"""
//////////////////////////////////////////////////////////////////////////////////////////////
// Public Domain Parametric Involute Spur Gear (and involute helical gear and involute rack)
// version 1.1
// by Leemon Baird, 2011, Leemon@Leemon.com
//http://www.thingiverse.com/thing:5505
//
// This file is public domain.  Use it for any purpose, including commercial
// applications.  Attribution would be nice, but is not required.  There is
// no warranty of any kind, including its correctness, usefulness, or safety.
//
// This is parameterized involute spur (or helical) gear.  It is much simpler and less powerful than
// others on Thingiverse.  But it is public domain.  I implemented it from scratch from the
// descriptions and equations on Wikipedia and the web, using Mathematica for calculations and testing,
// and I now release it into the public domain.
//
//        http://en.wikipedia.org/wiki/Involute_gear
//        http://en.wikipedia.org/wiki/Gear
//        http://en.wikipedia.org/wiki/List_of_gear_nomenclature
//        http://gtrebaol.free.fr/doc/catia/spur_gear.html
//        http://www.cs.cmu.edu/~rapidproto/mechanisms/chpt7.html
//
// The module gear() gives an involute spur gear, with reasonable defaults for all the parameters.
// Normally, you should just choose the first 4 parameters, and let the rest be default values.
// The module gear() gives a gear in the XY plane, centered on the origin, with one tooth centered on
// the positive Y axis.  The various functions below it take the same parameters, and return various
// measurements for the gear.  The most important is pitch_radius, which tells how far apart to space
// gears that are meshing, and adendum_radius, which gives the size of the region filled by the gear.
// A gear has a "pitch circle", which is an invisible circle that cuts through the middle of each
// tooth (though not the exact center). In order for two gears to mesh, their pitch circles should
// just touch.  So the distance between their centers should be pitch_radius() for one, plus pitch_radius()
// for the other, which gives the radii of their pitch circles.
//
// In order for two gears to mesh, they must have the same mm_per_tooth and pressure_angle parameters.
// mm_per_tooth gives the number of millimeters of arc around the pitch circle covered by one tooth and one
// space between teeth.  The pitch angle controls how flat or bulged the sides of the teeth are.  Common
// values include 14.5 degrees and 20 degrees, and occasionally 25.  Though I've seen 28 recommended for
// plastic gears. Larger numbers bulge out more, giving stronger teeth, so 28 degrees is the default here.
//
// The ratio of number_of_teeth for two meshing gears gives how many times one will make a full
// revolution when the the other makes one full revolution.  If the two numbers are coprime (i.e.
// are not both divisible by the same number greater than 1), then every tooth on one gear
// will meet every tooth on the other, for more even wear.  So coprime numbers of teeth are good.
//
// The module rack() gives a rack, which is a bar with teeth.  A rack can mesh with any
// gear that has the same mm_per_tooth and pressure_angle.
//
// Some terminology:
// The outline of a gear is a smooth circle (the "pitch circle") which has mountains and valleys
// added so it is toothed.  So there is an inner circle (the "root circle") that touches the
// base of all the teeth, an outer circle that touches the tips of all the teeth,
// and the invisible pitch circle in between them.  There is also a "base circle", which can be smaller than
// all three of the others, which controls the shape of the teeth.  The side of each tooth lies on the path
// that the end of a string would follow if it were wrapped tightly around the base circle, then slowly unwound.
// That shape is an "involute", which gives this type of gear its name.
//
//////////////////////////////////////////////////////////////////////////////////////////////

//An involute spur gear, with reasonable defaults for all the parameters.
//Normally, you should just choose the first 4 parameters, and let the rest be default values.
//Meshing gears must match in mm_per_tooth, pressure_angle, and twist,
//and be separated by the sum of their pitch radii, which can be found with pitch_radius(). """

# ported to Blendercam by Alain Pelletier Jan 2022


import bpy
from bpy.props import *
from bpy.types import Operator

from cam import utils, polygon_utils_cam, simple
import shapely
from shapely.geometry import Point, LineString, Polygon
import mathutils
import math


# convert gear_polar to cartesian coordinates
def gear_polar(r, theta):
    return r * math.sin(theta), r * math.cos(theta)


