如何在表面图上投影一条线？ [英] How to project a line on a surfaceplot?

问题描述

我有一个根据存储在CSV文件中的点数据创建的曲面图。如果要在3D创建的曲面上投影一条线（浮在曲面上方）。用什么方法？

我尝试了

我已经生成了一个曲面，给定的分散点存储在CSV文件中。现在，我想将曲面（红线）上的线投影到曲面（如绿线）上。

解决方案

让我们构建一个通用的MCVE，首先我们导入所需的软件包：

  import numpy as np 
 from scipy import interpolate 
 as plt 
从mpl_toolkits导入matplotlib.pyplot导入mplot3d 
 import matplotlib.tri as mtri 
 np.random.seed（123456）＃修复随机种子
  

现在，我们生成表面 S 的3D点集合（注意它是不规则的网格）：

  NS = 100 
 Sx = np.random.uniform（low = -1 。，high = 1。，size =（NS，））
 Sy = np.random.uniform（low = -1。，high = 1。，size =（NS，））
 Sz = -（Sx ** 2 + Sy ** 2）+ 0.1 * np.random.normal（size =（NS，））
  

和参数曲线 P ：

  NP = 100 
t = np.linspace（-1，1，NP）
 Px = t 
 Py = t ** 2-2- 0.5 
 Pz = t ** 3 + 1 
  

解决问题的关键是

完整的3D结果显示如下：

  axe = plt.axes（projection ='3d'）
 axe.plot_trisurf（tri，Sz，cmap ='jet'，alpha = 0.5）
 axe.plot（Px，Py， Pz）
 axe.plot（Px，Py，PSz，线宽= 2，color ='黑色'）
 axe.scatter（Sx，Sy，Sz）
 axe.view_init（elev = 25，azim = -45）
  

  axe.view_init（elev = 75，azim = -45）
  

I Have a surface plot created from point data stored in a CSV file. If I want to project a line (which is floating above the surface) on the surface created in 3D. What is the method?

I have tried a code from the following post for projecting a line on xy-xz-yz plane.
I can see that it is projecting the endpoint of line on the xy-xz-yz plane.

If I want to project on the surface created with point data. I don't have an equation of the surface. I have created with point data available.

Here is a mockup image of what I'm trying to achieve:

I have generated a curved surface with given scattered points stored in a CSV file. Now I want to project the line on top of the surface(red line) to the surface(as a green line).

解决方案

Lets build a generic MCVE, first we import required packages:

import numpy as np
from scipy import interpolate
import matplotlib.pyplot as plt
from mpl_toolkits import mplot3d
import matplotlib.tri as mtri
np.random.seed(123456) # Fix the random seed

Now we generate a collection of 3D points for a surface S (notice it is an irregular mesh):

NS = 100
Sx = np.random.uniform(low=-1., high=1., size=(NS,))
Sy = np.random.uniform(low=-1., high=1., size=(NS,))
Sz = -(Sx**2 + Sy**2) + 0.1*np.random.normal(size=(NS,))

And a parametric curve P:

NP = 100
t = np.linspace(-1, 1, NP)
Px = t
Py = t**2 - 0.5
Pz = t**3 + 1

The key to solve your problem is LinearNDInterpolator which performs a piecewise linear interpolation in N dimensions:

PSz = interpolate.LinearNDInterpolator(list(zip(Sx, Sy)), Sz)(list(zip(Px,Py)))

There is just the need to reshape data to fit the method signature from separate vectors to matrix of shape (Nsample,Ndims) which can be translated to:

list(zip(Sx, Sy))

We can check the data from the top:

tri = mtri.Triangulation(Sx, Sy)
fig, axe = plt.subplots()
axe.plot(Sx, Sy, '+')
axe.plot(Px, Py)
axe.triplot(tri, linewidth=1, color='gray')
axe.set_aspect('equal')
axe.grid()

The complete 3D result is shown bellow:

axe = plt.axes(projection='3d')
axe.plot_trisurf(tri, Sz, cmap='jet', alpha=0.5)
axe.plot(Px, Py, Pz)
axe.plot(Px, Py, PSz, linewidth=2, color='black')
axe.scatter(Sx, Sy, Sz)
axe.view_init(elev=25, azim=-45)

axe.view_init(elev=75, azim=-45)

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