mirror of
https://github.com/3b1b/manim.git
synced 2025-09-01 00:48:45 +00:00
Tweaks to Cramer's rule animations for video publication
This commit is contained in:
Grant Sanderson
parent
dc18845a44
commit
7d9336f9ff
1 changed files with 136 additions and 17 deletions
|
|
@ -7,6 +7,9 @@ OUTPUT_COLOR = YELLOW
|
|||
INPUT_COLOR = MAROON_B
|
||||
|
||||
|
||||
OUTPUT_DIRECTORY = "eola2/cramer"
|
||||
|
||||
|
||||
def get_cramer_matrix(matrix, output_vect, index=0):
|
||||
"""
|
||||
The inputs matrix and output_vect should be Matrix mobjects
|
||||
|
|
@ -71,6 +74,43 @@ class LinearSystem(VGroup):
|
|||
# Scenes
|
||||
|
||||
|
||||
class AltOpeningQuote(OpeningQuote):
|
||||
def construct(self):
|
||||
kw = {
|
||||
"tex_to_color_map": {
|
||||
"Jerry": YELLOW,
|
||||
"Kramer": BLUE,
|
||||
},
|
||||
"arg_separator": "",
|
||||
"alignment": "",
|
||||
}
|
||||
parts = VGroup(
|
||||
TextMobject("Jerry: Ah, you're crazy!", **kw),
|
||||
TextMobject(
|
||||
"Kramer:",
|
||||
"{} Am I? Or am I so sane that\\\\",
|
||||
"you just blew your mind?",
|
||||
**kw
|
||||
),
|
||||
TextMobject("Jerry: It's impossible!", **kw),
|
||||
TextMobject(
|
||||
"Kramer:", "{} Is it?! Or is it so possible\\\\",
|
||||
"your head is spinning like a top?",
|
||||
**kw
|
||||
)
|
||||
)
|
||||
for part in parts[1::2]:
|
||||
part[-1].align_to(part[-2], LEFT)
|
||||
|
||||
parts.arrange(DOWN, buff=MED_LARGE_BUFF, aligned_edge=LEFT)
|
||||
|
||||
self.add(parts[0])
|
||||
self.play(FadeIn(parts[1], lag_ratio=0.1, run_time=2))
|
||||
self.play(FadeIn(parts[2], lag_ratio=0))
|
||||
self.play(FadeIn(parts[3], lag_ratio=0.1, run_time=2))
|
||||
self.wait()
|
||||
|
||||
|
||||
class CramerOpeningQuote(OpeningQuote):
|
||||
CONFIG = {
|
||||
"quote": ["Computers are useless. They \\\\ can only give you answers."],
|
||||
|
|
@ -90,15 +130,16 @@ class LeaveItToComputers(TeacherStudentsScene):
|
|||
system.target.scale(0.5)
|
||||
system.target.to_corner(UL)
|
||||
|
||||
colors = [X_COLOR, Y_COLOR, Z_COLOR]
|
||||
cramer_groups = VGroup()
|
||||
for i in range(3):
|
||||
numer_matrix = get_cramer_matrix(
|
||||
system.matrix_mobject, system.output_vect_mob,
|
||||
index=i
|
||||
)
|
||||
VGroup(*numer_matrix.mob_matrix[:, i]).set_color(colors[i])
|
||||
VGroup(*numer_matrix.mob_matrix[:, i]).set_stroke(colors[i], 1)
|
||||
# color = colors[i]
|
||||
color = YELLOW
|
||||
VGroup(*numer_matrix.mob_matrix[:, i]).set_color(color)
|
||||
VGroup(*numer_matrix.mob_matrix[:, i]).set_stroke(color, 1)
|
||||
numer = VGroup(
|
||||
get_det_text(numer_matrix, initial_scale_factor=3),
|
||||
numer_matrix
|
||||
|
|
@ -167,7 +208,7 @@ class LeaveItToComputers(TeacherStudentsScene):
|
|||
ReplacementTransform(
|
||||
system.output_vect_mob.elements.copy(),
|
||||
VGroup(*numer[1].mob_matrix[:, 0]),
|
||||
path_arc=180 * DEGREES
|
||||
path_arc=90 * DEGREES
|
||||
),
|
||||
self.teacher.change, "happy",
|
||||
)
|
||||
|
|
@ -204,6 +245,19 @@ class LeaveItToComputers(TeacherStudentsScene):
|
|||
self.wait(3)
|
||||
|
||||
|
||||
class ShowComputer(ThreeDScene):
|
||||
def construct(self):
|
||||
laptop = Laptop()
|
||||
laptop.add_updater(lambda m, dt: m.rotate(0.1 * dt, axis=UP))
|
||||
self.play(DrawBorderThenFill(
|
||||
laptop,
|
||||
lag_ratio=0.1,
|
||||
