168 lines
6.2 KiB
Python
168 lines
6.2 KiB
Python
from manim import *
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import numpy as np
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import sys
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# 确保中文显示正常
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print("设置UTF-8编码以支持中文显示")
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sys.stdout.reconfigure(encoding='utf-8')
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sys.stderr.reconfigure(encoding='utf-8')
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class AnimatedFunctionPlot(Scene):
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def construct(self):
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print("=== 开始构建动画场景 ===")
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# 添加片头
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print("0. 显示片头：东师理想数学动画AI制作平台作品")
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title = Text("东师理想数学动画AI制作平台作品", font_size=60, color=WHITE)
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subtitle = Text("正弦和余弦关系动画演示", font_size=36, color=BLUE).next_to(title, DOWN, buff=0.5)
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# 淡入标题和副标题
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self.play(FadeIn(title, run_time=2))
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self.play(FadeIn(subtitle, run_time=1.5))
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# 等待2秒
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self.wait(2)
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# 淡出标题和副标题
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self.play(FadeOut(title), FadeOut(subtitle), run_time=1.5)
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# 创建坐标系（修正数学符号显示）
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print("1. 创建坐标系：范围从-3.5π到3.5π，步长为π/2，y轴范围从-1.5到1.5")
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axes = Axes(
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x_range=[-3.5 * PI, 3.5 * PI, PI / 2],
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y_range=[-1.5, 1.5, 0.5],
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axis_config={"color": BLUE},
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x_axis_config={
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# 清空要显示的数字列表
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"numbers_to_include": [],
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"numbers_with_elongated_ticks": np.arange(-3 * PI, 3.5 * PI, PI),
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"decimal_number_config": {
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"num_decimal_places": 0,
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"include_sign": True,
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},
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# 禁用默认数字标签
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"include_numbers": False,
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},
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y_axis_config={
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"decimal_number_config": {
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"num_decimal_places": 1,
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}
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},
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tips=False,
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).scale(0.9)
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# 修正1：使用MathTex并正确转义π符号
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print("2. 添加x轴标签：使用MathTex正确显示π符号")
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x_labels = VGroup(*[
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MathTex(r"%d\pi" % i if i != 0 else "0").scale(0.7).move_to(axes.c2p(i * PI, 0))
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for i in range(-3, 4)
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])
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print("3. 播放创建坐标系和标签的动画，持续2秒")
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self.play(
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Create(axes, run_time=2),
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LaggedStart(*[Write(label) for label in x_labels], lag_ratio=0.3),
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)
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self.wait(0.5)
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# 修正2：使用MathTex包装数学公式
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print("4. 绘制正弦函数图像：使用绿色表示sin(x)")
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sin_graph = axes.plot(lambda x: np.sin(x), color=GREEN)
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sin_label = axes.get_graph_label(
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sin_graph,
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MathTex(r"\sin(x)", color=GREEN), # 使用MathTex替代Tex
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x_val=-3 * PI,
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direction=UP
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)
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print("5. 播放绘制正弦曲线和标签的动画，持续3秒")
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self.play(
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Create(sin_graph, run_time=3),
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Write(sin_label, run_time=1),
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rate_func=linear
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)
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self.wait()
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# 修正3：余弦公式同样使用MathTex
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print("6. 绘制余弦函数图像：使用红色表示cos(x)")
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cos_graph = axes.plot(lambda x: np.cos(x), color=RED)
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cos_label = axes.get_graph_label(
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cos_graph,
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MathTex(r"\cos(x)", color=RED), # 使用MathTex替代Tex
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x_val=3 * PI,
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direction=DOWN
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)
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print("7. 播放从正弦曲线变换到余弦曲线的动画，持续3秒")
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self.play(
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TransformFromCopy(sin_graph, cos_graph, path_arc=PI / 2, run_time=3),
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FadeIn(cos_label, shift=DOWN),
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)
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self.wait()
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# 动态垂直线（追踪动画）
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print("8. 创建动态垂直线和跟踪点：用于展示任意x值对应的sin和cos函数值")
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tracker = ValueTracker(-3 * PI)
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vert_line = always_redraw(lambda:
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DashedLine(
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axes.c2p(tracker.get_value(), -1.5),
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axes.c2p(tracker.get_value(), 1.5),
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color=YELLOW
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)
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)
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dot_sin = always_redraw(lambda:
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Dot(color=GREEN).move_to(axes.i2gp(tracker.get_value(), sin_graph))
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)
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dot_cos = always_redraw(lambda:
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Dot(color=RED).move_to(axes.i2gp(tracker.get_value(), cos_graph))
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)
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print("9. 播放创建垂直线和跟踪点的动画")
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self.play(
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Create(vert_line),
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GrowFromCenter(dot_sin),
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GrowFromCenter(dot_cos)
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)
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print("10. 播放垂直线从-3π移动到3π的动画，持续6秒，展示函数值随x变化")
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self.play(
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tracker.animate.set_value(3 * PI),
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run_time=6,
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rate_func=linear
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)
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self.wait()
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# 修正4：相位差公式使用正确数学环境
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print("11. 展示相位差公式：cos(x) = sin(x + π/2)")
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equation = MathTex(
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r"\cos(x) = \sin\left(x + \frac{\pi}{2}\right)", # 使用MathTex
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color=YELLOW
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).to_edge(UP)
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print("12. 播放写入公式和移动正弦曲线的动画，持续2秒")
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self.play(
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Write(equation),
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sin_graph.animate.shift(LEFT * PI / 2).set_color(ORANGE),
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run_time=2
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)
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print("13. 等待2秒，让观众理解相位差概念")
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self.wait(2)
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print("\n=== 动画场景构建完成 ===")
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if __name__ == '__main__':
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print("设置渲染配置：高质量、预览模式、输出目录为./output")
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config = {
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"quality": "high_quality",
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"preview": True,
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"media_dir": "./output",
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"pixel_height": 1080,
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"pixel_width": 1920,
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"background_color": "#1E1E1E"
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}
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print("使用临时配置渲染场景")
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with tempconfig(config):
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scene = AnimatedFunctionPlot()
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scene.render() |