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可视化库之三 3brown1blue 秘密利器 manim

可视化库之三 3brown1blue 秘密利器 manim

作者: Python_Camp | 来源:发表于2022-03-23 12:36 被阅读0次

这个图库包含了一系列的最佳实践代码片段,以及相应的视频/图片输出,说明了整个库的不同功能。这些都是在MIT许可下的,所以可以随意复制和粘贴到你的项目中。请享受这个Manim的味道!

提示

在我们的文档中,这个画廊并不是唯一可以看到明确的代码和视频例子的地方:在我们的参考手册中还有很多--例如,参见我们关于tex_mobject, geometry, moving_camera_scene等模块的文档。

看看我们的交互式Jupyter环境,它允许在线运行这些例子,而不需要本地安装。

另外,请访问我们的推,以获得更多的演示文稿。

image.png
from manim import *

class ExampleRotation(Scene):
    def construct(self):
        self.camera.background_color = WHITE
        m1a = Square().set_color(RED).shift(LEFT)
        m1b = Circle().set_color(RED).shift(LEFT)
        m2a= Square().set_color(BLUE).shift(RIGHT)
        m2b= Circle().set_color(BLUE).shift(RIGHT)

        points = m2a.points
        points = np.roll(points, int(len(points)/4), axis=0)
        m2a.points = points

        self.play(Transform(m1a,m1b),Transform(m2a,m2b), run_time=1)
image.png
from manim import *

class PointMovingOnShapes(Scene):
    def construct(self):
        circle = Circle(radius=1, color=BLUE)
        dot = Dot()
        dot2 = dot.copy().shift(RIGHT)
        self.add(dot)

        line = Line([3, 0, 0], [5, 0, 0])
        self.add(line)

        self.play(GrowFromCenter(circle))
        self.play(Transform(dot, dot2))
        self.play(MoveAlongPath(dot, circle), run_time=2, rate_func=linear)
        self.play(Rotating(dot, about_point=[2, 0, 0]), run_time=1.5)
        self.wait()
image.png
from manim import *

class MovingGroupToDestination(Scene):
    def construct(self):
        group = VGroup(Dot(LEFT), Dot(ORIGIN), Dot(RIGHT, color=RED), Dot(2 * RIGHT)).scale(1.4)
        dest = Dot([4, 3, 0], color=YELLOW)
        self.add(group, dest)
        self.play(group.animate.shift(dest.get_center() - group[2].get_center()))
        self.wait(0.5)
image.png
from manim import *

class MovingFrameBox(Scene):
    def construct(self):
        text=MathTex(
            "\\frac{d}{dx}f(x)g(x)=","f(x)\\frac{d}{dx}g(x)","+",
            "g(x)\\frac{d}{dx}f(x)"
        )
        self.play(Write(text))
        framebox1 = SurroundingRectangle(text[1], buff = .1)
        framebox2 = SurroundingRectangle(text[3], buff = .1)
        self.play(
            Create(framebox1),
        )
        self.wait()
        self.play(
            ReplacementTransform(framebox1,framebox2),
        )
        self.wait()
image.png
from manim import *

class SinAndCosFunctionPlot(Scene):
    def construct(self):
        axes = Axes(
            x_range=[-10, 10.3, 1],
            y_range=[-1.5, 1.5, 1],
            x_length=10,
            axis_config={"color": GREEN},
            x_axis_config={
                "numbers_to_include": np.arange(-10, 10.01, 2),
                "numbers_with_elongated_ticks": np.arange(-10, 10.01, 2),
            },
            tips=False,
        )
        axes_labels = axes.get_axis_labels()
        sin_graph = axes.plot(lambda x: np.sin(x), color=BLUE)
        cos_graph = axes.plot(lambda x: np.cos(x), color=RED)

        sin_label = axes.get_graph_label(
            sin_graph, "\\sin(x)", x_val=-10, direction=UP / 2
        )
        cos_label = axes.get_graph_label(cos_graph, label="\\cos(x)")

        vert_line = axes.get_vertical_line(
            axes.i2gp(TAU, cos_graph), color=YELLOW, line_func=Line
        )
        line_label = axes.get_graph_label(
            cos_graph, "x=2\pi", x_val=TAU, direction=UR, color=WHITE
        )

        plot = VGroup(axes, sin_graph, cos_graph, vert_line)
        labels = VGroup(axes_labels, sin_label, cos_label, line_label)
        self.add(plot, labels)
image.png
from manim import *

class GraphAreaPlot(Scene):
    def construct(self):
        ax = Axes(
            x_range=[0, 5],
            y_range=[0, 6],
            x_axis_config={"numbers_to_include": [2, 3]},
            tips=False,
        )

        labels = ax.get_axis_labels()

        curve_1 = ax.plot(lambda x: 4 * x - x ** 2, x_range=[0, 4], color=BLUE_C)
        curve_2 = ax.plot(
            lambda x: 0.8 * x ** 2 - 3 * x + 4,
            x_range=[0, 4],
            color=GREEN_B,
        )