rate_func=smooth
|
||||
))
|
||||
self.wait(8)
|
||||
self.play(FadeOut(laptop))
|
||||
|
||||
|
||||
class PrerequisiteKnowledge(TeacherStudentsScene):
|
||||
CONFIG = {
|
||||
"camera_config": {"background_opacity": 1}
|
||||
|
|
@ -264,6 +318,20 @@ class NotTheMostComputationallyEfficient(Scene):
|
|||
self.wait()
|
||||
|
||||
|
||||
class GaussTitle(Scene):
|
||||
def construct(self):
|
||||
title = TextMobject("Gaussian Elimination")
|
||||
title.scale(1.5)
|
||||
title.to_edge(UP)
|
||||
line = Line(LEFT, RIGHT).scale(7)
|
||||
line.next_to(title, DOWN)
|
||||
self.play(
|
||||
FadeIn(title, lag_ratio=0.2),
|
||||
ShowCreation(line),
|
||||
)
|
||||
self.wait()
|
||||
|
||||
|
||||
class WhyLearnIt(TeacherStudentsScene):
|
||||
def construct(self):
|
||||
self.student_says(
|
||||
|
|
@ -474,8 +542,8 @@ class SetupSimpleSystemOfEquations(LinearTransformationScene):
|
|||
for column, column_mob, m in zip(columns, column_mobs, matrices):
|
||||
column_mob.save_state()
|
||||
column_mob[0].scale(0).move_to(matrix_mobject)
|
||||
Transform(column_mob.elements, column).update(1)
|
||||
Transform(column_mob.brackets, matrix_mobject.brackets).update(1)
|
||||
column_mob.elements.become(column)
|
||||
column_mob.brackets.become(matrix_mobject.brackets)
|
||||
self.add_foreground_mobject(column_mob)
|
||||
self.apply_matrix(m, added_anims=[
|
||||
ApplyMethod(column_mob.restore, path_arc=90 * DEGREES)
|
||||
|
|
@ -553,6 +621,13 @@ class SetupSimpleSystemOfEquations(LinearTransformationScene):
|
|||
return system
|
||||
|
||||
|
||||
class FloatingMinus(Scene):
|
||||
def construct(self):
|
||||
minus = TexMobject("-")
|
||||
self.add(minus)
|
||||
self.play(minus.shift, 2.9 * UP, run_time=1)
|
||||
|
||||
|
||||
class ShowZeroDeterminantCase(LinearTransformationScene):
|
||||
CONFIG = {
|
||||
"show_basis_vectors": True,
|
||||
|
|
@ -1172,14 +1247,17 @@ class OrthonormalWords(Scene):
|
|||
class ShowSomeOrthonormalTransformations(LinearTransformationScene):
|
||||
CONFIG = {
|
||||
"random_seed": 1,
|
||||
"n_angles": 5
|
||||
"n_angles": 7,
|
||||
}
|
||||
|
||||
def construct(self):
|
||||
for x in range(self.n_angles):
|
||||
angle = TAU * np.random.random() - TAU / 2
|
||||
matrix = rotation_matrix(angle, OUT)[:2, :2]
|
||||
self.apply_matrix(matrix)
|
||||
if x in [2, 4]:
|
||||
matrix[:, 1] *= -1
|
||||
self.apply_matrix(matrix, run_time=1)
|
||||
self.wait()
|
||||
|
||||
|
||||
class SolvingASystemWithOrthonormalMatrix(LinearTransformationScene):
|
||||
|
|
@ -2046,7 +2124,7 @@ class WriteCramersRule(Scene):
|
|||
|
||||
class CramersYEvaluation(Scene):
|
||||
def construct(self):
|
||||
frac = TexMobject("{(2)(2) - (4)(0) \\over (2)(1) - (-1)(0)}")
|
||||
frac = TexMobject("{(2)(2) - (4)(0) \\over (2)(1) - (-1)(0)}")[0]
|
||||
VGroup(frac[1], frac[11], frac[15], frac[26]).set_color(GREEN)
|
||||
VGroup(frac[4], frac[8]).set_color(MAROON_B)
|
||||
VGroup(frac[18], frac[22], frac[23]).set_color(RED)
|
||||
|
|
@ -2056,7 +2134,6 @@ class CramersYEvaluation(Scene):
|
|||
TexMobject("= \\frac{4}{2}"), TexMobject("=2")
|
||||
)
|
||||
group.arrange(RIGHT)
|
||||
group.add_to_back(BackgroundRectangle(group))
|
||||
|
||||
self.add(group)
|
||||
self.wait(1)
|
||||
|
|
@ -2065,7 +2142,7 @@ class CramersYEvaluation(Scene):
