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uwezi/20240524_glyphmap.py

Created May 24, 2024 11:27
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[transform glyph map] Helper made by dudewaldo4 to animate LaTeX. #manim #latex #tex #mathtext #transform
Raw
20240524_glyphmap.py
from manim import *
# by dudewaldo4
# https://discord.com/channels/581738731934056449/976376734935048223/1161709114154569819
# https://www.youtube.com/watch?v=Bg999qefIic
#
def ir(a,b): # inclusive range, useful for TransformByGlyphMap
return list(range(a,b+1))
class TransformByGlyphMap(AnimationGroup):
def __init__(self, mobA, mobB, *glyph_map, replace=True, from_copy=False, show_indices=False, **kwargs):
# replace=False does not work properly
if from_copy:
self.mobA = mobA.copy()
self.replace = True
else:
self.mobA = mobA
self.replace = replace
self.mobB = mobB
self.glyph_map = glyph_map
self.show_indices = show_indices
animations = []
mentioned_from_indices = []
mentioned_to_indices = []
for from_indices, to_indices in self.glyph_map:
print(from_indices, to_indices)
if len(from_indices) == 0 and len(to_indices) == 0:
self.show_indices = True
continue
elif len(to_indices) == 0:
animations.append(FadeOut(
VGroup(*[self.mobA[0][i] for i in from_indices]),
shift = self.mobB.get_center()-self.mobA.get_center()
))
elif len(from_indices) == 0:
animations.append(FadeIn(
VGroup(*[self.mobB[0][j] for j in to_indices]),
shift = self.mobB.get_center() - self.mobA.get_center()
))
else:
animations.append(Transform(
VGroup(*[self.mobA[0][i].copy() if i in mentioned_from_indices else self.mobA[0][i] for i in from_indices]),
VGroup(*[self.mobB[0][j] for j in to_indices]),
replace_mobject_with_target_in_scene=self.replace
))
mentioned_from_indices.extend(from_indices)
mentioned_to_indices.extend(to_indices)
print(mentioned_from_indices, mentioned_to_indices)
remaining_from_indices = list(set(range(len(self.mobA[0]))) - set(mentioned_from_indices))
remaining_from_indices.sort()
remaining_to_indices = list(set(range(len(self.mobB[0]))) - set(mentioned_to_indices))
remaining_to_indices.sort()
print(remaining_from_indices, remaining_to_indices)
if len(remaining_from_indices) == len(remaining_to_indices) and not self.show_indices:
for from_index, to_index in zip(remaining_from_indices, remaining_to_indices):
animations.append(Transform(
self.mobA[0][from_index],
self.mobB[0][to_index],
replace_mobject_with_target_in_scene=self.replace
))
super().__init__(*animations, **kwargs)
else:
print(f"From indices: {len(remaining_from_indices)} To indices: {len(remaining_to_indices)}")
print("Showing indices...")
super().__init__(
Create(index_labels(self.mobA[0], color=PINK)),
FadeIn(self.mobB.next_to(self.mobA, DOWN), shift=DOWN),
Create(index_labels(self.mobB[0], color=PINK)),
Wait(5),
lag_ratio=0.5
)
class CisCube(Scene):
def construct(self):
expA = MathTex("\\left( \\cos(x) + i\\sin(x) \\right)^3")
expB = MathTex("\\cos(3x) + i\\sin(3x)")
self.add(expA)
self.play(TransformByGlyphMap(expA,expB,
([16], [4]),
([16], [13]),
([0,15], [])
))
class MultiplyingBinomials(Scene):
def construct(self):
expA = MathTex("(x+3)(x+4)")
expB = MathTex("x(x+4) + 3(x+4)")
expC = MathTex("x^2 + 4x + 3x + 12")
expD = MathTex("x^2 + 7x + 12")
VGroup(expA, expB, expC, expD).arrange(DOWN)
self.add(expA)
self.play(
TransformByGlyphMap(expA, expB,
([0,4],[]),
([1],[0]),
([2], [6]),
([3], [7]),
([5,6,7,8,9], [1,2,3,4,5]),
([5,6,7,8,9], [8,9,10,11,12]),
from_copy=True
)
)
self.wait()
self.play(
TransformByGlyphMap(expB, expC,
([1,5,8,12], []),
([0,2], [0,1]),
([0,4], [3,4]),
([7,9], [6,7]),
([7,11], [9,10]),
from_copy=True
)
)
self.wait()
self.play(
TransformByGlyphMap(expC, expD,
([3,4,5,6,7], [3,4]),