        line_1 = ax.get_vertical_line(ax.input_to_graph_point(2, curve_1), color=YELLOW)
        line_2 = ax.get_vertical_line(ax.i2gp(3, curve_1), color=YELLOW)

        riemann_area = ax.get_riemann_rectangles(curve_1, x_range=[0.3, 0.6], dx=0.03, color=BLUE, fill_opacity=0.5)
        area = ax.get_area(curve_2, [2, 3], bounded_graph=curve_1, color=GREY, opacity=0.5)

        self.add(ax, labels, curve_1, curve_2, line_1, line_2, riemann_area, area)
image.png
from manim import *

class ThreeDSurfacePlot(ThreeDScene):
    def construct(self):
        resolution_fa = 42
        self.set_camera_orientation(phi=75 * DEGREES, theta=-30 * DEGREES)

        def param_gauss(u, v):
            x = u
            y = v
            sigma, mu = 0.4, [0.0, 0.0]
            d = np.linalg.norm(np.array([x - mu[0], y - mu[1]]))
            z = np.exp(-(d ** 2 / (2.0 * sigma ** 2)))
            return np.array([x, y, z])

        gauss_plane = Surface(
            param_gauss,
            resolution=(resolution_fa, resolution_fa),
            v_range=[-2, +2],
            u_range=[-2, +2]
        )

        gauss_plane.scale(2, about_point=ORIGIN)
        gauss_plane.set_style(fill_opacity=1,stroke_color=GREEN)
        gauss_plane.set_fill_by_checkerboard(ORANGE, BLUE, opacity=0.5)
        axes = ThreeDAxes()
        self.add(axes,gauss_plane)
image.png
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()
image.png
from manim import *

class SineCurveUnitCircle(Scene):
    # contributed by heejin_park, https://infograph.tistory.com/230
    def construct(self):
        self.show_axis()
        self.show_circle()
        self.move_dot_and_draw_curve()
        self.wait()

    def show_axis(self):
        x_start = np.array([-6,0,0])
        x_end = np.array([6,0,0])

        y_start = np.array([-4,-2,0])
        y_end = np.array([-4,2,0])

        x_axis = Line(x_start, x_end)
        y_axis = Line(y_start, y_end)

        self.add(x_axis, y_axis)
        self.add_x_labels()

        self.origin_point = np.array([-4,0,0])
        self.curve_start = np.array([-3,0,0])

    def add_x_labels(self):
        x_labels = [
            MathTex("\pi"), MathTex("2 \pi"),
            MathTex("3 \pi"), MathTex("4 \pi"),
        ]

        for i in range(len(x_labels)):
            x_labels[i].next_to(np.array([-1 + 2*i, 0, 0]), DOWN)
            self.add(x_labels[i])

    def show_circle(self):
        circle = Circle(radius=1)
        circle.move_to(self.origin_point)
        self.add(circle)
        self.circle = circle

    def move_dot_and_draw_curve(self):
        orbit = self.circle
        origin_point = self.origin_point

        dot = Dot(radius=0.08, color=YELLOW)
        dot.move_to(orbit.point_from_proportion(0))
        self.t_offset = 0
        rate = 0.25

        def go_around_circle(mob, dt):
            self.t_offset += (dt * rate)
            # print(self.t_offset)
            mob.move_to(orbit.point_from_proportion(self.t_offset % 1))

        def get_line_to_circle():
            return Line(origin_point, dot.get_center(), color=BLUE)

        def get_line_to_curve():
            x = self.curve_start[0] + self.t_offset * 4
            y = dot.get_center()[1]
            return Line(dot.get_center(), np.array([x,y,0]), color=YELLOW_A, stroke_width=2 )


        self.curve = VGroup()
        self.curve.add(Line(self.curve_start,self.curve_start))
        def get_curve():
            last_line = self.curve[-1]
            x = self.curve_start[0] + self.t_offset * 4
            y = dot.get_center()[1]
            new_line = Line(last_line.get_end(),np.array([x,y,0]), color=YELLOW_D)
            self.curve.add(new_line)

            return self.curve

        dot.add_updater(go_around_circle)

        origin_to_circle_line = always_redraw(get_line_to_circle)
        dot_to_curve_line = always_redraw(get_line_to_curve)
        sine_curve_line = always_redraw(get_curve)

        self.add(dot)
        self.add(orbit, origin_to_circle_line, dot_to_curve_line, sine_curve_line)
        self.wait(8.5)

        dot.remove_updater(go_around_circle)

场景
场景类是manim的连接组织。每个mobject都必须被添加到一个场景中才能被显示,或者从场景中移除才能停止显示。每个动画都必须由一个场景来播放,每个没有动画发生的时间间隔都由调用wait()来决定。你的视频的所有代码都必须包含在一个派生自Scene的类的construct()方法中。最后,如果要同时渲染多个场景,一个文件可以包含多个Scene子类。

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