🐍 1. 安装 Python 解释器
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官网下载地址：https://www.python.org/downloads/参考下图进行下载安装（如不熟悉可查找高阅读量教程）：
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https://i-blog.csdnimg.cn/direct/2c64bb62f06f47488d451b589acecb21.png
https://i-blog.csdnimg.cn/direct/eb7b92f41a42459dbb9c11b50696724a.png
如果不会，你就找阅读量最大的别人教程，很简单的
安装好后win+R 打开黑窗口输入python --version 出现版本好就ok了
如果没有出现也没有报错，那么就需要查看环境变量里面配置的路径是否正确（你应该找得到环境变量在哪里），以及删除系统注册表的老旧的解释器。（win+R 然后输入regedit，具体在哪里找到问AI，基本不会错的）
2.安装manim
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pip install manim如果下载慢，自己配置镜像源。
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常用镜像源地址
镜像源 地址 特点
清华大学 https://pypi.tuna.tsinghua.edu.cn/simple 学术友好，更新及时，最常用
阿里云 https://mirrors.aliyun.com/pypi/simple/ 云服务商，CDN节点覆盖全
腾讯云 https://mirrors.cloud.tencent.com/pypi/simple 稳定性高，智能路由
华为云 https://repo.huaweicloud.com/repository/pypi/simple 企业级支持
中国科技大学 https://pypi.mirrors.ustc.edu.cn/simple/ 支持历史版本查询
豆瓣 http://pypi.douban.com/simple/ 老牌镜像源3.安装ffmpeg
打开这个链接
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https://www.gyan.dev/ffmpeg/builds/
给我下载他，推荐Internet downmanager。获取下载链接丢给这个下载器32倍速下载老爽了。
解压下载的 ZIP 文件到指定目录（例如 C:\ffmpeg）。
添加到系统路径（可选但推荐）：
右键点击"此电脑" → "属性" → "高级系统设置" → "环境变量"。
在"系统变量"中找到 Path，点击"编辑"。
新建一条路径，填入 FFmpeg 的 bin 文件夹路径（例如 C:\ffmpeg\bin）。
验证安装：
打开命令行输入：
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ffmpeg -version若显示版本信息，则安装成功。、
4.安装Latex
打开它
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https://miktex.org/download点击下载安装就行。
5.运行你的文件：
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manim -p .\sample.py如果报错丢给AI缺少啥安装啥
一下是我的参考代码：圆的方程推导演示（做的没那么细哈~）
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from manim import *
import numpy as np
import os
# =========================
# 全局风格配置
# =========================
config.background_color = "#0B1020"
# 设置 LaTeX 编译器路径到环境变量
os.environ["PATH"] += os.pathsep + r"D:\CodingSoftWare\Miktex\miktex\bin\x64"
# 自定义 TeX 模板类 - 只设置名称，不设置完整路径
class CustomTexTemplate(TexTemplate):
def __init__(self):
super().__init__()
# 使用编译器名称，而不是完整路径
self.tex_compiler = "latex" # 或者 "pdflatex"
# 确保使用正确的参数
self.compiler_arguments = [
"-interaction=batchmode",
"-halt-on-error",
"-output-directory={}",
"{}",
]
class CircleEquationDerivation(Scene):
"""
两点距离公式推导圆的标准方程
Professional Mathematical Visualization
"""
def construct(self):
# ------------------------------------------------
# 1. 场景初始化
# ------------------------------------------------
self.camera.background_color = "#0B1020"
self.setup_color_palette()
# 标题动画
self.show_title_sequence()
# 坐标系建立
plane = self.create_coordinate_system()
self.play(
FadeIn(plane),
run_time=2,
)
self.wait(0.5)
# ------------------------------------------------
# 2. 创建圆心与动态点
# ------------------------------------------------
center_point = np.array([2, 1, 0])
radius_value = 3
radius_tracker = ValueTracker(0)
# 圆心
center_dot = Dot(
plane.c2p(*center_point[:2]),
color=self.primary_color,
radius=0.09,
)
# 使用自定义模板的 MathTex
center_label = MathTex("C(a,b)", tex_template=CustomTexTemplate()).scale(0.8)
center_label.next_to(center_dot, DOWN)
# 动态角度
theta_tracker = ValueTracker(0)
# 动态点P
moving_point = always_redraw(
lambda: Dot(
plane.c2p(
center_point[0] + radius_value * np.cos(theta_tracker.get_value()),
center_point[1] + radius_value * np.sin(theta_tracker.get_value()),
),
color=self.accent_color,
radius=0.08,
)
)
moving_label = always_redraw(
lambda: MathTex("P(x,y)", tex_template=CustomTexTemplate())
.scale(0.8)
.next_to(moving_point, UP)
)
# 动态圆
dynamic_circle = always_redraw(
lambda: Circle(
radius=plane.x_axis.n2p(radius_value)[0] - plane.x_axis.n2p(0)[0],
color=self.secondary_color,
stroke_width=4,
).move_to(plane.c2p(*center_point[:2]))
)
# 半径线
radius_line = always_redraw(
lambda: Line(
center_dot.get_center(),
moving_point.get_center(),
color=self.radius_color,
stroke_width=4,
)
)
# 半径数值
radius_text = always_redraw(
lambda: DecimalNumber(
radius_value,
num_decimal_places=1,
color=self.radius_color,
)
