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README.md

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 # Robotics_with_Python
-Learning Robotics with Python
+将基础的线性代数与Python结合，练习机器人中的基础概念。本套教程适合有一定编程基础的学习者。
+建议学习者边学习边观看3Blue1Brown中有关线性代数的视频教程。

lesson003python封装/framelib.py

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+import numpy as np
+import matplotlib.pyplot as plt
+
+
+def frame_show(label, Point_A, Point_B, ax, size):
+    R90 = np.array([[0, -1], [1, 0]])
+    Line_AB = Point_B - Point_A
+    norm_Line_AB = np.linalg.norm(Line_AB)
+    if norm_Line_AB != 1:
+        Line_AB = Line_AB / norm_Line_AB * size
+    ax.arrow(Point_A[0], Point_A[1], Line_AB[0], Line_AB[1], head_width=0.5, length_includes_head=True, color="red")
+    R90 = np.array([[0, -1], [1, 0]])  # 旋转公式
+    Line_AB_Rot90 = R90.dot(Line_AB)  # 点乘
+    ax.arrow(Point_A[0], Point_A[1], Line_AB_Rot90[0], Line_AB_Rot90[1], head_width=0.5, length_includes_head=True,
+             color="green")
+    plt.scatter(Point_A[0], Point_A[1])
+    label = "{" + str(label) + "}"
+    plt.text(Point_A[0], Point_A[1], label)
+
+
+def Rot_func(angle):
+    angle = np.deg2rad(angle)
+    R90 = np.array([[0, -1], [1, 0]])
+    elem_sim = lambda elem: np.around(elem, 0) if (elem - np.around(elem, 0)) < 1e-10 else elem
+    A11 = elem_sim(np.cos(angle))
+    A12 = elem_sim(-np.sin(angle))
+    A21 = elem_sim(np.sin(angle))
+    A22 = A11
+    Rot = np.array([[A11, A12], [A21, A22]])
+    return Rot
+
+
+def frame_show_angle_center(label, center, angle, ax, size):
+    Rot = Rot_func(angle)
+    x = np.array([1, 0])
+    x = Rot.dot(x)
+    frame_show(label, center, x + center, ax, size)
+    print("center" + str(center))
+    print("center+edge" + str(x + center))

lesson003python封装/frameworks.py

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+import framelib
+import numpy as np
+import matplotlib.pyplot as plt
+class frame2D:
+    def __init__(self):
+        self.center=np.array([0,0])
+        self.x_axis=np.array([1,0])
+        self.y_axis=np.array([0,1])
+        self.angle=0
+    def show(self,ax,label,size,color):
+        framelib.frame_show_angle_center(label,self.center,self.angle,ax,size)

lesson003python封装/lesson003part000总览

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+本节主要是通过代码封装中的类方法进行的。
+试着通过本节了解类的使用方法。
+part 1 主要完成类的定义
+part 2 主要完成通过文件导入函数
+part 3 将类也封装到文件当中
+如果有丰富的编程经验建议直接看part 3

lesson004_动画/Lesson004.py

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+import frameworks as fm
+import time
+# 进一步将类的封装定义在frameworks当中
+import numpy as np
+import matplotlib.pyplot as plt
+
+prev = fm.frame2D()
+tmp_list = []
+step = 1
+for i in range(0, 90, step):
+    tmp_list.append(fm.frame2D())
+    tmp_list[i].angle = i
+# run_time_max = 0
+# run_time_max_index = 0
+for i in range(0, 90, step):
+    plt.clf()
+    ax = plt.axes()
+    xlimit = 10
+    ylimit = 10
+    plt.axis('equal')  # 等轴
+
+    plt.xlim([-xlimit, xlimit])
+    plt.ylim([-ylimit, ylimit])
+    # start_time = time.time()
+    tmp_list[i].show(ax, "A", 2, "red")
+    # end_time = time.time()
+    # run_time = end_time - start_time
+    # print(str(i) + ":" + str(run_time))
+    # debug
+    # if run_time_max < run_time:
+    #     run_time_max = run_time
+    #     run_time_max_index = i
+
+    plt.pause(0.1)
+# print(run_time_max)
+# print(run_time_max_index)
+# plt.show()

lesson004_动画/README.md

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+- 该节中主要利用了matplotlib.pyplot中的clf()函数进行图像清除，利用pause()函数进行暂停设值进行的。
+- 其中主要练习过程当中的debug能力。需要通过测试擦看代码中的错误具体的位置。
+- 相似问题可以通过相同的方法对数学公式或者建模进行检测。
+- 由于jupyterlab中显示动画较为繁琐，请将所有文件放到同一文件夹下。这里我用的是PyCharm打开。

lesson004_动画/framelib.py

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+import numpy as np
+import matplotlib.pyplot as plt
+def frame_show(label, Point_A, Point_B, ax, size):
+    R90 = np.array([[0, -1], [1, 0]])
+    Line_AB = Point_B - Point_A
+    norm_Line_AB = np.linalg.norm(Line_AB)
+    if norm_Line_AB != 1:
+        Line_AB = Line_AB / norm_Line_AB * size
+    ax.arrow(Point_A[0], Point_A[1], Line_AB[0], Line_AB[1], head_width=0.5, length_includes_head=True, color="red")
+    R90 = np.array([[0, -1], [1, 0]])  # 旋转公式
+    Line_AB_Rot90 = R90.dot(Line_AB)  # 点乘
+    ax.arrow(Point_A[0], Point_A[1], Line_AB_Rot90[0], Line_AB_Rot90[1], head_width=0.5, length_includes_head=True,
+             color="green")
+    plt.scatter(Point_A[0], Point_A[1])
+    label = "{" + str(label) + "}"
+    plt.text(Point_A[0], Point_A[1], label)
+
+
+def Rot_func(angle):
+    angle = np.deg2rad(angle)
+    R90 = np.array([[0, -1], [1, 0]])
+    # elem_sim = lambda elem: np.around(elem, 0) if (elem - np.around(elem, 0)) < 1e-16 else elem
+    # A11 = elem_sim(np.cos(angle)).copy()
+    # A12 = elem_sim(-np.sin(angle)).copy()
+    # A21 = elem_sim(np.sin(angle)).copy()
+    # A22 = A11.copy()
+    A11=np.cos(angle).copy()
+    A12=-np.sin(angle).copy()
+    A21=np.sin(angle).copy()
+    A22=A11.copy()
+    Rot = np.array([[A11, A12], [A21, A22]]).copy()
+    print(np.rad2deg(angle))
+    print(np.cos(angle))
+    print(np.sin(angle))
+    return Rot
+
+
+def frame_show_angle_center(label, center, angle, ax, size):
+    Rot = Rot_func(angle)
+    x = np.array([1, 0])
+    x = Rot.dot(x)
+    x_norm=np.linalg.norm(x)
+    if x_norm!=1:
+        x=x.copy()/x_norm
+    frame_show(label, center, x + center, ax, size)
+    print("angle:"+str(angle))
+    print("center" + str(center))
+    print("center+edge" + str(x + center))

lesson004_动画/frameworks.py

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+import framelib
+import numpy as np
+import matplotlib.pyplot as plt
+class frame2D:
+    def __init__(self):
+        self.center=np.array([0,0])
+        self.x_axis=np.array([1,0])
+        self.y_axis=np.array([0,1])
+        self.angle=0
+    def show(self,ax,label,size,color):
+        framelib.frame_show_angle_center(label,self.center,self.angle,ax,size)