manim
2024-09-08 13:54:16
from manim import *
#导入manim命名空间
#这是一个最基本的manim结构，类名叫做BaseFrame，传入一个场景Scene，并且包含一个construct方法，传入self
class BaseFrame(Scene):
def construct(self):
self.wait()
class CreateCircle(Scene):
def construct(self):
circle = Circle() # 创建了一个Circle对象：circle
circle.set_fill(PINK, opacity=0.5) # set the color and transparency
self.play(Create(circle)) # show the circle on screen
class SquareToCircle(Scene):
def construct(self):
circle = Circle() # create a circle
circle.set_fill(PINK, opacity=0.5) # set color and transparency
square = Square() # create a square
square.rotate(PI / 4) # rotate a certain amount
self.play(Create(square)) # animate the creation of the square
self.play(Transform(square, circle)) # interpolate the square into the circle
self.play(FadeOut(square)) # fade out animation
class SquareAndCircle(Scene):
def construct(self):
circle = Circle() # create a circle
circle.set_fill(PINK, opacity=0.5) # set the color and transparency
square = Square() # create a square
square.set_fill(BLUE, opacity=0.5) # set the color and transparency
square.next_to(circle, RIGHT, buff=0.5) # set the position
self.play(Create(circle), Create(square)) # show the shapes on screen
class ThreePar(Scene):
def construct(self):
circle = Circle()
circle.set_fill(RED, opacity=0.6)
star = Star()
star.set_fill(BLUE, opacity=0.4)
square = Square()
square.set_fill(BLUE, opacity=0.5)
circle.next_to(star, LEFT, buff=0.5)
square.next_to(star, RIGHT, buff=0.5)
#占用1秒的时长，
#如果你的Create方法是在play里面的，他就会占用一秒钟的时间去展示创建对象的过程
self.add(star)
self.add(circle)#无意义的，后面的Create(circle)会创建，系统会删除次代码
self.play(Create(circle),Create(square))
self.wait(1)
self.remove(star)
self.wait(1)
class AnimatedSquareToCircle(Scene):
def construct(self):
circle = Circle() # create a circle
square = Square() # create a square
#Play_Scripts_Start
self.play(Create(square)) # show the square on screen
self.play(square.animate.rotate(PI / 4)) # 旋转图形，参数是弧度制
self.play(
ReplacementTransform(square, circle)
) # transform the square into a circle
self.play(
circle.animate.set_fill(PINK, opacity=0.5)
) # color the circle on screen
#Play_Scripts_End
class DifferentRotations(Scene):
def construct(self):
left_square = Square(color=BLUE, fill_opacity=0.7).shift(2 * LEFT)
right_square = Square(color=GREEN, fill_opacity=0.7).shift(2 * RIGHT)
self.play(
left_square.animate.rotate(PI), Rotate(right_square, angle=PI), run_time=2
)
self.wait()
#默认情况下，对象会生成在屏幕中心点
class Learn01_move(Scene):
def construct(self):
circle = Circle()
triangle = Triangle()
self.add(circle,triangle)
print ("移动")
self.wait(1)
circle.shift(LEFT*3 + UP*2)
#瞬间移动,LEFT,UP是单位方向向量
#以自身为参考
self.wait(1)
triangle.next_to(circle,RIGHT)
#瞬间移动
#以传入对象为参考
self.wait(1)
circle.move_to(DOWN)
#瞬间移动
#以屏幕中心为参考
self.wait(1)
triangle.align_to(circle,DOWN)
#瞬间移动
#以传入对象的假想边界作为调整
#传入DOWN(0,-1)，那么物体的纵坐标就会"对其"对象的下边界
#这个假想的边界一般以物体以中心为原点的第二象限区域
self.wait(1)
class Learn02_beauty(Scene):
def construct(self):
circle = Circle().shift(LEFT*2)
star = Star().shift(RIGHT*2)
self.play(Create(circle), Create(star))
self.wait(1)
#set_fill() 改变图形的内部
#set_stroke()改变图形的边框
star.set_stroke(color=YELLOW, width=20)
circle.set_stroke(color=BLUE, width=20)
star.set_fill(YELLOW, opacity=0.7)
circle.set_fill(YELLOW, opacity=0.7)
self.wait(1)
class Learn03_animations(Scene):
def construct(self):
star = Star()
self.play(FadeIn(star))#渐入特效
#self.play(FadeIn(star),run_time = 5)可以设置时间
self.wait(1)
self.play(Rotate(star, 2*PI))#旋转特效
self.wait(1)
self.play(FadeOut(star))#渐出特效
#animate方法
#这样就可以
class Learn04_animateMethod(Scene):
def construct(self):
star = Star()
self.play(star.animate.set_fill(YELLOW, opacity=0.4))
self.wait(1)
self.play(star.animate.set_fill(WHITE))
self.wait(1)
#也可以同时进行animate方法
self.play(
star.animate
.shift(UP+LEFT)
.rotate(2/3*PI)
.set_fill(RED)
)
self.wait(1)
#也可以在play中添加run_time参数，修改动画持续时间
self.play(
star.animate
.shift(-UP-LEFT)
.rotate(2/3*PI)
.set_fill(BLUE)
,run_time = 5
)
self.wait(1)
#创建自定义动画
#重写interpolate_mobject()方法
class Countqq(Animation):
#kwargs是可变参数，此处暂时用不上
def __init__(self, number: DecimalNumber, start: float, end: float, **kwargs):
# Pass number as the mobject of the animation
#这个是构造方法，使用到我们这个Countqq这个类的时候就会自动把参数传入此方法中
