#! /usr/bin/python3
# Last edited on 2024-07-27 00:47:07 by stolfi

from math import sin, cos, tan, atan2, asin, acos, hypot, sqrt, pi, inf, floor, sqrt
import rn
import sys

def points(dBase, dMin, dMax, np):
  # Generates a list of {np+1} points {v[i] = (x_i,y_i)}
  # on an involute of a circle with diameter {dBase}
  # centered at abscissa {-dBase/2}.
  # The points span the range of diameters {[dMin _ dMax]}.
  assert dMin >= dBase, "invalid dMin"
  assert dMax >= dBase, "invalid dMax"
  rBase = dBase/2
  v = []
  for k in range(np+1):
    f = k/np
    d = (1-f)*dMin + f*dMax
    alpha_d = alpha_at_given_d(d, dBase)
    omega_d = omega_from_alpha(alpha_d)
    x_d = 0.5*d*cos(omega_d) - rBase
    y_d = 0.5*d*sin(omega_d)
    v.append((x_d, y_d))
  return v
  
def dPitch_from_pCirc(N, pCirc):
  # Computes the pitch diameter {dPitch} from the circular pitch {pCirc}
  # and the number of teeth {N}.
  dPitch = N*pCirc/pi
  return dPitch

def dBase_from_dPitch(dPitch, theta):
  # Computes the base circle diameter {dBase} (mm) from the desired 
  # pitch diameter {dPitch} (mm) and the desired pressure angle {theta}
  # at the latter (radians):
  dBase = dPitch*cos(theta)
  return dBase

def omega_from_alpha(alpha):
  # Computes the polar angle {omega} ("inv alpha", radians) 
  # from the curve parameter {alpha}, the angle between local 
  # tangent and local radius (radians):
  omega = tan(alpha) - alpha
  return omega

def alpha_at_given_d(d, dBase):
  # Computes the the curve parameter {alpha},
  # the angle between local tangent and local radius (radians),
  # at a specific diameter {d} (mm), given the 
  # base diameter {dBase} (mm):
  alpha = acos(dBase/d)
  return alpha

def thickness_at_given_d(d, dPitch, theta, N):
  # Computes the the tooth thickness {th} (mm)
  # at a specific diameter {d}, given the pitch diameter {dPitch}
  # the pressure angle {theta} (radians), and the number of teeth {N}:
  dBase = dBase_from_dPitch(dPitch, theta)
  alpha = alpha_at_given_d(d, dBase)
  omega_0 = omega_from_alpha(theta*pi/180)
  omega = omega_from_alpha(alpha)
  th = d*((pi/(2*N)) + omega_0 - omega)
  return th