Manim/study_backup2.py

from manim import *
import math

class FadeInExample(MovingCameraScene):
    def construct(self):
        # —— 1. 文本淡入淡出（略） —— #
        self.wait(0.5)
        tex = Tex("Inverse ", "Proportion ", "Function").scale(1)
        self.play(Write(tex), run_time=2)
        self.wait(1)
        self.play(
            AnimationGroup(
                FadeOut(tex[0], shift=DOWN),
                FadeOut(tex[1], shift=DOWN),
                lag_ratio=0.09
            )
        )
        self.play(tex[2].animate.to_corner(UL))
        self.wait(0.3)

        # —— 2. 定义坐标系 & 函数 —— #
        axes = Axes(
            x_range=[-6, 8, 1],
            y_range=[-3, 5, 1],
            x_length=13,
            y_length=6,
            axis_config={
                "include_tip": False,
                "numbers_to_include": [],
                "color": WHITE
            }
        ).add_coordinates()
        labels = axes.get_axis_labels()
        func1 = axes.plot(lambda x: 1/x, x_range=[0.1, 11], color=YELLOW)
        func2 = axes.plot(lambda x: 1/x, x_range=[-25, -0.1], color=YELLOW)
        credits = Tex("Made with Manim by David", font_size=24)

        # —— 3. 播放坐标系 & 函数动画 —— #
        self.add(credits.to_corner(DR))
        self.play(
            Create(axes, run_time=3, lag_ratio=0.1),
            Write(credits, run_time=1),
        )
        self.add(labels)
        self.play(Write(labels))
        self.play(Create(func1, run_time=3), Create(func2, run_time=1))

        # —— 4. 相机缩放前的公式高亮（略） —— #
        equation = MathTex("y", "=", r"\frac{1}{x}")
        equation.move_to(UR)
        self.play(Write(equation), run_time=1)
        self.wait(0.5)
        rect = SurroundingRectangle(equation[0], color=YELLOW)
        self.play(Create(rect), run_time=0.6)
        self.wait(0.5)
        new_equation = MathTex(r"f(x)", "=", r"\frac{1}{x}")
        new_equation.move_to(equation)
        new_rect = SurroundingRectangle(new_equation[0], color=YELLOW)
        self.play(
            Transform(equation, new_equation),
            Transform(rect, new_rect),
            run_time=1
        )
        self.play(FadeOut(rect), run_time=0.5)

        # —— 5. 相机移动与缩放 —— #
        self.camera.frame.save_state()
        center = axes.c2p(
            (axes.x_range[0] + axes.x_range[1]) / 2,
            (axes.y_range[0] + axes.y_range[1]) / 2
        )
        shift_vec = RIGHT * 1.6 + UP * 0.7
        scale_factor = 0.6
        self.play(
            self.camera.frame.animate
                .move_to(center)
                .shift(shift_vec)
                .scale(scale_factor),
            run_time=1.4
            
        )
        self.remove(credits)
        self.add(credits.to_corner(DR))
        self.play(Write(credits), run_time=1)
        self.wait(0.3)

        # —— 6. 新增积分区域动画 —— #
        # ValueTracker 跟踪 x（初始值设为 e）
        t = ValueTracker(math.e)

        # 点 updater：始终在 (t, 1/t) 上
        dot = Dot().set_z_index(10)
        dot.add_updater(lambda d: d.move_to(
            axes.c2p(t.get_value(), 1 / t.get_value())
        ))

        # 动态多边形：积分区域从 x=1 到 current_x
        def make_polygon():
            x = t.get_value()
            y = 1 / x
            # 顶点为 (1,0), (x,0), (x, y), (1, 1)
            p0 = axes.c2p(1, 0)
            p1 = axes.c2p(x, 0)
            p2 = axes.c2p(x, y)
            p3 = axes.c2p(1, 1)
            poly = Polygon(p0, p1, p2, p3)
            poly.set_fill(BLUE, opacity=0.5)
            poly.set_stroke(YELLOW, width=2)
            return poly
        polygon = always_redraw(make_polygon)

        # 实时显示面积（积分面积）
        area_text = always_redraw(lambda: MathTex(
            rf"x = {t.get_value():.2f}", 
            rf"\text{{Area}} = \ln(x) = {math.log(t.get_value()):.2f}"
        ).arrange(DOWN).scale(0.6).next_to(dot, RIGHT).shift(UP*1.5))

        # 添加元素到场景
        self.add(dot, polygon)
        self.play(
            Create(polygon), 
            run_time = 1.5
        )

        self.add(area_text)
        self.play(
            Write(area_text),
            run_time = 3
        )

        # 动画：x 在 e±0.5 之间滑动，最后停在 e
        self.play(t.animate.set_value(math.e + 0.5), run_time=1)
        self.play(t.animate.set_value(math.e - 0.5), run_time=1)
        self.play(t.animate.set_value(math.e), run_time=1)
        self.wait(1)

        # —— 7. 转换为积分形式并高亮 x —— #
        self.play(
            Transform(equation, MathTex(
                r"\int_{1}^{x} \frac{1}{t}\,dt = \ln(x)"
            ).move_to(RIGHT * 1.3 + UP)),
            run_time=1.5
        )

        # 高亮 x
        highlight_rect = SurroundingRectangle(equation[-2][1], color=YELLOW)
        self.play(Create(highlight_rect), run_time=0.6)
        self.wait(0.5)

        # 将 x 替换为 e
        self.play(
            Transform(equation, MathTex(
                r"\int_{1}^{e} \frac{1}{t}\,dt = 1"
            ).move_to(equation)),
            run_time=1.5
        )
        self.wait(0.5)

        # 清除并添加 x = e
        self.play(
            Transform(equation, MathTex("x = e").move_to(equation)),
            FadeOut(highlight_rect, shift=DOWN),
            FadeOut(area_text, shift=DOWN),  # 同时移除面积文本
            run_time=1
        )
        self.wait(1)