直观数学-3blue1brown动画的制作

相信很多人都知道3Blue1Brown，这是一个由斯坦福大学的数学系学生Grant Sanderson 创建的YouTube 频道。该频道从独特的视觉角度解说高等数学，内容包括线性代数、微积分、神经网络、黎曼猜想、傅里叶变换以及四元数等等。

本人通过该视频频道获得了很多启发，同时也对其精良的视频制作技术产生了浓厚的兴趣。偶然的机会，得知其在Github上有专门开设了一个动画制作引擎：manim,地址在：

https://github.com/leekunhwee/manimhttps://github.com/leekunhwee/manim

3blue1brown制作的数学解析动画观点高，起点低，把非常复杂的数学原理讲述的非常生动形象，让没有太多数学基础的人也能够感受到数学的美感，今天我们就在UBUNTU18.04上，尝试安装一下3B1B的动画制作环境，说不定某天会用到。

安装环境：

Ubuntu 18.04.5 LTS
Anaconda Python 3.8.5

安装过程：

下载manim

git clone https://github.com/leekunhwee/manim.git

安装依赖，ffmpeg

这一步通过apt-get安装FFMPEG预编译包或者从源码开始编译都可以，从源码安装可以参考

ubuntu18.04编译FFMPEG_tugouxp的专栏-CSDN博客https://blog.csdn.net/tugouxp/article/details/115491843安装依赖，miktex

Getting MiKTeX

下载地址页面有安装说明，按照说明安装即可。

最后执行miktexsetup finish

验证安装依赖包的版本信息

安装python依赖包：

python -m pip install -r requirements.txt

(base) caozilong@caozilong-Vostro-3268:~/mimal/manim$ python -m pip install -r requirements.txt
Ignoring pycairo: markers 'sys_platform == "win32"' don't match your environment
Ignoring pyreadline: markers 'sys_platform == "win32"' don't match your environment
Collecting argparseDownloading argparse-1.4.0-py2.py3-none-any.whl (23 kB)
Collecting colourDownloading colour-0.1.5-py2.py3-none-any.whl (23 kB)
Requirement already satisfied: numpy in /home/caozilong/anaconda3/lib/python3.8/site-packages (from -r requirements.txt (line 3)) (1.19.2)
Requirement already satisfied: Pillow in /home/caozilong/anaconda3/lib/python3.8/site-packages (from -r requirements.txt (line 4)) (8.0.1)
Collecting progressbarDownloading progressbar-2.5.tar.gz (10 kB)
Requirement already satisfied: scipy in /home/caozilong/anaconda3/lib/python3.8/site-packages (from -r requirements.txt (line 6)) (1.5.2)
Requirement already satisfied: tqdm in /home/caozilong/anaconda3/lib/python3.8/site-packages (from -r requirements.txt (line 7)) (4.50.2)
Requirement already satisfied: opencv-python in /home/caozilong/anaconda3/lib/python3.8/site-packages (from -r requirements.txt (line 8)) (4.5.3.56)
Collecting pycairo==1.17.1Downloading pycairo-1.17.1.tar.gz (194 kB)|████████████████████████████████| 194 kB 453 kB/s
Collecting pydub==0.23.0Downloading pydub-0.23.0-py2.py3-none-any.whl (28 kB)
Building wheels for collected packages: progressbar, pycairoBuilding wheel for progressbar (setup.py) ... doneCreated wheel for progressbar: filename=progressbar-2.5-py3-none-any.whl size=12074 sha256=11707eec90e81c753d7d715ef81831bd0c497ff6a0322fd68fda3ce62789b021Stored in directory: /home/caozilong/.cache/pip/wheels/2c/67/ed/d84123843c937d7e7f5ba88a270d11036473144143355e2747Building wheel for pycairo (setup.py) ... doneCreated wheel for pycairo: filename=pycairo-1.17.1-cp38-cp38-linux_x86_64.whl size=258204 sha256=a72ee395c86fa713bad8c6df805187eaee0019fb47831de54b3bcbceeb37987fStored in directory: /home/caozilong/.cache/pip/wheels/92/a5/7c/b88429bb8e47045f531dd3b5dedf5c4202c2750b502c29fb29
Successfully built progressbar pycairo
Installing collected packages: argparse, colour, progressbar, pycairo, pydub
Successfully installed argparse-1.4.0 colour-0.1.5 progressbar-2.5 pycairo-1.17.1 pydub-0.23.0
(base) caozilong@caozilong-Vostro-3268:~/mimal/manim$

