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# difference_of_squares_final.py
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from manim import *
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import numpy as np
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class SquareDifference(Scene):
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def create_bubble(self, text, direction=UP):
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"""创建自定义对话气泡（完全兼容版）"""
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# 基础形状组件
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bubble = VGroup()
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# 文本内容（确保中文字体可用）
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text_mob = Text(text, font="Microsoft YaHei", font_size=24)
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text_mob.scale(0.8)
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# 背景框
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rect = RoundedRectangle(
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width=text_mob.width + 0.5,
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height=text_mob.height + 0.3,
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corner_radius=0.2,
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fill_color=WHITE,
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fill_opacity=1,
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stroke_color=BLACK,
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stroke_width=2
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)
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# 箭头方向处理
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arrow = Triangle().scale(0.3)
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arrow.set_fill(WHITE, 1)
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arrow.set_stroke(BLACK, 2)
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# 使用向量判断方向
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if np.array_equal(direction, UP):
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arrow.rotate(-PI/2)
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bubble.add(rect, arrow)
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bubble.arrange(DOWN, buff=0.1)
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elif np.array_equal(direction, DOWN):
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arrow.rotate(PI/2)
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bubble.add(arrow, rect)
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bubble.arrange(DOWN, buff=0.1)
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else: # 默认上方
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arrow.rotate(-PI/2)
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bubble.add(rect, arrow)
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bubble.arrange(DOWN, buff=0.1)
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# 定位文本
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text_mob.move_to(rect)
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bubble.add(text_mob)
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return bubble
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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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# 创建小熊角色（优化动画版）
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bear = VGroup(
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Circle(radius=0.5, color=GOLD, fill_opacity=1), # 头
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Circle(radius=0.1, fill_opacity=1).shift(UR*0.3), # 右耳
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Circle(radius=0.1, fill_opacity=1).shift(UL*0.3), # 左耳
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Ellipse(width=0.8, height=1.2, fill_opacity=1).shift(DOWN*0.8) # 身体
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).set_color([GOLD_E, LIGHT_BROWN])
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bear.scale(0.8).to_corner(DL)
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# 场景1：小熊出场
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self.play(DrawBorderThenFill(bear), run_time=1.5)
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self.play(
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bear.animate.shift(UP*0.5).scale(1.2),
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rate_func=there_and_back_with_pause,
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run_time=1.5
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)
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# 创建对话气泡
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bubble = self.create_bubble("大家好！今天我们来认识一个神奇的三角形")
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bubble.next_to(bear, UP, buff=0.3)
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self.play(
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LaggedStart(
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DrawBorderThenFill(bubble[0]),
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DrawBorderThenFill(bubble[1]),
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Write(bubble[2]),
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lag_ratio=0.3
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),
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run_time=2
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)
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self.wait(2)
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self.play(FadeOut(bubble))
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# 创建3-4-5直角三角形
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triangle = Polygon(
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[-2, -1, 0], [2, -1, 0], [2, 2, 0],
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color=WHITE,
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fill_opacity=0.5,
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stroke_width=4
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)
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labels = VGroup(
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MathTex("3").next_to(triangle, LEFT, buff=0.3),
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MathTex("4").next_to(triangle, DOWN, buff=0.3),
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MathTex("5", color=YELLOW).next_to(triangle.get_center(), UR, buff=0.3)
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)
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self.play(DrawBorderThenFill(triangle), run_time=2)
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self.play(LaggedStart(*[Write(l) for l in labels], lag_ratio=0.3))
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self.play(
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triangle.animate.shift(LEFT*2),
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bear.animate.look_at(triangle),
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run_time=1.5
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)
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self.wait()
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# 场景2：构建正方形
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square3 = Square(side_length=3, color=PINK, fill_opacity=0.3)
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square4 = Square(side_length=4, color=BLUE, fill_opacity=0.3)
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square5 = Square(side_length=5, color=GREEN, fill_opacity=0.3)
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square3.next_to(triangle, LEFT, buff=0.5)
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square4.next_to(triangle, DOWN, buff=0.5)
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square5.rotate(np.arctan(3/4)).next_to(triangle, UR, buff=0.5)
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self.play(
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LaggedStart(
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DrawBorderThenFill(square3),
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DrawBorderThenFill(square4),
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DrawBorderThenFill(square5),
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lag_ratio=0.5
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),
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bear.animate.wave(rate_func=there_and_back),
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run_time=3
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)
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# 添加面积标签
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area_text = VGroup(
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MathTex("3^2=9", color=PINK),
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MathTex("4^2=16", color=BLUE),
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MathTex("5^2=25", color=GREEN)
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).arrange(DOWN, buff=0.5, aligned_edge=LEFT).to_edge(UR)
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self.play(TransformFromCopy(square3, area_text[0]))
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self.play(Indicate(square3, scale_factor=1.2))
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self.play(TransformFromCopy(square4, area_text[1]))
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self.play(Indicate(square4, scale_factor=1.2))
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self.play(TransformFromCopy(square5, area_text[2]))
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self.play(Indicate(square5, scale_factor=1.2))
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self.wait()
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# 场景3：组合动画
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self.play(
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square3.animate.shift(UP*2 + LEFT*1).rotate(PI/3),
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square4.animate.shift(RIGHT*3 + DOWN*1).rotate(-PI/4),
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bear.animate.blink(rate_func=there_and_back),
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run_time=2
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)
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magic_text = Text("看！9 + 16 = 25", font="Microsoft YaHei", color=YELLOW).scale(0.8)
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self.play(Write(magic_text))
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self.play(
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square3.animate.move_to(ORIGIN).set_opacity(0.3),
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square4.animate.move_to(ORIGIN).set_opacity(0.3),
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square5.animate.move_to(ORIGIN).set_opacity(0.3),
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run_time=2
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)
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self.wait()
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# 场景4：公式推导
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equation = MathTex("3^2 + 4^2 = 5^2", color=YELLOW).scale(1.5)
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equation_box = SurroundingRectangle(equation, color=BLUE, buff=0.5, corner_radius=0.2)
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self.play(
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ReplacementTransform(magic_text, equation),
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Create(equation_box),
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bear.animate.jump(rate_func=there_and_back),
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run_time=2
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)
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self.wait(2)
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# 场景5：告别
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bye_bubble = self.create_bubble("下次再见啦！")
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bye_bubble.next_to(bear, UP, buff=0.3)
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self.play(
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FadeOut(VGroup(triangle, square3, square4, square5, equation_box, labels, area_text)),
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LaggedStart(
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DrawBorderThenFill(bye_bubble[0]),
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DrawBorderThenFill(bye_bubble[1]),
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Write(bye_bubble[2]),
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lag_ratio=0.3
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),
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bear.animate.happy().scale(1.2),
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run_time=2
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)
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self.play(
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bear.animate.rotate(PI/2, about_point=bear.get_center()).shift(DOWN*2),
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run_time=2
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)
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self.wait(2)
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if __name__ == "__main__":
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config.background_color = "#F0F8FF" # 浅蓝背景
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config.frame_width = 16
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config.frame_height = 9
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config.pixel_width = 1280
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config.pixel_height = 720
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config.media_dir = "./output"
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scene = SquareDifference()
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scene.render() |
