import mpmath as mp
import json

mp.dps = 50  # 设置精度为50位小数

kSegLength1 = mp.mpf('2.86')
kSegLength2 = mp.mpf('1.65')
kAlpha = mp.mpf('0.55') / (2 * mp.pi)

def Theta2C(theta):
  tmp = mp.sqrt(1 + theta**2)
  return kAlpha * 0.5 * (theta * tmp - mp.log(-theta + tmp))

def Theta2Dot(theta):
  return (kAlpha * theta * mp.cos(theta), kAlpha * theta * mp.sin(theta))

init_C=Theta2C(2*mp.pi*16)
def GenerateFirstNodeTheta(time_point, last_theta):
  cur_C = init_C - time_point
  def f(theta):
    return Theta2C(theta) - cur_C
  return mp.findroot(f, last_theta, solver='secant')

def GenerateFollowNodeTheta(cur_node_theta, expected_distance):
  cur_node_dot = Theta2Dot(cur_node_theta)
  def f(theta):
    test_node_dot = Theta2Dot(theta)
    actual_distance = mp.sqrt((cur_node_dot[0]-test_node_dot[0])**2 + (cur_node_dot[1]-test_node_dot[1])**2)
    return actual_distance - expected_distance
  return mp.findroot(f, cur_node_theta + 0.1, solver='secant')

def CalcMoveList(time_point, last_theta):
  first_node_theta = GenerateFirstNodeTheta(time_point, last_theta)
  first_node_dot = Theta2Dot(first_node_theta)
  first_node_C = Theta2C(first_node_theta)

  node_list = [{"theta": first_node_theta, "node": first_node_dot, "C": first_node_C, "v": mp.mpf('1.0')}]

  for i in range(1, 224):
    expected_distance = kSegLength1 if i == 1 else kSegLength2
    cur_node_theta = GenerateFollowNodeTheta(node_list[-1]["theta"], expected_distance)
    cur_node_dot = Theta2Dot(cur_node_theta)
    cur_node_C = Theta2C(cur_node_theta)
    node_list.append({"theta": cur_node_theta, "node": cur_node_dot, "C": cur_node_C})
  for i in range(223):
    AA = kSegLength1 if i == 0 else kSegLength2
    theta_i = node_list[i]["theta"]
    theta_ip1 = node_list[i+1]["theta"]
    alpha_i = mp.atan(theta_i)
    alpha_ip1 = mp.atan(theta_ip1)
    beta_i = mp.acos(((kAlpha*theta_i)**2 + AA**2 - (kAlpha*theta_ip1)**2) / (2*kAlpha*theta_i*AA))
    gama_i = mp.acos(((kAlpha*theta_ip1)**2 + AA**2 - (kAlpha*theta_i)**2) / (2*kAlpha*theta_ip1*AA))
    node_list[i+1]["v"] = node_list[i]["v"] * (-mp.cos(alpha_i + beta_i) / mp.cos(alpha_ip1 - gama_i))

  return node_list, first_node_theta

res_list = []
last_theta = 2 * mp.pi * 16

for time_point in range(301):
  print(f"calculating time_point={time_point}")
  move_list, last_theta = CalcMoveList(time_point, last_theta)
  res_list.append(move_list)

# 将结果转换为float并保留6位小数
float_res_list = [
  [
    {k: round(float(v), 6) if isinstance(v, mp.mpf) else 
      [round(float(x), 6) for x in v] if isinstance(v, tuple) else v
     for k, v in node.items()}
    for node in time_point
  ]
  for time_point in res_list
]

with open("A1_res.json", "w") as file:
  json.dump(float_res_list, file, indent=4)