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7b841c27cc* Optimized manim.utils.partial_bezier_points() * Added split_bezier, subdivide_bezier and bezier_remap, and tests * Use bezier_remap() in VMobject and OpenGLVMobject() * Note that partial_bezier_points is similar to calling split_bezier twice
215 lines
5 KiB
Python
215 lines
5 KiB
Python
import numpy as np
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# Defined because pre-commit is inserting an unacceptable line-break
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# between the "1" (or "2") and the "/ 3"
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one_third = 1 / 3
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two_thirds = 2 / 3
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# Expected values for matrices in split_bezier
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SPLIT_MATRICES = {
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# For 0-degree Béziers
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0: {
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0: np.array([[1], [1]]),
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one_third: np.array([[1], [1]]),
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two_thirds: np.array([[1], [1]]),
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1: np.array([[1], [1]]),
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},
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# For linear Béziers
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1: {
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0: np.array(
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[
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[1, 0],
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[1, 0],
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[1, 0],
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[0, 1],
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]
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),
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one_third: np.array(
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[
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[3, 0],
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[2, 1],
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[2, 1],
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[0, 3],
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]
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)
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/ 3,
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two_thirds: np.array(
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[
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[3, 0],
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[1, 2],
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[1, 2],
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[0, 3],
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]
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)
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/ 3,
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1: np.array(
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[
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[1, 0],
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[0, 1],
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[0, 1],
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[0, 1],
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]
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),
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},
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# For quadratic Béziers
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2: {
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0: np.array(
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[
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[1, 0, 0],
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[1, 0, 0],
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[1, 0, 0],
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[1, 0, 0],
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[0, 1, 0],
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[0, 0, 1],
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]
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),
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one_third: np.array(
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[
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[9, 0, 0],
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[6, 3, 0],
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[4, 4, 1],
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[4, 4, 1],
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[0, 6, 3],
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[0, 0, 9],
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]
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)
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/ 9,
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two_thirds: np.array(
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[
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[9, 0, 0],
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[3, 6, 0],
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[1, 4, 4],
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[1, 4, 4],
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[0, 3, 6],
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[0, 0, 9],
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]
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)
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/ 9,
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1: np.array(
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[
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[1, 0, 0],
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[0, 1, 0],
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[0, 0, 1],
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[0, 0, 1],
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[0, 0, 1],
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[0, 0, 1],
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]
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),
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},
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# For cubic Béziers
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3: {
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0: np.array(
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[
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[1, 0, 0, 0],
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[1, 0, 0, 0],
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[1, 0, 0, 0],
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[1, 0, 0, 0],
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[1, 0, 0, 0],
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[0, 1, 0, 0],
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[0, 0, 1, 0],
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[0, 0, 0, 1],
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]
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),
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one_third: np.array(
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[
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[27, 0, 0, 0],
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[18, 9, 0, 0],
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[12, 12, 3, 0],
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[8, 12, 6, 1],
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[8, 12, 6, 1],
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[0, 12, 12, 3],
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[0, 0, 18, 9],
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[0, 0, 0, 27],
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]
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)
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/ 27,
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two_thirds: np.array(
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[
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[27, 0, 0, 0],
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[9, 18, 0, 0],
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[3, 12, 12, 0],
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[1, 6, 12, 8],
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[1, 6, 12, 8],
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[0, 3, 12, 12],
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[0, 0, 9, 18],
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[0, 0, 0, 27],
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]
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)
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/ 27,
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1: np.array(
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[
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[1, 0, 0, 0],
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[0, 1, 0, 0],
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[0, 0, 1, 0],
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[0, 0, 0, 1],
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[0, 0, 0, 1],
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[0, 0, 0, 1],
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[0, 0, 0, 1],
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[0, 0, 0, 1],
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]
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),
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},
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# Test case with a quartic Bézier
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# to check if the fallback algorithms work
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4: {
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0: np.array(
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[
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[1, 0, 0, 0, 0],
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[1, 0, 0, 0, 0],
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[1, 0, 0, 0, 0],
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[1, 0, 0, 0, 0],
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[1, 0, 0, 0, 0],
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[1, 0, 0, 0, 0],
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[0, 1, 0, 0, 0],
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[0, 0, 1, 0, 0],
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[0, 0, 0, 1, 0],
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[0, 0, 0, 0, 1],
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]
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),
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one_third: np.array(
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[
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[81, 0, 0, 0, 0],
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[54, 27, 0, 0, 0],
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[36, 36, 9, 0, 0],
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[24, 36, 18, 3, 0],
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[16, 32, 24, 8, 1],
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[16, 32, 24, 8, 1],
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[0, 24, 36, 18, 3],
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[0, 0, 36, 36, 9],
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[0, 0, 0, 54, 27],
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[0, 0, 0, 0, 81],
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]
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)
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/ 81,
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two_thirds: np.array(
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[
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[81, 0, 0, 0, 0],
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[27, 54, 0, 0, 0],
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[9, 36, 36, 0, 0],
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[3, 18, 36, 24, 0],
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[1, 8, 24, 32, 16],
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[1, 8, 24, 32, 16],
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[0, 3, 18, 36, 24],
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[0, 0, 9, 36, 36],
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[0, 0, 0, 27, 54],
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[0, 0, 0, 0, 81],
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]
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)
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/ 81,
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1: np.array(
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[
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[1, 0, 0, 0, 0],
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[0, 1, 0, 0, 0],
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[0, 0, 1, 0, 0],
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[0, 0, 0, 1, 0],
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[0, 0, 0, 0, 1],
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[0, 0, 0, 0, 1],
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[0, 0, 0, 0, 1],
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[0, 0, 0, 0, 1],
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[0, 0, 0, 0, 1],
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[0, 0, 0, 0, 1],
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]
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),
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},
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}
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