python one-to-one tutorial: PyGeM Tutorials analysis 1

The author introduces himself: Da Shuangge, The small UP owner of station b, Live programming + red Police three, python 1 to 1 tutor.
This blog is a lesson plan for one-to-one tutoring of students on Python code. It is made public with the permission of the students.
The current specific tutoring content is PyGeM

This article is an explanation and analysis ofPyGeM tutorial-1-ffd
Tutorial 1 shows how to apply the free-form deformation to mesh nodes.

0 preparation

Prepare software

Must be installed

1. python 3.8 or above
   https://www.python.org/downloads/
2. conda
   conda is divided into Anaconda and Miniconda
   If the computer performance is good enough, it is recommended to install Anaconda (this is a big software)https://docs.conda.io/en/latest/miniconda.html Miniconda: https://www.anaconda .com/products/individual Anaconda:
   If the performance is average or you don’t want to install too many big things, you can try to install Miniconda
   
   

Recommended installation
3. Pycharm
https://blog.csdn.net/python1639er/article/details/122629870

Install third-party library pygem

PyGeM cannot be installed directly usingpip. You need to follow the steps below. (To be precise, the pip installation does not meet the requirements and the version is too old)

It is recommended to use Pycharm to create the project first,
and then install it in Pycharm's Terminal. (This is also equivalent to the command line)
When creating a Pycharm projectPython Interpreter it is recommended to choose the following

1. Choose Conda< a i=5> 2Choose according to the location of Conda on your computer

Install dependent libraries first

1. The ones that can be installed directly through pip are
   numpy, scipy, matplotlib, sphinx, pytest
   The installation command is as follows (run in the command line)

pip install numpy
pip install scipy
pip install matplotlib
pip install sphinx
pip install pytest

If you cannot install it, you may need to use a mirror.
Specific recommended reading:
Dashuang Python Introduction Tutorial 8-2 Python Library (Library) and Packages (Package), module (Module)’s third-party library part.

2. Manual installation pythonocc-core
   To use the submodule submodule you need to install this.
   You can use the conda command to install
   . The installation command is as follows (run in the command line)

conda install -c conda-forge pythonocc-core=7.4.0

3. Install PyGeM manually

The installation command is as follows (run in the command line)

git clone https://github.com/mathLab/PyGeM

Then switch the current path of the console to the folder of this project
If you run the above code in the Terminal of the Pycharm project,
At this time, the command to switch paths in Terminal is

cd PyGeM

Then enter the following command to install PyGeM

python setup.py install

It’s basically installed here.

1 beginning

first paragraph

Original text and translation

Free Form Deformation on a sphere
Free Form Deformation on a sphere
In this tutorial we will show the typical workflow to perform a deformation on a generic geometry using the free-form deformation method implemented within PyGeM.
In this tutorial, we will show a typical deformation of generic geometry using the free-form deformation (FFD) method implemented within PyGeM. work process.
A brief theoretical overview of the method is introduced in the pygem.ffd module,
pygem.ffd ,
while in the README you can find several references that focus on FFD.
And in README you can find some references focusing on FFD.

First of all, we import the required PyGeM class and we set matplotlib for 3D plots.
First of all, we import the required PyGeM class and we set matplotlib for 3D plots.
The version of PyGeM we are using in this tutorial is the 2.0.0.
The version of PyGeM we are using in this tutorial is the 2.0.0.

import

Original code

%matplotlib inline
import numpy as np
import mpl_toolkits.mplot3d
import matplotlib.pyplot as plt

import pygem
print(pygem.__version__)
from pygem import FFD

The first line%matplotlib inline is for Ipython compiler (can be used for embedded drawing in web pages),
is usually Jupyter or colab< /span>ipynbNotebook will be used.

Generally, .py files do not need this command. It is best to comment or delete it.

