1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
| from manim import *
import numpy as np
class CircleTangent(Scene):
def construct(self):
# 第一部分：封面
title = Text("圆的切线：几何关系与推导", font_size=48, color=BLUE)
subtitle = Text("几何直观与数学推导", font_size=36, color=GREEN)
subtitle.next_to(title, DOWN, buff=0.5)
self.play(Write(title), Write(subtitle))
self.wait(2)
self.play(FadeOut(title), FadeOut(subtitle))
# 第二部分：几何演示
# 创建坐标系
axes = Axes(
x_range=[-4, 4, 1],
y_range=[-3, 3, 1],
x_length=8,
y_length=6,
axis_config={"color": WHITE, "stroke_width": 2},
)
axes.add_coordinates()
# 创建圆：圆心(0,0)，半径2
circle = Circle(radius=2, color=YELLOW, stroke_width=4)
circle.move_to(ORIGIN)
# 圆心标记
center = Dot(ORIGIN, color=RED, radius=0.08)
center_label = MathTex("O", color=RED).next_to(ORIGIN, DL, buff=0.1)
# 圆上一点P
p_angle = PI / 3# 60度
p_point = circle.point_at_angle(p_angle)
p_dot = Dot(p_point, color=GREEN, radius=0.08)
p_label = MathTex("P", color=GREEN).next_to(p_point, UR, buff=0.1)
# 显示坐标系和圆
self.play(Create(axes), run_time=1.5)
self.play(Create(circle), run_time=2)
self.play(FadeIn(center), Write(center_label))
self.play(FadeIn(p_dot), Write(p_label))
self.wait(1)
# 绘制半径OP
radius = Line(ORIGIN, p_point, color=RED, stroke_width=4)
radius_label = MathTex("\\text{半径 } OP", color=RED).next_to(radius.get_center(), LEFT, buff=0.2)
self.play(Create(radius), Write(radius_label))
self.wait(1)
# 绘制切线（垂直于半径）
radius_vector = p_point - ORIGIN
tangent_vector = np.array([-radius_vector[1], radius_vector[0], 0]) # 旋转90度
tangent_vector = tangent_vector / np.linalg.norm(tangent_vector) # 单位化
# 绘制切线（长度为4）
tangent_line = Line(
p_point - 2 * tangent_vector,
p_point + 2 * tangent_vector,
color=BLUE,
stroke_width=4
)
tangent_label = MathTex("\\text{切线}", color=BLUE).next_to(tangent_line.get_center(), UP, buff=0.2)
self.play(Create(tangent_line), Write(tangent_label))
self.wait(1)
# 显示垂直符号
right_angle = RightAngle(radius, tangent_line, length=0.3, color=GREEN, stroke_width=4,quadrant=(-1, 1))
self.play(Create(right_angle))
# 垂直关系文本
perpendicular_text = MathTex("OP \\perp \\text{切线}", color=GREEN, font_size=36)
perpendicular_text.next_to(right_angle,RIGHT,buff=0.5)
self.play(Write(perpendicular_text))
self.wait(2)
# 第三部分：缩小几何图形并移至左上角，同时显示数学推导
# 创建几何图形组
geometry_group = VGroup(axes, circle, center, center_label, p_dot, p_label,
radius, radius_label, tangent_line, tangent_label,
right_angle, perpendicular_text)
# 缩小并移动几何图形到左上角
self.play(
geometry_group.animate.scale(0.6).to_corner(LEFT, buff=0.5),
run_time=2
)
# 显示数学推导标题
derivation_title = Text("数学推导", font_size=36, color=ORANGE)
derivation_title.to_edge(UP).shift(DOWN * 0.5)
self.play(Write(derivation_title))
# 推导步骤
steps = VGroup(
MathTex("\\text{1. 已知：圆方程 } (x-a)^2 + (y-b)^2 = r^2"),
MathTex("\\text{2. 圆心 } O(a,b), \\text{ 切点 } P(x_0, y_0)"),
MathTex("\\text{3. 半径斜率: } k_{OP} = \\frac{y_0 - b}{x_0 - a}"),
MathTex("\\text{4. 切线斜率: } k = -\\frac{1}{k_{OP}} = -\\frac{x_0 - a}{y_0 - b}"),
MathTex("\\text{5. 切线方程: } y - y_0 = k(x - x_0)"),
MathTex("\\text{6. 代入得: } y - y_0 = -\\frac{x_0 - a}{y_0 - b}(x - x_0)"),
MathTex("\\text{7. 整理: } (x_0 - a)(x - a) + (y_0 - b)(y - b) = r^2")
)
steps.arrange(DOWN, aligned_edge=LEFT, buff=0.3)
steps.scale(0.7)
steps.next_to(derivation_title, DOWN, buff=0.5).to_edge(RIGHT, buff=1)
# 逐步显示推导过程
for step in steps:
self.play(Write(step), run_time=1.5)
self.wait(0.5)
self.wait(2)
# 第四部分：具体实例 - 清除前面的所有内容
self.play(
FadeOut(geometry_group),
FadeOut(derivation_title),
FadeOut(steps)
)原作者的代码还要长一些，我做了适当的修改，主要是用来做圆的切斜的一些知识，渲染的过程中，会出现一些**LaTeX**文件包的提示，和我们第一次安装完Manim之后进行代码测试的时候一样，例如提示安装**CTEX.sty**文件，从提示来看是ctex宏包的一部分，点击安装就可以
|
