120 lines
4.0 KiB
Python
120 lines
4.0 KiB
Python
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from manim import *
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class SineDefinition(Scene):
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def construct(self):
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# 第一部分：标题淡入（2秒）
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title = Text("正弦函数的几何意义", font_size=48, color=BLUE)
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self.play(FadeIn(title, run_time=2))
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self.wait(0.5)
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self.play(FadeOut(title, run_time=0.5))
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# 第二部分：直角三角形展示（5秒）
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# 创建三角形和标签
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triangle = Polygon(ORIGIN, [3, 0, 0], [3, 2, 0], color=WHITE)
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opposite = Line([3, 0, 0], [3, 2, 0], color=GREEN)
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hypotenuse = Line(ORIGIN, [3, 2, 0], color=RED)
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angle_arc = Arc(radius=0.5, start_angle=0, angle=PI / 3.5, color=YELLOW)
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theta = MathTex(r"\theta", color=YELLOW).next_to(angle_arc, DOWN, buff=0.1)
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# 添加标签文本
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opposite_label = Text("对边", color=GREEN).next_to(opposite, RIGHT, buff=0.1)
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hypotenuse_label = Text("斜边", color=RED).next_to(hypotenuse, UP, buff=0.2).shift(LEFT * 0.5)
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# 动画展示
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self.play(Create(triangle), run_time=1)
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self.play(Create(angle_arc), Write(theta), run_time=1)
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self.play(Create(opposite), Write(opposite_label), run_time=1.5)
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self.play(Create(hypotenuse), Write(hypotenuse_label), run_time=1.5)
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self.wait(0.5)
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# 第三部分：单位圆动态演示（8秒）
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# 创建坐标系
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axes = Axes(
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x_range=[-1.5, 1.5],
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y_range=[-1.5, 1.5],
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axis_config={"color": BLUE},
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x_length=5,
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y_length=5
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)
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axes_labels = axes.get_axis_labels(
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x_label=Text("角度 θ", font_size=32),
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y_label=Text("正弦值", font_size=32)
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)
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# 创建单位圆
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unit_circle = Circle(radius=1, color=WHITE)
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radius_vector = Line(ORIGIN, [1, 0, 0], color=RED)
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# 创建正弦曲线坐标系
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sin_axes = Axes(
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x_range=[0, 2 * PI, PI / 2],
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y_range=[-1, 1, 0.5],
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x_length=5,
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y_length=3,
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axis_config={"color": BLUE}
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).to_edge(RIGHT)
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sin_axes_labels = sin_axes.get_axis_labels(
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x_label=Text("角度 θ", font_size=32),
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y_label=Text("正弦值", font_size=32)
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)
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# 动画转换
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self.play(
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ReplacementTransform(triangle, unit_circle),
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ReplacementTransform(hypotenuse, radius_vector),
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FadeOut(opposite),
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FadeOut(angle_arc),
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FadeOut(theta),
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FadeOut(opposite_label),
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FadeOut(hypotenuse_label),
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run_time=2
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)
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self.play(
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Create(axes),
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Create(sin_axes),
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Write(axes_labels),
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Write(sin_axes_labels),
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run_time=2
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)
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# 动态轨迹
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dot = Dot(color=YELLOW)
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sin_dot = Dot(color=YELLOW)
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trace = TracedPath(dot.get_center, stroke_color=YELLOW, stroke_width=4)
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# 更新函数
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def update_dot(mob, alpha):
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angle = alpha * 2 * PI
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x = np.cos(angle)
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y = np.sin(angle)
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mob.move_to(axes.c2p(x, y))
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sin_x = alpha * 2 * PI
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sin_y = np.sin(angle)
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sin_dot.move_to(sin_axes.c2p(sin_x, sin_y))
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return mob
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# 运行动画
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self.add(trace, dot, sin_dot)
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self.play(
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UpdateFromAlphaFunc(dot, update_dot),
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rate_func=linear,
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run_time=8
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)
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self.remove(trace, dot, sin_dot)
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# 第四部分：总结公式（3秒）
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formula = MathTex(r"\sin\theta = \frac{\text{对边}}{\text{斜边}}", font_size=60)
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formula.set_color_by_tex("对边", GREEN)
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formula.set_color_by_tex("斜边", RED)
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self.play(Write(formula), run_time=2)
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self.wait(1)
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# 末尾静止帧（3秒）
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self.wait(3)
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if __name__ == "__main__":
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scene = SineDefinition()
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scene.render()
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