Orbit OK

A/4/loong.py

@@ -1,7 +1,7 @@
 import mpmath as mp
 import numba as nb
 
-mp.dps = 25  # 设置精度为25位小数
+mp.dps = 50  # 设置精度为50位小数
 
 class Orbit:
   def __init__(self):

A/4/simulator.py

@@ -3,6 +3,10 @@ import json
 import numpy as np
 import sys
 import matplotlib.pyplot as plt
+import io
+from PIL import Image
+from matplotlib.patches import Rectangle
+import multiprocessing
 
 
 class GoodOrbit(Orbit):
@@ -18,10 +22,14 @@ class GoodOrbit(Orbit):
     self.point_B_cartesian = (-self.kAlpha * self.kCriticalTheta * mp.cos(self.kCriticalTheta),
                               -self.kAlpha * self.kCriticalTheta * mp.sin(self.kCriticalTheta))
     self.kPhi = mp.atan(self.kCriticalTheta)
+    print(f"Phi={self.kPhi}", file=sys.stderr)
     dx, dy = self.point_A_cartesian[0] - self.point_B_cartesian[0], self.point_A_cartesian[1] - self.point_B_cartesian[1]
     self.angle = mp.atan2(dy, dx)
-    self.point_C1_cartesian = (self.point_A_cartesian[0] - 2 * self.r * dx, self.point_A_cartesian[1] - 2 * self.r * dy)
+    print(f"angle={self.angle}", file=sys.stderr)
-    self.point_C2_cartesian = (self.point_B_cartesian[0] + 1 * self.r * dx, self.point_B_cartesian[1] + 1 * self.r * dy)
+    self.point_C1_cartesian = (self.point_A_cartesian[0] + 2 * self.r * mp.cos(self.angle + 0.5 * mp.pi + self.kPhi),
+                               self.point_A_cartesian[1] + 2 * self.r * mp.sin(self.angle + 0.5 * mp.pi + self.kPhi))
+    self.point_C2_cartesian = (self.point_B_cartesian[0] + 1 * self.r * mp.cos(self.angle - 0.5 * mp.pi + self.kPhi),
+                               self.point_B_cartesian[1] + 1 * self.r * mp.sin(self.angle - 0.5 * mp.pi + self.kPhi))
     self.radius_of_C1 = 2 * self.r
     self.radius_of_C2 = 1 * self.r
     self.arclength = 6 * self.r * self.kPhi
@@ -66,7 +74,31 @@ class GoodOrbit(Orbit):
       return -self.kAlpha * 0.5 * (theta * tmp - mp.log(-theta + tmp)) + self.edge_raw_C - self.arclength
 
   def Idx2Cartesian(self, idx):
-    return mp.matrix([mp.cos(idx), mp.sin(idx)])
+    if idx >= 0:
+      theta = idx + self.kCriticalTheta
+      return [self.kAlpha * theta * mp.cos(theta), self.kAlpha * theta * mp.sin(theta)]
+    elif idx >= -2 * self.kCriticalTheta:
+      c = self.Idx2C(idx) + self.arclength
+      # if c < 0 or c > self.arclength:
+      # raise Exception(f"idx={idx}, c={c}")
+      if c <= self.arclength / 3:
+        # In C2
+        delta_angle = c / self.radius_of_C2
+        actual_angle = self.angle + 0.5 * mp.pi + self.kPhi - delta_angle
+        return [
+            self.point_C2_cartesian[0] + self.radius_of_C2 * mp.cos(actual_angle),
+            self.point_C2_cartesian[1] + self.radius_of_C2 * mp.sin(actual_angle)
+        ]
+      else:
+        delta_angle = (c - self.arclength / 3) / self.radius_of_C1
+        actual_angle = self.angle - 0.5 * mp.pi - self.kPhi + delta_angle
+        return [
+            self.point_C1_cartesian[0] + self.radius_of_C1 * mp.cos(actual_angle),
+            self.point_C1_cartesian[1] + self.radius_of_C1 * mp.sin(actual_angle)
+        ]
+    else:
+      theta = -idx - self.kCriticalTheta
+      return [-self.kAlpha * theta * mp.cos(theta), -self.kAlpha * theta * mp.sin(theta)]
 
   def C2Idx(self, C):
 
@@ -75,48 +107,82 @@ class GoodOrbit(Orbit):
 
     return mp.findroot(f, 0, solver='secant')
 
