评估半球内点的函数并在 Python 中绘制幻灯片
我正在尝试评估一个函数，该函数取决于从球体中心到半球体内任意点的半径。
我首先定义三个数组，分别对应沿半径、仰角和方位角的点。在 for 循环中，我计算 x、y 和 z 坐标来评估函数。
我不确定我是否正确进行了映射。我需要将求值函数的值存储在与 x、y 和 z 坐标相对应的 3D 矩阵中，以便在后处理步骤中绘制切片，但我一直在确定如何定义函数矩阵的大小。
在笛卡尔坐标系中非常容易，因为可以将每个坐标与矩阵的维数联系起来。这就是为什么我需要一些关于如何滑动矩阵的指导，因为我没有带有笛卡尔坐标的 3D 矩阵。我如何从球坐标构建这个矩阵？
任何帮助将不胜感激！
这是我的（没有成果的）尝试：
import numpy as np
beta = 1
rho = np.linspace(0, 1, 20)
phi = np.linspace(0, 2*np.pi, 20)
theta = np.linspace(0, np.pi/2, 10)
f = np.empty([len(theta), len(theta), len(phi)], dtype=complex)
for i in range(len(rho)):
for j in range(len(phi)):
for k in range(len(theta)):
x = rho[i] * np.sin(theta[k]) * np.cos(phi[j])
y = rho[i] * np.sin(theta[k]) * np.sin(phi[j])
z = rho[i] * np.cos(theta[k])
R = np.sqrt(x**2 + y**2 + z**2)
f[k, i, j] = -1j*((z/R)/(z/R + beta)) * (np.exp(1j*k*R)/R)
I am trying to evaluate a function that depends on the radius from the center of a sphere to any point inside half a sphere.
I start by defining three arrays corresponding to the points along the radius, the elevation and azimuthal angles. In a for loop I compute the x, y and z coordinates to evaluate the function.
I am not sure if I am doing the mapping properly. I need to store the values of the evaluated function in a 3D matrix corresponding to the x, y, and z coordinates to plot slices in a postprocessing step, but I am stuck identifying how I can define the size of my function matrix.
In cartesian coordinates is really easy since one can link every coordinate with the dimension of the matrix. That's why I need some guidance in how I can slide the matrix since I don't have a 3D matrix with the cartesian coordinates. How I can construct this matrix from the spherical coordintaes?
Any help will be more than appreciated!
Here is my (unfruitful) attempt:
import numpy as np
beta = 1
rho = np.linspace(0, 1, 20)
phi = np.linspace(0, 2*np.pi, 20)
theta = np.linspace(0, np.pi/2, 10)
f = np.empty([len(theta), len(theta), len(phi)], dtype=complex)
for i in range(len(rho)):
for j in range(len(phi)):
for k in range(len(theta)):
x = rho[i] * np.sin(theta[k]) * np.cos(phi[j])
y = rho[i] * np.sin(theta[k]) * np.sin(phi[j])
z = rho[i] * np.cos(theta[k])
R = np.sqrt(x**2 + y**2 + z**2)
f[k, i, j] = -1j*((z/R)/(z/R + beta)) * (np.exp(1j*k*R)/R)
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评论（1）
你只是有一个错字，第二个维度又是 len(theta) 而不是 len(rho)。还应该
注意的是，如果我没记错的话，你根本不需要
R，它只是rho[i]。You just have a typo, the second dimension is again len(theta) isntead of len(rho). It should be
Note also that, if I am not mistaken, you don't need
Rat all, it's justrho[i].