如何移动二次线？

Question

如何将二次蓝线移动到较低的位置？现在曲线之间的空间是不一样的，因为二次函数。

import matplotlib.pyplot as plt
import numpy as np

fig, ax = plt.subplots()
plt.rcParams["figure.figsize"] = [8, 8]

x = np.linspace(-1, 1, 100)
y = x**2
ax.set_ylim(-0.3, 1.06)
ax.plot(x, y)
ax.scatter(1/2*(ax.get_xlim()[0] + ax.get_xlim()[1]), 0.15, marker = 'o', s=900, facecolors='none')
width_l = ax.get_ylim()[1] - ax.get_ylim()[0]
ax.plot(x, y - 0.1*width_l)

plt.show()

想要的结果是两条平行线：

Answer 1

这是一种从曲线计算法线的方法，并在给定距离处绘制平行线，该距离指定为法线的length：

import matplotlib.pyplot as plt
import numpy as np
import math

def get_parallels(length=.1):
    
    px, py = [], []
    
    for idx in range(len(x)-1):
        x0, y0, xa, ya = x[idx], y[idx], x[idx+1], y[idx+1]
        dx, dy = xa-x0, ya-y0
        norm = math.hypot(dx, dy) * 1/length
        dx /= norm
        dy /= norm        
        px.append(x0-dy)
        py.append(y0+dx)
    return px, py


fig, ax = plt.subplots()
plt.rcParams["figure.figsize"] = [8, 8]

x = np.linspace(-1, 1, 100)
y = x**2
ax.set_ylim(-0.3, 1.06)
ax.plot(x, y)
for length in (-.3, -.2, -.1, .1, .2, .3, .4):
    ax.plot(*get_parallels(length=length))


plt.show()

或绘制一个不合理的数字：

for length in (ndx*.025 for ndx in range(-100, 20) if ndx != 0 ):
    ax.plot(*get_parallels(length=length))