#self在构造的时候不需要传递
super().__init__(number, **kwargs)
# Set start and end
self.start = start
self.end = end
def interpolate_mobject(self, alpha: float):
# Set value of DecimalNumber according to alpha
#这一行是增长的 这个是manim系统内部调用的，我们就不管他了。
value = self.start + (alpha * (self.end - self.start))
self.mobject.set_value(value)
class Learn05_CountingScene(Scene):
def construct(self):
#创建一个Decimal数字，设置颜色，缩放比
number = DecimalNumber().set_color(BLUE).scale(5).move_to(LEFT)
#添加一个定时更新器,ORIGIN相当于[0,0,0],移动到屏幕中心点
#匿名函数lambda构建方法 lambda XXX:___
number.add_updater(lambda number: number)
self.add(number)
self.wait(1)
# Play the Count Animation to count from 0 to 314 in 4 seconds
#Count传入数字范围从0到100，设置持续时间4秒，线性增长
#play可以传递一个Animation类型的参数，用于动画的播放，参数可设置：run_time,rate_func there_and_back
self.play(Countqq(number, 0, 100), run_time=4, rate_func=linear)
self.wait(1)
class Learn06_MobjectExample(Scene):
def construct(self):
p1= [-1,-1,0]
p2= [1,-1,0]
p3= [1,1,0]
p4= [-1,1,0]
#append_points()方法是增加节点，连成折线。
#方法中传入起点与终点的Line的points
a = Line(p1,p2).append_points(Line(p2,p3).points).append_points(Line(p3,p4).points)
#寻找线的开头&结尾&重心 get_start get_end get_center
point_start= a.get_start()
point_end = a.get_end()
point_center = a.get_center()
#这个self.mobjects[-1]是指上一个add的对象
#np是numpy的意思，manim中，numpy as np，即数学库
#UR指的是UP+RIGHT，在边界的右上角
self.add(Text(f"a.get_start() = {np.round(point_start,2).tolist()}", font_size=24).to_edge(UR).set_color(YELLOW))
self.add(Text(f"a.get_end() = {np.round(point_end,2).tolist()}", font_size=24).next_to(self.mobjects[-1],DOWN).set_color(RED))
self.add(Text(f"a.get_center() = {np.round(point_center,2).tolist()}", font_size=24).next_to(self.mobjects[-1],DOWN).set_color(BLUE))
#还可以get各种位置 get_bottom get_center point_from_proportion是线的中点
self.add(Dot(a.get_start()).set_color(YELLOW).scale(2))
self.add(Dot(a.get_end()).set_color(RED).scale(2))
self.add(Dot(a.get_top()).set_color(GREEN_A).scale(2))
self.add(Dot(a.get_bottom()).set_color(GREEN_D).scale(2))
self.add(Dot(a.get_center()).set_color(BLUE).scale(2))
self.add(Dot(a.point_from_proportion(0.5)).set_color(ORANGE).scale(2))
self.add(*[Dot(x) for x in a.points])
self.add(a)
#测试，不用管这里
class Learn07_MobjectTest(Scene):
def construct(self):
p1=[-1,-1,0]
p2=[1,1,0]
p3=[-1,1,0]
a =Line(p1,p2).append_points(Line(p2,p3).points)
self.add(Dot(a.point_from_proportion(0.5)).set_color(ORANGE).scale(2))
self.add(*[Dot(x) for x in a.points])
self.add(a)
class Learn08_Transform(Scene):
def construct(self):
#设置摄像机的背景颜色，即屏幕背景
self.camera.background_color = GREEN_A
#创建一个正方形
m1 = Circle().set_color(RED)
#创建一个矩形，旋转一定角度
m2 = Rectangle().set_color(RED).rotate(PI/6)
#转变图形
self.play(Transform(m1,m2))
#会直接把m1变成m2的外观，m2不会显示
class Test_Transform(Scene):
def construct(self):
#渐变色
mobj1 = Text(f"早上好，我是？", font_size=93,t2g={'[1:-1]': (RED,GREEN),}).shift(UP*2)
self.play(FadeIn(mobj1),run_time=1)
mobj2 = Text(f"傻逼！", font_size=256).next_to(self.mobjects[-1],DOWN).set_color(BLUE)
self.play(Transform(mobj1,mobj2),run_time=2)
class Learn09_roll(Scene):
def construct(self):
self.camera.background_color = WHITE
m1a = Square().set_color(RED).shift(LEFT)
m1b = Circle().set_color(RED).shift(LEFT)
m2a= Square().set_color(BLUE).shift(RIGHT)
m2b= Circle().set_color(BLUE).shift(RIGHT)
points = m2a.points
points = np.roll(points, int(len(points)/4), axis=0)
m2a.points = points
self.play(Transform(m1a,m1b),Transform(m2a,m2b), run_time=1)
#隔离分组字串
class Learn10_HelloLaTeX(Scene):
def construct(self):
tex = MathTex(
r"\sum_{i=0}^{n}{\frac{x^n}{n!}}"
)
text = Text('指数函数的泰勒展开.',font_size=32,
t2c={"指数函数": BLUE, "泰勒": ORANGE}).next_to(tex,UP)
#for x in text:
#x.set_color(random_color())
#x.set_color(random_bright_color())
tex2 = MathTex(
r"e^x = x^0 + x^1 + \frac{1}{2} x^2 + \frac{1}{6} x^3 + \cdots + \frac{1}{n!} x^n + \cdots"
,substrings_to_isolate="x"#隔离x作为字串，后面就可以单独渲染它的颜色了
).next_to(tex,DOWN)
tex2.set_color_by_tex("x", YELLOW)
self.add(tex,text,tex2)
#坐标轴的显示
class Learn11_Plane(ThreeDScene):
def construct(self):
numberplane = NumberPlane(
#关于直角坐标的一些相关设置
#坐标偏移
#x_range The [x_min, x_max, x_step]-10 10 1
#y_range The [y_min, y_max, y_step]-10 10 1
x_range=[-10,10,1],
y_range=[-10,10,1],
#坐标缩放边界，默认是20
x_length=20,
y_length=20,