.scale(0.7)
.next_to(radius_line, RIGHT)
)
# 动画进入
self.play(
LaggedStart(
GrowFromCenter(center_dot),
Write(center_label),
Create(dynamic_circle),
lag_ratio=0.25,
),
run_time=2,
)
self.play(
FadeIn(moving_point),
FadeIn(moving_label),
Create(radius_line),
FadeIn(radius_text),
run_time=1.5,
)
# ------------------------------------------------
# 3. 点沿圆运动
# ------------------------------------------------
self.play(
theta_tracker.animate.set_value(TAU),
rate_func=rate_functions.ease_in_out_sine,
run_time=8,
)
self.wait(0.5)
# ------------------------------------------------
# 4. 引出距离公式
# ------------------------------------------------
distance_formula = MathTex(
"d",
"=",
"\\sqrt{",
"(x_2-x_1)^2",
"+",
"(y_2-y_1)^2",
"}",
tex_template=CustomTexTemplate(),
).scale(1.1)
distance_formula.to_edge(UP)
formula_bg = SurroundingRectangle(
distance_formula,
color=self.secondary_color,
buff=0.3,
corner_radius=0.15,
)
self.play(
AnimationGroup(
FadeIn(formula_bg),
Write(distance_formula),
lag_ratio=0.1,
),
run_time=2,
)
self.wait(1)
# ------------------------------------------------
# 5. 替换坐标
# ------------------------------------------------
substitution_formula = MathTex(
"r",
"=",
"\\sqrt{",
"(x-a)^2",
"+",
"(y-b)^2",
"}",
tex_template=CustomTexTemplate(),
).scale(1.1)
substitution_formula.move_to(distance_formula)
self.play(
TransformMatchingTex(
distance_formula,
substitution_formula,
path_arc=PI / 4,
),
run_time=2.5,
)
self.wait(1)
# ------------------------------------------------
# 6. 两边平方
# ------------------------------------------------
squared_formula = MathTex(
"r^2",
"=",
"(x-a)^2",
"+",
"(y-b)^2",
tex_template=CustomTexTemplate(),
).scale(1.2)
squared_formula.move_to(substitution_formula)
self.play(
TransformMatchingTex(
substitution_formula,
squared_formula,
),
run_time=2,
)
self.wait(1)
# ------------------------------------------------
# 7. 标准形式整理
# ------------------------------------------------
final_formula = MathTex(
"(x-a)^2",
"+",
"(y-b)^2",
"=",
"r^2",
tex_template=CustomTexTemplate(),
).scale(1.4)
final_formula.set_color_by_gradient(
self.primary_color,
self.accent_color,
)
final_formula.move_to(squared_formula)
# 聚焦镜头效果
focus_rect = SurroundingRectangle(
final_formula,
color=self.accent_color,
buff=0.4,
stroke_width=3,
)
self.play(
Succession(
FadeOut(formula_bg),
TransformMatchingTex(
squared_formula,
final_formula,
),
),
run_time=2.5,
)
self.play(
Create(focus_rect),
Flash(
final_formula,
color=self.accent_color,
flash_radius=1.2,
),
run_time=1.5,
)
self.wait(2)
# ------------------------------------------------
# 8. 最终镜头
# ------------------------------------------------
explanation = Text(
"所有到圆心距离为 r 的点的集合",
font="Microsoft YaHei",
color=GREY_A,
).scale(0.55)
explanation.next_to(final_formula, DOWN, buff=0.6)
self.play(
FadeIn(explanation, shift=UP * 0.2),
run_time=1.2,
)
self.wait(3)
# ====================================================
# 工具函数
# ====================================================
def setup_color_palette(self):
"""颜色系统"""
self.primary_color = "#4FC3F7"
self.secondary_color = "#7C4DFF"
self.accent_color = "#00E5A8"
self.radius_color = "#FFB74D"
def create_coordinate_system(self):
"""创建坐标系"""
plane = NumberPlane(
x_range=[-5, 9, 1],
y_range=[-4, 6, 1],
background_line_style={
"stroke_color": BLUE_E,
"stroke_opacity": 0.25,
"stroke_width": 1,
},
axis_config={
"stroke_color": GREY_B,
"stroke_width": 2,
},
)
return plane
def show_title_sequence(self):
"""标题动画"""
title = Text(
"圆的基本方程",
font="Microsoft YaHei",
color=WHITE,
weight=BOLD,
).scale(1.3)
subtitle = Text(
"Deriving the Equation of a Circle",
color=GREY_B,
).scale(0.45)
subtitle.next_to(title, DOWN)
title_group = VGroup(title, subtitle)
glow = SurroundingRectangle(
title_group,
color=self.secondary_color,
buff=0.4,
corner_radius=0.2,
)
self.play(
LaggedStart(
FadeIn(title, shift=UP),
FadeIn(subtitle),
lag_ratio=0.2,
),
run_time=2,
)
self.play(
Create(glow),
run_time=1,
)
self.wait(1)
self.play(
FadeOut(title_group),
FadeOut(glow),
run_time=1.5,
)