conda install pycairo

(base) caozilong@caozilong-Vostro-3268:~/mimal/manim$ conda install pycairo
Collecting package metadata (current_repodata.json): done
Solving environment: -
The environment is inconsistent, please check the package plan carefully
The following packages are causing the inconsistency:- defaults/linux-64::anaconda==2020.11=py38_0- defaults/linux-64::spyder==4.1.5=py38_0- defaults/linux-64::astroid==2.4.2=py38_0- defaults/noarch::python-language-server==0.35.1=py_0- defaults/linux-64::pylint==2.6.0=py38\
done## Package Plan ##environment location: /home/caozilong/anaconda3added / updated specs:- pycairoThe following packages will be downloaded:package                    |            build---------------------------|-----------------_anaconda_depends-2020.07  |           py38_0           6 KBanaconda-custom            |           py38_1          35 KBastroid-2.5                |   py38h06a4308_1         284 KBca-certificates-2021.7.5   |       h06a4308_1         113 KBcertifi-2021.5.30          |   py38h06a4308_0         138 KBconda-4.10.3               |   py38h06a4308_0         2.9 MBlibllvm9-9.0.1             |       h4a3c616_1        21.0 MBopenssl-1.1.1l             |       h7f8727e_0         2.5 MBpycairo-1.19.1             |   py38h708ec4a_0          73 KBsnappy-1.1.8               |       he6710b0_0          40 KBwrapt-1.12.1               |   py38h7b6447c_1          50 KB------------------------------------------------------------Total:        27.1 MBThe following NEW packages will be INSTALLED:_anaconda_depends  pkgs/main/linux-64::_anaconda_depends-2020.07-py38_0h5py               pkgs/main/linux-64::h5py-2.10.0-py38h7918eee_0libllvm9           pkgs/main/linux-64::libllvm9-9.0.1-h4a3c616_1pycairo            pkgs/main/linux-64::pycairo-1.19.1-py38h708ec4a_0snappy             pkgs/main/linux-64::snappy-1.1.8-he6710b0_0wrapt              pkgs/main/linux-64::wrapt-1.12.1-py38h7b6447c_1The following packages will be UPDATED:astroid                                      2.4.2-py38_0 --> 2.5-py38h06a4308_1ca-certificates                              2020.10.14-0 --> 2021.7.5-h06a4308_1certifi            pkgs/main/noarch::certifi-2020.6.20-p~ --> pkgs/main/linux-64::certifi-2021.5.30-py38h06a4308_0conda                                4.9.2-py38h06a4308_0 --> 4.10.3-py38h06a4308_0openssl                                 1.1.1h-h7b6447c_0 --> 1.1.1l-h7f8727e_0The following packages will be DOWNGRADED:anaconda                                   2020.11-py38_0 --> custom-py38_1Proceed ([y]/n)? yDownloading and Extracting Packages
anaconda-custom      | 35 KB     | ##################################### | 100%
openssl-1.1.1l       | 2.5 MB    | ##################################### | 100%
wrapt-1.12.1         | 50 KB     | ##################################### | 100%
certifi-2021.5.30    | 138 KB    | ##################################### | 100%
pycairo-1.19.1       | 73 KB     | ##################################### | 100%
ca-certificates-2021 | 113 KB    | ##################################### | 100%
astroid-2.5          | 284 KB    | ##################################### | 100%
_anaconda_depends-20 | 6 KB      | ##################################### | 100%
snappy-1.1.8         | 40 KB     | ##################################### | 100%
libllvm9-9.0.1       | 21.0 MB   | ##################################### | 100%
conda-4.10.3         | 2.9 MB    | ##################################### | 100%
Preparing transaction: done
Verifying transaction: done
Executing transaction: done
(base) caozilong@caozilong-Vostro-3268:~/mimal/manim$