background_line_style={
"stroke_color":RED,
"stroke_width":4,
"stroke_opacity":0.6
},
#坐标密度
faded_line_ratio=1,
).add_coordinates([0,1,2,3],[-1,0,1,2,3])
#展示部分坐标标签
self.play(FadeIn(numberplane),run_time=2)
self.play(FadeOut(numberplane),run_time=1.5)
#添加默认的坐标轴标签
numberplane = PolarPlane().add_coordinates()
self.play(FadeIn(numberplane),run_time=2)
self.play(FadeOut(numberplane),run_time=1.5)
#如果要使用3维坐标，则需要使用3d scene
ax = ThreeDAxes()
lab = ax.get_z_axis_label(Tex("$z$-label"))
self.set_camera_orientation(phi=2*PI/5, theta=-PI/5)
self.add(ax, lab).wait(1)
class Learn12_indication(Scene):
def construct(self):
#波浪文字
testStr = MathTex(r"WaveWavexxxxyyyyzzzz").scale(2)
#ApplyWave
self.play(ApplyWave(testStr))
self.play(ApplyWave(
testStr,
direction=RIGHT,
time_width=0.5,
amplitude=0.3
))
self.play(ApplyWave(
testStr,
rate_func=linear,
ripples=4
))
#强调，划重点
self.play(Circumscribe(testStr))
self.play(Circumscribe(testStr, Circle))
self.play(Circumscribe(testStr, fade_out=True))
self.play(Circumscribe(testStr, time_width=2))
self.play(Circumscribe(testStr, Circle, True))
#高亮 Indicate
self.play(Indicate(tex))
self.wait()
#放大、摇晃Wiggle
self.play(Wiggle(tex))
self.wait()
#实际例子1--Logo图案设计--#mathbb mathscr mathtt
class RemooLogo(Scene):
def construct(self):
self.add(NumberPlane())
self.camera.background_color='#758a99'
logo_green = "#87c2a5"
logo_blue = "#525893"
logo_red = "#e07a5f"
logo_black = "#343434"
MT_R = MathTex(r"\mathscr{R}", fill_color=logo_black)\
.scale(7)\
.shift(LEFT+UP)
MT_ee = MathTex(r"\mathtt{E}", fill_color=logo_blue)\
.scale(4)
circle0 = Circle(color=GREEN_A, fill_opacity=0.7).shift(RIGHT)
circle1 = Circle(color=logo_green, fill_opacity=1).shift(RIGHT*2)
square = Square(color=YELLOW, fill_opacity=1)
triangle = Triangle(color=logo_red, fill_opacity=1).shift(LEFT)
logo = VGroup(triangle,square,circle0,circle1,MT_ee,MT_R)#order matters~
logo.move_to(ORIGIN).scale(2)
self.add(logo)
#实际例子2--微分、斜率示意
class DyAndDx(Scene):
def construct(self):
dot = Dot([-2, -1,0])
dot2 = Dot([2, 1, 0])
dot3 = Dot([2,-1,0])
line = Line(dot.get_center(), dot2.get_center()).set_color(ORANGE)
#线变成括号{ -- Brace
b1 = Brace(line)
b1text = b1.get_tex("x_0+dx")
b2 = Brace(line, direction=line.copy().rotate(PI / 2).get_unit_vector())
b2text = b2.get_tex(r"\sqrt{(dx)^2+(dy)^2}")
b3 = Brace(line,direction=[1,0,0])
b3text = b3.get_tex("y_0+dy")
#self.add(line, dot, dot2, b1, b2, b3, b1text, b2text, b3text)
sets = VGroup( dot, dot2, b1, b2, b3, b1text, b2text, b3text)
self.play(FadeIn(line,shift=DOWN))
for mobj in sets:
self.play(Write(mobj),run_time=0.2)
self.wait(1)
#实际例子3--向量-基础
class VectorArrow(Scene):
def construct(self):
numberplane = NumberPlane()
dot = Dot([0,0,0])
arrow = Arrow([0,0,0],[2,2,0],buff = 0)
origin_text = Text('(0.0,0.0)').next_to(dot,DOWN+RIGHT)
tip_text = Text(f'({np.round(arrow.get_vector()[0])},{np.round(arrow.get_vector()[1])})').next_to(arrow,UP+RIGHT)
self.add(numberplane, dot, arrow, origin_text, tip_text)
#实际例子4-方框文字颜色
class RectangleSelected(Scene):
def construct(self):
rectangle = Rectangle(color = RED)
text=Text("你好，我是remoo\n这里是manim学习笔记",
t2c={"我是remoo":BLUE,"manim学习笔记":GREEN,},
line_spacing=2)
selectText = "remoo"
print(selectText)
rectangle.surround(text)
group1 = VGroup(rectangle,text)
self.play(Write(text))
self.play(FadeIn(rectangle))
self.wait(0.3)
self.play(ApplyMethod(group1.scale,2))
self.wait(0.2)
self.play(ApplyMethod(group1.scale,0.5))
self.wait(1)
class BooleanDevice(Scene):
def construct(self):
circle1 = Circle(
radius=2,fill_opacity=0.5,color=BLUE,stroke_width=10
).move_to(LEFT*2.5)
circle2 = Circle(
radius=2,fill_opacity=0.5,color=YELLOW,stroke_width=10
).move_to(LEFT*0.5)
group1 = VGroup(circle1,circle2)
self.play(GrowFromCenter(group1))
self.play(group1.animate.shift(LEFT))
#求交集
intersection = Intersection(circle1,circle2,color=GREEN,fill_opacity=0.8)
Text_inter = Text("交集")
self.play(intersection.animate.scale(0.25).move_to(RIGHT * 5 + UP * 2.5),
Text_inter.animate.move_to(RIGHT * 3 + UP * 2.5))
#求并集
union = Union(circle1, circle2, color=ORANGE, fill_opacity=0.8)
Text_uni = Text("并集")
self.play(union.animate.scale(0.25).move_to(RIGHT * 5 + UP),
Text_uni.animate.move_to(RIGHT * 3 + UP))