# unwind a string this many degrees to go from radius r1 to radius r2
def gear_iang(r1, r2):
    return math.sqrt((r2 / r1) * (r2 / r1) - 1) - math.acos(r1 / r2)


#  radius a fraction f up the curved side of the tooth
def gear_q7(f, r, b, r2, t, s):
    return gear_q6(b, s, t, (1-f) * max(b, r) + f * r2)


# point at radius d on the involute curve
def gear_q6(b, s, t, d):
    return gear_polar(d, s * (gear_iang(b, d) + t))

# mm_per_tooth = this is the "circular pitch", the circumference of the pitch circle divided by the number of teeth
# number_of_teeth = total number of teeth around the entire perimeter
# hole_diameter =  diameter of the hole in the center, in mm
# pressure_angle = Controls how straight or bulged the tooth sides are. In radians.
# clearance = gap between top of a tooth on one gear and bottom of valley on a meshing gear( in millimeters)
# backlash = gap between two meshing teeth, in the direction along the  circumference of the pitch circle


def gear(mm_per_tooth=0.003, number_of_teeth=5, hole_diameter=0.003175,
         pressure_angle=0.3488, clearance=0.0, backlash=0.0, rim_size=0.0005, hub_diameter=0.006, spokes=4):
    simple.deselect()
    pi = math.pi
    p = mm_per_tooth * number_of_teeth / pi / 2  # radius of pitch circle
    c = p + mm_per_tooth / pi - clearance        # radius of outer circle
    b = p * math.cos(pressure_angle)  # radius of base circle
    r = p-(c-p)-clearance   # radius of root circle
    t = mm_per_tooth / 2 - backlash / 2  # tooth thickness at pitch circle
    k = - gear_iang(b, p) - t / 2 / p    # angle to where involute meets base circle on each side of tooth
    shapely_gear = Polygon([
                            (0, 0),
                            gear_polar(r, k if r < b else -pi / number_of_teeth),
                            gear_q7(0, r, b, c, k, 1),
                            gear_q7(0.1, r, b, c, k, 1),
                            gear_q7(0.2, r, b, c, k, 1),
                            gear_q7(0.3, r, b, c, k, 1),
                            gear_q7(0.4, r, b, c, k, 1),
                            gear_q7(0.5, r, b, c, k, 1),
                            gear_q7(0.6, r, b, c, k, 1),
                            gear_q7(0.7, r, b, c, k, 1),
                            gear_q7(0.8, r, b, c, k, 1),
                            gear_q7(0.9, r, b, c, k, 1),
                            gear_q7(1.0, r, b, c, k, 1),
                            gear_q7(1.0, r, b, c, k, -1),
                            gear_q7(0.9, r, b, c, k, -1),
                            gear_q7(0.8, r, b, c, k, -1),
                            gear_q7(0.7, r, b, c, k, -1),
                            gear_q7(0.6, r, b, c, k, -1),
                            gear_q7(0.5, r, b, c, k, -1),
                            gear_q7(0.4, r, b, c, k, -1),
                            gear_q7(0.3, r, b, c, k, -1),
                            gear_q7(0.2, r, b, c, k, -1),
                            gear_q7(0.1, r, b, c, k, -1),
                            gear_q7(0.0, r, b, c, k, -1),
                            gear_polar(r, -k if r < b else pi / number_of_teeth)
                            ])
    utils.shapelyToCurve('tooth', shapely_gear, 0.0)
    i = number_of_teeth
    while i > 1:
        simple.duplicate()
        simple.rotate(2 * math.pi / number_of_teeth)
        i -= 1
    simple.join_multiple('tooth')
    simple.active_name('_teeth')

    bpy.ops.curve.simple(align='WORLD', location=(0, 0, 0), rotation=(0, 0, 0), Simple_Type='Circle',
                         Simple_radius=r, shape='3D', use_cyclic_u=True, edit_mode=False)
    simple.active_name('_hub')
    simple.union('_')
    simple.active_name('_gear')
    simple.remove_doubles()

