[英]How to plot normal vectors in each point of the curve with a given length?
How to plot normal vectors in each point of the curve with a given length?如何在给定长度的曲线的每个点上 plot 法向量?
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)
plt.show()
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
# Calculating the gradient
L=.1 # gradient length
grad = np.ones(shape = (2, x.shape[0]))
grad[0, :] = -2*x
grad /= np.linalg.norm(grad, axis=0) # normalizing to unit vector
nx = np.vstack((x - L/2 * grad[0], x + L/2 * grad[0]))
ny = np.vstack((y - L/2 * grad[1], y + L/2 * grad[1]))
# ax.set_ylim(-0.3, 1.06)
ax.plot(x, y)
ax.plot(nx, ny, 'r')
ax.axis('equal')
plt.show()
To plot the normals
, you need to calculate the slope at each point;对于 plot 的normals
,您需要计算每个点的斜率; from there, you get the tangent vector that you can rotate by pi/2
.从那里,您可以得到可以旋转pi/2
的切线向量。
here is one approach using python i/o np, which makes it probably easier to understand at first.这是使用 python i/o np 的一种方法,起初它可能更容易理解。
Changing the length will adjust the size of the normals to properly scale with your plot.更改长度将调整法线的大小以与 plot 正确缩放。
import matplotlib.pyplot as plt
import numpy as np
import math
def get_normals(length=.1):
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
ax.plot((x0, x0-dy), (y0, y0+dx)) # plot the normals
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)
get_normals()
plt.show()
or longer normals, directed downwards: get_normals(length=-.3)
(use ax.set_aspect('equal')
to maintain angles)或更长的法线,向下: get_normals(length=-.3)
(使用ax.set_aspect('equal')
保持角度)
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