Finished preliminary animations for eola intro video

This commit is contained in:
Grant Sanderson
2016-07-13 13:09:18 -07:00
parent d35a8f76ac
commit fa708dd92a
5 changed files with 547 additions and 24 deletions

View File

@ -38,13 +38,47 @@ class OpeningQuote(Scene):
words.to_edge(UP)
for mob in words.submobjects[48:49+13]:
mob.highlight(GREEN)
author = TextMobject("-Hermann Weyl")
author = TextMobject("-Jean Dieudonn\\'e")
author.highlight(YELLOW)
author.next_to(words, DOWN)
self.play(FadeIn(words))
self.dither(3)
self.play(Write(author))
self.play(Write(author, run_time = 5))
self.dither()
class VideoIcon(SVGMobject):
def __init__(self, **kwargs):
SVGMobject.__init__(self, "video_icon", **kwargs)
self.center()
self.scale_to_fit_width(2*SPACE_WIDTH/12.)
self.set_stroke(color = WHITE, width = 0)
self.set_fill(color = WHITE, opacity = 1)
class UpcomingSeriesOfVidoes(Scene):
def construct(self):
icons = [VideoIcon() for x in range(10)]
colors = Color(BLUE_A).range_to(BLUE_D, len(icons))
for icon, color in zip(icons, colors):
icon.set_fill(color, opacity = 1)
icons = VMobject(*icons)
icons.arrange_submobjects(RIGHT)
icons.to_edge(LEFT)
icons.shift(UP)
icons = icons.split()
def rate_func_creator(offset):
return lambda a : min(max(2*(a-offset), 0), 1)
self.play(*[
FadeIn(
icon,
run_time = 5,
rate_func = rate_func_creator(offset)
)
for icon, offset in zip(icons, np.linspace(0, 0.5, len(icons)))
])
self.dither()
@ -612,12 +646,300 @@ class PhysicsExample(Scene):
class LinearAlgebraIntuitions(Scene):
def construct(self):
pass
title = TextMobject("Preview of core visual intuitions")
title.to_edge(UP)
h_line = Line(SPACE_WIDTH*LEFT, SPACE_WIDTH*RIGHT)
h_line.next_to(title, DOWN)
h_line.highlight(BLUE_E)
intuitions = [
"Matrices transform space",
"Matrix multiplication corresponds to applying " +
"one transformation after another",
"The determinant gives the factor by which areas change",
]
self.play(
Write(title),
ShowCreation(h_line),
run_time = 2
)
for count, intuition in enumerate(intuitions, 3):
intuition += " (details coming in chapter %d)"%count
mob = TextMobject(intuition)
mob.scale(0.7)
mob.next_to(h_line, DOWN)
self.play(FadeIn(mob))
self.dither(4)
self.play(FadeOut(mob))
self.remove(mob)
self.dither()
class MatricesAre(Scene):
def construct(self):
matrix = matrix_to_mobject([[1, -1], [1, 2]])
matrix.scale_to_fit_height(6)
arrow = Arrow(LEFT, RIGHT, stroke_width = 8, preserve_tip_size_when_scaling = False)
arrow.scale(2)
arrow.to_edge(RIGHT)
matrix.next_to(arrow, LEFT)
self.play(Write(matrix, run_time = 1))
self.play(ShowCreation(arrow, submobject_mode = "one_at_a_time"))
self.dither()
class ExampleTransformationForIntuitionList(LinearTransformationScene):
def construct(self):
self.setup()
self.apply_matrix([[1, -1], [1, 2]])
self.dither()
class MatrixMultiplicationIs(Scene):
def construct(self):
matrix1 = matrix_to_mobject([[1, -1], [1, 2]])
matrix1.highlight(BLUE)
matrix2 = matrix_to_mobject([[2, 1], [1, 2]])
matrix2.highlight(GREEN)
for m in matrix1, matrix2:
m.scale_to_fit_height(3)
arrow = Arrow(LEFT, RIGHT, stroke_width = 6, preserve_tip_size_when_scaling = False)
arrow.scale(2)
arrow.to_edge(RIGHT)
matrix1.next_to(arrow, LEFT)
matrix2.next_to(matrix1, LEFT)
brace1 = Brace(matrix1, UP)
apply_first = TextMobject("Apply first").next_to(brace1, UP)
brace2 = Brace(matrix2, DOWN)
apply_second = TextMobject("Apply second").next_to(brace2, DOWN)
self.play(
Write(matrix1),
ShowCreation(arrow),
GrowFromCenter(brace1),
Write(apply_first),
run_time = 1
)
self.dither()
self.play(
Write(matrix2),
