QingLong/AI/Manim/L11_PythagoreanProof.py

from manim import *
import numpy as np


class PythagoreanProof(Scene):
    def update_step(self, current_text, new_content, duration=1.5):
        """带淡入淡出效果的步骤更新"""
        new_text = Text(new_content, font="Microsoft YaHei", font_size=32).to_edge(UP, buff=0.8)
        new_text.set_color_by_gradient(GOLD, ORANGE)

        if current_text:
            self.play(
                FadeOut(current_text, shift=UP * 0.3),
                FadeIn(new_text, shift=DOWN * 0.3),
                run_time=0.8
            )
        else:
            self.play(FadeIn(new_text, shift=DOWN))

        self.wait(duration)
        return new_text

    def create_polygon(self, points, color, fill_opacity=0.8):
        """创建带样式的多边形"""
        return Polygon(*points,
                       color=color,
                       fill_opacity=fill_opacity,
                       stroke_width=4)

    def construct(self):
        current_step = None
        elements = VGroup()

        # === 步骤1：使用NumPy数组定义坐标 ===
        current_step = self.update_step(None, "步骤1：绘制直角三角形")

        # 定义三角形顶点（使用NumPy数组）
        A = np.array([-2.0, -1.0, 0.0])
        B = np.array([2.0, -1.0, 0.0])
        C = np.array([1.0, 1.5, 0.0])

        triangle = self.create_polygon([A, B, C], BLUE)
        elements.add(triangle)
        self.play(Create(triangle), run_time=2)
        self.wait()

        # === 步骤2：构建三个正方形 ===
        current_step = self.update_step(current_step, "步骤2：构建三个正方形")

        # 计算向量
        vector_AC = C - A
        vector_BC = C - B

        # 构建正方形坐标点（使用向量运算）
        square_a = Square(side_length=4, color=ORANGE).shift(DOWN * 2)

        square_b_points = [
            A,
            C,
            C + vector_AC * 0.8,
            A + vector_AC * 0.8
        ]
        square_b = self.create_polygon(square_b_points, ORANGE)

        square_c_points = [
            B,
            C,
            C + vector_BC * 0.8,
            B + vector_BC * 0.8
        ]
        square_c = self.create_polygon(square_c_points, ORANGE)

        self.play(
            LaggedStart(
                Create(square_a),
                Create(square_b),
                Create(square_c),
                lag_ratio=0.4
            ),
            run_time=3
        )
        elements.add(square_a, square_b, square_c)
        self.wait()

        # === 步骤3：面积变换演示 ===
        current_step = self.update_step(current_step, "步骤3：面积恒等变换")

        # 创建可移动三角形
        moving_tri_points = [C, A, A + (A - C) * 0.8]
        moving_tri = self.create_polygon(moving_tri_points, YELLOW)

        self.play(Create(moving_tri), run_time=1)
        self.play(
            Rotate(
                moving_tri,
                angle=-PI / 2,
                about_point=A,
                rate_func=smooth
            ),
            run_time=2
        )
        self.wait()

        # === 步骤4：最终结论 ===
        current_step = self.update_step(current_step, "步骤4：得出结论")

        # 数学公式
        formula = MathTex(r"a^2 + b^2 = c^2", color=GOLD).scale(2)
        formula_box = SurroundingRectangle(formula, color=WHITE, buff=0.5)

        self.play(
            FadeOut(elements),
            FadeOut(moving_tri),
            run_time=1
        )
        self.play(
            DrawBorderThenFill(formula_box),
            Write(formula),
            run_time=2
        )
        self.wait(3)


if __name__ == "__main__":
    config = {
        "quality": "high_quality",
        "preview": True,
        "media_dir": "./output",
        "pixel_height": 1080,
        "pixel_width": 1920,
        "background_color": "#333333",  # 深色背景
        "format": "png"  # 解决部分系统渲染问题
    }

    with tempconfig(config):
        scene = PythagoreanProof()
        scene.render()