|
|||
# Largely copy-pasted. Not great, but what are you gonna do.
|
||||
class CramersXEvaluation(Scene):
|
||||
def construct(self):
|
||||
frac = TexMobject("{(4)(1) - (-1)(2) \\over (2)(1) - (-1)(0)}")
|
||||
frac = TexMobject("{(4)(1) - (-1)(2) \\over (2)(1) - (-1)(0)}")[0]
|
||||
VGroup(frac[1], frac[12]).set_color(MAROON_B)
|
||||
VGroup(frac[4], frac[8], frac[9]).set_color(RED)
|
||||
VGroup(frac[16], frac[27]).set_color(GREEN)
|
||||
|
|
@ -2082,6 +2159,25 @@ class CramersXEvaluation(Scene):
|
|||
self.wait(1)
|
||||
|
||||
|
||||
class FourPlusTwo(Scene):
|
||||
def construct(self):
|
||||
p1 = TexMobject("(4)(1)")
|
||||
p2 = TexMobject("-(-1)(2)")
|
||||
p2.next_to(p1, RIGHT, SMALL_BUFF)
|
||||
b1 = Brace(p1, UP)
|
||||
b2 = Brace(p2, UP)
|
||||
t1 = b1.get_tex("4", buff=SMALL_BUFF)
|
||||
t2 = b2.get_tex("+2", buff=SMALL_BUFF)
|
||||
|
||||
for b, t in (b1, t1), (b2, t2):
|
||||
t.set_stroke(BLACK, 3, background=True)
|
||||
self.play(
|
||||
GrowFromCenter(b),
|
||||
Write(t)
|
||||
)
|
||||
self.wait()
|
||||
|
||||
|
||||
class Equals2(Scene):
|
||||
def construct(self):
|
||||
self.add(TexMobject("=2").add_background_rectangle())
|
||||
|
|
@ -2096,8 +2192,8 @@ class Equals3(Scene):
|
|||
|
||||
class Introduce3DSystem(SetupSimpleSystemOfEquations):
|
||||
CONFIG = {
|
||||
"matrix": [[3, 2, 7], [-1, 2, -4], [4, 0, 1]],
|
||||
"output_vect": [-4, -2, 5],
|
||||
"matrix": [[3, 2, -7], [1, 2, -4], [4, 0, 1]],
|
||||
"output_vect": [4, 2, 5],
|
||||
"compare_to_big_system": False,
|
||||
"transition_to_geometric_view": False,
|
||||
}
|
||||
|
|
@ -2108,6 +2204,17 @@ class Introduce3DSystem(SetupSimpleSystemOfEquations):
|
|||
self.from_system_to_matrix()
|
||||
|
||||
|
||||
class MysteryInputLabel(Scene):
|
||||
def construct(self):
|
||||
brace = Brace(Line(ORIGIN, RIGHT), DOWN)
|
||||
text = brace.get_text("Mystery input")
|
||||
self.play(
|
||||
GrowFromCenter(brace),
|
||||
Write(text)
|
||||
)
|
||||
self.wait()
|
||||
|
||||
|
||||
class ThinkItThroughYourself(TeacherStudentsScene):
|
||||
def construct(self):
|
||||
self.teacher_says(
|
||||
|
|
@ -2144,17 +2251,29 @@ class AreYouPausingAndPondering(TeacherStudentsScene):
|
|||
self.wait(6)
|
||||
|
||||
|
||||
class Thumbnail(TransformingAreasYCoord):
|
||||
class Thumbnail(TransformingAreasYCoord, MovingCameraScene):
|
||||
CONFIG = {
|
||||
"background_plane_kwargs": {
|
||||
"y_max": 6,
|
||||
},
|
||||
}
|
||||
|
||||
def setup(self):
|
||||
TransformingAreasYCoord.setup(self)
|
||||
MovingCameraScene.setup(self)
|
||||
|
||||
def construct(self):
|
||||
self.matrix = np.array(self.matrix)
|
||||
vect = self.add_vector([1, 1.5], color=MAROON_B)
|
||||
ip = self.get_input_parallelogram(vect)
|
||||
self.add_transformable_mobject(ip)
|
||||
self.apply_transposed_matrix([[2, -0.5], [1, 2]])
|
||||
# self.square.set_fill(YELLOW, 0.7)
|
||||
self.camera_frame.shift(UP)
|
||||
|
||||
words = TextMobject("Cramer's", "rule")
|
||||
words.set_width(7)
|
||||
# words.add_background_rectangle_to_submobjects()
|
||||
words.scale(3)
|
||||
words.set_stroke(BLACK, 6, background=True)
|
||||
words.to_edge(UP, buff=-MED_LARGE_BUFF)
|
||||
words.add_background_rectangle()
|
||||
words.to_edge(UP)
|
||||
self.add(words)
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue