Python，matplotlib。 繪制兩點之間的函數

Question

我想使用 matplotlib 在 2 個點之間繪制一個函數。 類似的問題，但對於 3d 情況沒有工作答案： 如何繪制面向局部 x 軸 matplotlib 3d 的函數？

我認為它應該像這樣工作：

import matplotlib.pyplot as plt
import math

def foo(x, L):
    # some polynomial on [0, L]
    return x**2  # usually it's more difficult


def magic(plt, foo, point1, point2):
    """
    Plot foo from point1 to point2
    :param plt: matplotlib.pyplot
    :param foo: function
    :param point1: tuple (x1, y1) or list [x1, y1]
    :param point2: tuple (x2, y2) or list [x2, y2]
    :return:
    """
    # do magic
    # create modified function along new local x' axis using points in initial x,y axis?
    # create new axis, rotate and move them?
    pass

x1, y1 = 1, 1  # first point coordinates
x2, y2 = 2, 2  # second point coordinates
dx = x1 - x2
dy = y1 - y2
# length, this ratio is always True in my case (see picture below)
L = math.sqrt(dx * dx + dy * dy)

ax, fig = plt.subplots()
magic(plt, foo, (x1,y1), (x2, y2))
plt.show()

重要：沿新軸的長度不會改變。 如果[0, L]上有一個函數[0, L]則意味着它在旋轉/移動或沿新軸表示后將具有相同的域（或“長度”）。

這是我正在嘗試做的事情的圖像

Answer 1

不涉及魔法。 只是從 (0,0) 到 (x1,y1) 的平移和由 dx 和 dy 定義的角度旋轉。 該角度的正弦是 dy/L，余弦是 dx/L。 使用numpy數組既可以方便地編寫函數，又可以加快計算速度。

在下面的代碼中，我更改了示例函數，以更清楚地說明函數是如何轉換的。 此外，縱橫比設置為“相等”。 否則旋轉后的函數看起來會失真。

import matplotlib.pyplot as plt
import numpy as np

def foo(x):
    # some function on [0, L]
    return np.sin(x*20)/(x+1)

def function_on_new_axis(foo, point1, point2):
    """
    Plot foo from point1 to point2
    :param foo: function
    :param point1: tuple (x1, y1) or list [x1, y1]
    :param point2: tuple (x2, y2) or list [x2, y2]
    :return:
    """
    # create modified function along new local x' axis using points in initial x,y axis?
    # create new axis, rotate and move them?
    dx = x2 - x1
    dy = y2 - y1
    L = np.sqrt(dx * dx + dy * dy)
    XI = np.linspace(0, L, 500)  # initial coordinate system
    YI = foo(XI)
    s =  dy  / L  # sine of the rotation angle
    c =  dx  / L  # cosine of the rotation angle
    XM = c * XI - s * YI + x1  # modified coordinate system
    YM = s * XI + c * YI + y1
    plt.plot(XI, YI, color='crimson', alpha=0.3)
    plt.plot(XM, YM, color='crimson')
    plt.plot([x1, x2], [y1, y2], 'go')

x1, y1 = 1, 1  # first point coordinates
x2, y2 = 2, 3  # second point coordinates


fig, ax = plt.subplots()
function_on_new_axis(foo, (x1,y1), (x2, y2))
ax.axis('equal')  # equal aspect ratio between x and y axis to prevent that the function would look skewed
# show the axes at (0,0)
ax.spines['left'].set_position('zero')
ax.spines['right'].set_color('none')
ax.spines['bottom'].set_position('zero')
ax.spines['top'].set_color('none')
plt.show()