    if spokes > 0:
        bpy.ops.curve.simple(align='WORLD', location=(0, 0, 0), rotation=(0, 0, 0), Simple_Type='Circle',
                             Simple_radius=r-rim_size, shape='3D', use_cyclic_u=True, edit_mode=False)
        simple.active_name('_hole')
        simple.difference('_', '_gear')
        bpy.ops.curve.simple(align='WORLD', location=(0, 0, 0), rotation=(0, 0, 0), Simple_Type='Circle',
                             Simple_radius=hub_diameter/2, shape='3D', use_cyclic_u=True, edit_mode=False)
        simple.active_name('_hub')
        bpy.ops.curve.simple(align='WORLD', location=(0, 0, 0), rotation=(0, 0, 0), Simple_Type='Circle',
                             Simple_radius=hole_diameter/2, shape='3D', use_cyclic_u=True, edit_mode=False)
        simple.active_name('_hub_hole')
        simple.difference('_hub', '_hub')

        simple.join_multiple('_')

        simple.add_rectangle(r-rim_size-((hub_diameter-hole_diameter)/4 + hole_diameter/2), hub_diameter/2, center_x=False)
        simple.move(x=(hub_diameter-hole_diameter)/4 + hole_diameter/2)
        simple.active_name('_spoke')

        angle = 2 * pi / spokes
        while spokes > 0:
            simple.duplicate()
            simple.rotate(angle)
            spokes -= 1
        simple.union('_spoke')
        simple.remove_doubles()
        simple.union('_')
    else:
        bpy.ops.curve.simple(align='WORLD', location=(0, 0, 0), rotation=(0, 0, 0), Simple_Type='Circle',
                             Simple_radius=hole_diameter, shape='3D', use_cyclic_u=True, edit_mode=False)
        simple.active_name('_hole')
        simple.difference('_', '_gear')

    name = 'gear-' + str(round(mm_per_tooth*1000, 1))
    name += 'mm-pitch-' + str(number_of_teeth)
    name += 'teeth-PA-' + str(round(math.degrees(pressure_angle), 1))
    simple.active_name(name)


def rack(mm_per_tooth=0.01, number_of_teeth=11, height=0.012, pressure_angle=0.3488, backlash=0.0,
         hole_diameter=0.003175, tooth_per_hole=4):
    simple.deselect()
    pi = math.pi
    mm_per_tooth *= 1000
    a = mm_per_tooth / pi  # addendum
    t = (a * math.sin(pressure_angle))         # tooth side is tilted so top/bottom corners move this amount
    a /= 1000
    mm_per_tooth /= 1000
    t /= 1000

    shapely_gear = Polygon([
                            (-mm_per_tooth * 2/4*1.001, a-height),
                            (-mm_per_tooth * 2/4*1.001 - backlash, -a),
                            (-mm_per_tooth * 1/4 + backlash - t, -a),
                            (-mm_per_tooth * 1/4 + backlash + t, a),
                            (mm_per_tooth * 1/4 - backlash - t, a),
                            (mm_per_tooth * 1/4 - backlash + t, -a),
                            (mm_per_tooth * 2/4*1.001 + backlash, -a),
                            (mm_per_tooth * 2/4*1.001, a-height)
                            ])

    utils.shapelyToCurve('_tooth', shapely_gear, 0.0)
    i = number_of_teeth
    while i > 1:
        simple.duplicate(x=mm_per_tooth)
        i -= 1
    simple.union('_tooth')
    simple.move(y=height/2)
    if hole_diameter > 0:
        bpy.ops.curve.simple(align='WORLD', location=(mm_per_tooth/2, 0, 0), rotation=(0, 0, 0), Simple_Type='Circle',
                             Simple_radius=hole_diameter/2, shape='3D', use_cyclic_u=True, edit_mode=False)
        simple.active_name('_hole')
        distance = (number_of_teeth-1) * mm_per_tooth
        while distance > tooth_per_hole * mm_per_tooth:
            simple.duplicate(x=tooth_per_hole * mm_per_tooth)
            distance -= tooth_per_hole * mm_per_tooth
        simple.difference('_', '_tooth')

    name = 'rack-' + str(round(mm_per_tooth * 1000, 1))
    name += '-PA-' + str(round(math.degrees(pressure_angle), 1))
    simple.active_name(name)