GrowFromCenter(brace2),
Write(apply_second),
run_time = 1
)
self.dither()
class ComposedTransformsForIntuitionList(LinearTransformationScene):
def construct(self):
self.setup()
self.apply_matrix([[1, -1], [1, 2]])
self.dither()
self.apply_matrix([[2, 1], [1, 2]])
self.dither()
class DeterminantsAre(Scene):
def construct(self):
tex_mob = TexMobject("""
\\text{Det}\\left(\\left[
\\begin{array}{cc}
1 & -1 \\\\
1 & 2
\\end{array}
\\right]\\right)
""")
tex_mob.scale_to_fit_height(4)
arrow = Arrow(LEFT, RIGHT, stroke_width = 8, preserve_tip_size_when_scaling = False)
arrow.scale(2)
arrow.to_edge(RIGHT)
tex_mob.next_to(arrow, LEFT)
self.play(
Write(tex_mob),
ShowCreation(arrow, submobject_mode = "one_at_a_time"),
run_time = 1
)
class TransformationForDeterminant(LinearTransformationScene):
def construct(self):
self.setup()
square = Square(side_length = 1)
square.shift(-square.get_corner(DOWN+LEFT))
square.set_fill(YELLOW_A, 0.5)
self.add_transformable_mobject(square)
self.apply_matrix([[1, -1], [1, 2]])
class ProfessorsTry(Scene):
def construct(self):
morty = Mortimer()
morty.to_corner(DOWN+RIGHT)
morty.shift(3*LEFT)
speech_bubble = morty.get_bubble("speech", height = 4, width = 8)
speech_bubble.shift(RIGHT)
words = TextMobject(
"It really is beautiful! I want you to \\\\" + \
"see it the way I do...",
)
speech_bubble.position_mobject_inside(words)
thought_bubble = ThoughtBubble(width = 4, height = 3.5)
thought_bubble.next_to(morty, UP)
thought_bubble.to_edge(RIGHT)
randy = Randolph()
randy.scale(0.8)
randy.to_corner()
self.add(randy, morty)
self.play(
ApplyMethod(morty.change_mode, "speaking"),
FadeIn(speech_bubble),
FadeIn(words)
)
self.play(Blink(randy))
self.play(FadeIn(thought_bubble ))
self.play(Blink(morty))
class ExampleMatrixMultiplication(NumericalMatrixMultiplication):
CONFIG = {
"left_matrix" : [[-3, 1], [2, 5]],
"right_matrix" : [[5, 3], [7, -3]]
}
class TableOfContents(Scene):
def construct(self):
title = TextMobject("Essence of Linear Algebra")
title.highlight(BLUE)
title.to_corner(UP+LEFT)
h_line = Line(SPACE_WIDTH*LEFT, SPACE_WIDTH*RIGHT)
h_line.next_to(title, DOWN)
h_line.to_edge(LEFT, buff = 0)
chapters = VMobject(*map(TextMobject, [
"Chapter 1: Vectors, what even are they?",
"Chapter 2: Linear combinations, span and bases",
"Chapter 3: Matrices as linear transformations",
"Chapter 4: Matrix multiplication as composition",
"Chapter 5: The determinant",
"Chapter 6: Inverse matrices, column space and null space",
"Chapter 7: Dot products and cross products",
"Chapter 8: Change of basis",
"Chapter 9: Eigenvectors and eigenvalues",
"Chapter 10: Abstract vector spaces",
]))
chapters.arrange_submobjects(DOWN)
chapters.scale(0.7)
chapters.next_to(h_line, DOWN)
self.play(
Write(title),
ShowCreation(h_line)
)
for chapter in chapters.split():
chapter.to_edge(LEFT, buff = 1)
self.play(FadeIn(chapter))
self.dither(2)
entry3 = chapters.split()[2]
added_words = TextMobject("(Personally, I'm most excited \\\\ to do this one)")
added_words.scale(0.5)
added_words.highlight(YELLOW)
added_words.next_to(h_line, DOWN)
added_words.to_edge(RIGHT)
arrow = Arrow(added_words.get_bottom(), entry3)
self.play(
ApplyMethod(entry3.highlight, YELLOW),
ShowCreation(arrow, submobject_mode = "one_at_a_time"),
Write(added_words),
run_time = 1
)
self.dither()
removeable = VMobject(added_words, arrow, h_line, title)
self.play(FadeOut(removeable))
self.remove(removeable)
self.series_of_videos(chapters)
def series_of_videos(self, chapters):
icon = SVGMobject("video_icon")
icon.center()
icon.scale_to_fit_width(2*SPACE_WIDTH/12.)
