import mpmath as mp
import json

mp.dps = 15  # 设置精度为15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)

    delta_theta = mp.mpf('1e-8')
    virtual_first_node_theta = first_node_theta + delta_theta
    virtual_first_node_C = Theta2C(virtual_first_node_theta)
    delta_T = virtual_first_node_C - first_node_C

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

    for i in range(1, 225):
        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)

        virtual_cur_node_theta = GenerateFollowNodeTheta(virtual_first_node_theta, expected_distance)
        virtual_cur_node_C = Theta2C(virtual_cur_node_theta)
        v = (virtual_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_first_node_theta = virtual_cur_node_theta

    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)