验证用例：

python -m manim example_scenes.py SquareToCircle -pl

python -m manim example_scenes.py WarpSquare -pl

以一个例子说明3B1B的动画制作原理

from manimlib.imports import *
import os
import pyclbrclass Shapes(Scene):#A few simple shapes#Python 2.7 version runs in Python 3.7 without changesdef construct(self):circle = Circle()square = Square()line=Line(np.array([3,0,0]),np.array([5,0,0]))triangle=Polygon(np.array([0,0,0]),np.array([1,1,0]),np.array([1,-1,0]))self.play(ShowCreation(circle))self.play(FadeOut(circle))self.play(GrowFromCenter(square))self.play(Transform(square,triangle))self.add(line)class MoreShapes(Scene):#A few more simple shapes#2.7 version runs in 3.7 without any changes#Note: I fixed my 'play command not found' issue by installing soxdef construct(self):circle = Circle(color=PURPLE_A)square = Square(fill_color=GOLD_B, fill_opacity=1, color=GOLD_A)square.move_to(UP+LEFT)circle.surround(square)rectangle = Rectangle(height=2, width=3)ellipse=Ellipse(width=3, height=1, color=RED)ellipse.shift(2*DOWN+2*RIGHT)pointer = CurvedArrow(2*RIGHT,5*RIGHT,color=MAROON_C)arrow = Arrow(LEFT,UP)arrow.next_to(circle,DOWN+LEFT)rectangle.next_to(arrow,DOWN+LEFT)ring=Annulus(inner_radius=.5, outer_radius=1, color=BLUE)ring.next_to(ellipse, RIGHT)self.add(pointer)self.play(FadeIn(square))self.play(Rotating(square),FadeIn(circle))self.play(GrowArrow(arrow))self.play(GrowFromCenter(rectangle), GrowFromCenter(ellipse), GrowFromCenter(ring))class MovingShapes(Scene):#Show the difference between .shift() and .move_todef construct(self):circle=Circle(color=TEAL_A)circle.move_to(LEFT)square=Circle()square.move_to(LEFT+3*DOWN)self.play(GrowFromCenter(circle), GrowFromCenter(square), rate=5)self.play(ApplyMethod(circle.move_to,RIGHT), ApplyMethod(square.shift,RIGHT))self.play(ApplyMethod(circle.move_to,RIGHT+UP), ApplyMethod(square.shift,RIGHT+UP))self.play(ApplyMethod(circle.move_to,LEFT+UP), ApplyMethod(square.shift,LEFT+UP))class AddingText(Scene):#Adding text on the screendef construct(self):my_first_text=TextMobject("Writing with manim is fun")second_line=TextMobject("and easy to do!")second_line.next_to(my_first_text,DOWN)third_line=TextMobject("for me and you!")third_line.next_to(my_first_text,DOWN)self.add(my_first_text, second_line)self.wait(2)self.play(Transform(second_line,third_line))self.wait(2)second_line.shift(3*DOWN)self.play(ApplyMethod(my_first_text.shift,3*UP))###Try uncommenting the following####self.play(ApplyMethod(second_line.move_to, LEFT_SIDE-2*LEFT))#self.play(ApplyMethod(my_first_text.next_to,second_line))class AddingMoreText(Scene):#Playing around with text propertiesdef construct(self):quote = TextMobject("Imagination is more important than knowledge")quote.set_color(RED)quote.to_edge(UP)quote2 = TextMobject("A person who never made a mistake never tried anything new")quote2.set_color(YELLOW)author=TextMobject("-Albert Einstein")author.scale(0.75)author.next_to(quote.get_corner(DOWN+RIGHT),DOWN)self.add(quote)self.add(author)self.wait(2)self.play(Transform(quote,quote2),ApplyMethod(author.move_to,quote2.get_corner(DOWN+RIGHT)+DOWN+2*LEFT))self.play(ApplyMethod(author.scale,1.5))author.match_color(quote2)self.play(FadeOut(quote))class RotateAndHighlight(Scene):#Rotation of text and highlighting with surrounding geometriesdef construct(self):square=Square(side_length=5,fill_color=YELLOW, fill_opacity=1)label=TextMobject("Text at an angle")label.bg=BackgroundRectangle(label,fill_opacity=1)label_group=VGroup(label.bg,label)  #Order matterslabel_group.rotate(TAU/8)label2=TextMobject("Boxed text",color=BLACK)label2.bg=SurroundingRectangle(label2,color=BLUE,fill_color=RED, fill_opacity=.5)label2_group=VGroup(label2,label2.bg)label2_group.next_to(label_group,DOWN)label3=TextMobject("Rainbow")label3.scale(2)label3.