icon.set_stroke(color = WHITE, width = 0)
icons = [icon.copy() for chapter in chapters.split()]
colors = Color(BLUE_A).range_to(BLUE_D, len(icons))
for icon, color in zip(icons, colors):
icon.set_fill(color, opacity = 1)
icons = VMobject(*icons)
icons.arrange_submobjects(RIGHT)
icons.to_edge(LEFT)
icons.shift(UP)
randy = Randolph()
randy.to_corner()
bubble = randy.get_bubble()
new_icons = icons.copy().scale(0.2)
bubble.position_mobject_inside(new_icons)
self.play(Transform(
chapters, icons,
path_arc = np.pi/2,
))
self.clear()
self.add(icons)
self.play(FadeIn(randy))
self.play(Blink(randy))
self.dither()
self.play(
ShowCreation(bubble),
Transform(icons, new_icons)
)
self.dither()
class ResourceForTeachers(Scene):
def construct(self):
morty = Mortimer(mode = "speaking")
morty.to_corner(DOWN + RIGHT)
bubble = morty.get_bubble("speech")
bubble.write("I'm assuming you \\\\ know linear algebra\\dots")
words = bubble.content
bubble.clear()
randys = VMobject(*[
Randolph(color = c)
for c in BLUE_D, BLUE_C, BLUE_E
])
randys.arrange_submobjects(RIGHT)
randys.scale(0.8)
randys.to_corner(DOWN+LEFT)
self.add(randys, morty)
self.play(FadeIn(bubble), Write(words), run_time = 3)
for randy in np.array(randys.split())[[2,0,1]]:
self.play(Blink(randy))
self.dither()
class PauseAndPonder(Scene):
def construct(self):
pause = TexMobject("=").rotate(np.pi/2)
pause.stretch(0.5, 1)
pause.scale_to_fit_height(1.5)
bubble = ThoughtBubble().scale_to_fit_height(2)
pause.shift(LEFT)
bubble.next_to(pause, RIGHT, buff = 1)
self.play(FadeIn(pause))
self.play(ShowCreation(bubble))
self.dither()
class NextVideo(Scene):
def construct(self):
title = TextMobject("Next video: Vectors, what even are they?")
title.to_edge(UP)
rect = Rectangle(width = 16, height = 9, color = BLUE)
rect.scale_to_fit_height(6)
rect.next_to(title, DOWN)
self.add(title)
self.play(ShowCreation(rect))
self.dither()

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@ -1,11 +1,14 @@
import numpy as np
from scene import Scene
from mobject import Mobject
from mobject.vectorized_mobject import VMobject
from mobject.tex_mobject import TexMobject, TextMobject
from animation.transform import ApplyPointwiseFunction, Transform
from animation.transform import ApplyPointwiseFunction, Transform, \
ApplyMethod, FadeOut
from animation.simple_animations import ShowCreation
from topics.number_line import NumberPlane
from topics.geometry import Vector
from topics.geometry import Vector, Line, Circle
from helpers import *
@ -32,8 +35,13 @@ class LinearTransformationScene(Scene):
"foreground_plane_kwargs" : {
"x_radius" : 2*SPACE_WIDTH,
"y_radius" : 2*SPACE_HEIGHT,
"secondary_line_ratio" : 0
},
"background_plane_kwargs" : {
"color" : GREY,
"secondary_color" : DARK_GREY,
"axes_color" : GREY,
},
"background_plane_kwargs" : {},
"show_coordinates" : False,
"show_basis_vectors" : True,
"i_hat_color" : GREEN_B,
@ -45,29 +53,27 @@ class LinearTransformationScene(Scene):
self.moving_vectors = []
self.background_plane = NumberPlane(
color = GREY,
secondary_color = DARK_GREY,
**self.background_plane_kwargs
)
if self.show_coordinates:
self.background_plane.add_coordinates()
if self.include_background_plane:
self.add_to_background(self.background_plane)
self.add_background_mobject(self.background_plane)
if self.include_foreground_plane:
self.plane = NumberPlane(**self.foreground_plane_kwargs)
self.add_to_transformable(self.plane)
self.add_transformable_mobject(self.plane)
