python - 如何使用 manim 创建正确的饼图

Question

无论如何，我正在尝试(这实际上是我的第一个 manim 程序)。

from manim import *
import copy
import numpy as np
import random

color_palette = [BLUE, GREEN, YELLOW, GREY_BROWN]

class TestPie(Scene):
    def construct(self):
        n_elements = 3
        radius = 1
        weights = np.random.rand(n_elements)
        weights /= weights.sum()
        angles = weights*np.pi*2
        angles_offset = [0]+np.cumsum(weights*np.pi*2)[:-1].tolist()
        arcs = [Arc(angles_offset[i], angles[i]) for i in range(n_elements)]
        arcs2 = copy.deepcopy(arcs)
        triangles = [Polygon(*[
            # first element
            (radius*np.cos(angles_offset[i]), radius*np.sin(angles_offset[i]),0),
            (0, 0, 0), # second element
            # third element
            (radius*np.cos(angles_offset[(i+1)%n_elements]),
             radius*np.sin(angles_offset[(i+1)%n_elements]), 0)], stroke_width=0)
                    for i in range(n_elements)]
        lines = [Line((0,0,0),
                      (radius*np.cos(angles_offset[i]), radius*np.sin(angles_offset[i]), 0))
                 for i in range(n_elements)]
        for i in range(n_elements):
            arcs2[i].set_fill(color_palette[i%len(color_palette)], opacity=0.5)
            triangles[i].set_fill(color_palette[i%len(color_palette)], opacity=0.5)

        self.play(
            *map(lambda obj: ShowCreation(obj, run_time=1), arcs),
            *map(lambda obj: ShowCreation(obj, run_time=1), lines),
        )
        self.play(
            *map(lambda i: Transform(arcs[i], arcs2[i], runtime=1), range(n_elements)),
            *map(lambda obj: FadeIn(obj, run_time=1), triangles),

        )

        self.wait()
        weights = np.random.rand(n_elements)
        weights /= weights.sum()
        angles = weights*np.pi*2
        angles_offset = [0]+np.cumsum(weights*np.pi*2)[:-1].tolist()
        arcs2 = [Arc(angles_offset[i], angles[i]) for i in range(n_elements)]
        lines2 = [Line((0,0,0),
                       (radius*np.cos(angles_offset[i]), radius*np.sin(angles_offset[i]), 0))
                  for i in range(n_elements)]
        triangles2 = [Polygon(*[
            # first element
            (radius*np.cos(angles_offset[i]), radius*np.sin(angles_offset[i]),0),
            (0, 0, 0), # second element
            # third element
            (radius*np.cos(angles_offset[(i+1)%n_elements]),
             radius*np.sin(angles_offset[(i+1)%n_elements]), 0)], stroke_width=0)
                    for i in range(n_elements)]

        for i in range(n_elements):
            arcs2[i].set_fill(color_palette[i%len(color_palette)], opacity=0.5)
            triangles2[i].set_fill(color_palette[i%len(color_palette)], opacity=0.5)

        self.play(
            *map(lambda i: Transform(lines[i], lines2[i],
                                     runtime=1), range(n_elements)),
            *map(lambda i: Transform(arcs[i], arcs2[i],
                                     runtime=1), range(n_elements)),
            *map(lambda i: Transform(triangles[i], triangles2[i],
                                     runtime=1), range(n_elements)),
        )
        self.wait(2)
        

输出:

因此，我当前的程序有两个问题。我会很感激一点帮助。
1. 由于我使用的是三角形和圆弧，因此您可以在下图中看到一个难看的间隙。

2. 我正在使用 Arc 进行丑陋的转换, Triange和 Line类，转换应该遵循圆周，现在不是这种情况。您可以在下图中欣赏更多中间丑陋步骤之一。 (如你所见，它不再是圆形的了)

Answer 1

对于第一个问题，避免通过精确排列单独的形状来创建形状。事实上，完全避免完全排列单独的形状:图形渲染引擎通常 have trouble rendering such situations .不是从圆形线段和三角形中创建一个圆形扇区，而是创建一个单一的形状来表示将作为单个单元绘制的整个扇区。在这种情况下，请使用 Sector类来表示扇区而不是单独的 Arc和 Polygon .
对于第二个问题，问题是默认 manim逐点计算中间形状。插值行为由形状的 interpolate 控制方法。通过对形状进行子类化，您可以覆盖 interpolate方法，而是根据定义形状的更自然的高级参数计算中间形状:在这种情况下，是中心、角度和半径。
这两个修复都包含在下面的示例中。

from manim import *
import numpy as np

class MySector(Sector):
    """ Circular sector shape with a custom interpolation method. """

    def interpolate(self, mobject1, mobject2, alpha, path_func=straight_path):
        if not (isinstance(mobject1, MySector) and isinstance(mobject2, MySector)):
            return super().interpolate(mobject1, mobject2, alpha, path_func=path_func)

        for attr in (
            'start_angle', 'angle',
            'inner_radius', 'outer_radius',
        ):
            v1 = getattr(mobject1, attr)
            v2 = getattr(mobject2, attr)
            setattr(self, attr, path_func(v1, v2, alpha))

        self.arc_center = path_func(
            mobject1.get_arc_center(),
            mobject2.get_arc_center(),
            alpha
        )
        self.interpolate_color(mobject1, mobject2, alpha)
        self.clear_points()
        self.generate_points()
        return self


color_palette = [BLUE, GREEN, YELLOW, GREY_BROWN]

class TestPie(Scene):
    def construct(self):
        weights = np.array([2.0, 3.0, 4.0])
        weights /= weights.sum()

        angles = weights * TAU
        angles_offset = np.cumsum((0, *angles[:-1]))

        sectors1 = [
            MySector(start_angle=ao, angle=a,
                stroke_width=DEFAULT_STROKE_WIDTH,
                fill_opacity=0)
            for ao, a in zip(angles_offset, angles)
        ]

        sectors2 = [
            MySector(start_angle=ao, angle=a,
                stroke_width=DEFAULT_STROKE_WIDTH,
                fill_color=color_palette[i % len(color_palette)], fill_opacity=0.5)
            for i, (ao, a) in enumerate(zip(angles_offset, angles))
        ]

        self.play(
            *(ShowCreation(a1, run_time=1) for a1 in sectors1)
        )

        self.play(
            *(Transform(a1, a2, runtime=1) for (a1, a2) in zip(sectors1, sectors2))
        )

        self.wait()

        weights = np.array([4.0, 3.0, 2.0])
        weights /= weights.sum()

        angles = weights * TAU
        angles_offset = np.cumsum((0, *angles[:-1]))

        sectors2 = [
            MySector(start_angle=ao, angle=a,
                stroke_width=DEFAULT_STROKE_WIDTH,
                fill_color=color_palette[i % len(color_palette)], fill_opacity=0.5)
            for i, (ao, a) in enumerate(zip(angles_offset, angles))
        ]

        self.play(
            *(Transform(a1, a2, runtime=1) for (a1, a2) in zip(sectors1, sectors2))
        )
        self.wait(2)

这是由此产生的动画:

以上不保留构成饼图扇区的线条的初始绘制动画。您可以覆盖 pointwise_become_partial恢复它的方法，或者您可以简单地恢复 Line原始代码中的形状。