Dashuang Python introductory tutorial 8-1 Importimport

import math
print(math.pi)

from math import pi
print(pi)

import math as m
print(m.pi)

2 mesh_points

Then, the other ingredient is the original geometry we want to deform.
Then, the other ingredient is the original geometry we want to deform.
In this simple tutorial we just span some points around a sphere and morph their coordinates using the FFD class.
In this simple tutorial, we just span a Some points around the sphere and change their coordinates using the FFD class.

def mesh_points(num_pts = 2000):
    indices = np.arange(0, num_pts, dtype=float) + 0.5

    phi = np.arccos(1 - 2*indices/num_pts)
    theta = np.pi * (1 + 5**0.5) * indices

    return np.array([np.cos(theta) * np.sin(phi), np.sin(theta) * np.sin(phi), np.cos(phi)]).T

mesh = mesh_points()
plt.figure(figsize=(8,8)).add_subplot(111, projection='3d').scatter(*mesh.T);
plt.show()

phi

numpy.arange(start, stop, dtype = None)
Return evenly spaced values ​​within a given interval.
Return evenly spaced values ​​within a given interval.

>>> import numpy as np
>>> np.arange(0, 5, dtype=float)
array([0., 1., 2., 3., 4.])
np.arange(0, 5, dtype=float) + 0.5
array([0.5, 1.5, 2.5, 3.5, 4.5])
>>> np.arange(0, 2000, dtype=float) + 0.5
array([5.0000e-01, 1.5000e+00, 2.5000e+00, ..., 1.9975e+03, 1.9985e+03,
       1.9995e+03])

Aboute: Da Shuang Python Introduction Tutorial 1-2 Numbers and Strings

num_ptsTake the default value2000
indices = np.arange(0, 2000, dtype=float) + 0.5
and get an array of 0.5, 1.5, 2.5 until 1999.5

indices/num_pts gets an array of 1 divided into num_pts parts
1 - 2* indices/num_pts gets an array of [-1, 1] divided into num_pts parts

np.arccos(1 - 2*indices/num_pts)obtainable is$[0,An\; array\; composed\; of\; numbers\; between\; \pi ]$ (not equally separated at this time)
is the abscissa of points on the curve corresponding to equally spaced points on the y-axis.

phi corresponds to the spherical coordinate system$\varphi$
For details, see the ellipsoid formula below

theta

np.pi * (1 + 5**0.5) * indices
This is where you are$Pi\ast (1+\sqrt{5})$

This is used to get the coordinates,
It is probably the golden spiral method
I don’t understand the detailed principle, a>
I won’t go into detail here, as long as it works.

If you are interested, you can check this out:
evenly-distributing-n-points-on-a-sphere

return

np.array([np.cos(theta) * np.sin(phi), np.sin(theta) * np.sin(phi), np.cos(phi)])
will get a 3 rowsnum_pts column

[[ 0.05111927 -0.21801231  0.29980505 -0.19082906  ......  -0.17335079  0.14097948]
 [-0.13147935  0.10756687  0.08727502 -0.31414053  ......  0.17043915 -0.0049786 ]
 [ 0.99        0.97        0.95        0.93        ......  -0.97       -0.99      ]]

additional .Tobtained num_ptsrow 3 column

[[ 0.05111927 -0.13147935  0.99      ]
 [-0.21801231  0.10756687  0.97      ]
 [ 0.29980505  0.08727502  0.95      ]
 [-0.19082906 -0.31414053  0.93      ]
 ......
 [-0.17335079  0.17043915 -0.97      ]
 [ 0.14097948 -0.0049786  -0.99      ]]

Official official

ellipsoid

Spherical coordinate system, where$\phi$here is the sky,$\theta$Observe the equation, which is the equivalent of the equation:
$$\begin{gathered} x=a\sin Phi\cos \theta ; \\ and=b\sin Phi\sin \theta ; \\ With=c\cos \phi ; \\ 0\le Phi\le 180^{\circ };0\le i\le 360^{\circ }; \end{gathered}$$

