向量场的环流量

1from manim import *2import numpy as np3 4config.tex_template = TexTemplateLibrary.ctex5config.tex_template.add_to_preamble(r"\setCJKmainfont{STSong}")6 7class Circulation(ThreeDScene):8    def construct(self):9        # 创建标题10        title = Text("向量场的环流量", font="STSong", font_size=48)11        self.add_fixed_in_frame_mobjects(title)12        self.play(Write(title))13        self.wait(1)14        self.play(FadeOut(title))15 16        # 创建3D坐标系17        axes = ThreeDAxes(18            x_range=[-3, 3, 1],19            y_range=[-3, 3, 1],20            z_range=[-3, 3, 1],21            x_length=6,22            y_length=6,23            z_length=624        )25 26        # 设置相机视角27        self.set_camera_orientation(28            phi=70*DEGREES,29            theta=-45*DEGREES30        )31 32        self.play(Create(axes))33        self.wait(1)34 35        # 创建旋转向量场36        def vector_field_func(point):37            x, y, z = point38            return np.array([-y, x, 0]) / 239 40        # 创建向量场（蓝色箭头）- 减少向量数量41        vector_field = VGroup()42        for x in np.linspace(-2, 2, 5):  # 减少为5x5的网格43            for y in np.linspace(-2, 2, 5):44                for z in [0]:45                    point = np.array([x, y, z])46                    vector = vector_field_func(point)47                    arrow = Arrow3D(48                        start=point,49                        end=point + vector,50                        color=BLUE,51                        thickness=0.0252                    )53                    vector_field.add(arrow)54 55        # 添加向量场说明 - 添加向量符号56        field_label = MathTex(57            "\\vec{F}", 58            tex_template=TexTemplateLibrary.ctex,59            color=BLUE60        ).scale(1.2)61        field_label.shift(LEFT * 3.5)  # 向中间平移62 63        self.add_fixed_in_frame_mobjects(field_label)64        self.play(Create(vector_field), Write(field_label))65        self.wait(1)66 67        # 创建圆形路径68        radius = 1.569        circle = Circle(radius=radius, color=YELLOW)70        circle.shift(OUT*0.01)  # 稍微抬高以便看清71        72        # 创建路径箭头（表示路径方向）73        path_arrows = VGroup()74        n_arrows = 24  # 增加箭头数量75        for i in range(n_arrows):76            angle = i * TAU / n_arrows77            point = np.array([78                radius * np.cos(angle),79                radius * np.sin(angle),80                0.0181            ])82            next_angle = (i + 1) * TAU / n_arrows83            next_point = np.array([84                radius * np.cos(next_angle),85                radius * np.sin(next_angle),86                0.0187            ])88            arrow = Arrow3D(89                start=point,90                end=next_point,91                color=YELLOW,92                thickness=0.0293            )94            path_arrows.add(arrow)95 96        # 修改路径说明位置97        path_label = Text("闭合路径 C", font="STSong", font_size=30, color=YELLOW)98        path_label.shift(RIGHT * 3.5)  # 向中间平移99        self.add_fixed_in_frame_mobjects(path_label)100 101        self.play(Create(circle), Create(path_arrows), Write(path_label))102        self.wait(1)103 104        # 创建移动的点和切向量105        dot = Sphere(radius=0.08, color=RED)106        dot.move_to(circle.point_from_proportion(0))107        108        # 创建切向量（显示做功）109        def get_work_vector(point):110            field_vector = vector_field_func(point)111            return Arrow3D(112                start=point,113                end=point + field_vector,114                color=GREEN,115                thickness=0.03116            )117 118        work_vector = get_work_vector(circle.point_from_proportion(0))119 120        # 添加做功说明121        work_label = Text("向量场沿路径做功", font="STSong", font_size=30, color=GREEN)122        work_label.next_to(path_label, DOWN)123        self.add_fixed_in_frame_mobjects(work_label)124 125        self.play(Create(dot), Create(work_vector), Write(work_label))126        self.wait(1)127 128        # 创建环流量公式129        circulation_formula = MathTex(130            "\\text{环流量} = \\oint_C \\vec{F} \\cdot d\\vec{r}",131            tex_template=TexTemplateLibrary.ctex132        ).scale(0.8)133        circulation_formula.to_corner(UR)134        135        explanation = Text(136            "环流量表示向量场沿闭合路径的总做功",137            font="STSong",138            font_size=24139        ).next_to(circulation_formula, DOWN+LEFT*0.5)140 141        self.add_fixed_in_frame_mobjects(circulation_formula, explanation)142        self.play(Write(circulation_formula), Write(explanation))143        self.wait(1)144 145        # 创建点的运动动画146        def update_dot_and_vector(mob, alpha):147            new_point = circle.point_from_proportion(alpha)148            dot.move_to(new_point)149            new_vector = get_work_vector(new_point)150            work_vector.become(new_vector)151 152        # 执行动画153        self.play(154            UpdateFromAlphaFunc(dot, update_dot_and_vector),155            run_time=8,156            rate_func=linear157        )158        self.wait(1)159 160        # 相机旋转161        self.begin_ambient_camera_rotation(rate=0.2)162        self.wait(4)163        self.stop_ambient_camera_rotation()164        self.wait(2)165 166def main():167    import os168    os.system("manim -pqh circulation.py Circulation")169 170if __name__ == "__main__":171    main()