#求容斥
union = Exclusion(circle1, circle2, color=PINK, fill_opacity=0.8)
Text_uni = Text("容斥")
self.play(union.animate.scale(0.25).move_to(RIGHT * 5 - UP),
Text_uni.animate.move_to(RIGHT * 3 - UP))
#求异
union = Difference(circle1, circle2, color=RED, fill_opacity=0.8)
Text_uni = Text("求异")
self.play(union.animate.scale(0.25).move_to(RIGHT * 5 - UP * 2.5),
Text_uni.animate.move_to(RIGHT * 3 - UP * 2.5))
class PointMovingOnShapes(Scene):
def construct(self):
circle = Circle(radius=1, color=BLUE)
dot = Dot()
dot2 = dot.copy().shift(RIGHT)
self.add(dot)
line = Line([1, 0, 0], [7, 0, 0])
self.add(line)
self.play(GrowFromCenter(circle))
self.play(Transform(dot, dot2))
self.play(MoveAlongPath(dot, circle), run_time=2, rate_func=there_and_back)
self.play(MoveAlongPath(dot, circle), run_time=1, rate_func=linear)
#根据某一点旋转
self.play(Rotating(dot, about_point=[4, 0, 0]), run_time=1.5)
self.wait(1)
class MovingFrameBox(Scene):
def construct(self):
text=MathTex(
"\\frac{d}{dx}f(x)g(x)=","f(x)\\frac{d}{dx}g(x)","+",
"g(x)\\frac{d}{dx}f(x)"
)
self.play(Write(text))
framebox1 = SurroundingRectangle(text[1], buff = .1)
framebox2 = SurroundingRectangle(text[3], buff = .1)
self.play(
Create(framebox1),
)
self.wait()
self.play(
ReplacementTransform(framebox1,framebox2),
)
self.wait()
class ArrangeSumobjectsExample(Scene):
def construct(self):
s= VGroup(*[Dot().shift(i*0.1*RIGHT+UP) for i in range(0,15)])
s.shift(UP).set_color(BLUE)
s2= s.copy().set_color(RED)
s2.arrange_submobjects()
s2.shift(DOWN)
self.add(s,s2)
class InvertSumobjectsExample(Scene):
def construct(self):
s = VGroup(*[Dot().shift(i*0.1*RIGHT) for i in range(-20,20)])
s2 = s.copy()
s2.invert()
s2.shift(DOWN)
self.play(Write(s), Write(s2))
class BooleanOperations(Scene):
def construct(self):
ellipse1 = Ellipse(
width=4.0, height=5.0, fill_opacity=0.5, color=BLUE, stroke_width=10
).move_to(LEFT)
ellipse2 = ellipse1.copy().set_color(color=RED).move_to(RIGHT)
bool_ops_text = MarkupText("<u>Boolean Operation</u>").next_to(ellipse1, UP * 3)
ellipse_group = Group(bool_ops_text, ellipse1, ellipse2).move_to(LEFT * 3)
self.play(FadeIn(ellipse_group))
i = Intersection(ellipse1, ellipse2, color=GREEN, fill_opacity=0.5)
self.play(i.animate.scale(0.25).move_to(RIGHT * 5 + UP * 2.5))
intersection_text = Text("Intersection", font_size=23).next_to(i, UP)
self.play(FadeIn(intersection_text))
u = Union(ellipse1, ellipse2, color=ORANGE, fill_opacity=0.5)
union_text = Text("Union", font_size=23)
self.play(u.animate.scale(0.3).next_to(i, DOWN, buff=union_text.height * 3))
union_text.next_to(u, UP)
self.play(FadeIn(union_text))
e = Exclusion(ellipse1, ellipse2, color=YELLOW, fill_opacity=0.5)
exclusion_text = Text("Exclusion", font_size=23)
self.play(e.animate.scale(0.3).next_to(u, DOWN, buff=exclusion_text.height * 3.5))
exclusion_text.next_to(e, UP)
self.play(FadeIn(exclusion_text))
d = Difference(ellipse1, ellipse2, color=PINK, fill_opacity=0.5)
difference_text = Text("Difference", font_size=23)
self.play(d.animate.scale(0.3).next_to(u, LEFT, buff=difference_text.height * 3.5))
difference_text.next_to(d, UP)
self.play(FadeIn(difference_text))
class SumFuncG_p1(Scene):
def construct(self):
P1Group = VGroup()
axes = Axes(
x_range=[-1.2, 1.2, .5],
y_range=[-0.3, 10, 1],
x_length=10,
axis_config={"color": GREEN},
x_axis_config={
"numbers_to_include": np.arange(-1, 1.2, .5),
"numbers_with_elongated_ticks": np.arange(-0.3, 3, 1),
},
)
Background_Frame = SurroundingRectangle(axes,color=ORANGE)
labels = axes.get_axis_labels(x_label="", y_label="")
Tex01 = MathTex(
r"\sum_{n=0}^{\infty}\frac{4n^2+4n+3}{2n+1}x^{2n}").shift(UP*1.6)
S_Tex01 = SurroundingRectangle(Tex01,color=GREEN_A,fill_color=PINK,fill_opacity=0.3)
self.play(Write(axes),FadeIn(labels),Write(Tex01),FadeIn(S_Tex01),GrowFromCenter(Background_Frame))
#原本是x: (4*n**2+4*n+3)/(2*n+1)*x**(2*n)
#但是指数增长过快，所以造了个假！！～～(2*n)*x**(2*n)
sum_func = lambda x: x**(2*n)
for n in range(1,16):
text = Text(f"n = {n}")
sum_graph = axes.plot(
sum_func,
discontinuities=[-1.1, 1.1],
dt=0.0001
, color=random_bright_color())
self.add(text)
self.play(Write(sum_graph),run_time=0.5,rate_func=there_and_back)
self.remove(text)
#dot1_axes = Dot(axes.coords_to_point(1, 0))
