202 lines
7.8 KiB
Python
202 lines
7.8 KiB
Python
from loong import *
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import json
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import numpy as np
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import sys
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import matplotlib.pyplot as plt
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import io
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from PIL import Image
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from matplotlib.patches import Rectangle
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import multiprocessing
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class GoodOrbit(Orbit):
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def __init__(self):
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self.kAlpha = mp.mpf("1.7") / (2 * mp.pi)
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self.kCriticalTheta = 2.86 / ((2 / 3) * self.kAlpha) - 0.1
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self.r = (1 / 3) * self.kAlpha * mp.sqrt(1 + self.kCriticalTheta**2)
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self.point_A_cartesian = (
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self.kAlpha * self.kCriticalTheta * mp.cos(self.kCriticalTheta),
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self.kAlpha * self.kCriticalTheta * mp.sin(self.kCriticalTheta),
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)
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self.point_B_cartesian = (-self.kAlpha * self.kCriticalTheta * mp.cos(self.kCriticalTheta),
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-self.kAlpha * self.kCriticalTheta * mp.sin(self.kCriticalTheta))
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self.kPhi = mp.atan(self.kCriticalTheta)
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print(f"Phi={self.kPhi}", file=sys.stderr)
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dx, dy = self.point_A_cartesian[0] - self.point_B_cartesian[0], self.point_A_cartesian[1] - self.point_B_cartesian[1]
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self.angle = mp.atan2(dy, dx)
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print(f"angle={self.angle}", file=sys.stderr)
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self.point_C1_cartesian = (self.point_A_cartesian[0] + 2 * self.r * mp.cos(self.angle + 0.5 * mp.pi + self.kPhi),
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self.point_A_cartesian[1] + 2 * self.r * mp.sin(self.angle + 0.5 * mp.pi + self.kPhi))
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self.point_C2_cartesian = (self.point_B_cartesian[0] + 1 * self.r * mp.cos(self.angle - 0.5 * mp.pi + self.kPhi),
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self.point_B_cartesian[1] + 1 * self.r * mp.sin(self.angle - 0.5 * mp.pi + self.kPhi))
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self.radius_of_C1 = 2 * self.r
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self.radius_of_C2 = 1 * self.r
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self.arclength = 6 * self.r * self.kPhi
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self.edge_k = self.kAlpha * mp.sqrt(1 + self.kCriticalTheta * self.kCriticalTheta)
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self.n = -1
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for i in range(3, 20, 2):
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self.a = (self.arclength - 2 * self.edge_k * self.kCriticalTheta) / (2 * (1 - i) * self.kCriticalTheta**i)
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self.b = (i * self.arclength - 2 * self.edge_k * self.kCriticalTheta) / (2 * (i - 1) * self.kCriticalTheta)
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if self.a > 0 and self.b > 0:
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self.n = i
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break
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print(f"arclength={self.arclength}", file=sys.stderr)
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print(f"edge_k={self.edge_k}", file=sys.stderr)
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print(f"a={self.a}", file=sys.stderr)
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print(f"b={self.b}", file=sys.stderr)
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print(f"n={self.n}", file=sys.stderr)
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print(f"now k={self.n*self.a*self.kCriticalTheta**(self.n-1)+self.b}", file=sys.stderr)
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if self.n == -1:
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raise Exception("n must be set")
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self.edge_raw_C = self.kAlpha * 0.5 * (
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self.kCriticalTheta * mp.sqrt(1 + self.kCriticalTheta * self.kCriticalTheta) -
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mp.log(-self.kCriticalTheta + mp.sqrt(1 + self.kCriticalTheta * self.kCriticalTheta)))
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def InitIdx(self):
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return mp.mpf("0.0")
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def InitC(self):
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return mp.mpf("0.0")
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def Idx2C(self, idx): # this function must be monotonically increasing
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if idx >= 0:
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theta = idx + self.kCriticalTheta
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tmp = mp.sqrt(1 + theta * theta)
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return self.kAlpha * 0.5 * (theta * tmp - mp.log(-theta + tmp)) - self.edge_raw_C
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elif idx >= -2 * self.kCriticalTheta:
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x = idx + self.kCriticalTheta
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y = (self.a * (x**self.n) + self.b * x) - 0.5 * self.arclength
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return y
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else:
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theta = -idx - self.kCriticalTheta
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tmp = mp.sqrt(1 + theta * theta)
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return -self.kAlpha * 0.5 * (theta * tmp - mp.log(-theta + tmp)) + self.edge_raw_C - self.arclength
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def Idx2Cartesian(self, idx):
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if idx >= 0:
