manimの備忘録シェルピンスキーのギャスケット

from manimlib.imports import *
import numpy as np

class Sierpinski(MovingCameraScene):

def construct(self):
    def b_afin(Cx,Cy):
        b_afin = np.array([
            [1,0,-Cx],
            [0,1,-Cy],
            [0,0,1],
        ]) 
        return b_afin

    def a_afin(Cx,Cy):
        a_afin = np.array([
            [1,0,Cx],
            [0,1,Cy],
            [0,0,1]
        ])
        return a_afin
    
    def rotate_matrix(rad):
            r_matrix = np.array([
                [np.cos(rad),-1*np.sin(rad),0],
                [np.sin(rad),np.cos(rad),0],
                [0,0,1],
            ]) 
            return r_matrix

    def create_tri(a,b,c):
        
        length = b[0]-a[0]
        c = [0,0,0]
        c[0] = a[0] + length / 2 
        c[1] = a[1] + np.sqrt(3)*length / 2 
        c = np.array([c[0],c[1],1])
        n1 = (a + c)/2
        n2 = (b + a)/2
        n3 = (c + b )/2

        line1 = Line(n1,n2,stroke_width =1).set_color(BLUE_A)
        line2 = Line(n2,n3,stroke_width =1).set_color(BLUE_A)
        line3 = Line(n3,n1,stroke_width =1).set_color(BLUE_A)
        
        length = np.linalg.norm(n2-a)
        length2 = np.linalg.norm(b-n2)
        length3 = np.linalg.norm(n3-n1)
        
        dots = [a,n2,n1,n2,b,n3,n1,n3,c]

        if length < 0.125/2:
            return
        else:
            lines = VGroup(line1,line2,line3)
            self.add(lines)
            self.wait(0.1)
            
            create_tri(a,n2,n1)
            create_tri(n2,b,n3)
            create_tri(n1,n3,c)
            return dots 


    a = np.array([-3,-2,1])
    Ax = a[0]
    Ay = a[1]
    b = [0,0,1]
    b[0] = a[0] + 6
    b[1] = a[1]
    b[2] = 1
    b = np.array([b[0],b[1],b[2]])
    c = a_afin(Ax,Ay)@(rotate_matrix(np.pi/3)@(b_afin(Ax,Ay)@b))
    tri = Polygon(a,b,c,stroke_width =1)
    self.play(ShowCreation(tri))
    create_tri(a,b,c)
    self.wait(1)