#dot2_axes = Dot(axes.coords_to_point(-1, 0))
line1_graph = axes.get_lines_to_point(axes.c2p(1,10.16))
line2_graph = axes.get_lines_to_point(axes.c2p(-1,10.17))
Tex = MathTex(f"\\frac{{4\\cdot{n}^2+4\\cdot{n}+3}}{{2\\cdot{n}+1}}x^{{2\\cdot{n}}}")
st = SurroundingRectangle(Tex,color=GREEN_A,fill_color=GREEN_C,fill_opacity=0.3)
self.play(Write(line1_graph),Write(line2_graph),GrowFromCenter(st))
for n in range(1,20):
Tex = MathTex(f"\\frac{{4\\cdot{n}^2+4\\cdot{n}+3}}{{2\\cdot{n}+1}}x^{{2\\cdot{n}}}")
sum_graph = axes.plot(
sum_func,
discontinuities=[-1.1, 1.1],
dt=0.0001
, color=random_bright_color())
P1Group.add(sum_graph)
self.add(Tex,st)
self.play(Write(sum_graph),run_time=0.2,rate_func=linear)
self.remove(Tex)
P1Group.add(Background_Frame,axes,labels,Tex01,S_Tex01,line1_graph,line2_graph,Tex,st)
class SumFuncShow001(Scene):
def construct(self):
text01 = Text("今天来看一道2012年数学3的考研题\n颇有技巧～Remoo",t2c={"数学3":RED,"～Remoo":BLUE})
self.play(Write(text01),run_time=2)
self.play(text01.animate.shift(LEFT*2+UP*3.2))
#题目
Qs01_p1 = Text("求幂级数").align_to(text01,DL).shift(DOWN)
Tex01 = MathTex(
r"\sum_{n=0}^{\infty}\frac{4n^2+4n+3}{2n+1}x^{","2n","}").next_to(Qs01_p1,RIGHT)
Qs01_p2 = Text("的收敛半径与和函数",t2c={"收敛半径":RED,"和函数":RED}).next_to(Tex01,RIGHT)
group01 = VGroup (Qs01_p1,Tex01,Qs01_p2)
self.play(GrowFromCenter(group01))
self.wait(2)
#此时题目已经展示出来了，需要把废话弄掉。
text02 = Text("2012数三").scale(0.5).move_to(text01,UL)
for letter in text02:
letter.set_color(random_bright_color())
self.play(Transform(text01,text02),group01.animate.move_to(text01,DL).shift(DOWN*0.4))
text02 = Text("解:",font_size=84,t2c={"解:":PINK})
self.play(text02.animate.move_to(group01,DL*2).shift(DOWN))
#缺奇次幂，直接用比值审敛法
mk_Rectangle_01 = Rectangle(color=RED, fill_opacity=0)
mk_Rectangle_01.surround(Tex01[1])
self.play(FadeOut(mk_Rectangle_01),run_time=0.5)
for x in range(2):
self.play(FadeOut(mk_Rectangle_01),run_time=0.5)
self.play(FadeIn(mk_Rectangle_01),run_time=0.5)
text03 = Text("由于这里是缺奇次幂，直接用比值审敛法",
t2c={"比值审敛法":RED,"缺奇次幂":RED,}).next_to(text02,RIGHT)
self.play(ReplacementTransform(Tex01[1].copy(),text03),FadeOut(mk_Rectangle_01),run_time=1)
Tex02 = MathTex(
r"\lim _{n \rightarrow \infty}\frac{\left|\frac{4(n+1)^{2}+4(n+1)+3}{2(n+1)+1} x^{2(n+1)}\right|}{\left|\frac{4 n^{2}+4 n+3}{2 n+1} x^{2 n}\right| } ",r"="
,font_size=64)
self.wait(1)
Tex02.move_to(ORIGIN)
self.play(Write(Tex02))
self.wait(1)
##代入比值审敛法公式
#高亮题目Un部分
Tex1_temp = Tex01[0][5:18].copy()
self.add(Tex1_temp)
for x in range(2):
self.play(Tex1_temp.animate.set_fill(BLUE),run_time=0.8,rate_func=there_and_back)
#传给分子
self.play(ReplacementTransform(Tex1_temp,Tex02[0][6:44]))
#高亮题目Un部分
Tex1_temp = Tex01[0][5:18].copy()
self.add(Tex1_temp)
for x in range(1):
self.play(Tex1_temp.animate.set_fill(BLUE),run_time=0.8,rate_func=there_and_back)
#传给分母
self.play(ReplacementTransform(Tex1_temp,Tex02[0][45:80]))
self.wait(1)
#self.play(Write(Tex02))
##式子往左边移动一点
self.play(Tex02.animate.align_to(text02,LEFT))
self.wait(1.5)
##式子化简
#高亮化简部分
Tex1_temp = Tex02[0][6:44].copy()
Tex2_temp = Tex02[0][45:80].copy()
self.add(Tex1_temp)
for x in range(2):
self.play(
Tex1_temp.animate.set_fill(BLUE),
Tex2_temp.animate.set_fill(BLUE),
run_time=0.4,rate_func=there_and_back)
##化简结果展示
#Tex03放在Tex02的右边
Tex03 = MathTex(
r"\lim _{n \rightarrow \infty} \frac{\left|x^{2(n+1)}\right|}{\left|x^{2 n}\right|}", r"=")\
.next_to(Tex02,RIGHT)
self.play(
ReplacementTransform(Tex1_temp,Tex03),
ReplacementTransform(Tex2_temp,Tex03),
)
##把 解:XXX 隐去
self.play(
FadeOut(text02),FadeOut(text03),
Tex02.animate.shift(UP*0.8),Tex03.animate.shift(UP*0.8))
self.wait(2)
##把Tex02隐去，得出收敛半径
self.play(FadeOut(Tex02),Tex03.animate.align_to(text02,LEFT))
Tex04 = MathTex(
r" =\left | x^2 \right | "
,font_size=64)\
.next_to(Tex03,RIGHT).shift(LEFT*0.5)
self.play(ReplacementTransform(Tex03[1],Tex04))
self.wait(2)
Tex05 = MathTex(
r" =\left | x^2 \right |< 1 "
,font_size=64)\
.next_to(Tex03,RIGHT).shift(LEFT*2)
self.play(ReplacementTransform(Tex04,Tex05))
self.wait(2)
text04 = Text(",于是，收敛半径 R=1 ",t2c={"收敛半径":RED})
text04.next_to(Tex05,RIGHT)
self.play(Write(text04))
self.wait(2)
##代入端点验算
text05 = Text("当x = ±1时，",t2c={"±1":RED}).next_to(Tex03,DOWN).shift(DOWN)
