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数学动画们

camera.py

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+from manim import *
+
+class MoveCameraToCorner(Scene):
+    def construct(self):
+        # 创建坐标轴
+        axes = Axes(
+            x_range=[0, 10, 1],
+            y_range=[0, 10, 1],
+            x_length=6,
+            y_length=6,
+            axis_config={"include_numbers": True},
+        )
+        self.add(axes)
+
+        # 等待一会儿观察默认位置
+        self.wait(1)
+
+        # 将相机移到让原点在左下角的位置，并缩放
+        self.camera.frame.save_state()  # 保存初始状态（可选）
+        self.camera.frame.move_to(axes.c2p(5, 5))  # 把坐标系中心移到画面中心
+        self.camera.frame.shift(LEFT * 5.5 + DOWN * 3.2)  # 向左下移动
+        self.camera.frame.scale(0.5)  # 缩小画面，相当于放大坐标轴
+
+        self.wait(1)  # 等待动画前静止
+
+        # 动画执行移动和缩放
+        self.play(self.camera.frame.animate.move_to(axes.c2p(5, 5)).shift(LEFT * 5.5 + DOWN * 3.2).scale(0.5), run_time=3)
+
+        self.wait(2)

cartasin.py

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+from manim import *
+import numpy as np
+
+class CartesianPlaneScene(Scene):
+    def construct(self):
+        # 一、创建坐标平面，先隐藏网格和数字
+        plane = NumberPlane(
+            x_range=[-5, 5, 1],
+            y_range=[-3, 3, 1],
+            background_line_style={
+                "stroke_color": GREY,
+                "stroke_width": 1,
+                "stroke_opacity": 1,
+            },
+            axis_config={
+                "include_tip": True,
+                "tip_length": 0.15,
+            }
+        )
+        # 生成坐标数字，但先透明
+        plane.add_coordinates()
+        plane.background_lines.set_opacity(0)
+        plane.coordinate_labels.set_opacity(0)
+
+        # 二、动画绘制 X 轴和 Y 轴
+        self.play(
+            Create(plane.x_axis, run_time=2),
+            Create(plane.y_axis, run_time=2),
+        )
+        self.wait(1)
+
+        # 三、写出刻度数字
+        self.play(
+            FadeIn(plane.coordinate_labels, shift=DOWN*0.2),
+            run_time=2
+        )
+        self.wait(1)
+
+        # 四、绘制网格线
+        self.play(
+            Create(plane.background_lines, run_time=3),
+        )
+        self.wait(1)
+
+        # 五、突出原点
+        origin_dot = Dot(plane.c2p(0, 0), color=RED)
+        self.play(FadeIn(origin_dot), run_time=1)
+        self.wait(2)

simple_scene.py

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+from manim import *
+
+class OpeningManim(Scene):
+    def construct(self):
+        title = Tex(r"This is some \LaTeX")
+        basel = MathTex(r"\sum_{n=1}^\infty \frac{1}{n^2} = \frac{\pi^2}{6}")
+        VGroup(title, basel).arrange(DOWN)
+        self.play(
+            Write(title),
+            FadeIn(basel, shift=DOWN),
+        )
+        self.wait()
+
+        transform_title = Tex("That was a transform")
+        transform_title.to_corner(UP + LEFT)
+        self.play(
+            Transform(title, transform_title),
+            LaggedStart(*[FadeOut(obj, shift=DOWN) for obj in basel]),
+        )
+        self.wait()
+
+        grid = NumberPlane()
+        grid_title = Tex("This is a grid", font_size=72)
+        grid_title.move_to(transform_title)
+
+        self.add(grid, grid_title)  # Make sure title is on top of grid
+        self.play(
+            FadeOut(title),
+            FadeIn(grid_title, shift=UP),
+            Create(grid, run_time=3, lag_ratio=0.1),
+        )
+        self.wait()
+
+        grid_transform_title = Tex(
+            r"That was a non-linear function \\ applied to the grid"
+        )
+        grid_transform_title.move_to(grid_title, UL)
+        grid.prepare_for_nonlinear_transform()
+        self.play(
+            grid.animate.apply_function(
+                lambda p: p
+                          + np.array(
+                    [
+                        np.sin(p[1]),
+                        np.sin(p[0]),
+                        0,
+                    ]
+                )
+            ),
+            run_time=3,
+        )
+        self.wait()
+        self.play(Transform(grid_title, grid_transform_title))
+        self.wait()

