Screw thread (závit) in blender

screw-thread.py

import bpy
from math import *

def createMeshFromData(name, origin, verts, edges, faces):
    # Create mesh and object
    me = bpy.data.meshes.new(name+'Mesh')
    ob = bpy.data.objects.new(name, me)
    ob.location = origin
    ob.show_name = False
    # Link object to scene and make active
    bpy.context.collection.objects.link(ob)
    ob.select_set(True)
    # Create mesh from given verts, faces.
    me.from_pydata(verts, edges, faces)
    # Update mesh with new data
    me.update()

# Parameters
VerticesPerLoop = 256
Loops = 5
R = 32.2 # Outer radius
r = 20 # Inner radius
# thread profile (h1, h2, h3, h4 of the 4 points defining the profile)
h1 = 4
h2 = 1
h3 = 4
h4 = 5
falloffRate = 2

# Code
H = h1 + h2 + h3 + h4

#build array of profile points
ProfilePoints = []
ProfilePoints.append( [r, 0, 0] )
ProfilePoints.append( [R, 0, h1] )
if h2 > 0:
    ProfilePoints.append( [R, 0, h1 + h2] )
ProfilePoints.append( [r, 0, h1 + h2 + h3] )
if h4 > 0:
    ProfilePoints.append( [r, 0, h1 + h2 + h3 + h4] )

N = len(ProfilePoints)
verts = [[0, 0, 0] for _ in range(N * (VerticesPerLoop + 1)  * Loops)]
faces = [[0, 0, 0, 0] for _ in range(( N - 1) * VerticesPerLoop * Loops) ]

# go around a cirle. for each point in ProfilePoints array, create a vertex
angle = 0
for i in range(VerticesPerLoop * Loops + 1):
    for j in range(N):
        angle = i * 2 * pi / VerticesPerLoop
        # falloff applies to outer rings only
        u = i / (VerticesPerLoop * Loops)
        radius = r + (R - r) * (1 - 6*(pow(2 * u - 1, falloffRate * 4)/2 - pow(2 * u - 1, falloffRate * 6)/3)) if ProfilePoints[j][0] == R else r

        x = radius * cos(angle)
        y = radius * sin(angle)
        z = ProfilePoints[j][2] + i / VerticesPerLoop * H

        verts[N*i + j][0] = x
        verts[N*i + j][1] = y
        verts[N*i + j][2] = z
# now build face array
for i in range(VerticesPerLoop * Loops):
    for j in range(N - 1):
        faces[(N - 1) * i + j][0] = N * i + j
        faces[(N - 1) * i + j][1] = N * i + 1 + j
        faces[(N - 1) * i + j][2] = N * (i + 1) + 1 + j
        faces[(N - 1) * i + j][3] =  N * (i + 1) + j

createMeshFromData( 'Thread', [0, 0, 0], verts, [], faces )

This is what it looks like