Try to plot three dimensional graph of the function z=2*x^2+y^2 , where x=sin3t and y=cos3t . The range of t should be set to [-3, 3], and the ranges of x and y axes are both [-1.2, 1.2]. Requirement: Plot the three-dimensional (3-D) mesh graph, 3-D surface graph and 3-D surface graph with contour lines, respectively. In addition, plot the 2-D sectional view graph for x=1.
时间: 2023-12-02 18:04:48 浏览: 32
Sure, I can help you with that. Here's the code in Python using matplotlib and numpy libraries:
```python
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
# Define the function
def f(x, y):
return 2*x**2 + y**2
# Define the range of t
t = np.linspace(-3, 3, 100)
# Calculate the x and y values
x = np.sin(3*t)
y = np.cos(3*t)
# Calculate the z values
z = f(x, y)
# Create a meshgrid for the x and y values
X, Y = np.meshgrid(x, y)
# Create a figure and three subplots for the different types of plots
fig = plt.figure(figsize=(12, 6))
ax1 = fig.add_subplot(2, 3, 1, projection='3d')
ax1.plot_wireframe(X, Y, z)
ax1.set_xlabel('X')
ax1.set_ylabel('Y')
ax1.set_zlabel('Z')
ax1.set_title('3D Mesh Graph')
ax2 = fig.add_subplot(2, 3, 2, projection='3d')
ax2.plot_surface(X, Y, z, cmap='viridis')
ax2.set_xlabel('X')
ax2.set_ylabel('Y')
ax2.set_zlabel('Z')
ax2.set_title('3D Surface Graph')
ax3 = fig.add_subplot(2, 3, 3, projection='3d')
ax3.plot_surface(X, Y, z, cmap='viridis')
ax3.contour(X, Y, z, zdir='z', offset=-1, cmap='viridis')
ax3.set_xlabel('X')
ax3.set_ylabel('Y')
ax3.set_zlabel('Z')
ax3.set_title('3D Surface Graph with Contour Lines')
# Create a 2D sectional view graph for x=1
x1 = 1
y1 = np.linspace(-1.2, 1.2, 100)
z1 = f(x1, y1)
ax4 = fig.add_subplot(2, 3, 4)
ax4.plot(y1, z1)
ax4.set_xlabel('Y')
ax4.set_ylabel('Z')
ax4.set_title('2D Sectional View Graph for x=1')
plt.show()
```
This code will generate a figure with six subplots. The first three subplots are the 3D mesh graph, 3D surface graph, and 3D surface graph with contour lines, respectively. The fourth subplot is the 2D sectional view graph for x=1. The ranges of the x and y axes are both [-1.2, 1.2], and the range of t is set to [-3, 3].