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Beginning eola project
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Grant Sanderson
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3 changed files with 389 additions and 0 deletions
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eola/__init__.py
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eola/__init__.py
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eola/chapter0.py
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eola/chapter0.py
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from mobject.tex_mobject import TexMobject
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from mobject import Mobject
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from mobject.image_mobject import ImageMobject
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from mobject.vectorized_mobject import VMobject
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from animation.animation import Animation
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from animation.transform import *
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from animation.simple_animations import *
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from animation.playground import *
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from topics.geometry import *
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from topics.characters import *
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from topics.functions import *
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from topics.number_line import *
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from topics.combinatorics import *
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from scene import Scene
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from camera import Camera
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from mobject.svg_mobject import *
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from mobject.tex_mobject import *
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from eola.utils import *
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EXAMPLE_TRANFORM = [[0, 1], [-1, 1]]
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TRANFORMED_VECTOR = [[1], [2]]
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class OpeningQuote(Scene):
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def construct(self):
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words = TextMobject(
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"""
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``There is hardly any theory which is more elementary
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than linear algebra, in spite of the fact that generations
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of professors and textbook writers have obscured its
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simplicity by preposterous calculations with matrices.''
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""",
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organize_left_to_right = False
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)
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words.scale_to_fit_width(2*(SPACE_WIDTH-1))
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words.to_edge(UP)
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for mob in words.submobjects[48:49+13]:
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mob.highlight(GREEN)
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words.show()
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author = TextMobject("-Hermann Weyl")
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author.highlight(YELLOW)
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author.next_to(words, DOWN)
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self.play(Write(words))
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self.dither()
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self.play(FadeIn(author))
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self.dither()
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class AboutLinearAlgebra(Scene):
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def construct(self):
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self.show_dependencies()
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self.linalg_is_confusing()
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self.ask_questions()
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def show_dependencies(self):
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linalg = TextMobject("Linear Algebra")
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subjects = map(TextMobject, [
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"Computer science",
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"Physics",
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"Electrical engineering",
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"Mechanical engineering",
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"Statistics",
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"\\vdots"
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])
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prev = subjects[0]
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for subject in subjects[1:]:
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subject.next_to(prev, DOWN, aligned_edge = LEFT)
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prev = subject
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all_subs = VMobject(*subjects)
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linalg.to_edge(LEFT)
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all_subs.next_to(linalg, RIGHT, buff = 2)
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arrows = VMobject(*[
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Arrow(linalg, sub)
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for sub in subjects
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])
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self.play(Write(linalg, run_time = 1))
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self.dither()
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self.play(
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ShowCreation(arrows, submobject_mode = "lagged_start"),
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FadeIn(all_subs),
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run_time = 2
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)
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self.dither()
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self.linalg = linalg
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def linalg_is_confusing(self):
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linalg = self.linalg
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all_else = list(self.mobjects)
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all_else.remove(linalg)
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randy = Randolph()
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randy.to_corner()
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bubble = randy.get_bubble(width = 10)
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new_linalg = bubble.position_mobject_inside(linalg.copy())
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self.play(*map(FadeOut, all_else))
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self.remove(*all_else)
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self.play(
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Transform(linalg, new_linalg),
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Write(bubble),
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FadeIn(randy)
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)
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self.play(ApplyMethod(randy.change_mode, "confused"))
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self.dither()
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self.play(Blink(randy))
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self.play(FadeOut(linalg))
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self.remove(linalg)
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self.randy, self.bubble = randy, bubble
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def ask_questions(self):
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randy, bubble = self.randy, self.bubble
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matrix_multiplication = TexMobject("""
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\\left[
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\\begin{array}{cc}
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a & b \\\\
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c & d
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\\end{array}
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\\right]
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\\left[
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\\begin{array}{cc}
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e & f \\\\
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g & h
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\\end{array}
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\\right]
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=
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\\left[
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\\begin{array}{cc}
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ae + bg & af + bh \\\\
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ce + dg & cf + dh
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\\end{array}
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\\right]
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""")
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cross = TexMobject("\\vec{v} \\times \\vec{w}")
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left_right_arrow = DoubleArrow(Point(LEFT), Point(RIGHT))
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det = TextMobject("Det")
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q_mark = TextMobject("?")
