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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
167 lines
3.8 KiB
Python
167 lines
3.8 KiB
Python
import numpy as np
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# Expected values for matrices in subdivide_bezier and others
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# Note that in bezier.py this is a list of dicts,
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# not a dict of dicts!
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SUBDIVISION_MATRICES = {
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# For 0-degree Béziers
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0: {
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2: np.array([[1], [1]]),
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3: np.array([[1], [1], [1]]),
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4: np.array([[1], [1], [1], [1]]),
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},
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# For linear Béziers
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1: {
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2: np.array(
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[
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[2, 0],
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[1, 1],
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[1, 1],
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[0, 2],
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]
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)
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/ 2,
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3: 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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[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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4: np.array(
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[
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[4, 0],
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[3, 1],
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[3, 1],
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[2, 2],
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[2, 2],
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[1, 3],
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[1, 3],
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[0, 4],
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]
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)
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/ 4,
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},
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# For quadratic Béziers
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2: {
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2: np.array(
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[
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[4, 0, 0],
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[2, 2, 0],
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[1, 2, 1],
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[1, 2, 1],
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[0, 2, 2],
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[0, 0, 4],
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]
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)
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/ 4,
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3: 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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[2, 5, 2],
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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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4: np.array(
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[
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[16, 0, 0],
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[12, 4, 0],
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[9, 6, 1],
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[9, 6, 1],
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[6, 8, 2],
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[4, 8, 4],
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[4, 8, 4],
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[2, 8, 6],
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[1, 6, 9],
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[1, 6, 9],
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[0, 4, 12],
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[0, 0, 16],
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]
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)
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/ 16,
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},
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# For cubic Béziers
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3: {
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2: np.array(
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[
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[8, 0, 0, 0],
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[4, 4, 0, 0],
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[2, 4, 2, 0],
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[1, 3, 3, 1],
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[1, 3, 3, 1],
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[0, 2, 4, 2],
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[0, 0, 4, 4],
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[0, 0, 0, 8],
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]
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)
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/ 8,
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3: 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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[4, 12, 9, 2],
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[2, 9, 12, 4],
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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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4: np.array(
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[
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[64, 0, 0, 0],
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[48, 16, 0, 0],
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[36, 24, 4, 0],
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[27, 27, 9, 1],
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[27, 27, 9, 1],
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[18, 30, 14, 2],
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[12, 28, 20, 4],
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[8, 24, 24, 8],
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[8, 24, 24, 8],
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[4, 20, 28, 12],
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[2, 14, 30, 18],
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[1, 9, 27, 27],
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[1, 9, 27, 27],
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[0, 4, 24, 36],
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[0, 0, 16, 48],
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[0, 0, 0, 64],
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]
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)
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/ 64,
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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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2: np.array(
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[
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[16, 0, 0, 0, 0],
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[8, 8, 0, 0, 0],
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[4, 8, 4, 0, 0],
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[2, 6, 6, 2, 0],
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[1, 4, 6, 4, 1],
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[1, 4, 6, 4, 1],
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[0, 2, 6, 6, 2],
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[0, 0, 4, 8, 4],
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[0, 0, 0, 8, 8],
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[0, 0, 0, 0, 16],
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]
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)
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/ 16,
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},
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}
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