Manim：使用Python绘制数学动画

Manim是一个由3Blue1Brown的Grant Sanderson开发的开源框架，用户可以通过编写Python代码来创建数学动画，适用于教学、科研和科普宣传等多个领域。

Manim的核心功能之一是动画效果的创建和控制。它提供了多种动画效果，如创建、变换、淡入淡出等，用户可以通过简单的代码实现复杂的动画效果，此外还支持自定义动画效果，以满足用户的特定需求。

Manim官网：Manim Community

在安装Manim前需要先安装ffmpeg和MikTeX。

ffmpeg下载网址:Download FFmpeg

MikTeX下载网址:Getting MiKTeX

下载完成后需要配置下Path环境

我为Manim使用Anaconda创建了一个3.10版本的Python虚拟环境，随后在虚拟环境中直接安装Manim:

pip install manim

有些时候运行Manim脚本会产生报错，只要在 MikTeX Console 中安装相应的宏包即可

接下来整三段官方教学代码和一段我写的Jumping第一定律教学动画

代码一：绘制文本

这里先创建一个BraceAnnotation类，它继承自 Scene 类，这是 Manim 中用于构建动画场景的基础类。随后创建场景construct，将对象添加到场景中即可：

python">from manim import *

class BraceAnnotation(Scene):
    def construct(self):
        dot = Dot([-2, -1, 0])
        dot2 = Dot([2, 1, 0])
        line = Line(dot.get_center(), dot2.get_center()).set_color(ORANGE)
        b1 = Brace(line)
        b1text = b1.get_text("Horizontal distance")
        b2 = Brace(line, direction=line.copy().rotate(PI / 2).get_unit_vector())
        b2text = b2.get_tex("x-x_1")
        self.add(line, dot, dot2, b1, b2, b1text, b2text)

运行效果如下：

输入命令可以将脚本转换为动画：

python">manim test.py BraceAnnotation # 类名

脚本运行后，会生成一系列文件夹，在video文件夹中可以找到生成的动画

代码二：图形动画

这里展示了两个椭圆之间的布尔运算。先创建两个不同颜色的椭圆，并添加了标题文本，接着依次通过动画展示了这两个椭圆的交集、并集、排除和差集，同时为每种运算结果添加了相应的文本标签。

python">from manim import *

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))

代码三：动态展示角度

python">from manim import *

class MovingAngle(Scene):
    def construct(self):
        rotation_center = LEFT

        theta_tracker = ValueTracker(110)
        line1 = Line(LEFT, RIGHT)
        line_moving = Line(LEFT, RIGHT)
        line_ref = line_moving.copy()
        line_moving.rotate(
            theta_tracker.get_value() * DEGREES, about_point=rotation_center
        )
        a = Angle(line1, line_moving, radius=0.5, other_angle=False)
        tex = MathTex(r"\theta").move_to(
            Angle(
                line1, line_moving, radius=0.5 + 3 * SMALL_BUFF, other_angle=False
            ).point_from_proportion(0.5)
        )

        self.add(line1, line_moving, a, tex)
        self.wait()

        line_moving.add_updater(
            lambda x: x.become(line_ref.copy()).rotate(
                theta_tracker.get_value() * DEGREES, about_point=rotation_center
            )
        )

        a.add_updater(
            lambda x: x.become(Angle(line1, line_moving, radius=0.5, other_angle=False))
        )
        tex.add_updater(
            lambda x: x.move_to(
                Angle(
                    line1, line_moving, radius=0.5 + 3 * SMALL_BUFF, other_angle=False
                ).point_from_proportion(0.5)
            )
        )

        self.play(theta_tracker.animate.set_value(40))
        self.play(theta_tracker.animate.increment_value(140))
        self.play(tex.animate.set_color(RED), run_time=0.5)
        self.play(theta_tracker.animate.set_value(350))

代码四：Jumping第一定律

python">from manim import Scene, ImageMobject, ORIGIN, FadeIn, FadeOut, Text, config  
from manim import *  
  
class JumpingLaw(Scene):  
    def construct(self):  
        config.tex_template.add_to_preamble(r'\usepackage[utf8]{inputenc}')  
        config.tex_template.add_to_preamble(r'\usepackage{amsmath}')  
        config.tex_template.add_to_preamble(r'\usepackage{amssymb}')  
        config.tex_template.add_to_preamble(r'\usepackage{unicode-math}')  
        config.tex_template.add_to_preamble(r'\setmainfont{SimHei}')  # 使用黑体字体  
  
        mathematician_image = ImageMobject("jumping.png").scale(1)  
        mathematician_image.move_to(ORIGIN)  
        text = Text("Jumping第一定律").scale(0.75).next_to(mathematician_image, DOWN)  
   
        formula1 = Text("宇宙最终答案 = 42").scale(0.75)  
        formula2 = Text("一周有 7 天").scale(0.75)  
        formula3 = Text("42 ÷ 7 = 6").scale(0.75)  
        formula4 = Text("主 = 6").scale(0.75)  
        formula1.move_to(3 * LEFT + 2 * UP)  
        formula2.move_to(3 * LEFT + UP)  
        formula3.move_to(3 * LEFT)  
        formula4.move_to(3 * LEFT + DOWN)  
  
        self.play(FadeIn(mathematician_image), FadeIn(text))  
        self.wait()  
        self.play(  
            mathematician_image.animate.move_to(np.array([3, 1.5, 0])),  # 用3D坐标，z坐标设为0  
            text.animate.move_to(np.array([3, -2, 0])) 
        )  
        self.wait()  
  
        self.play(FadeIn(formula1))  
        self.wait()  
        self.play(FadeIn(formula2))  
        self.wait()  
        self.play(FadeIn(formula3))  
        self.wait()  
        self.play(FadeIn(formula4))  
        self.wait(2)  
        self.play(  
            FadeOut(mathematician_image),  
            FadeOut(text),  
            FadeOut(formula1),  
            FadeOut(formula2),  
            FadeOut(formula3)  
        )  
        self.wait()  
        formula4.scale(2) 
        formula4.move_to(ORIGIN) 
        self.play(formula4.animate.scale(2).move_to(ORIGIN))  
        self.wait(2)

运行后效果如下：