189 lines
5.5 KiB
Python
189 lines
5.5 KiB
Python
from manim import *
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class ParabolaLesson(Scene):
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# 坐标常量定义
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LEFT_MARGIN = 3.2
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AXIS_RANGE = [-4, 4, -1, 3]
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# 颜色定义
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BG_COLOR = "#F5F5F5"
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CURVE_COLOR = "#00BFFF"
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FOCUS_COLOR = "#FF4500"
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DIRECTRIX_COLOR = "#AAAAAA"
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def construct(self):
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self.camera.background_color = self.BG_COLOR
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self._intro()
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self._discovery()
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self._proof()
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self._practice()
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def _intro(self):
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# 创建坐标系
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axes = Axes(
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x_range=[-4, 4, 1],
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y_range=[-1, 3, 1],
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axis_config={"color": BLACK},
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tips=False
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)
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axes_labels = axes.get_axis_labels(x_label="x", y_label="y")
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# 初始抛物线 (a=1)
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a_value = ValueTracker(1)
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parabola = always_redraw(lambda: axes.plot(
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lambda x: a_value.get_value() * x ** 2,
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color=self.CURVE_COLOR
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))
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# 添加所有元素
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self.add(axes, axes_labels, parabola)
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def _discovery(self):
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# 标题
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title = Tex("$a$是正数，开口向上", color=BLUE).to_edge(UP)
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# 公式
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formula = MathTex("y = a x^2", color=BLACK).next_to(title, DOWN)
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# 滑杆
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slider = NumberLine(
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x_range=[0, 2, 0.5],
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length=4,
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color=BLACK,
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include_numbers=True
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).to_edge(DOWN)
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slider_label = Tex("$a$值:", color=BLACK).next_to(slider, LEFT)
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# 滑杆指示器
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dot = Dot(color=RED).move_to(slider.n2p(1))
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a_value = ValueTracker(1)
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dot.add_updater(lambda d: d.move_to(slider.n2p(
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a_value.get_value()
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)))
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a_text = always_redraw(lambda: DecimalNumber(
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a_value.get_value(),
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color=RED
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).next_to(dot, UP))
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# 添加元素
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self.play(
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Write(title),
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Write(formula),
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Create(slider),
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Write(slider_label)
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)
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self.add(dot, a_text)
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# 动画：a值变化 (0.5 -> 1 -> 2)
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self.play(
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a_value.animate.set_value(0.5),
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run_time=5,
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rate_func=rate_functions.ease_in_out_sine
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)
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self.play(
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a_value.animate.set_value(1),
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run_time=5,
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rate_func=rate_functions.ease_in_out_sine
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)
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self.play(
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a_value.animate.set_value(2),
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run_time=5,
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rate_func=rate_functions.ease_in_out_sine
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)
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# 5秒静止帧
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self.wait(5)
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def _proof(self):
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# 更新标题
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new_title = Tex("$a$是负数，开口向下", color=BLUE).to_edge(UP)
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# 滑杆范围变为负数
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slider = NumberLine(
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x_range=[-2, 0, 0.5],
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length=4,
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color=BLACK,
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include_numbers=True
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).to_edge(DOWN)
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slider_label = Tex("$a$值:", color=BLACK).next_to(slider, LEFT)
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# 更新滑杆指示器
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a_value = ValueTracker(-1)
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dot = Dot(color=RED).move_to(slider.n2p(-1))
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dot.add_updater(lambda d: d.move_to(slider.n2p(
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a_value.get_value()
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)))
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a_text = always_redraw(lambda: DecimalNumber(
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a_value.get_value(),
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color=RED
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).next_to(dot, UP))
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# 更新公式
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formula = MathTex("y = a x^2", color=BLACK).next_to(new_title, DOWN)
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# 焦点和准线
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focus = always_redraw(lambda: Dot(
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color=self.FOCUS_COLOR
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).move_to([0, 1 / (4 * a_value.get_value()), 0]))
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directrix = always_redraw(lambda: DashedLine(
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start=[-4, -1 / (4 * a_value.get_value()), 0],
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end=[4, -1 / (4 * a_value.get_value()), 0],
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color=self.DIRECTRIX_COLOR
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))
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# 切换元素
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self.play(
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Transform(self.mobjects[0], new_title),
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Transform(self.mobjects[1], formula),
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Transform(self.mobjects[2], slider),
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Transform(self.mobjects[3], slider_label)
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)
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self.add(focus, directrix)
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# 动画：a值变化 (-0.5 -> -1 -> -2)
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self.play(
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a_value.animate.set_value(-0.5),
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run_time=5,
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rate_func=rate_functions.ease_in_out_sine
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)
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self.play(
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a_value.animate.set_value(-1),
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run_time=5,
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rate_func=rate_functions.ease_in_out_sine
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)
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self.play(
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a_value.animate.set_value(-2),
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run_time=5,
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rate_func=rate_functions.ease_in_out_sine
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)
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# 5秒静止帧
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self.wait(5)
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def _practice(self):
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# 添加练习题文本
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practice = Tex(
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"思考题：当$a=-1$时，\\\\焦点和准线在哪里？",
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color=BLUE
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).scale(0.8).to_edge(DOWN)
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# 显示练习题
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self.play(Write(practice))
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self.wait(5)
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if __name__ == "__main__":
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# 全局指定 ctex 模板（一次性）
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config.tex_template = TexTemplateLibrary.ctex
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# 使用临时配置渲染场景（配置只在with块内有效）
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with tempconfig({
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"quality": "low_quality",
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"preview": True,
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"output_file": "ParabolaLesson"
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}):
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# 实例化场景类
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scene = ParabolaLesson()
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# 执行渲染流程（包含文件生成和预览）
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scene.render() |