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left_right_arrow.next_to(cross)
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det.next_to(left_right_arrow)
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q_mark.next_to(left_right_arrow, UP)
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cross_question = VMobject(cross, left_right_arrow, q_mark, det)
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cross_question.get_center = lambda : left_right_arrow.get_center()
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eigen_q = TextMobject("Eigen?")
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for mob in matrix_multiplication, cross_question, eigen_q:
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bubble.position_mobject_inside(mob)
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self.play(FadeIn(mob))
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if randy.mode is not "pondering":
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self.play(ApplyMethod(randy.change_mode, "pondering"))
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self.dither()
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else:
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self.dither(2)
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self.remove(mob)
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class NumericVsGeometric(Scene):
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def construct(self):
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self.setup()
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self.specifics_concepts()
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self.clear_way_for_geometric()
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self.list_geometric_benefits()
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def setup(self):
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numeric = TextMobject("Numeric operations")
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geometric = TextMobject("Geometric intuition")
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for mob in numeric, geometric:
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mob.to_corner(UP+LEFT)
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geometric.shift(SPACE_WIDTH*RIGHT)
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hline = Line(SPACE_WIDTH*LEFT, SPACE_WIDTH*RIGHT)
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hline.next_to(numeric, DOWN)
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hline.to_edge(LEFT, buff = 0)
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vline = Line(SPACE_HEIGHT*UP, SPACE_HEIGHT*DOWN)
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for mob in hline, vline:
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mob.highlight(GREEN)
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self.play(ShowCreation(VMobject(hline, vline)))
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digest_locals(self)
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def specifics_concepts(self):
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matrix_vector_product = TexMobject(" ".join([
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matrix_to_tex_string(EXAMPLE_TRANFORM),
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matrix_to_tex_string(TRANFORMED_VECTOR),
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"&=",
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matrix_to_tex_string([
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["1 \\cdot 1 + 0 \\cdot 2"],
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["1 \\cdot 1 + (-1)\\cdot 2"]
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]),
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"\\\\ &=",
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matrix_to_tex_string([[1], [-1]]),
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]))
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matrix_vector_product.scale_to_fit_width(SPACE_WIDTH-0.5)
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matrix_vector_product.next_to(self.vline, LEFT)
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self.play(
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Write(self.numeric),
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FadeIn(matrix_vector_product),
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run_time = 2
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)
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self.dither()
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self.play(Write(self.geometric, run_time = 2))
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### Paste in linear transformation
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self.dither()
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digest_locals(self)
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def clear_way_for_geometric(self):
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new_line = Line(SPACE_HEIGHT*LEFT, SPACE_HEIGHT*RIGHT)
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new_line.shift((SPACE_HEIGHT+1)*DOWN)
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self.play(
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Transform(self.vline, new_line),
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Transform(self.hline, new_line),
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ApplyMethod(self.numeric.shift, (2*SPACE_HEIGHT+1)*DOWN),
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ApplyMethod(
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self.matrix_vector_product.shift,
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(2*SPACE_HEIGHT+1)*DOWN
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),
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ApplyMethod(self.geometric.to_edge, LEFT)
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)
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def list_geometric_benefits(self):
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follow_words = TextMobject("is helpful for \\dots")
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follow_words.next_to(self.geometric)
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#Ugly hack
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diff = follow_words.submobjects[0].get_bottom()[1] - \
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self.geometric.submobjects[0].get_bottom()[1]
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follow_words.shift(diff*DOWN)
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randys = [
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Randolph(mode = "speaking"),
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Randolph(mode = "surprised"),
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Randolph(mode = "pondering")
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]
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bulb = SVGMobject("light_bulb")
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bulb.scale_to_fit_height(1)
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bulb.highlight(YELLOW)
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thoughts = [
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matrix_to_mobject(EXAMPLE_TRANFORM),
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bulb,
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TextMobject("So therefore...").scale(0.5)
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]
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self.play(Write(follow_words, run_time = 1.5))
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curr_randy = None
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for randy, thought in zip(randys, thoughts):
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randy.shift(DOWN)
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thought.next_to(randy, UP+RIGHT, buff = 0)
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if curr_randy:
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self.play(
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Transform(curr_randy, randy),
