From 3cbd6471718055229a5186d3c2db7371a9312f33 Mon Sep 17 00:00:00 2001
From: easternDay <849919718@qq.com>
Date: Wed, 19 Jun 2019 12:25:27 +0800
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+# 物理曲线的Pytthon绘制
+## 所需Lib
+1. matplotlib
+2. numpy
+## 所绘制曲线
+1. 重力势能曲线
+2. 抛体运动曲线
+3. 点电荷电力线分布
+4. 电偶极子电力线和等势面分布
+5. 简谐振动
+6. 李萨如图形
+## 代码实现
+```Python
+#coding:utf-8
+import numpy as np
+import matplotlib.pyplot as plt
+
+# 支持中文
+plt.rcParams['font.sans-serif'] = ['SimHei']  # 用来正常显示中文标签
+
+
+# 控制图形的长和宽单位为英寸，
+# 调用figure创建一个绘图对象，并且使它成为当前的绘图对象。
+plt.figure(figsize=(5,5))
+# 设置X轴的范围
+plt.xlim(0,10)
+# 设置Y轴的范围
+plt.ylim(0,100)
+
+# 曲线设置
+x=np.linspace(0,10,10)
+y=np.array(9.8*x)
+
+#$可以让字体变得跟好看
+#给所绘制的曲线一个名字，此名字在图示(legend)中显示。
+# 只要在字符串前后添加"$"符号，matplotlib就会使用其内嵌的latex引擎绘制的数学公式。
+#color : 指定曲线的颜色
+#linewidth : 指定曲线的宽度
+plt.plot(x,y, '--c',marker='o',label="$9.8*x$",color="red",linewidth=2, markersize=5)
+#设置X轴的文字
+plt.xlabel("High(下落高度)")
+#设置Y轴的文字
+plt.ylabel("Ep(重力势能)")
+#设置图表的标题
+plt.title("重力势能曲线")
+
+
+#显示图示
+plt.legend()
+#显示出我们创建的所有绘图对象。
+plt.show()
+```
+```Python
+import numpy as np
+import matplotlib.pyplot as plt
+
+def projectile(V_initial, theta, bouyancy=True, drag=True):
+    g = 9.81
+    m = 1
+    C = 0.47
+    r = 0.5
+    S = np.pi*pow(r, 2)
+    ro_mars = 0.0175
+
+    time = np.linspace(0, 100, 10000)
+    tof = 0.0
+    dt = time[1] - time[0]
+    bouy = ro_mars*g*(4/3*np.pi*pow(r, 3))
+    gravity = -g * m
+    V_ix = V_initial * np.cos(theta)
+    V_iy = V_initial * np.sin(theta)
+    v_x = V_ix
+    v_y = V_iy
+    r_x = 0.0
+    r_y = 0.0
+    r_xs = list()
+    r_ys = list()
+    r_xs.append(r_x)
+    r_ys.append(r_y)
+    # This gets a bit 'hand-wavy' but as dt -> 0 it approaches the analytical solution.
+    # Just make sure you use sufficiently small dt (dt is change in time between steps)
+    for t in time:
+        F_x = 0.0
+        F_y = 0.0
+        if (bouyancy == True):
+            F_y = F_y + bouy
+        if (drag == True):
+            F_y = F_y - 0.5*C*S*ro_mars*pow(v_y, 2)
+            F_x = F_x - 0.5*C*S*ro_mars*pow(v_x, 2) * np.sign(v_y)
+        F_y = F_y + gravity
+
+        r_x = r_x + v_x * dt + (F_x / (2 * m)) * dt**2
+        r_y = r_y + v_y * dt + (F_y / (2 * m)) * dt**2
+        v_x = v_x + (F_x / m) * dt
+        v_y = v_y + (F_y / m) * dt
+        if (r_y >= 0.0):
+            r_xs.append(r_x)
+            r_ys.append(r_y)
+        else:
+            tof = t
+            r_xs.append(r_x)
+            r_ys.append(r_y)
+            break
+
+    return r_xs, r_ys, tof
+
+v = 30
+theta = np.pi/4
+
+fig = plt.figure(figsize=(8,4), dpi=100)
+r_xs, r_ys, tof = projectile(v, theta, True, True)
+plt.plot(r_xs, r_ys, 'g:', label="Gravity, Buoyancy, and Drag")
+r_xs, r_ys, tof = projectile(v, theta, False, True)
+plt.plot(r_xs, r_ys, 'b:', label="Gravity and Drag")
+r_xs, r_ys, tof = projectile(v, theta, False, False)
+plt.plot(r_xs, r_ys, 'k:', label="Gravity")
+plt.title("Trajectory", fontsize=14)
+plt.xlabel("Displacement in x-direction (m)")
+plt.ylabel("Displacement in y-direction (m)")
+plt.ylim(bottom=0.0)
+plt.legend()
+plt.show()
+```
+```Python
+#coding:utf-8
+import numpy as np
+import matplotlib.pyplot as plt
+import math
+
+# 支持中文
+plt.rcParams['font.sans-serif'] = ['SimHei']  # 用来正常显示中文标签
+#显示负号
+plt.rcParams['axes.unicode_minus'] = False
+
+
+# 控制图形的长和宽单位为英寸，
+# 调用figure创建一个绘图对象，并且使它成为当前的绘图对象。
+plt.figure(figsize=(5,5))
+# 设置X轴的范围
+plt.xlim(-10,10)
+# 设置Y轴的范围
+plt.ylim(-10,10)
+
+# 曲线设置
+x=np.linspace(0,10,10)
+y=np.array(x)
+
+#$可以让字体变得跟好看
+#给所绘制的曲线一个名字，此名字在图示(legend)中显示。
+# 只要在字符串前后添加"$"符号，matplotlib就会使用其内嵌的latex引擎绘制的数学公式。
+#color : 指定曲线的颜色
+#linewidth : 指定曲线的宽度
+rad = 0
+for i in range(-50,50):
+    y = math.tan(rad)*x
+    rad += math.pi/6
+    plt.plot(x,y, '--c',marker='^',color="red",linewidth=2, markersize=5)
+    plt.plot(-x,y, '--c',marker='^',color="red",linewidth=2, markersize=5)
+plt.plot(0,0, '--c',marker='o',label="点电荷",color="blue",linewidth=2, markersize=15)
+#设置图表的标题
+plt.title("点电荷电力线分布")
+
+
+#显示图示
+plt.legend()
+#显示出我们创建的所有绘图对象。
+plt.show()
+```
+```Python
+from matplotlib.tri import (
+  Triangulation, UniformTriRefiner, CubicTriInterpolator)
+import matplotlib.pyplot as plt
+import matplotlib.cm as cm
+import numpy as np
+
+#-----------------------------------------------------------------------------
+# Electrical potential of a dipole
+#-----------------------------------------------------------------------------
+def dipole_potential(x, y):
+  """ The electric dipole potential V """
+  r_sq = x**2 + y**2
+  theta = np.arctan2(y, x)
+  z = np.cos(theta)/r_sq
+  return (np.max(z) - z) / (np.max(z) - np.min(z))
+
+#-----------------------------------------------------------------------------
+# Creating a Triangulation
+#-----------------------------------------------------------------------------
+# First create the x and y coordinates of the points.