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)label3.to_edge(DOWN)self.add(square)self.play(FadeIn(label_group))self.play(FadeIn(label2_group))self.play(FadeIn(label3))class BasicEquations(Scene):#A short script showing how to use Latex commandsdef construct(self):eq1=TextMobject("$\\vec{X}_0 \\cdot \\vec{Y}_1 = 3$")eq1.shift(2*UP)eq2=TexMobject(r"\vec{F}_{net} = \sum_i \vec{F}_i")eq2.shift(2*DOWN)self.play(Write(eq1))self.play(Write(eq2))class ColoringEquations(Scene):#Grouping and coloring parts of equationsdef construct(self):line1=TexMobject(r"\text{The vector } \vec{F}_{net} \text{ is the net }",r"\text{force }",r"\text{on object of mass }")line1.set_color_by_tex("force", BLUE)line2=TexMobject("m", "\\text{ and acceleration }", "\\vec{a}", ".  ")line2.set_color_by_tex_to_color_map({"m": YELLOW,"{a}": RED})sentence=VGroup(line1,line2)sentence.arrange_submobjects(DOWN, buff=MED_LARGE_BUFF)self.play(Write(sentence))class UsingBraces(Scene):#Using braces to group text togetherdef construct(self):eq1A = TextMobject("4x + 3y")eq1B = TextMobject("=")eq1C = TextMobject("0")eq2A = TextMobject("5x -2y")eq2B = TextMobject("=")eq2C = TextMobject("3")eq1B.next_to(eq1A,RIGHT)eq1C.next_to(eq1B,RIGHT)eq2A.shift(DOWN)eq2B.shift(DOWN)eq2C.shift(DOWN)eq2A.align_to(eq1A,LEFT)eq2B.align_to(eq1B,LEFT)eq2C.align_to(eq1C,LEFT)eq_group=VGroup(eq1A,eq2A)braces=Brace(eq_group,LEFT)eq_text = braces.get_text("A pair of equations")self.add(eq1A, eq1B, eq1C)self.add(eq2A, eq2B, eq2C)self.play(GrowFromCenter(braces),Write(eq_text))class UsingBracesConcise(Scene):#A more concise block of code with all columns aligneddef construct(self):eq1_text=["4","x","+","3","y","=","0"]eq2_text=["5","x","-","2","y","=","3"]eq1_mob=TexMobject(*eq1_text)eq2_mob=TexMobject(*eq2_text)eq1_mob.set_color_by_tex_to_color_map({"x":RED_B,"y":GREEN_C})eq2_mob.set_color_by_tex_to_color_map({"x":RED_B,"y":GREEN_C})for i,item in enumerate(eq2_mob):item.align_to(eq1_mob[i],LEFT)eq1=VGroup(*eq1_mob)eq2=VGroup(*eq2_mob)eq2.shift(DOWN)eq_group=VGroup(eq1,eq2)braces=Brace(eq_group,LEFT)eq_text = braces.get_text("A pair of equations")self.play(Write(eq1),Write(eq2))self.play(GrowFromCenter(braces),Write(eq_text))class PlotFunctions(GraphScene):CONFIG = {"x_min" : -10,"x_max" : 10.3,"y_min" : -1.5,"y_max" : 1.5,"graph_origin" : ORIGIN ,"function_color" : RED ,"axes_color" : GREEN,"x_labeled_nums" :range(-10,12,2),}   def construct(self):self.setup_axes(animate=True)func_graph=self.get_graph(self.func_to_graph,self.function_color)func_graph2=self.get_graph(self.func_to_graph2)vert_line = self.get_vertical_line_to_graph(TAU,func_graph,color=YELLOW)graph_lab = self.get_graph_label(func_graph, label = "\\cos(x)")graph_lab2=self.get_graph_label(func_graph2,label = "\\sin(x)", x_val=-10, direction=UP/2)two_pi = TexMobject("x = 2 \\pi")label_coord = self.input_to_graph_point(TAU,func_graph)two_pi.next_to(label_coord,RIGHT+UP)self.play(ShowCreation(func_graph),ShowCreation(func_graph2))self.play(ShowCreation(vert_line), ShowCreation(graph_lab), ShowCreation(graph_lab2),ShowCreation(two_pi))def func_to_graph(self,x):return np.cos(x)def func_to_graph2(self,x):return np.sin(x)class ExampleApproximation(GraphScene):CONFIG = {"function" : lambda x : np.cos(x), "function_color" : BLUE,"taylor" : [lambda x: 1, lambda x: 1-x**2/2, lambda x: 1-x**2/math.factorial(2)+x**4/math.factorial(4), lambda x: 1-x**2/2+x**4/math.factorial(4)-x**6/math.factorial(6),lambda x: 1-x**2/math.factorial(2)+x**4/math.factorial(4)-x**6/math.factorial(6)+x**8/math.factorial(8), lambda x: 1-x**2/math.factorial(2)+x**4/math.factorial(4)-x**6/math.factorial(6)+x**8/math.factorial(8) - x**10/math.factorial(10)],"center_point" : 0,"approximation_color" : GREEN,"x_min" : -10,"x_max" : 10,"y_min" : -1,"y_max" : 1,"graph_origin" : ORIGIN ,"x_labeled_nums" :range(-10,12,2),}def construct(self):self.setup_axes(animate=True)func_graph = self.get_graph(self.function,self.function_color,)approx_graphs = [self.get_graph(f,self.approximation_color)for f in self.taylor]term_num = [TexMobject("n = " + str(n),aligned_edge=TOP)for