166 lines
5.4 KiB
Python
166 lines
5.4 KiB
Python
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（略） —— #
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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 —— #
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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 —— #
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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（略） —— #
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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 —— #
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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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self.wait(0.3)
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# —— 6. 新增积分区域动画 —— #
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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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# 点 updater：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 d: d.move_to(
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axes.c2p(t.get_value(), 1 / t.get_value())
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))
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# 动态多边形：积分区域从 x=1 到 current_x
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def make_polygon():
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x = t.get_value()
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y = 1 / x
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# 顶点为 (1,0), (x,0), (x, y), (1, 1)
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p0 = axes.c2p(1, 0)
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p1 = axes.c2p(x, 0)
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p2 = axes.c2p(x, y)
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p3 = axes.c2p(1, 1)
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poly = Polygon(p0, p1, p2, p3)
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poly.set_fill(BLUE, opacity=0.5)
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poly.set_stroke(YELLOW, width=2)
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return poly
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polygon = always_redraw(make_polygon)
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# 实时显示面积（积分面积）
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area_text = always_redraw(lambda: MathTex(
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rf"x = {t.get_value():.2f}",
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rf"\text{{Area}} = \ln(x) = {math.log(t.get_value()):.2f}"
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).arrange(DOWN).scale(0.6).next_to(dot, RIGHT).shift(UP*1.5))
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# 添加元素到场景
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self.add(dot, polygon)
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self.play(
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Create(polygon),
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run_time = 1.5
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)
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self.add(area_text)
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self.play(
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Write(area_text),
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run_time = 3
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)
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# 动画：x 在 e±0.5 之间滑动，最后停在 e
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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 x —— #
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self.play(
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Transform(equation, MathTex(
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r"\int_{1}^{x} \frac{1}{t}\,dt = \ln(x)"
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).move_to(RIGHT * 1.3 + UP)),
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run_time=1.5
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)
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# 高亮 x
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highlight_rect = SurroundingRectangle(equation[-2][1], color=YELLOW)
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self.play(Create(highlight_rect), run_time=0.6)
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self.wait(0.5)
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# 将 x 替换为 e
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self.play(
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Transform(equation, MathTex(
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r"\int_{1}^{e} \frac{1}{t}\,dt = 1"
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).move_to(equation)),
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run_time=1.5
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)
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self.wait(0.5)
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# 清除并添加 x = e
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self.play(
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Transform(equation, MathTex("x = e").move_to(equation)),
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FadeOut(highlight_rect, shift=DOWN),
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FadeOut(area_text, shift=DOWN), # 同时移除面积文本
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run_time=1
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)
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self.wait(1) |