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Transform(curr_thought, thought)
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)
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else:
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self.play(
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FadeIn(randy),
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Write(thought, run_time = 1)
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)
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curr_randy = randy
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curr_thought = thought
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self.dither(1.5)
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class ExampleTransformation(LinearTransformationScene):
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def construct(self):
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self.setup()
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self.apply_matrix(EXAMPLE_TRANFORM)
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self.dither()
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class NumericToComputations(Scene):
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def construct(self):
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top = TextMobject("Numeric understanding")
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arrow = Arrow(UP, DOWN)
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bottom = TextMobject("Actual computations")
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top.next_to(arrow, UP)
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bottom.next_to(arrow, DOWN)
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self.add(top)
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self.play(ShowCreation(arrow, submobject_mode = "one_at_a_time"))
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self.play(FadeIn(bottom))
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self.dither()
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90
eola/utils.py
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eola/utils.py
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import numpy as np
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from scene import Scene
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from mobject.vectorized_mobject import VMobject
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from mobject.tex_mobject import TexMobject, TextMobject
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from animation.transform import ApplyMatrix, ApplyMethod
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from topics.number_line import NumberPlane
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from topics.geometry import Vector
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from helpers import *
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def matrix_to_tex_string(matrix):
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matrix = np.array(matrix).astype("string")
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n_rows, n_cols = matrix.shape
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prefix = "\\left[ \\begin{array}{%s}"%("c"*n_cols)
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suffix = "\\end{array} \\right]"
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rows = [
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" & ".join(row)
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for row in matrix
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]
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return prefix + " \\\\ ".join(rows) + suffix
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def matrix_to_mobject(matrix):
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return TexMobject(matrix_to_tex_string(matrix))
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class LinearTransformationScene(Scene):
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CONFIG = {
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"include_background_plane" : True,
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"include_foreground_plane" : True,
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"foreground_plane_kwargs" : {
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"x_radius" : 2*SPACE_WIDTH,
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"y_radius" : 2*SPACE_HEIGHT,
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},
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"background_plane_kwargs" : {},
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"show_coordinates" : False,
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"show_basis_vectors" : True,
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"i_hat_color" : GREEN_B,
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"j_hat_color" : RED,
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}
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def setup(self):
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self.background_mobjects = []
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self.foreground_mobjects = []
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self.background_plane = NumberPlane(
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color = GREY,
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secondary_color = DARK_GREY,
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**self.background_plane_kwargs
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)
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if self.show_coordinates:
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self.background_plane.add_coordinates()
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if self.include_background_plane:
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self.add_to_background(self.background_plane)
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if self.include_foreground_plane:
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self.plane = NumberPlane(**self.foreground_plane_kwargs)
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self.add_to_foreground(self.plane)
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if self.show_basis_vectors:
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i_hat = Vector(self.background_plane.num_pair_to_point((1, 0)))
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j_hat = Vector(self.background_plane.num_pair_to_point((0, 1)))
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i_hat.highlight(self.i_hat_color)
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j_hat.highlight(self.j_hat_color)
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self.add_to_foreground(i_hat, j_hat)
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def add_to_background(self, *mobjects):
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for mobject in mobjects:
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if mobject not in self.background_mobjects:
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self.background_mobjects.append(mobject)
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self.add(mobject)
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def add_to_foreground(self, *mobjects):
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for mobject in mobjects:
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if mobject not in self.foreground_mobjects:
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self.foreground_mobjects.append(mobject)
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self.add(mobject)
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def apply_matrix(self, matrix, **kwargs):
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self.play(ApplyMatrix(
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matrix,
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VMobject(*self.foreground_mobjects),
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**kwargs
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))
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