n in range(0,8)]#[t.to_edge(BOTTOM,buff=SMALL_BUFF) for t in term_num]#term = TexMobject("")#term.to_edge(BOTTOM,buff=SMALL_BUFF)term = VectorizedPoint(3*DOWN)approx_graph = VectorizedPoint(self.input_to_graph_point(self.center_point, func_graph))self.play(ShowCreation(func_graph),)for n,graph in enumerate(approx_graphs):self.play(Transform(approx_graph, graph, run_time = 2),Transform(term,term_num[n]))self.wait()class DrawAnAxis(Scene):CONFIG = { "plane_kwargs" : { "x_line_frequency" : 2,"y_line_frequency" :2}}def construct(self):my_plane = NumberPlane(**self.plane_kwargs)my_plane.add(my_plane.get_axis_labels())self.add(my_plane)#self.wait()class SimpleField(Scene):CONFIG = {"plane_kwargs" : {"color" : RED},}def construct(self):plane = NumberPlane(**self.plane_kwargs) #Create axes and gridplane.add(plane.get_axis_labels())  #add x and y labelself.add(plane)  #Place grid on screenpoints = [x*RIGHT+y*UPfor x in np.arange(-5,5,1)for y in np.arange(-5,5,1)]     #List of vectors pointing to each grid pointvec_field = []  #Empty list to use in for loopfor point in points:field = 0.5*RIGHT + 0.5*UP   #Constant field up and to rightresult = Vector(field).shift(point)   #Create vector and shift it to grid pointvec_field.append(result)   #Append to listdraw_field = VGroup(*vec_field)   #Pass list of vectors to create a VGroupself.play(ShowCreation(draw_field))   #Draw VGroup on screenclass FieldWithAxes(Scene):CONFIG = {"plane_kwargs" : {"color" : RED_B},"point_charge_loc" : 0.5*RIGHT-1.5*UP,}def construct(self):plane = NumberPlane(**self.plane_kwargs)#plane.main_lines.fade(.9)  #doesn't work in most recent commitplane.add(plane.get_axis_labels())self.add(plane)field = VGroup(*[self.calc_field(x*RIGHT+y*UP)for x in np.arange(-9,9,1)for y in np.arange(-5,5,1)])self.play(ShowCreation(field))def calc_field(self,point):#This calculates the field at a single point.x,y = point[:2]Rx,Ry = self.point_charge_loc[:2]r = math.sqrt((x-Rx)**2 + (y-Ry)**2)efield = (point - self.point_charge_loc)/r**3#efield = np.array((-y,x,0))/math.sqrt(x**2+y**2)  #Try one of these two fields#efield = np.array(( -2*(y%2)+1 , -2*(x%2)+1 , 0 ))/3  #Try one of these two fieldsreturn Vector(efield).shift(point)class ExampleThreeD(ThreeDScene):CONFIG = {"plane_kwargs" : {"color" : RED_B},"point_charge_loc" : 0.5*RIGHT-1.5*UP,}def construct(self):plane = NumberPlane(**self.plane_kwargs)#plane.main_lines.fade(.9)   #Doesn't work in most recent commitplane.add(plane.get_axis_labels())self.add(plane)field2D = VGroup(*[self.calc_field2D(x*RIGHT+y*UP)for x in np.arange(-9,9,1)for y in np.arange(-5,5,1)])self.set_camera_orientation(phi=PI/3,gamma=PI/5)self.play(ShowCreation(field2D))self.wait()#self.move_camera(gamma=0,run_time=1)   #Doesn't work in most recent commit#self.move_camera(phi=3/4*PI, theta=-PI/2)   #Doesn't work in most recent commitself.begin_ambient_camera_rotation(rate=0.1)self.wait(6)def calc_field2D(self,point):x,y = point[:2]Rx,Ry = self.point_charge_loc[:2]r = math.sqrt((x-Rx)**2 + (y-Ry)**2)efield = (point - self.point_charge_loc)/r**3return Vector(efield).shift(point)class EFieldInThreeD(ThreeDScene):CONFIG = {"plane_kwargs" : {"color" : RED_B},"point_charge_loc" : 0.5*RIGHT-1.5*UP,}def construct(self):plane = NumberPlane(**self.plane_kwargs)#plane.main_lines.fade(.9)  #Doesn't work in most recent commitplane.add(plane.get_axis_labels())self.add(plane)field2D = VGroup(*[self.calc_field2D(x*RIGHT+y*UP)for x in np.arange(-9,9,1)for y in np.arange(-5,5,1)])field3D = VGroup(*[self.calc_field3D(x*RIGHT+y*UP+z*OUT)for x in np.arange(-9,9,1)for y in np.arange(-5,5,1)for z in np.arange(-5,5,1)])self.play(ShowCreation(field3D))self.wait()#self.move_camera(0.8*np.pi/2, -0.45*np.pi)   #Doesn't work in most recent commitself.begin_ambient_camera_rotation()self.wait(6)def calc_field2D(self,point):x,y = point[:2]Rx,Ry = self.point_charge_loc[:2]r = math.sqrt((x-Rx)**2 + (y-Ry)**2)efield = (point - self.point_charge_loc)/r**3return Vector(efield).shift(point)def calc_field3D(self,point):x,y,z = pointRx,Ry,Rz = self.point_charge_locr = math.sqrt((x-Rx)**2 + (y-Ry)**2+(z-Rz)**2)efield = (point - self.point_charge_loc)/r**3#efield = np.array((-y,x,z))/math.sqrt(x**2+y**2+z**2)return Vector(efield).shift(point)class MovingCharges(Scene):CONFIG = {"plane_kwargs" : {"color" : RED_B},"point_charge_loc" : 0.5*RIGHT-1.5*UP,}def construct(self):plane = NumberPlane(**self.plane_kwargs)#plane.main_lines.fade(.9)  #Doesn't work in most recent commitplane.add(plane.get_axis_labels())self.add(plane)field = VGroup(*[self.calc_field(x*RIGHT+y*UP)for x in np.arange(-9,9,1)for y in np.arange(-5,5,1)])self.field=fieldsource_charge = self.Positron().move_to(self.point_charge_loc)self.play(FadeIn(source_charge))self.play(ShowCreation(field))self.moving_charge()def calc_field(self,point):x,y = point[:2]Rx,Ry = self.point_charge_loc[:2]r = math.sqrt((x-Rx)**2 + (y-Ry)**2)efield = (point - self.point_charge_loc)/r**3return Vector(efield).shift(point)def moving_charge(self):numb_charges=4possible_points = [v.get_start() for v in self.field]points = random.sample(possible_points, numb_charges)particles = VGroup(*[self.Positron().move_to(point)for point in points])for particle in particles:particle.velocity = np.array((0,0,0))self.play(FadeIn(particles))self.moving_particles = particlesself.add_foreground_mobjects(self.moving_particles )self.always_continually_update = Trueself.wait(10)def field_at_point(self,point):x,y = point[:2]Rx,Ry = self.point_charge_loc[:2]r = math.sqrt((x-Rx)**2 + (y-Ry)**2)efield = (point - self.point_charge_loc)/r**3return efielddef continual_update(self, *args, **kwargs):if hasattr(self, "moving_particles"):dt = self.frame_durationfor p in self.moving_particles:accel = self.field_at_point(p.get_center())p.velocity = p.velocity + accel*dtp.shift(p.velocity*dt)class Positron(Circle):CONFIG = {"radius" : 0.2,"stroke_width" : 3,"color" : RED,"fill_color" : RED,"fill_opacity" : 0.5,}def __init__(self, **kwargs):Circle.__init__(self, **kwargs)plus = TexMobject("+")plus.scale(0.7)plus.move_to(self)self.add(plus)class FieldOfMovingCharge(Scene):CONFIG = {"plane_kwargs" : {"color" : RED_B},"point_charge_start_loc" : 5.5*LEFT-1.5*UP,}def construct(self):plane = NumberPlane(**self.plane_kwargs)#plane.main_lines.fade(.9)   #Doesn't work in most recent commitplane.add(plane.get_axis_labels())self.add(plane)field = VGroup(*[self.create_vect_field(self.point_charge_start_loc,x*RIGHT+y*UP)for x in np.arange(-9,9,1)for y in np.arange(-5,5,1)])self.field=fieldself.source_charge = self.Positron().move_to(self.point_charge_start_loc)self.source_charge.velocity = np.array((1,0,0))self.play(FadeIn(self.source_charge))self.play(ShowCreation(field))self.moving_charge()def create_vect_field(self,source_charge,observation_point):return Vector(self.calc_field(source_charge,observation_point)).shift(observation_point)def calc_field(self,source_point,observation_point):x,y,z = observation_pointRx,Ry,Rz = source_pointr = math.sqrt((x-Rx)**2 + (y-Ry)**2 + (z-Rz)**2)if r<0.0000001:   #Prevent divide by zeroefield = np.array((0,0,0))  else:efield = (observation_point - source_point)/r**3return efielddef moving_charge(self):numb_charges=3possible_points = [v.get_start() for v in self.field]points = random.sample(possible_points, numb_charges)particles = VGroup(self.source_charge, *[self.Positron().move_to(point)for point in points])for particle in particles[1:]:particle.velocity = np.array((0,0,0))self.play(FadeIn(particles[1:]))self.moving_particles = particlesself.add_foreground_mobjects(self.moving_particles )self.always_continually_update = Trueself.wait(10)def continual_update(self, *args, **kwargs):Scene.continual_update(self, *args, **kwargs)if hasattr(self, "moving_particles"):dt = self.frame_durationfor v in self.field:field_vect=np.zeros(3)for p in self.moving_particles:field_vect = field_vect + self.calc_field(p.get_center(), v.get_start())v.put_start_and_end_on(v.get_start(), field_vect+v.get_start())for p in self.moving_particles:accel = np.zeros(3)p.velocity = p.velocity + accel*dtp.shift(p.velocity*dt)class Positron(Circle):CONFIG = {"radius" : 0.2,"stroke_width" : 3,"color" : RED,"fill_color" : RED,"fill_opacity" : 0.5,}def __init__(self, **kwargs):Circle.__init__(self, **kwargs)plus = TexMobject("+")plus.scale(0.7)plus.move_to(self)self.add(plus)HEAD_INDEX   = 0
