150 lines
4.7 KiB
Python
150 lines
4.7 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_CENTER = LEFT * LEFT_MARGIN
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TITLE_POS = UP * 3.2
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FORMULA_POS = UP * 2.2
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SLIDER_POS = UP * 1.2
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GRAPH_POS = LEFT * LEFT_MARGIN
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def construct(self):
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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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# 创建坐标轴
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axes = Axes(
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x_range=[-3, 3, 1],
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y_range=[0, 8, 2],
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axis_config={"color": BLUE},
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tips=False
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).shift(self.GRAPH_POS)
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# 初始曲线 y=x²
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curve = axes.plot(lambda x: x ** 2, color=YELLOW)
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# 标题和公式
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title = Tex("$a$是正数，开口向上", color=GREEN).to_edge(self.TITLE_POS)
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formula = MathTex("y = x^2", color=RED).to_edge(self.FORMULA_POS)
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# 动画序列
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self.play(Create(axes), run_time=1.5)
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self.play(Create(curve), Write(formula), run_time=2)
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self.play(Write(title), run_time=1.5)
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self.wait(1)
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# 保存对象
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self.axes = axes
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self.curve = curve
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self.formula = formula
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self.title = title
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def _discovery(self):
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# 创建滑杆数值显示
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a_value = DecimalNumber(1.0, num_decimal_places=1)
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a_text = Tex("$a = $").next_to(a_value, LEFT)
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a_display = VGroup(a_text, a_value).to_edge(self.SLIDER_POS)
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# 更新公式为 y=ax²
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new_formula = MathTex("y = a x^2", color=RED).to_edge(self.FORMULA_POS)
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self.play(Transform(self.formula, new_formula), FadeIn(a_display))
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# 创建滑杆
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slider = NumberLine(x_range=[0.5, 2.5], length=4, include_numbers=True)
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slider.to_edge(self.SLIDER_POS).shift(DOWN * 0.6)
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dot = Dot(color=RED).move_to(slider.n2p(1))
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# 添加滑杆动画
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self.play(Create(slider), Create(dot))
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# 定义曲线更新函数
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def update_curve(mob):
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a = a_value.get_value()
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new_curve = self.axes.plot(lambda x: a * x ** 2, color=YELLOW)
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mob.become(new_curve)
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# 设置数值更新器
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self.curve.add_updater(update_curve)
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# 参数变化动画序列
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a_values = [0.5, 1.0, 2.0]
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for a in a_values:
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self.play(
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a_value.animate.set_value(a),
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dot.animate.move_to(slider.n2p(a)),
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run_time=3
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)
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self.wait(0.5)
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# 移除更新器
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self.curve.remove_updater(update_curve)
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# 保持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$是负数，开口向下", color=GREEN).to_edge(self.TITLE_POS)
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self.play(Transform(self.title, new_title))
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# 更新公式
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new_formula = MathTex("y = a x^2", color=RED).to_edge(self.FORMULA_POS)
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self.play(Transform(self.formula, new_formula))
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# 创建新的滑杆数值显示
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a_value = DecimalNumber(-0.5, num_decimal_places=1)
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a_text = Tex("$a = $").next_to(a_value, LEFT)
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a_display = VGroup(a_text, a_value).to_edge(self.SLIDER_POS)
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# 创建新滑杆
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slider = NumberLine(x_range=[-2.5, -0.5], length=4, include_numbers=True)
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slider.to_edge(self.SLIDER_POS).shift(DOWN * 0.6)
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dot = Dot(color=RED).move_to(slider.n2p(-0.5))
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# 添加滑杆动画
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self.play(FadeIn(a_display), Create(slider), Create(dot))
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# 定义曲线更新函数
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def update_curve(mob):
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a = a_value.get_value()
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new_curve = self.axes.plot(lambda x: a * x ** 2, color=YELLOW)
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mob.become(new_curve)
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# 设置数值更新器
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self.curve.add_updater(update_curve)
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# 参数变化动画序列
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a_values = [-0.5, -1.0, -2.0]
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for a in a_values:
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self.play(
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a_value.animate.set_value(a),
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dot.animate.move_to(slider.n2p(a)),
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run_time=3
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)
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self.wait(0.5)
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# 移除更新器
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self.curve.remove_updater(update_curve)
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# 保持5秒静止帧
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self.wait(5)
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def _practice(self):
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# 练习环节留空
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pass
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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({"preview": True, "quality": "high_quality"}):
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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() |