概要

manimの作法、調べてみた。
ComplexPlane使ってみた。

サンプルコード

from manimlib.imports import *

class test(Scene):
    CONFIG = {
        "plane_config": {
            "x_radius": 9,
            "y_radius": 9,
            "stroke_width": 3,
        },
        "background_plane_config": {
            "color": LIGHT_GREY,
            "secondary_color": DARK_GREY,
            "stroke_width": 0.5,
            "stroke_opacity": 0.5,
            "secondary_line_ratio": 0,
        }
    }
    def construct(self):
        self.add_planes()
        z_tuples = [(complex(2, 1), "2 + i", UP), (complex(5, 2), "5 + 2i", LEFT), (complex(-np.sqrt(2) / 2, np.sqrt(2) / 2), "-\\frac{\\sqrt{2}}{2} + \\frac{\\sqrt{2}}{2} i", LEFT, ), (complex(-4, 1.5), "-4 + 1.5i", RIGHT), (complex(3, 0), "3 + 0i", UP), (complex(4, -3), "4 + -3i", UP), ]
        for z, z_tex, label_vect in z_tuples:
            self.show_multiplication(z, z_tex, label_vect)
    def add_planes(self, include_title = True):
        plane = ComplexPlane(**self.plane_config)
        self.plane = plane
        background_plane = ComplexPlane(**self.background_plane_config)
        background_plane.add_coordinates()
        self.background_plane = background_plane
        self.add(background_plane)
        self.add(plane)
        if include_title:
            title = TextMobject("Complex plane")
            title.scale(1.5)
            title.to_corner(UL, buff = MED_LARGE_BUFF)
            title.shift(SMALL_BUFF * UR)
            self.title = title
            self.add_foreground_mobjects(title)
    def show_multiplication(self, z, z_tex, label_vect):
        z_color = WHITE
        plane = self.plane
        new_plane = plane.deepcopy()
        real_tex, imag_tex = z_tex.split("+")
        label = TexMobject("\\text{Multiply by}\\\\", real_tex, "+", imag_tex, alignment = "", )
        label[1].set_color(GREEN)
        label[3].set_color(RED)
        label.scale(1.2)
        h_line = Line(plane.number_to_point(0), plane.number_to_point(z.real), color = GREEN, stroke_width = 5, )
        v_line = Line(plane.number_to_point(z.real), plane.number_to_point(z), color = RED, stroke_width = 5, )
        lines = VGroup(h_line, v_line)
        z_point = plane.number_to_point(z)
        z_dot = Dot(z_point)
        z_dot.set_color(z_color)
        label[1:].next_to(z_dot, label_vect)
        label[0].next_to(label[1:], UP)
        for mob in label:
            label.add_to_back(BackgroundRectangle(mob))
        one_dot = Dot(plane.number_to_point(1))
        one_dot.set_color(YELLOW)
        for dot in z_dot, one_dot:
            dot.save_state()
            dot.scale(5)
            dot.set_fill(opacity = 0)
            dot.set_stroke(width = 1, opacity = 0.5)
        to_fade_out = VGroup(plane, label, lines, z_dot, one_dot)
        self.play(ShowCreation(lines), FadeInFromDown(label), Restore(z_dot), )
        self.play(Restore(one_dot))
        angle = np.log(z).imag
        self.play(one_dot.move_to, z_dot, plane.apply_complex_function, lambda w: z * w, path_arc = angle, run_time = 3)
        self.wait()
        self.play(FadeOut(to_fade_out), FadeIn(new_plane), )
        self.plane = new_plane

生成した動画

以上。