BODY_INDEX   = 1
ARMS_INDEX   = 2
LEGS_INDEX   = 3class StickMan(SVGMobject):CONFIG = {"color" : BLUE_E,"file_name_prefix": "stick_man","stroke_width" : 2,"stroke_color" : WHITE,"fill_opacity" : 1.0,"height" : 3,}def __init__(self, mode = "plain", **kwargs):digest_config(self, kwargs)self.mode = modeself.parts_named = Falsetry:svg_file = os.path.join(SVG_IMAGE_DIR,"%s_%s.svg" % (self.file_name_prefix, mode))SVGMobject.__init__(self, file_name=svg_file, **kwargs)except:warnings.warn("No %s design with mode %s" %(self.file_name_prefix, mode))svg_file = os.path.join(SVG_IMAGE_DIR,"stick_man_plain.svg",)SVGMobject.__init__(self, mode="plain", file_name=svg_file, **kwargs)def name_parts(self):self.head = self.submobjects[HEAD_INDEX]self.body = self.submobjects[BODY_INDEX]self.arms = self.submobjects[ARMS_INDEX]self.legs = self.submobjects[LEGS_INDEX]self.parts_named = Truedef init_colors(self):SVGMobject.init_colors(self)if not self.parts_named:self.name_parts()self.head.set_fill(self.color, opacity = 1)self.body.set_fill(RED, opacity = 1)self.arms.set_fill(YELLOW, opacity = 1)self.legs.set_fill(BLUE, opacity = 1)return selfclass Waving(Scene):def construct(self):start_man = StickMan()plain_man = StickMan()waving_man = StickMan("wave")self.add(start_man)self.wait()self.play(Transform(start_man,waving_man))self.play(Transform(start_man,plain_man))self.wait()class CirclesAndSquares(SVGMobject):CONFIG = {"color" : BLUE_E,"file_name_prefix": "circles_and_squares","stroke_width" : 2,"stroke_color" : WHITE,"fill_opacity" : 1.0,"height" : 3,"start_corner" : None,"circle_index" : 0,"line1_index" :1,"line2_index" : 2,"square1_index" : 3,"square2_index" : 4,}def __init__(self, mode = "plain", **kwargs):digest_config(self, kwargs)self.mode = modeself.parts_named = Falsetry:svg_file = os.path.join(SVG_IMAGE_DIR,"%s_%s.svg" % (self.file_name_prefix, mode))SVGMobject.__init__(self, file_name=svg_file, **kwargs)except:warnings.warn("No %s design with mode %s" %(self.file_name_prefix, mode))svg_file = os.path.join(SVG_IMAGE_DIR,"circles_and_squares_plain.svg",)SVGMobject.__init__(self, mode="plain", file_name=svg_file, **kwargs)def name_parts(self):self.circle = self.submobjects[self.circle_index]self.line1 = self.submobjects[self.line1_index]self.line2 = self.submobjects[self.line2_index]self.square1 = self.submobjects[self.square1_index]self.square2 = self.submobjects[self.square2_index]self.parts_named = Truedef init_colors(self):SVGMobject.init_colors(self)self.name_parts()self.circle.set_fill(RED, opacity = 1)self.line1.set_fill(self.color, opacity = 0)self.line2.set_fill(self.color, opacity = 0)self.square1.set_fill(GREEN, opacity = 1)self.square2.set_fill(BLUE, opacity = 1)return selfclass SVGCircleAndSquare(Scene):def construct(self):thingy = CirclesAndSquares()self.add(thingy)self.wait()if __name__ == "__main__":# Call this file at command line to make sure all scenes work with version of manim# type "python manim_tutorial_P37.py" at command line to run all scenes in this file#Must have "import os" and  "import pyclbr" at start of file to use this###Using Python class browser to determine which classes are defined in this filemodule_name = 'manim_tutorial_P37'   #Name of current filemodule_info = pyclbr.readmodule(module_name)for item in module_info.values():if item.module==module_name:print(item.name)os.system("python -m manim manim_tutorial_P37.py %s -l" % item.name)  #Does not play files

