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from manim import *
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import numpy as np
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class AnimatedFunctionPlot(Scene):
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def construct(self):
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# 创建坐标系（修正数学符号显示）
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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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"numbers_to_include": np.arange(-3 * PI, 3.5 * PI, PI),
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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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},
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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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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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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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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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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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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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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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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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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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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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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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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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self.wait(2)
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if __name__ == '__main__':
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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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with tempconfig(config):
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scene = AnimatedFunctionPlot()
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scene.render()
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