Tex06 = MathTex(r"\pm 1").next_to(Tex03,DOWN).shift(DOWN)
Tex07 = MathTex(r"\sum_{n=1}^{\infty} \frac{4 n^{2}+4 n+3}{2 n+1}(\pm 1)^{2 n}").next_to(text05,RIGHT)
Tex07[0][19:21].set_color(RED)
self.play(Write(text05))
self.wait(1)
self.play(Transform(Tex06,Tex01))
self.play(Transform(Tex06,Tex07))
#化简
Tex08 = MathTex(r"=\sum_{n=1}^{\infty} \frac{4 n^{2}+4 n+3}{2 n+1}").next_to(Tex06,RIGHT)
self.play(Write(Tex08))
text06 = Text("显然，该级数发散，故收敛域:(-1,1)",t2c={"收敛域:(-1,1)":PINK}).next_to(text05,DOWN).align_to(text05,LEFT).shift(DOWN*0.8)
self.play(Write(text06))
class SumFuncPart2(Scene):
def construct(self):
#题目
text01 = Text("2012数三").scale(0.5).to_edge(UL)
for letter in text01:
letter.set_color(random_bright_color())
Qs01_p1 = Text("求幂级数").align_to(text01,DL).shift(DOWN)
Tex01 = MathTex(
r"\sum_{n=0}^{\infty}\frac{4n^2+4n+3}{2n+1}x^{","2n","}").next_to(Qs01_p1,RIGHT)
Qs01_p2 = Text("的收敛半径与和函数",t2c={"收敛半径":GREEN,"和函数":RED}).next_to(Tex01,RIGHT)
group01 = VGroup (Qs01_p1,Tex01,Qs01_p2,text01)
self.add(group01)
##开始求和函数
Tex02 = MathTex(r"let:s(x)=\sum_{n=0}^{\infty} \frac{4 n^{2}+4 n+3}{2 n+1} x^{2 n} \quad(|x|<1)")\
.align_to(text01,LEFT)
Tex03 = MathTex(r"=\sum_{n=0}^{\infty} \frac{(2 n+1)^{2}+2}{2 n+1} x^{2 n}")
#14 21
self.play(ReplacementTransform(Tex02[0][14:21]))
#实际例子40--灰阶显示
class GradientImageFromArray(Scene):
def construct(self):
n = 256
imageArray = np.uint8(
[[i * 256 / n for i in range(0, n)] for _ in range(0, n)]
)
image = ImageMobject(imageArray).scale(2)
image.background_rectangle = SurroundingRectangle(image, GREEN)
self.add(image, image.background_rectangle)
#MathTex公式在内存中的存储方式！！
class MathTexTest(Scene):
def construct(self):
Tex02_p1 = MathTex(
"\\lim _{n \\rightarrow \\infty}"
,font_size=64)
Tex02_p2 = MathTex(
r"\lim _{n \rightarrow \infty}\frac{\left|\frac{4(n+1)^{2}+4(n+1)+3}{2(n+1)+1} x^{2(n+1)}\right|}{\left|\frac{4 n^{2}+4 n+3}{2 n+1} x^{2 n}\right|}"
,font_size=64)
self.play(GrowFromCenter(Tex02_p2))
self.wait(2)
#for x in range(60):
#self.play(Tex02_p2[0][x].copy().animate.shift(DOWN*2))
self.play(Tex02_p2[0][6:44].copy().animate.shift(DOWN*2))
class foo( Scene ):
def construct( self ):
lines1 = MathTex(r'\frac{1}{2}', r'\divisionsymbol', r'\frac{2}{3}')
lines2 = MathTex(r'2 \divisionsymbol 3')
lines3 = MathTex(r'\frac{2}{1} \times \frac{1}{3}')
lines2.move_to(lines1[2], RIGHT)
lines2.shift(RIGHT)
lines3.move_to(lines2)
self.play(Write(lines1))
self.play(ReplacementTransform(lines1[2], lines2))
self.wait(1)
self.play(ReplacementTransform(lines2, lines3))
self.wait(3)
class SineCurveUnitCircle(Scene):
# contributed by heejin_park, https://infograph.tistory.com/230
#remoo注释
def construct(self):
self.show_axis()
self.show_circle()
self.move_dot_and_draw_curve()
self.wait()
def show_axis(self):
x_start = np.array([-6,0,0])
x_end = np.array([6,0,0])
y_start = np.array([-4,-2,0])
y_end = np.array([-4,2,0])
x_axis = Line(x_start, x_end)
y_axis = Line(y_start, y_end)
self.add(x_axis, y_axis)
self.add_x_labels()
self.origin_point = np.array([-4,0,0])
self.curve_start = np.array([-3,0,0])
def add_x_labels(self):
x_labels = [
MathTex("\pi"), MathTex("2 \pi"),
MathTex("3 \pi"), MathTex("4 \pi"),
]
for i in range(len(x_labels)):
x_labels[i].next_to(np.array([-1 + 2*i, 0, 0]), DOWN)
self.add(x_labels[i])
def show_circle(self):
circle = Circle(radius=1)
circle.move_to(self.origin_point)
self.add(circle)
self.circle = circle
def move_dot_and_draw_curve(self):
orbit = self.circle
origin_point = self.origin_point
dot = Dot(radius=0.08, color=YELLOW)
dot.move_to(orbit.point_from_proportion(0))
self.t_offset = 0
rate = 0.25
def go_around_circle(mob, dt):
self.t_offset += (dt * rate)
# print(self.t_offset)
mob.move_to(orbit.point_from_proportion(self.t_offset % 1))
def get_line_to_circle():
return Line(origin_point, dot.get_center(), color=BLUE)
def get_line_to_curve():
x = self.curve_start[0] + self.t_offset * 4
y = dot.get_center()[1]
return Line(dot.get_center(), np.array([x,y,0]), color=YELLOW_A, stroke_width=2 )
self.curve = VGroup()
self.curve.add(Line(self.curve_start,self.curve_start))
def get_curve():
last_line = self.curve[-1]
x = self.curve_start[0] + self.t_offset * 4
y = dot.get_center()[1]