执行测试

python -m manim manim_tutorial_P37.py MoreShapes -pl

效果：

还有其他一些例子，比如：

支持字体：

此时的环境不支持字体显示，执行带有字体处理的用例会失败，所以接下来需要支持字体处理

安装字体文件：

physics.sty：https://mirrors.ctan.org/macros/latex/contrib/physics/physics.sty
dsfont.sty：

将这两个文件下载到：

/usr/share/texlive/texmf-dist/tex/latex/physics/physics.sty

和

/usr/share/texlive/texmf-dist/tex/latex/dsfont/

最后执行sudo mktexlsr，如下图所示：

OK，现在可以支持字体显示了，我们重新运行用例：

python -m manim manim_tutorial_P37.py PlotFunctions  -pl

manim_tutorial_P37.py中有21个用例，安装字体后都可以运行

高端一些的例子：

git clone https://github.com/3b1b/manim.git

pip install -e .

验证命令：

manimgl example_scenes.py OpeningManimExample

或者

manim-render example_scenes.py OpeningManimExample

效果：

总结：

3B1B 动画的制作思路是：根据自己想在场景中展现的内容和效果编写一系列的类，然后通过命令行对每个类进行实例化，前面输入的测试命令其实就包含了类的实例化过程，而每个类被实例化后都将得到一个动画片段，通过视频制作软件将各个片段衔接起来并配音，就能得到大家喜闻乐见的 3B1B 教学动画了。

结束！