RADIUS
        y = cos(radians(i * Deg_Step)) * START_RADIUS
        z = Height_Offset - 0
        verts.append([x, y, z])
        Lowest_Z_Vert = min(Lowest_Z_Vert, z)
    Height_Offset -= Stright_Length
    Row += 1

    for i in range(DIV_COUNT + 1):
        x = sin(radians(i * Deg_Step)) * START_RADIUS
        y = cos(radians(i * Deg_Step)) * START_RADIUS
        z = Height_Offset - 0
        verts.append([x, y, z])
        Lowest_Z_Vert = min(Lowest_Z_Vert, z)
    Height_Offset -= Taper_Lentgh
    Row += 1