Lissajous 曲线是一个参数曲线，通常通过两个不同频率和相位的和谐振荡来描述。它是二维傅里叶变换的可视表示。
用 Trae 通过 DeepSeek V3-0324 自动生成代码，一次通过。
import numpy as np
import matplotlib . pyplot as plt
from matplotlib . animation import FuncAnimation
class LissajousCurve :
def __init__ ( self , ax , A , B , a , b , delta = 0 ):
"""
Create a Lissajous curve.
Parameters:
ax : axes object
A, B : amplitude for x and y oscillations
a, b : frequency for x and y oscillations
delta : phase difference
"""
self . ax = ax
self . A = A
self . B = B
self . a = a
self . b = b
self . delta = delta
self . t = np . linspace ( 0 , 2 * np . pi , 500 )
self . x = self . A * np . sin ( self . a * self . t + self . delta )
self . y = self . B * np . sin ( self . b * self . t )
# Initialize line and point with empty data
self . line , = ax .plot([], [], 'r-' ) # Red line
self . point , = ax .plot([], [], 'bo' ) # Blue point
def init ( self ):
""" Initialize the plot. Clear the line and point. """
self . line .set_data([], [])
self . point .set_data([], [])
return self . line , self . point ,
def update ( self , frame ):
"""
Update line and point based on the current frame.
"""
# 添加边界检查
if frame >= len ( self . x ):
frame = len ( self . x ) - 1
# 确保数据是序列类型
line_x = self . x [: frame + 1 ] if frame > 0 else []
line_y = self . y [: frame + 1 ] if frame > 0 else []
self . line .set_data( line_x , line_y )
self . point .set_data([ self . x [ frame ]], [ self . y [ frame ]]) # 确保传入的是序列
return self . line , self . point ,
# Create a figure and axis
fig , ax = plt . subplots ( figsize = ( 6 , 6 ))
ax . set_xlim ( - 2.5 , 2.5 )
ax . set_ylim ( - 2 , 2 )
ax . set_aspect ( 'equal' ) # Ensure the aspect ratio is equal
ax . set_title ( "Dynamic Lissajous Curve (A=2, B=1, a=3, b=4)" )
# Create the LissajousCurve object
lc = LissajousCurve ( ax , A = 2 , B = 1 , a = 3 , b = 4 , delta = np . pi / 2 )
# Call FuncAnimation to create an animation
ani = FuncAnimation ( fig , lc . update , frames = 500 , init_func = lc . init , blit = True , interval = 20 )
# 保存为 GIF 文件
ani . save ( 'd:/py_stu/test/lissajous.gif' , writer = 'pillow' , fps = 24 )
# Show the animation
plt . show ()