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数学动画们
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183
study.py
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183
study.py
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from manim import *
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import math
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class FadeInExample(MovingCameraScene):
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def construct(self):
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# —— 1. 文本淡入淡出（原样保留）—— #
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self.wait(0.5)
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tex = Tex("Inverse ", "Proportion ", "Function").scale(1)
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self.play(Write(tex), run_time=2)
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self.wait(1)
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self.play(
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AnimationGroup(
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FadeOut(tex[0], shift=DOWN),
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FadeOut(tex[1], shift=DOWN),
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lag_ratio=0.09
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)
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)
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self.play(tex[2].animate.to_corner(UL))
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self.wait(0.3)
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# —— 2. 定义坐标系 & 函数（原样保留）—— #
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axes = Axes(
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x_range=[-6, 8, 1],
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y_range=[-3, 5, 1],
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x_length=13,
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y_length=6,
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axis_config={
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"include_tip": False,
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"numbers_to_include": [],
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"color": WHITE
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}
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).add_coordinates()
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labels = axes.get_axis_labels()
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func1 = axes.plot(lambda x: 1/x, x_range=[0.1, 11], color=YELLOW)
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func2 = axes.plot(lambda x: 1/x, x_range=[-25, -0.1], color=YELLOW)
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credits = Tex("Made with Manim by David", font_size=24)
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# —— 3. 播放坐标系 & 函数动画（原样保留）—— #
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self.add(credits.to_corner(DR))
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self.play(
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Create(axes, run_time=3, lag_ratio=0.1),
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Write(credits, run_time=1),
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)
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self.add(labels)
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self.play(Write(labels))
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self.play(Create(func1, run_time=3), Create(func2, run_time=1))
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# —— 4. 相机缩放前的公式高亮（原样保留）—— #
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equation = MathTex("y", "=", r"\frac{1}{x}")
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equation.move_to(UR)
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self.play(Write(equation), run_time=1)
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self.wait(0.5)
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rect = SurroundingRectangle(equation[0], color=YELLOW)
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self.play(Create(rect), run_time=0.6)
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self.wait(0.5)
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new_equation = MathTex(r"f(x)", "=", r"\frac{1}{x}")
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new_equation.move_to(equation)
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new_rect = SurroundingRectangle(new_equation[0], color=YELLOW)
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self.play(
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Transform(equation, new_equation),
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Transform(rect, new_rect),
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run_time=1
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)
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self.play(FadeOut(rect), run_time=0.5)
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# —— 5. 相机移动与缩放（原样保留）—— #
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self.camera.frame.save_state()
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center = axes.c2p(
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(axes.x_range[0] + axes.x_range[1]) / 2,
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(axes.y_range[0] + axes.y_range[1]) / 2
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)
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shift_vec = RIGHT * 1.6 + UP * 0.7
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scale_factor = 0.6
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self.play(
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self.camera.frame.animate
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.move_to(center)
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.shift(shift_vec)
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.scale(scale_factor),
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run_time=1.4
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)
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self.remove(credits)
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self.add(credits.to_corner(DR))
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self.play(Write(credits), run_time=1)
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# —— 6. 新增积分区域动画（核心修复）—— #
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# ValueTracker 跟踪 x（初始值设为 e）
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t = ValueTracker(math.e)
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# dot：始终在 (t, 1/t) 上
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dot = Dot().set_z_index(10)
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dot.add_updater(lambda m: m.move_to(
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axes.c2p(t.get_value(), 1 / t.get_value())
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))
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# 动态积分区域
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integral = always_redraw(lambda: axes.get_area(
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func1,
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x_range=[1, t.get_value()],
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color=BLUE,
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opacity=0.5
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))
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integral_border = always_redraw(lambda: axes.plot(
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lambda x: 1/x,
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x_range=[1, t.get_value()],
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color=YELLOW,
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stroke_width=2
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))
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# 创建动态文本函数
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def create_text():
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x_val = t.get_value()
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area_val = math.log(x_val)
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return VGroup(
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MathTex(f"x = {x_val:.2f}"),
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MathTex(f"A = {area_val:.2f}")
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).arrange(DOWN, aligned_edge=LEFT)
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# 动态文本，并添加 updater
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dynamic_text = create_text()
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dynamic_text.next_to(dot, UR, buff=0.3)
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def update_text(group):
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x_val = t.get_value()
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area_val = math.log(x_val)
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group[0].become(MathTex(f"x = {x_val:.2f}"))
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group[1].become(MathTex(f"A = {area_val:.2f}"))
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group.arrange(DOWN, aligned_edge=LEFT)
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group.next_to(dot, UP + RIGHT * 5, buff=0.3)
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dynamic_text.add_updater(update_text)
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# 添加并播放
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self.add(dot, integral, integral_border)
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self.play(Create(integral), Create(integral_border), run_time=2)
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# 切换到动态文本
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self.add(dynamic_text)
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self.play(Write(dynamic_text), run_time=2)
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# x 在 e±0.5 之间滑动
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self.play(t.animate.set_value(math.e + 0.5), run_time=1)
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self.play(t.animate.set_value(math.e - 0.5), run_time=1)
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self.play(t.animate.set_value(math.e), run_time=1)
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self.wait(1)
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# —— 7. 转换为积分形式并高亮（原样保留）—— #
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integral_eq = MathTex(
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r"\int_{1}^{x} \frac{1}{x}\,dx = 1"
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).move_to(ORIGIN).shift(RIGHT * 1.3 + UP)
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def highlight(mobj):
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return Circumscribe(
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mobj,
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color=YELLOW,
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time_width=2,
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run_time=1.5,
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fade_out=True
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)
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def sync_hl():
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return (
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highlight(integral_eq[0][5]), # x
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highlight(integral_eq[0][-1]), # 1
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highlight(dynamic_text[0][-1]),# 动态 x
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highlight(dynamic_text[1][-1]) # 动态 A
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)
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self.play(Transform(equation, integral_eq), run_time=1.5)
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self.play(sync_hl(), run_time=2)
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final_eq = MathTex(
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r"\int_{1}^{e} \frac{1}{x}\,dx = 1"
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).move_to(integral_eq)
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self.play(
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Transform(equation, final_eq),
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highlight(final_eq[0][5]),
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highlight(dynamic_text[0][-1]),
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run_time=2
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)
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self.play(
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Indicate(final_eq[0][5], color=YELLOW),
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Indicate(dynamic_text[0][-1], color=YELLOW),
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run_time=1.5
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)
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self.wait(1)
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