if self.show_basis_vectors:
self.add_vector((1, 0), self.i_hat_color)
self.add_vector((0, 1), self.j_hat_color)
def add_to_background(self, *mobjects):
def add_background_mobject(self, *mobjects):
for mobject in mobjects:
if mobject not in self.background_mobjects:
self.background_mobjects.append(mobject)
self.add(mobject)
def add_to_transformable(self, *mobjects):
def add_transformable_mobject(self, *mobjects):
for mobject in mobjects:
if mobject not in self.transformable_mobject:
self.transformable_mobject.append(mobject)
@ -109,6 +115,190 @@ class LinearTransformationScene(Scene):
)
)
class Matrix(VMobject):
CONFIG = {
"v_buff" : 0.5,
"h_buff" : 1,
}
def __init__(self, matrix, **kwargs):
"""
Matrix can either either include numbres, tex_strings,
or mobjects
"""
VMobject.__init__(self, **kwargs)
matrix = np.array(matrix)
assert(matrix.ndim == 2)
if not isinstance(matrix[0][0], Mobject):
matrix = matrix.astype("string")
matrix = self.string_matrix_to_mob_matrix(matrix)
self.organize_mob_matrix(matrix)
self.add(*matrix.flatten())
self.add_brackets()
self.center()
self.mob_matrix = matrix
def string_matrix_to_mob_matrix(self, matrix):
return np.array([
map(TexMobject, row)
for row in matrix
])
def organize_mob_matrix(self, matrix):
for i, row in enumerate(matrix):
for j, elem in enumerate(row):
mob = matrix[i][j]
if i == 0 and j == 0:
continue
elif i == 0:
mob.next_to(matrix[i][j-1], RIGHT, self.h_buff)
else:
mob.next_to(matrix[i-1][j], DOWN, self.v_buff)
return self
def get_mob_matrix(self):
return self.mob_matrix
def add_brackets(self):
bracket_pair = TexMobject("\\big[ \\big]")
bracket_pair.scale(2)
bracket_pair.stretch_to_fit_height(self.get_height() + 0.5)
l_bracket, r_bracket = bracket_pair.split()
l_bracket.next_to(self, LEFT)
r_bracket.next_to(self, RIGHT)
self.add(l_bracket, r_bracket)
return self
class NumericalMatrixMultiplication(Scene):
CONFIG = {
"left_matrix" : [[1, 2], [3, 4]],
"right_matrix" : [[5, 6], [7, 8]]
}
def construct(self):
left_string_matrix, right_string_matrix = [
np.array(matrix).astype("string")
for matrix in self.left_matrix, self.right_matrix
]
if right_string_matrix.shape[0] != left_string_matrix.shape[1]:
raise Exception("Incompatible shapes for matrix multiplication")
left = Matrix(left_string_matrix)
right = Matrix(right_string_matrix)
result = self.get_result_matrix(
left_string_matrix, right_string_matrix
)
self.organize_matrices(left, right, result)
# self.add_lines(left, right)
self.animate_product(left, right, result)
def get_result_matrix(self, left, right):
(m, k), n = left.shape, right.shape[1]
mob_matrix = np.array([VMobject()]).repeat(m*n).reshape((m, n))
for a in range(m):
for b in range(n):
parts = [
prefix + "(%s)(%s)"%(left[a][c], right[c][b])
for c in range(k)
for prefix in ["" if c == 0 else "+"]
]
mob_matrix[a][b] = TexMobject(parts, next_to_buff = 0.1)
return Matrix(mob_matrix)
def add_lines(self, left, right):
line_kwargs = {
"color" : BLUE,
"stroke_width" : 2,
}
left_rows = [
VMobject(*row) for row in left.get_mob_matrix()
]
h_lines = VMobject()
for row in left_rows[:-1]:
h_line = Line(row.get_left(), row.get_right(), **line_kwargs)
h_line.next_to(row, DOWN, buff = left.v_buff/2.)
h_lines.add(h_line)
right_cols = [
VMobject(*col) for col in np.transpose(right.get_mob_matrix())
]
v_lines = VMobject()
for col in right_cols[:-1]:
v_line = Line(col.get_top(), col.get_bottom(), **line_kwargs)
v_line.next_to(col, RIGHT, buff = right.h_buff/2.)
