90 lines
2.5 KiB
Python
90 lines
2.5 KiB
Python
from manim import *
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import math
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def norm(vec):
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return math.sqrt(sum([xi ** 2 for xi in vec]))
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def normalize(vec):
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n = norm(vec)
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return [xi / n for xi in vec]
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def plus(v1, v2):
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return [x1 + x2 for x1, x2 in zip(v1, v2)]
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def minus(v1, v2):
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return [x1 - x2 for x1, x2 in zip(v1, v2)]
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def mult(v, c):
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return [xi * c for xi in v]
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def SegmentedLine(points):
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assert(len(points) >= 2)
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ret = []
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for p1, p2 in zip( points[:-1], points[1:] ):
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vec = minus(p2, p1)
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length = norm(vec)
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normalized = normalize(vec)
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rotated = [-normalized[1], normalized[0], 0]
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ret.append(p1)
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ret.append(plus(p1, mult(normalized, length * 1/3)))
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ret.append(plus(p1, plus(mult(normalized, length/2), mult(rotated, math.sqrt(3) * length / 6))))
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ret.append(plus(p1, mult(normalized, length * 2/3)))
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ret.append(points[-1])
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return ret
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class snowflake(Scene):
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def construct(self):
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points = [[-7, -1, 0],
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[ 7, -1, 0]]
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segment = VMobject(stroke_width=1)
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segment.set_points_as_corners(points)
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self.add(*[Dot(p) for p in points])
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self.play(Create(segment))
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self.wait(1)
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vg = VGroup()
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self.add(vg)
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for i in range(4):
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points = SegmentedLine(points)
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new_vg = VGroup(*[Dot(p, radius=0.1/(i+1)) for p in points])
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self.play(Create(new_vg))
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self.play(segment.animate.set_points_as_corners(points))
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self.wait(1)
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vg.add(*[e for e in new_vg])
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self.remove(new_vg)
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self.play(Uncreate(vg))
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segment2 = segment.copy()
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segment3 = segment.copy()
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segs = VGroup(segment, segment2, segment3)
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mid = -(math.sqrt(14**2 - 7**2))/ 2 + 1
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self.play(Rotate(segment2, 2 * PI / 3, axis=[0,0,1], about_point=[0, mid, 0]),
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Rotate(segment3, -2 * PI / 3, axis=[0,0,1], about_point=[0, mid, 0]))
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self.play(segs.animate.scale(0.5).center())
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lines = [
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Line(segment.get_all_points()[0], segment.get_all_points()[-1], color=RED),
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Line(segment2.get_all_points()[0], segment2.get_all_points()[-1], color=RED),
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Line(segment3.get_all_points()[0], segment3.get_all_points()[-1], color=RED)
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]
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self.play(Create(VGroup(*lines)))
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self.play(*[FadeOut(mob) for mob in self.mobjects])
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if __name__ == "__main__":
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sc = snowflake()
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sc.render(True)
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