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theta = idx + self.kCriticalTheta
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return [self.kAlpha * theta * mp.cos(theta), self.kAlpha * theta * mp.sin(theta)]
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elif idx >= -2 * self.kCriticalTheta:
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c = self.Idx2C(idx) + self.arclength
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# if c < 0 or c > self.arclength:
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# raise Exception(f"idx={idx}, c={c}")
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if c <= self.arclength / 3:
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# In C2
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delta_angle = c / self.radius_of_C2
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actual_angle = self.angle + 0.5 * mp.pi + self.kPhi - delta_angle
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return [
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self.point_C2_cartesian[0] + self.radius_of_C2 * mp.cos(actual_angle),
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self.point_C2_cartesian[1] + self.radius_of_C2 * mp.sin(actual_angle)
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]
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else:
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delta_angle = (c - self.arclength / 3) / self.radius_of_C1
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actual_angle = self.angle - 0.5 * mp.pi - self.kPhi + delta_angle
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return [
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self.point_C1_cartesian[0] + self.radius_of_C1 * mp.cos(actual_angle),
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self.point_C1_cartesian[1] + self.radius_of_C1 * mp.sin(actual_angle)
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]
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else:
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theta = -idx - self.kCriticalTheta
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return [-self.kAlpha * theta * mp.cos(theta), -self.kAlpha * theta * mp.sin(theta)]
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def C2Idx(self, C):
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def f(idx):
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return self.Idx2C(idx) - C
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return mp.findroot(f, (-100*2*mp.pi,100*2*mp.pi), solver='bisect')
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def GenerateNextPointIdx(self, cur_point_idx, expected_distance, guess=None):
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if guess is None:
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cur_point_C = self.Idx2C(cur_point_idx)
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guess = self.C2Idx(cur_point_C + expected_distance)
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cur_point_dot = self.Idx2Cartesian(cur_point_idx)
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def f(idx):
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test_point_dot = self.Idx2Cartesian(idx)
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return mp.sqrt((cur_point_dot[0] - test_point_dot[0])**2 +
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(cur_point_dot[1] - test_point_dot[1])**2) - expected_distance
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return mp.findroot(f, guess, solver='secant')
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def GenerateImg(self, node_list):
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fig = plt.figure(figsize=(12, 12))
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# 绘制轨道线
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idx_list = np.linspace(-12 * 2 * np.pi, 8 * 2 * np.pi, 10000)
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x = [float(self.Idx2Cartesian(t)[0]) for t in idx_list]
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y = [float(self.Idx2Cartesian(t)[1]) for t in idx_list]
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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, 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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# 创建一个 BytesIO 对象来存储图像
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buf = io.BytesIO()
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plt.savefig(buf, format='png')
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buf.seek(0)
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# 清除当前图形，释放内存
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plt.close(fig)
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# 返回图像对象
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return Image.open(buf)
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if __name__ == "__main__":
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orbit = GoodOrbit()
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loong = Loong(orbit, 224, mp.mpf("2.0"), mp.mpf("1e-8"))
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res_list = []
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for ti in np.arange(5, 10, 0.025):
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print(f"calculating time_point={ti}", file=sys.stderr)
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res_list.append(loong.CalcStatusListByTime(mp.mpf(ti), res_list[-1] if res_list else None))
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# 转换成内置浮点数并保留6位
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float_res_list = [[{
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"idx": round(float(node["idx"]), 6),
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"node": [
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round(float(node["node"][0]), 6),
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round(float(node["node"][1]), 6),
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],
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"C": round(float(node["C"]), 6),
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"v": round(float(node["v"]), 6),
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} for node in res] for res in res_list]
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with open("A4_res.json", "w") as file:
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json.dump(float_res_list, file, indent=4)
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img_list = [orbit.GenerateImg(res) for res in res_list]
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img_list[0].save("A4.gif", save_all=True, append_images=img_list[1:], duration=25, loop=0)
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