from_copy=True
)
)
class QuadraticFormula(Scene):
def construct(self):
exps = [
MathTex("ax^2 + bx + c = 0"),
MathTex("ax^2 + bx = -c"),
MathTex("x^2 + {b \\over a}x = - {c \\over a}"),
MathTex("x^2 + {b \\over a}x + \\left({b \\over 2a}\\right)^2 = - {c \\over a} + \\left({b \\over 2a}\\right)^2"),
MathTex("x^2 + {b \\over a}x + \\left({b \\over 2a}\\right)^2 = \\left({b \\over 2a}\\right)^2 - {c \\over a}"),
MathTex("x^2 + {b \\over a}x + \\left({b \\over 2a}\\right)^2 = {b^2 \\over 4a^2} - {c \\over a}"),
MathTex("x^2 + {b \\over a}x + \\left({b \\over 2a}\\right)^2 = {b^2 \\over 4a^2} - {4ac \\over 4a^2}"),
MathTex("x^2 + {b \\over a}x + \\left({b \\over 2a}\\right)^2 = {b^2 - 4ac \\over 4a^2}"),
MathTex("\\left( x + {b \\over 2a} \\right)^2 = {b^2 - 4ac \\over 4a^2}"),
MathTex("x + {b \\over 2a} = \\pm \\sqrt{ {b^2 - 4ac \\over 4a^2} }"),
MathTex("x + {b \\over 2a} = \\pm { \\sqrt{ b^2 - 4ac } \\over \\sqrt{ 4a^2 } }"),
MathTex("x + {b \\over 2a} = \\pm { \\sqrt{ b^2 - 4ac } \\over 2a } }"),
MathTex("x = - {b \\over 2a} \\pm { \\sqrt{ b^2 - 4ac } \\over 2a } }"),
MathTex("x = { - b \\pm \\sqrt{ b^2 - 4ac } \\over 2a }"),
]
for exp in exps:
exp.scale(1.5)
self.play(Write(exps[0]))
self.wait()
self.play(TransformByGlyphMap(exps[0], exps[1], # subtract c
([6,7], [7,8]),
([8], [6]),
([9], [])
))
self.wait()
self.play(TransformByGlyphMap(exps[1], exps[2], # divide by a
([0], [5,11]),
([], [4,10]),
))
self.wait()
self.play(TransformByGlyphMap(exps[2], exps[3], # complete the square
([], [*ir(7,14)]),
([], [*ir(20,27)]),
))
self.wait()
self.play(TransformByGlyphMap(exps[3], exps[4], # rhs reorder
([*ir(21,27)], [*ir(16,22)]),
([*ir(16,19)], [*ir(23,26)]),
([20], [])
))
self.wait()
self.play(TransformByGlyphMap(exps[4], exps[5], # rhs distribute square
([22], [17]),
([22], [21]),
([22,19], [19]),
([16,21], [])
))
self.wait()
self.play(TransformByGlyphMap(exps[5], exps[6], # rhs common denominator
([], [23,24,27,29]),
))
self.wait()
self.play(TransformByGlyphMap(exps[6], exps[7], # rhs combine fractions
([23,24,25], [19,20,21]),
([22], [18]),
([18], [22]),
([26], [22]),
([19,20,21], [23,24,25]),
([27,28,29], [23,24,25])
))
self.wait()
self.play(TransformByGlyphMap(exps[7], exps[8], # lhs rewrite
([0,6], [1]),
([2,7], [2]),
([3,4,5], [3,4,6]),
([9,10,11,12], [3,4,5,6]),
([1,14], [8]),
([8], [0]),
([13], [7]),
))
self.wait()
self.play(TransformByGlyphMap(exps[8], exps[9], # square root
([8], [7,8,9]),
([0,7], []),
))
self.wait()
self.play(TransformByGlyphMap(exps[9], exps[10], # rhs distribute square root
([8], [8,17]),
([9], [9,18]),
))
self.wait()
self.play(TransformByGlyphMap(exps[10], exps[11], # rhs simplify denominator
([17,18], []),
([19], [17]),
([20,21], [18])
))
self.wait()
self.play(TransformByGlyphMap(exps[11], exps[12], # final subtract
([*ir(1,5)], [*ir(2,6)]),
))
self.wait()
self.play(TransformByGlyphMap(exps[12], exps[13], # combine fractions
([4], [13]),
([16], [13]),
([5,6], [14,15]),
([17,18], [14,15])
))
self.wait()
self.play(Circumscribe(exps[-1]))
class SumChange(Scene):
def construct(self):
tex1 = MathTex("\\sum_{k=1}^{9}")
tex2 = MathTex("\\sum_{k=1}^{10}")
self.play(Write(tex1, run_time=0.75))
self.play(TransformByGlyphMap(tex1,tex2,
([0], [0,1]),
#show_indices=False
))
self.wait()
class TransformExample(Scene):
def construct(self):
table_title = Tex(
"ALL POSSIBLE INITIAL POSITIONS", font_size=30, fill_color=LIGHT_BROWN
)
table_title2 = Tex(
"ALL POSSIBLE POSITIONS", font_size=30, fill_color=LIGHT_BROWN
)
self.play(FadeIn(table_title, shift=DOWN))
self.wait(3)
self.play(
TransformByGlyphMap(table_title, table_title2,
([11,12,13,14,15,16,17],[]),
)
)
self.wait()
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