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# difference_of_squares_final.py
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from manim import *
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class SquareDifference(Scene):
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def construct(self):
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# 高清配置
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config.frame_width = 16
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config.frame_height = 9
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config.pixel_height = 1440
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config.pixel_width = 2560
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# 参数配置
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a = 4
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b = 1
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colors = {
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"a": "#1F77B4",
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"b": "#FF7F0E",
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"text": "#FFFFFF",
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"bg": "#2E2E2E"
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}
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self.camera.background_color = colors["bg"]
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step_delay = 2.5
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# ========== 标题部分 ==========
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title = Text("东师理想数学课件生成助手",
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font_size=48,
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color=colors["text"],
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weight=BOLD,
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stroke_width=8,
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stroke_color=BLACK)
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sub_title = Text("平方差公式可视化演示",
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font_size=32,
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color=colors["text"],
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stroke_width=4,
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stroke_color=BLACK).next_to(title, DOWN)
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self.play(
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Write(title, run_time=1.5),
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FadeIn(sub_title, shift=UP),
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run_time=2
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)
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self.wait(step_delay)
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self.play(
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FadeOut(title, shift=UP),
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FadeOut(sub_title, shift=DOWN),
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run_time=1.5
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)
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# ========== 公式推导部分 ==========
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formula_steps = VGroup(
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MathTex("(", "a", "+", "b", ")(", "a", "-", "b", ")", font_size=40),
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MathTex("=", "a", "^2", "-", "b", "^2", font_size=40),
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MathTex("=", f"{a**2}", "-", f"{b**2}", font_size=40),
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MathTex("=", f"{(a+b)*(a-b)}", font_size=48, color=GREEN)
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).arrange(DOWN, aligned_edge=LEFT, buff=0.8)
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formula_board = SurroundingRectangle(
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formula_steps,
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color=WHITE,
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stroke_width=2,
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fill_color=BLACK,
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fill_opacity=0.7,
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corner_radius=0.2
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)
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self.play(
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DrawBorderThenFill(formula_board),
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FadeIn(formula_steps, shift=UP),
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run_time=2
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)
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self.wait(step_delay)
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# ========== 坐标系部分（最终修复） ==========
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# 使用新版背景线直接生成网格
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axes = Axes(
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x_range=[0, a+b+1, 1],
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y_range=[0, a+b+1, 1],
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x_length=8,
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y_length=6,
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axis_config={
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"color": colors["text"],
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"stroke_width": 3,
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"include_numbers": True
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}
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).shift(DOWN*0.5)
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# 大正方形动画
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big_square = Rectangle(
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width=a+b,
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height=a+b,
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color=colors["a"],
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fill_opacity=0.4,
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stroke_width=4
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).move_to(axes.c2p((a+b)/2, (a+b)/2))
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self.play(
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formula_board.animate.scale(0.8).to_edge(UP, buff=0.5),
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Create(axes, run_time=2),
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DrawBorderThenFill(big_square),
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run_time=2
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)
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self.wait(step_delay)
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# ========== 剩余动画部分 ==========
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# 垂直分割线
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v_line = Line(
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start=axes.c2p(a, 0),
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end=axes.c2p(a, a+b),
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color=colors["text"],
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stroke_width=4
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)
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v_label = MathTex("a",
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color=colors["text"],
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stroke_width=3,
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stroke_color=BLACK).next_to(v_line, RIGHT, buff=0.2)
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# 水平分割线
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h_line = Line(
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start=axes.c2p(0, a),
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end=axes.c2p(a+b, a),
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color=colors["text"],
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stroke_width=4
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)
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h_label = MathTex("a",
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color=colors["text"],
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stroke_width=3,
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stroke_color=BLACK).next_to(h_line, UP, buff=0.2)
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self.play(
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Create(v_line),
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Write(v_label),
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Create(h_line),
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Write(h_label),
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run_time=2
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)
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self.wait(step_delay)
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# ========== 面积计算部分 ==========
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part_a = Rectangle(
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width=a,
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height=a,
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color=colors["a"],
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fill_opacity=0.6
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).move_to(axes.c2p(a/2, a/2))
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part_b = Rectangle(
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width=b,
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height=a+b,
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color=colors["b"],
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fill_opacity=0.6
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).move_to(axes.c2p(a + b/2, (a+b)/2))
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self.play(
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Transform(big_square, part_a),
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FadeIn(part_b),
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run_time=2
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)
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self.wait(step_delay)
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# 移动并计算面积差
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moved_part = part_b.copy().shift(DOWN*b)
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area_diff = Rectangle(
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width=b,
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height=2*b,
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color=RED,
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fill_opacity=0.3
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).move_to(axes.c2p(a + b/2, a - b))
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self.play(
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part_b.animate.shift(DOWN*b),
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FadeIn(area_diff),
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run_time=2
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)
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self.wait(step_delay)
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# ========== 最终联动 ==========
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final_formula = formula_steps[-1].copy()
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final_formula.generate_target()
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final_formula.target.scale(1.5).move_to(ORIGIN)
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self.play(
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MoveToTarget(final_formula),
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FadeOut(axes),
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FadeOut(part_a),
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FadeOut(part_b),
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FadeOut(area_diff),
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run_time=2
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)
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self.wait(step_delay*2)
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# 结束动画
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self.play(
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final_formula.animate.scale(0.5).to_edge(DOWN, buff=1),
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run_time=1.5
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)
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self.wait(2)
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# 版权信息
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copyright = Text("© 东师理想 版权所有",
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font_size=24,
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color=colors["text"],
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stroke_width=2,
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stroke_color=BLACK).to_edge(DOWN, buff=0.3)
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self.play(Write(copyright), run_time=1)
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self.wait(3)
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