v_lines.add(v_line)
self.play(ShowCreation(h_lines))
self.play(ShowCreation(v_lines))
self.dither()
self.show_frame()
def organize_matrices(self, left, right, result):
equals = TexMobject("=")
everything = VMobject(left, right, equals, result)
everything.arrange_submobjects()
everything.scale_to_fit_width(2*SPACE_WIDTH-1)
self.add(everything)
def animate_product(self, left, right, result):
l_matrix = left.get_mob_matrix()
r_matrix = right.get_mob_matrix()
result_matrix = result.get_mob_matrix()
circle = Circle(
radius = l_matrix[0][0].get_height(),
color = GREEN
)
circles = VMobject(*[
entry.get_point_mobject()
for entry in l_matrix[0][0], r_matrix[0][0]
])
(m, k), n = l_matrix.shape, r_matrix.shape[1]
for mob in result_matrix.flatten():
mob.highlight(BLACK)
lagging_anims = []
for a in range(m):
for b in range(n):
for c in range(k):
l_matrix[a][c].highlight(YELLOW)
r_matrix[c][b].highlight(YELLOW)
for c in range(k):
start_parts = VMobject(
l_matrix[a][c].copy(),
r_matrix[c][b].copy()
)
result_entry = result_matrix[a][b].split()[c]
new_circles = VMobject(*[
circle.copy().shift(part.get_center())
for part in start_parts.split()
])
self.play(Transform(circles, new_circles))
self.play(
Transform(
start_parts,
result_entry.copy().highlight(YELLOW),
path_arc = -np.pi/2
),
*lagging_anims
)
result_entry.highlight(YELLOW)
self.remove(start_parts)
lagging_anims = [
ApplyMethod(result_entry.highlight, WHITE)
]
for c in range(k):
l_matrix[a][c].highlight(WHITE)
r_matrix[c][b].highlight(WHITE)
self.play(FadeOut(circles), *lagging_anims)
self.dither()

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@ -11,6 +11,8 @@ from scipy import linalg
from constants import *
CLOSED_THRESHOLD = 0.01
def get_smooth_handle_points(points):
num_handles = len(points) - 1
dim = points.shape[1]
@ -76,7 +78,7 @@ def diag_to_matrix(l_and_u, diag):
return matrix
def is_closed(points):
return np.all(points[0] == points[-1])
return np.linalg.norm(points[0] - points[-1]) < CLOSED_THRESHOLD
def color_to_rgb(color):
return np.array(Color(color).get_rgb())

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@ -26,6 +26,7 @@ class PiCreature(SVGMobject):
"fill_opacity" : 1.0,
"initial_scale_val" : 0.01,
"corner_scale_factor" : 0.75,
"flip_at_start" : False,
}
def __init__(self, mode = "plain", **kwargs):
self.parts_named = False
@ -36,6 +37,8 @@ class PiCreature(SVGMobject):
digest_config(self, kwargs, locals())
SVGMobject.__init__(self, svg_file, **kwargs)
self.init_colors()
if self.flip_at_start:
self.flip()
def name_parts(self):
self.mouth = self.submobjects[MOUTH_INDEX]
@ -122,14 +125,11 @@ class Randolph(PiCreature):
class Mortimer(PiCreature):
CONFIG = {
"color" : "#736357"
"color" : "#736357",
"flip_at_start" : True,
}
def __init__(self, *args, **kwargs):
PiCreature.__init__(self, *args, **kwargs)
self.flip()
class Mathematician(PiCreature):
CONFIG = {
"color" : GREY,
@ -219,6 +219,7 @@ class Bubble(SVGMobject):
class SpeechBubble(Bubble):
CONFIG = {
"file_name" : "Bubbles_speech.svg",
"height" : 4
}
class ThoughtBubble(Bubble):
@ -226,3 +227,10 @@ class ThoughtBubble(Bubble):
"file_name" : "Bubbles_thought.svg",
}
def __init__(self, **kwargs):
Bubble.__init__(self, **kwargs)
self.submobjects.sort(
lambda m1, m2 : int((m1.get_bottom()-m2.get_bottom())[1])
)

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@ -8,7 +8,7 @@ class Arc(VMobject):
"radius" : 1.0,
"start_angle" : 0,
"num_anchors" : 8,
"anchors_span_full_range" : True
"anchors_span_full_range" : True,
}
def __init__(self, angle, **kwargs):
digest_locals(self)
@ -164,6 +164,7 @@ class Arrow(Line):
if self.preserve_tip_size_when_scaling:
self.remove(self.tip)
self.add_tip()
return self
class Vector(Arrow):
CONFIG = {