study.py

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+from manim import *
+import math
+
+class FadeInExample(MovingCameraScene):
+    def construct(self):
+        # —— 1. 文本淡入淡出（原样保留）—— #
+        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（原样保留）—— #
+        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（原样保留）—— #
+        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（原样保留）—— #
+        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（原样保留）—— #
+        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)
+
+        # —— 6. 新增积分区域动画（核心修复）—— #
+        # ValueTracker 跟踪 x（初始值设为 e）
+        t = ValueTracker(math.e)
+
+        # dot：始终在 (t, 1/t) 上
+        dot = Dot().set_z_index(10)
+        dot.add_updater(lambda m: m.move_to(
+            axes.c2p(t.get_value(), 1 / t.get_value())
+        ))
+
+        # 动态积分区域
+        integral = always_redraw(lambda: axes.get_area(
+            func1,
+            x_range=[1, t.get_value()],
+            color=BLUE,
+            opacity=0.5
+        ))
+        integral_border = always_redraw(lambda: axes.plot(
+            lambda x: 1/x,
+            x_range=[1, t.get_value()],
+            color=YELLOW,
+            stroke_width=2
+        ))
+
+        # 创建动态文本函数
+        def create_text():
+            x_val = t.get_value()
+            area_val = math.log(x_val)
+            return VGroup(
+                MathTex(f"x = {x_val:.2f}"),
+                MathTex(f"A = {area_val:.2f}")
+            ).arrange(DOWN, aligned_edge=LEFT)
+
+        # 动态文本，并添加 updater
+        dynamic_text = create_text()
+        dynamic_text.next_to(dot, UR, buff=0.3)
+        def update_text(group):
+            x_val = t.get_value()
+            area_val = math.log(x_val)
+            group[0].become(MathTex(f"x = {x_val:.2f}"))
+            group[1].become(MathTex(f"A = {area_val:.2f}"))
+            group.arrange(DOWN, aligned_edge=LEFT)
+            group.next_to(dot, UP + RIGHT * 5, buff=0.3)
+        dynamic_text.add_updater(update_text)
+
+        # 添加并播放
+        self.add(dot, integral, integral_border)
+        self.play(Create(integral), Create(integral_border), run_time=2)
+
+        # 切换到动态文本
+        self.add(dynamic_text)
+        self.play(Write(dynamic_text), run_time=2)
+
+        # x 在 e±0.5 之间滑动
+        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（原样保留）—— #
+        integral_eq = MathTex(
+            r"\int_{1}^{x} \frac{1}{x}\,dx = 1"
+        ).move_to(ORIGIN).shift(RIGHT * 1.3 + UP)
+
+        def highlight(mobj):
+            return Circumscribe(
+                mobj,
+                color=YELLOW,
+                time_width=2,
+                run_time=1.5,
+                fade_out=True
+            )
+
+        def sync_hl():
+            return (
+                highlight(integral_eq[0][5]),  # x
+                highlight(integral_eq[0][-1]), # 1
+                highlight(dynamic_text[0][-1]),# 动态 x
+                highlight(dynamic_text[1][-1]) # 动态 A
+            )
+
+        self.play(Transform(equation, integral_eq), run_time=1.5)
+        self.play(sync_hl(), run_time=2)
+
+        final_eq = MathTex(
+            r"\int_{1}^{e} \frac{1}{x}\,dx = 1"
+        ).move_to(integral_eq)
+        self.play(
+            Transform(equation, final_eq),
+            highlight(final_eq[0][5]),
+            highlight(dynamic_text[0][-1]),
+            run_time=2
+        )
+        self.play(
+            Indicate(final_eq[0][5], color=YELLOW),
+            Indicate(dynamic_text[0][-1], color=YELLOW),
+            run_time=1.5
+        )
+        self.wait(1)

study_backup2.py

@@ -0,0 +1,166 @@
+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)