-  def GenerateNextPointIdx(self, cur_point_idx, expected_distance):
+  def GenerateNextPointIdx(self, cur_point_idx, expected_distance, guess=None):
-    return cur_point_idx + expected_distance
+    if guess is None:
+      cur_point_C = self.Idx2C(cur_point_idx)
+      guess = self.C2Idx(cur_point_C + expected_distance)
+    cur_point_dot = self.Idx2Cartesian(cur_point_idx)
+
+    def f(idx):
+      test_point_dot = self.Idx2Cartesian(idx)
+      return mp.sqrt((cur_point_dot[0] - test_point_dot[0])**2 +
+                     (cur_point_dot[1] - test_point_dot[1])**2) - expected_distance
+
+    return mp.findroot(f, guess, solver='secant')
+
+  def GenerateImg(self, node_list):
+    fig = plt.figure(figsize=(12, 12))
+
+    # 绘制轨道线
+    idx_list = np.linspace(-8 * 2 * np.pi, 8 * 2 * np.pi, 10000)
+    x = [float(self.Idx2Cartesian(t)[0]) for t in idx_list]
+    y = [float(self.Idx2Cartesian(t)[1]) for t in idx_list]
+    plt.plot(x, y, color='gray', linewidth=0.5)
+
+    # 绘制节点、连接线和木板
+    for i in range(len(node_list) - 1):
+      x1, y1 = [float(coord) for coord in node_list[i]["node"]]
+      x2, y2 = [float(coord) for coord in node_list[i + 1]["node"]]
+
+      # 绘制红色节点
+      plt.plot(x1, y1, 'ro', markersize=3)
+
+      # 绘制蓝色连接线
+      plt.plot([x1, x2], [y1, y2], 'b-', linewidth=0.5)
+
+      # 计算并绘制木板（长方形）
+      dx = x2 - x1
+      dy = y2 - y1
+      length = np.sqrt(dx**2 + dy**2)
+      angle = np.arctan2(dy, dx)
+
+      rect_length = length + 0.55  # 总长度加上两端各延伸的0.275m
+      rect_width = 0.3
+
+      # 计算长方形的中心点
+      center_x = (x1 + x2) / 2
+      center_y = (y1 + y2) / 2
+
+      # 计算长方形的左下角坐标
+      rect_x = center_x - rect_length / 2 * np.cos(angle) + rect_width / 2 * np.sin(angle)
+      rect_y = center_y - rect_length / 2 * np.sin(angle) - rect_width / 2 * np.cos(angle)
+
+      rect = Rectangle((rect_x, rect_y), rect_length, rect_width, angle=angle * 180 / np.pi, fill=False, edgecolor='g')
+      plt.gca().add_patch(rect)
+
+    # 绘制最后一个节点
+    x, y = [float(coord) for coord in node_list[-1]["node"]]
+    plt.plot(x, y, 'ro', markersize=3)
+
+    plt.axis('equal')
+
+    # 创建一个 BytesIO 对象来存储图像
+    buf = io.BytesIO()
+    plt.savefig(buf, format='png')
+    buf.seek(0)
+
+    # 清除当前图形，释放内存
+    plt.close(fig)
+
+    # 返回图像对象
+    return Image.open(buf)
 
 
-orbit = GoodOrbit()
-
-
-def f(x):
-  return float(orbit.Idx2C(x))
-
-
-# 获取 kCriticalTheta
-kCriticalTheta = float(orbit.kCriticalTheta)
-print(f"kCriticalTheta={kCriticalTheta}")
-
-# 定义范围 [-kCriticalTheta-1, kCriticalTheta +1]
-start = -2.5 * kCriticalTheta - 1
-end = 0.5 * kCriticalTheta + 1
-
-# 生成范围内的点
-x_vals = np.linspace(start, end, 1000)
-
-# 计算 f(x) 的值
-y_vals = [f(mp.mpf(x)) for x in x_vals]
-
-# 绘制图像
-plt.figure(figsize=(10, 6))
-plt.plot(x_vals, y_vals, label='Idx2C(x)')
-plt.title('Idx2C function plot')
-plt.xlabel('Index (x)')
-plt.ylabel('C Value')
-plt.grid(True)
-plt.axhline(0, color='black', linewidth=0.5)
-plt.axvline(0, color='black', linewidth=0.5)
-plt.legend()
-plt.show()
-sys.exit()
 if __name__ == "__main__":
   orbit = GoodOrbit()
   loong = Loong(orbit, 224, mp.mpf("2.0"), mp.mpf("1e-8"))
   res_list = []
-  for ti in range(-100, 101):
+  for ti in range(-10, 2):
     print(f"calculating time_point={ti}")
     res_list.append(loong.CalcStatusListByTime(mp.mpf(ti)))
     # 转换成内置浮点数并保留6位
@@ -131,3 +197,5 @@ if __name__ == "__main__":
   } for node in res] for res in res_list]
   with open("A4_res.json", "w") as file:
     json.dump(float_res_list, file, indent=4)
+  img_list = [orbit.GenerateImg(res) for res in res_list]
+  img_list[0].save("A4.gif", save_all=True, append_images=img_list[1:], duration=1000, loop=0)