import sys
import json
import numba
import math

kSegLength1=2.86
kSegLength2=1.65
kAlpha=0.55/(2*math.pi)
if __name__ !="__main__":
  sys.exit()

@numba.njit
def Theta2C(theta):
  tmp=math.sqrt(1+theta*theta)
  return kAlpha*0.5*(theta*tmp-math.log(-theta+tmp))

@numba.njit
def Theta2Dot(theta):
  return (kAlpha*theta*math.cos(theta),kAlpha*theta*math.sin(theta))
res_list=[]
init_C=Theta2C(2*math.pi*16)
print(f"init_C={init_C}")
GenerateFirstNodeTheta_last_res_store=2*math.pi*16
@numba.njit
def GenerateFirstNodeTheta(time_point,GenerateFirstNodeTheta_last_res):
  cur_C=init_C-1*time_point
  R=GenerateFirstNodeTheta_last_res
  L=GenerateFirstNodeTheta_last_res-10.0
  if L<0:
    L=0
  M=(L+R)/2
  kEps=1e-10
  while True:
    test_C=Theta2C(M)
    # print(L,M,R,test_C-cur_C)
    if -kEps < test_C-cur_C <kEps:
      break
    if test_C<cur_C:
      L=M
      M=(L+R)/2
    elif test_C > cur_C:
      R=M
      M=(L+R)/2
  GenerateFirstNodeTheta_last_res=M
  return M

@numba.njit
def GenerateFollowNodeTheta(cur_node_theta,expected_distance):
  cur_node_dot= Theta2Dot(cur_node_theta)
  step=1.0
  res_node_theta=cur_node_theta
  kEps=1e-10
  # print(f"expected_distance={expected_distance}")
  while True:
    test_node_theta=res_node_theta+step
    test_node_dot=Theta2Dot(test_node_theta)
    actual_distance=math.sqrt((cur_node_dot[0]-test_node_dot[0])**2 + (cur_node_dot[1]-test_node_dot[1])**2)
    # print(f"actual_distance={actual_distance}, expected_distance={expected_distance}, step={step}")
    if actual_distance < expected_distance-kEps:
      res_node_theta+=step
    elif actual_distance < expected_distance+kEps:
      break
    else:
      pass
    step*=0.5
  return res_node_theta

def CalcMoveList(time_point):
  global GenerateFirstNodeTheta_last_res_store
  first_node_theta=GenerateFirstNodeTheta(time_point,GenerateFirstNodeTheta_last_res_store)
  GenerateFirstNodeTheta_last_res_store=first_node_theta
  first_node_dot=Theta2Dot(first_node_theta)
  first_node_C=Theta2C(first_node_theta)
  # print(f"\t{node_list}")
  delta_theta=1e-4
  virtual_first_node_theta=first_node_theta+delta_theta
  virtual_first_node_C=Theta2C(virtual_first_node_theta)
  virtual_lst_node_theta=virtual_first_node_theta
  delta_T=virtual_first_node_C-first_node_C
  node_list=[{"delta_theta":delta_theta,"delta_T":delta_T},{"theta":first_node_theta,"node":first_node_dot,"C":first_node_C,"v":1.0}]
  for i in range(1,225):
    if i==1:
      expected_distance=kSegLength1
    else:
      expected_distance=kSegLength2
    # print(f"i={i}, expected_distance={expected_distance}")
    cur_node_theta=GenerateFollowNodeTheta(node_list[-1]["theta"],expected_distance)
    cur_node_dot= Theta2Dot(cur_node_theta)
    cur_node_C=Theta2C(cur_node_theta)
    virtural_cur_node_theta=GenerateFollowNodeTheta(virtual_lst_node_theta,expected_distance)
    virtural_cur_node_C=Theta2C(virtural_cur_node_theta)
    v=(virtural_cur_node_C-cur_node_C)/delta_T
    node_list.append({"theta":cur_node_theta,"node":cur_node_dot,"C":cur_node_C,"v":v})
    virtual_lst_node_theta=virtural_cur_node_theta
    # print(f"\t{node_list[-1]}")
  return node_list

for time_point in range(0,301):
  print(f"calculating time_point={time_point}")
  res_list.append(CalcMoveList(time_point))

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