new_line = Line(last_line.get_end(),np.array([x,y,0]), color=YELLOW_D)
self.curve.add(new_line)
return self.curve
dot.add_updater(go_around_circle)
origin_to_circle_line = always_redraw(get_line_to_circle)
dot_to_curve_line = always_redraw(get_line_to_curve)
sine_curve_line = always_redraw(get_curve)
self.add(dot)
self.add(orbit, origin_to_circle_line, dot_to_curve_line, sine_curve_line)
self.wait(8.5)
dot.remove_updater(go_around_circle)from manim import *
#导入manim命名空间
#这是一个最基本的manim结构，类名叫做BaseFrame，传入一个场景Scene，并且包含一个construct方法，传入self
class BaseFrame(Scene):
def construct(self):
self.wait()
class CreateCircle(Scene):
def construct(self):
circle = Circle() # 创建了一个Circle对象：circle
circle.set_fill(PINK, opacity=0.5) # set the color and transparency
self.play(Create(circle)) # show the circle on screen
class SquareToCircle(Scene):
def construct(self):
circle = Circle() # create a circle
circle.set_fill(PINK, opacity=0.5) # set color and transparency
square = Square() # create a square
square.rotate(PI / 4) # rotate a certain amount
self.play(Create(square)) # animate the creation of the square
self.play(Transform(square, circle)) # interpolate the square into the circle
self.play(FadeOut(square)) # fade out animation
class SquareAndCircle(Scene):
def construct(self):
circle = Circle() # create a circle
circle.set_fill(PINK, opacity=0.5) # set the color and transparency
square = Square() # create a square
square.set_fill(BLUE, opacity=0.5) # set the color and transparency
square.next_to(circle, RIGHT, buff=0.5) # set the position
self.play(Create(circle), Create(square)) # show the shapes on screen
class ThreePar(Scene):
def construct(self):
circle = Circle()
circle.set_fill(RED, opacity=0.6)
star = Star()
star.set_fill(BLUE, opacity=0.4)
square = Square()
square.set_fill(BLUE, opacity=0.5)
circle.next_to(star, LEFT, buff=0.5)
square.next_to(star, RIGHT, buff=0.5)
#占用1秒的时长，
#如果你的Create方法是在play里面的，他就会占用一秒钟的时间去展示创建对象的过程
self.add(star)
self.add(circle)#无意义的，后面的Create(circle)会创建，系统会删除次代码
self.play(Create(circle),Create(square))
self.wait(1)
self.remove(star)
self.wait(1)
class AnimatedSquareToCircle(Scene):
def construct(self):
circle = Circle() # create a circle
square = Square() # create a square
#Play_Scripts_Start
self.play(Create(square)) # show the square on screen
self.play(square.animate.rotate(PI / 4)) # 旋转图形，参数是弧度制
self.play(
ReplacementTransform(square, circle)
) # transform the square into a circle
self.play(
circle.animate.set_fill(PINK, opacity=0.5)
) # color the circle on screen
#Play_Scripts_End
class DifferentRotations(Scene):
def construct(self):
left_square = Square(color=BLUE, fill_opacity=0.7).shift(2 * LEFT)
right_square = Square(color=GREEN, fill_opacity=0.7).shift(2 * RIGHT)
self.play(
left_square.animate.rotate(PI), Rotate(right_square, angle=PI), run_time=2
)
self.wait()
#默认情况下，对象会生成在屏幕中心点
class Learn01_move(Scene):
def construct(self):
circle = Circle()
triangle = Triangle()
self.add(circle,triangle)
print ("移动")
self.wait(1)
circle.shift(LEFT*3 + UP*2)
#瞬间移动,LEFT,UP是单位方向向量
#以自身为参考
self.wait(1)
triangle.next_to(circle,RIGHT)
#瞬间移动
#以传入对象为参考
self.wait(1)
circle.move_to(DOWN)
#瞬间移动
#以屏幕中心为参考
self.wait(1)
triangle.align_to(circle,DOWN)
#瞬间移动
#以传入对象的假想边界作为调整
#传入DOWN(0,-1)，那么物体的纵坐标就会"对其"对象的下边界
#这个假想的边界一般以物体以中心为原点的第二象限区域
self.wait(1)
class Learn02_beauty(Scene):
def construct(self):
circle = Circle().shift(LEFT*2)
star = Star().shift(RIGHT*2)
self.play(Create(circle), Create(star))
self.wait(1)
#set_fill() 改变图形的内部
#set_stroke()改变图形的边框
star.set_stroke(color=YELLOW, width=20)
circle.set_stroke(color=BLUE, width=20)
star.set_fill(YELLOW, opacity=0.7)
circle.set_fill(YELLOW, opacity=0.7)
self.wait(1)
class Learn03_animations(Scene):
def construct(self):
star = Star()
self.play(FadeIn(star))#渐入特效
#self.play(FadeIn(star),run_time = 5)可以设置时间
self.wait(1)
self.play(Rotate(star, 2*PI))#旋转特效
self.wait(1)
self.play(FadeOut(star))#渐出特效
#animate方法
#这样就可以
class Learn04_animateMethod(Scene):
def construct(self):
star = Star()
self.play(star.animate.set_fill(YELLOW, opacity=0.4))
self.wait(1)
self.play(star.animate.set_fill(WHITE))
self.wait(1)
#也可以同时进行animate方法
self.play(
star.animate
.shift(UP+LEFT)
.rotate(2/3*PI)