3 first picture

Original code

import numpy as np
import matplotlib.pyplot as plt

def mesh_points(num_pts = 2000):
    indices = np.arange(0, num_pts, dtype=float) + 0.5

    phi = np.arccos(1 - 2*indices/num_pts)
    theta = np.pi * (1 + 5**0.5) * indices

    return np.array([np.cos(theta) * np.sin(phi), np.sin(theta) * np.sin(phi), np.cos(phi)]).T

mesh = mesh_points()
plt.figure(figsize=(8,8)).add_subplot(111, projection='3d').scatter(*mesh.T);
plt.show()

The operation effect is as shown in the figure

Let’s take a detailed look at the drawing part of the code here.

plt.figure(figsize=(8,8)).add_subplot(111, projection='3d').scatter(*mesh.T);
plt.show()

figure

plt.figure(figsize=(8,8))
Create a new figure, or activate an existing figure.
figsize 指定 Width, height in inches.

figureIt can be thought of as a drawing window.

Sample code

import matplotlib.pyplot as plt
fig = plt.figure(figsize=(8,8))
plt.show()

The operation effect is as follows

an empty drawing window

subplot

This method is used to add or plan the axis in the windowfigureaxes

plt.subplot(*args, **kwargs)
Add an Axes to the current figure or retrieve an existing Axes.
Add an Axes to the current figure or retrieve an existing Axes.
This is a wrapper of Figure.add_subplot which provides additional behavior when working with the implicit API (see the notes section).
This is< a A wrapper for i=4> that provides additional behavior when using the implicit API (see comments section). Figure.add_subplot

Call signatures:

subplot(nrows, ncols, index, **kwargs)  # 位置
subplot(pos, **kwargs)  # 位置
subplot(**kwargs)
subplot(ax)

Example: tutorial_101d.pyLike below

import matplotlib.pyplot as plt

# 按 三行x二列 的布局分割窗口，
# 得到总共六块区域
# 在第1个区域，放下第1个轴线 ax1
# plt.subplot(321)
# 下面的和上面的效果相同，下面的写法更正式
ax1 = plt.subplot(3, 2, 1)

# 在第2个区域，放下第2个轴线 ax2
# 该轴线无边框
ax2 = plt.subplot(322, frameon=False)

# 在第3个区域，放下第3个轴线 ax3
# 该轴线为极坐标轴线
ax3 = plt.subplot(323, projection='polar')

# 在第4个区域，放下第4个轴线 ax4
# 该轴线背景色为红色
ax4 = plt.subplot(325, facecolor='red')

plt.show()

The running effect is as shown below

3d

fig.add_subplot(111, projection='3d')

• 111:Lay out the window by one row and one column, and place the axis in the first area.
• projection='3d':A 3D graph axis

Example code

import matplotlib.pyplot as plt

fig = plt.figure(figsize=(8,8))
ax = fig.add_subplot(111, projection='3d')

plt.show()

The running effect is as shown below

The three axes of the 3D diagram are as follows:

scatter

scatter(xs, ys, zs)
Draw a scatter plot
based on the specified x, y, z coordinates

Exampletutorial_101f.pyAs below

import matplotlib.pyplot as plt

fig = plt.figure(figsize=(8,8))

ax = fig.add_subplot(111, projection='3d')

xs = [i for i in range(10)]
ys = [0 for i in range(10)]
zs = [0 for i in range(10)]

ax.scatter(xs, ys, zs)

plt.show()

The operation effect is as follows

Drawing code disassembly

plt.figure(figsize=(8,8)).add_subplot(111, projection='3d').scatter(*mesh.T);

This long code, broken down into step-by-step words,
is equivalent to the following code

fig = plt.figure(figsize=(8,8))
ax = fig.add_subplot(111, projection='3d')
xs, ys, zs = mesh.T
ax.scatter(xs, ys, zs)

It can also be written in the following form.

plt.figure(figsize=(8,8))
plt.add_subplot(111, projection='3d')
xs, ys, zs = mesh.T
plt.scatter(xs, ys, zs)