129 lines
4.3 KiB
Python
129 lines
4.3 KiB
Python
import mpmath as mp
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import json
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import sys
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import matplotlib.pyplot as plt
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from matplotlib.patches import Rectangle
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import numpy as np
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if __name__ != "__main__":
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sys.exit()
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mp.dps = 15 # 设置精度为15位小数
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kSegLength1 = mp.mpf('2.86')
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kSegLength2 = mp.mpf('1.65')
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kAlpha = mp.mpf('0.55') / (2 * mp.pi)
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def Theta2C(theta):
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tmp = mp.sqrt(1 + theta**2)
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return kAlpha * 0.5 * (theta * tmp - mp.log(-theta + tmp))
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def Theta2Dot(theta):
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return (kAlpha * theta * mp.cos(theta), kAlpha * theta * mp.sin(theta))
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init_C=Theta2C(2*mp.pi*16)
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def GenerateFirstNodeTheta(time_point):
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cur_C = init_C - time_point
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def f(theta):
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return Theta2C(theta) - cur_C
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return mp.findroot(f, 2*mp.pi*16, solver='secant')
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def GenerateFollowNodeTheta(cur_node_theta, expected_distance):
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cur_node_dot = Theta2Dot(cur_node_theta)
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def f(theta):
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test_node_dot = Theta2Dot(theta)
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actual_distance = mp.sqrt((cur_node_dot[0]-test_node_dot[0])**2 + (cur_node_dot[1]-test_node_dot[1])**2)
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return actual_distance - expected_distance
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return mp.findroot(f, cur_node_theta + 0.1, solver='secant')
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def CalcMoveList(time_point):
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first_node_theta = GenerateFirstNodeTheta(time_point)
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first_node_dot = Theta2Dot(first_node_theta)
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first_node_C = Theta2C(first_node_theta)
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node_list = [{"theta": first_node_theta, "node": first_node_dot, "C": first_node_C, "v": mp.mpf('1.0')}]
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for i in range(1, 224):
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expected_distance = kSegLength1 if i == 1 else kSegLength2
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cur_node_theta = GenerateFollowNodeTheta(node_list[-1]["theta"], expected_distance)
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cur_node_dot = Theta2Dot(cur_node_theta)
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cur_node_C = Theta2C(cur_node_theta)
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node_list.append({"theta": cur_node_theta, "node": cur_node_dot, "C": cur_node_C})
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for i in range(223):
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AA = kSegLength1 if i == 0 else kSegLength2
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theta_i = node_list[i]["theta"]
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theta_ip1 = node_list[i+1]["theta"]
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alpha_i = mp.atan(theta_i)
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alpha_ip1 = mp.atan(theta_ip1)
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beta_i = mp.acos(((kAlpha*theta_i)**2 + AA**2 - (kAlpha*theta_ip1)**2) / (2*kAlpha*theta_i*AA))
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gama_i = mp.acos(((kAlpha*theta_ip1)**2 + AA**2 - (kAlpha*theta_i)**2) / (2*kAlpha*theta_ip1*AA))
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node_list[i+1]["v"] = node_list[i]["v"] * (-mp.cos(alpha_i + beta_i) / mp.cos(alpha_ip1 - gama_i))
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return node_list
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time_point= float(input())
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print(f"calculating time_point={time_point}",file=sys.stderr)
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time_point_list = CalcMoveList(time_point)
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# 将结果转换为float并保留6位小数
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float_res_list = [
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{k: round(float(v), 6) if isinstance(v, mp.mpf) else
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[round(float(x), 6) for x in v] if isinstance(v, tuple) else v
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for k, v in node.items()}
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for node in time_point_list
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]
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# print(float_res_list)
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json.dump(float_res_list, sys.stdout, indent=4)
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def visualize_spiral(node_list):
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plt.figure(figsize=(12, 12))
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# 绘制灰色螺旋线
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theta = np.linspace(0, float(node_list[-1]["theta"]), 1000)
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x = [float(Theta2Dot(t)[0]) for t in theta]
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y = [float(Theta2Dot(t)[1]) for t in theta]
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plt.plot(x, y, color='gray', linewidth=0.5)
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# 绘制节点、连接线和木板
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for i in range(len(node_list) - 1):
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x1, y1 = [float(coord) for coord in node_list[i]["node"]]
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x2, y2 = [float(coord) for coord in node_list[i+1]["node"]]
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# 绘制红色节点
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plt.plot(x1, y1, 'ro', markersize=3)
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# 绘制蓝色连接线
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plt.plot([x1, x2], [y1, y2], 'b-', linewidth=0.5)
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# 计算并绘制木板（长方形）
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dx = x2 - x1
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dy = y2 - y1
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length = np.sqrt(dx**2 + dy**2)
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angle = np.arctan2(dy, dx)
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rect_length = length + 0.55 # 总长度加上两端各延伸的0.275m
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rect_width = 0.3
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# 计算长方形的中心点
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center_x = (x1 + x2) / 2
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center_y = (y1 + y2) / 2
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# 计算长方形的左下角坐标
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rect_x = center_x - rect_length/2 * np.cos(angle) + rect_width/2 * np.sin(angle)
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rect_y = center_y - rect_length/2 * np.sin(angle) - rect_width/2 * np.cos(angle)
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rect = Rectangle((rect_x, rect_y), rect_length, rect_width,
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angle=angle*180/np.pi, fill=False, edgecolor='g')
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plt.gca().add_patch(rect)
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# 绘制最后一个节点
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x, y = [float(coord) for coord in node_list[-1]["node"]]
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plt.plot(x, y, 'ro', markersize=3)
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plt.axis('equal')
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plt.title(f"Spiral visualization at time={time_point}")
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plt.show()
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# 在计算完节点列表后调用可视化函数
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visualize_spiral(float_res_list) |