+n_angles = 30
+n_radii = 10
+min_radius = 0.2
+radii = np.linspace(min_radius, 0.95, n_radii)
+
+angles = np.linspace(0, 2 * np.pi, n_angles, endpoint=False)
+angles = np.repeat(angles[..., np.newaxis], n_radii, axis=1)
+angles[:, 1::2] += np.pi / n_angles
+
+x = (radii*np.cos(angles)).flatten()
+y = (radii*np.sin(angles)).flatten()
+V = dipole_potential(x, y)
+
+# Create the Triangulation; no triangles specified so Delaunay triangulation
+# created.
+triang = Triangulation(x, y)
+
+# Mask off unwanted triangles.
+triang.set_mask(np.hypot(x[triang.triangles].mean(axis=1),
+             y[triang.triangles].mean(axis=1))
+        < min_radius)
+
+#-----------------------------------------------------------------------------
+# Refine data - interpolates the electrical potential V
+#-----------------------------------------------------------------------------
+refiner = UniformTriRefiner(triang)
+tri_refi, z_test_refi = refiner.refine_field(V, subdiv=3)
+
+#-----------------------------------------------------------------------------
+# Computes the electrical field (Ex, Ey) as gradient of electrical potential
+#-----------------------------------------------------------------------------
+tci = CubicTriInterpolator(triang, -V)
+# Gradient requested here at the mesh nodes but could be anywhere else:
+(Ex, Ey) = tci.gradient(triang.x, triang.y)
+E_norm = np.sqrt(Ex**2 + Ey**2)
+
+#-----------------------------------------------------------------------------
+# Plot the triangulation, the potential iso-contours and the vector field
+#-----------------------------------------------------------------------------
+fig, ax = plt.subplots()
+ax.set_aspect('equal')
+# Enforce the margins, and enlarge them to give room for the vectors.
+ax.use_sticky_edges = False
+ax.margins(0.07)
+
+ax.triplot(triang, color='0.8')
+
+levels = np.arange(0., 1., 0.01)
+cmap = cm.get_cmap(name='hot', lut=None)
+ax.tricontour(tri_refi, z_test_refi, levels=levels, cmap=cmap,
+       linewidths=[2.0, 1.0, 1.0, 1.0])
+# Plots direction of the electrical vector field
+ax.quiver(triang.x, triang.y, Ex/E_norm, Ey/E_norm,
+     units='xy', scale=10., zorder=3, color='blue',
+     width=0.007, headwidth=3., headlength=4.)
+
+ax.set_title('Gradient plot: an electrical dipole')
+plt.show()
+```
+```Python
+import matplotlib.pyplot as plt
+import numpy as np
+
+
+def f(t):
+    return np.cos(2 * np.pi * t)
+
+
+a = np.arange(0.0, 5.0, 0.02)
+
+plt.plot(a, f(a))
+plt.xlabel('横坐标(时间)', fontproperties='Kaiti', fontsize=14, color='red')
+plt.ylabel('纵坐标(振幅)', fontproperties='SimHei', fontsize=18, color='red')
+plt.title('简谐运动 y=cos(2πx)', fontproperties='SimHei', fontsize=18, color='green')
+plt.grid(True)
+plt.axis([-1, 6, -2, 2])
+plt.annotate('简谐运动曲线', xy=(3, 1), xytext=(4, 1.5), arrowprops=dict(facecolor='black', shrink=0.2),
+             fontproperties='SimHei', fontsize=12, color='red')
+
+plt.show()
+```
+```Python
+import numpy as np
+from matplotlib.pyplot import plot
+from matplotlib.pyplot import show
+a = float(input())
+b = float(input())
+t = np.linspace(-np.pi, np.pi, 201)
+x = np.sin(a * t + np.pi/2)
+y = np.sin(b * t)
+plot(x, y)
+show()
+```
+## GITHUB链接
+[东方怂天的GitHub][1]
+
+
+[1]:https://github.com/easternDay/Physical-curve-drawing
-- 
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