.set_fill(RED)
)
self.wait(1)
#也可以在play中添加run_time参数，修改动画持续时间
self.play(
star.animate
.shift(-UP-LEFT)
.rotate(2/3*PI)
.set_fill(BLUE)
,run_time = 5
)
self.wait(1)
#创建自定义动画
#重写interpolate_mobject()方法
class Countqq(Animation):
#kwargs是可变参数，此处暂时用不上
def __init__(self, number: DecimalNumber, start: float, end: float, **kwargs):
# Pass number as the mobject of the animation
#这个是构造方法，使用到我们这个Countqq这个类的时候就会自动把参数传入此方法中
#self在构造的时候不需要传递
super().__init__(number, **kwargs)
# Set start and end
self.start = start
self.end = end
def interpolate_mobject(self, alpha: float):
# Set value of DecimalNumber according to alpha
#这一行是增长的 这个是manim系统内部调用的，我们就不管他了。
value = self.start + (alpha * (self.end - self.start))
self.mobject.set_value(value)
class Learn05_CountingScene(Scene):
def construct(self):
#创建一个Decimal数字，设置颜色，缩放比
number = DecimalNumber().set_color(BLUE).scale(5).move_to(LEFT)
#添加一个定时更新器,ORIGIN相当于[0,0,0],移动到屏幕中心点
#匿名函数lambda构建方法 lambda XXX:___
number.add_updater(lambda number: number)
self.add(number)
self.wait(1)
# Play the Count Animation to count from 0 to 314 in 4 seconds
#Count传入数字范围从0到100，设置持续时间4秒，线性增长
#play可以传递一个Animation类型的参数，用于动画的播放，参数可设置：run_time,rate_func there_and_back
self.play(Countqq(number, 0, 100), run_time=4, rate_func=linear)
self.wait(1)
class Learn06_MobjectExample(Scene):
def construct(self):
p1= [-1,-1,0]
p2= [1,-1,0]
p3= [1,1,0]
p4= [-1,1,0]
#append_points()方法是增加节点，连成折线。
#方法中传入起点与终点的Line的points
a = Line(p1,p2).append_points(Line(p2,p3).points).append_points(Line(p3,p4).points)
#寻找线的开头&结尾&重心 get_start get_end get_center
point_start= a.get_start()
point_end = a.get_end()
point_center = a.get_center()
#这个self.mobjects[-1]是指上一个add的对象
#np是numpy的意思，manim中，numpy as np，即数学库
#UR指的是UP+RIGHT，在边界的右上角
self.add(Text(f"a.get_start() = {np.round(point_start,2).tolist()}", font_size=24).to_edge(UR).set_color(YELLOW))
self.add(Text(f"a.get_end() = {np.round(point_end,2).tolist()}", font_size=24).next_to(self.mobjects[-1],DOWN).set_color(RED))
self.add(Text(f"a.get_center() = {np.round(point_center,2).tolist()}", font_size=24).next_to(self.mobjects[-1],DOWN).set_color(BLUE))
#还可以get各种位置 get_bottom get_center point_from_proportion是线的中点
self.add(Dot(a.get_start()).set_color(YELLOW).scale(2))
self.add(Dot(a.get_end()).set_color(RED).scale(2))
self.add(Dot(a.get_top()).set_color(GREEN_A).scale(2))
self.add(Dot(a.get_bottom()).set_color(GREEN_D).scale(2))
self.add(Dot(a.get_center()).set_color(BLUE).scale(2))
self.add(Dot(a.point_from_proportion(0.5)).set_color(ORANGE).scale(2))
self.add(*[Dot(x) for x in a.points])
self.add(a)
#测试，不用管这里
class Learn07_MobjectTest(Scene):
def construct(self):
p1=[-1,-1,0]
p2=[1,1,0]
p3=[-1,1,0]
a =Line(p1,p2).append_points(Line(p2,p3).points)
self.add(Dot(a.point_from_proportion(0.5)).set_color(ORANGE).scale(2))
self.add(*[Dot(x) for x in a.points])
self.add(a)
class Learn08_Transform(Scene):
def construct(self):
#设置摄像机的背景颜色，即屏幕背景
self.camera.background_color = GREEN_A
#创建一个正方形
m1 = Circle().set_color(RED)
#创建一个矩形，旋转一定角度
m2 = Rectangle().set_color(RED).rotate(PI/6)
#转变图形
self.play(Transform(m1,m2))
#会直接把m1变成m2的外观，m2不会显示
class Test_Transform(Scene):
def construct(self):
#渐变色
mobj1 = Text(f"早上好，我是？", font_size=93,t2g={'[1:-1]': (RED,GREEN),}).shift(UP*2)
self.play(FadeIn(mobj1),run_time=1)
mobj2 = Text(f"傻逼！", font_size=256).next_to(self.mobjects[-1],DOWN).set_color(BLUE)
self.play(Transform(mobj1,mobj2),run_time=2)
class Learn09_roll(Scene):
def construct(self):
self.camera.background_color = WHITE
m1a = Square().set_color(RED).shift(LEFT)
m1b = Circle().set_color(RED).shift(LEFT)
m2a= Square().set_color(BLUE).shift(RIGHT)
m2b= Circle().set_color(BLUE).shift(RIGHT)
points = m2a.points
points = np.roll(points, int(len(points)/4), axis=0)
m2a.points = points
self.play(Transform(m1a,m1b),Transform(m2a,m2b), run_time=1)
class Learn10_HelloLaTeX(Scene):
def construct(self):
tex = MathTex(
r"\sum_{i=1}^{n}{X_i}"
)
tex2 = MathTex(
r"e^x = x^0 + x^1 + \frac{1}{2} x^2 + \frac{1}{6} x^3 + \cdots + \frac{1}{n!} x^n + \cdots"
,substrings_to_isolate="x"#隔离x作为字串，后面就可以单独渲染它的颜色了
).next_to(tex,DOWN)
tex2.set_color_by_tex("x", YELLOW)
self.add(tex,tex2)最新文章
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