mirror of
https://github.com/3b1b/manim.git
synced 2025-08-02 02:35:22 +08:00
Footnote about 3d transformations
This commit is contained in:
Grant Sanderson
@ -48,11 +48,17 @@ class MatrixToBlank(Scene):
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matrix = Matrix([[3, 1], [0, 2]])
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arrow = Arrow(LEFT, RIGHT)
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matrix.to_edge(LEFT)
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arrow.next_to(matrix, LEFT)
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arrow.next_to(matrix, RIGHT)
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matrix.add(arrow)
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self.play(Write(matrix))
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self.dither()
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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_transposed_matrix([[3, 0], [1, 2]])
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self.dither(2)
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class RecapTime(TeacherStudentsScene):
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def construct(self):
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self.setup()
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@ -226,6 +232,13 @@ class RecapOver(TeacherStudentsScene):
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self.teacher_says("Recap over!")
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class TwoSuccessiveTransformations(LinearTransformationScene):
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CONFIG = {
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"foreground_plane_kwargs" : {
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"x_radius" : 2*SPACE_WIDTH,
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"y_radius" : 2*SPACE_WIDTH,
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"secondary_line_ratio" : 0
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},
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}
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def construct(self):
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self.setup()
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self.apply_transposed_matrix([[2, 1],[1, 2]])
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@ -1007,13 +1020,72 @@ class ThreeSuccessiveTransformationsAltParens(ThreeSuccessiveTransformations):
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"symbols_str" : "(AB)C"
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}
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class ThreeSuccessiveTransformationsSimple(ThreeSuccessiveTransformations):
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CONFIG = {
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"symbols_str" : "ABC"
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}
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class ExplanationTrumpsProof(Scene):
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def construct(self):
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greater = TexMobject(">")
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greater.shift(RIGHT)
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explanation = TextMobject("Good explanation")
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explanation.highlight(BLUE)
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proof = TextMobject("Symbolic proof")
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proof.highlight(LIGHT_BROWN)
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explanation.next_to(greater, LEFT)
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proof.next_to(greater, RIGHT)
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explanation.get_center = lambda : explanation.get_right()
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proof.get_center = lambda : proof.get_left()
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self.play(
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Write(explanation),
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Write(greater),
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Write(proof),
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run_time = 1
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)
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self.play(
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explanation.scale_in_place, 1.5,
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proof.scale_in_place, 0.7
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)
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self.dither()
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class GoPlay(TeacherStudentsScene):
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def construct(self):
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self.setup()
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self.teacher_says("Go play!", height = 3, width = 5)
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self.play(*[
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ApplyMethod(student.change_mode, "happy")
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for student in self.get_students()
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])
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self.random_blink()
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student = self.get_students()[-1]
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bubble = ThoughtBubble(direction = RIGHT, width = 6, height = 5)
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bubble.pin_to(student, allow_flipping = False)
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bubble.make_green_screen()
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self.play(
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ShowCreation(bubble),
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student.look, UP+LEFT,
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)
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self.play(student.change_mode, "pondering")
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for x in range(3):
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self.random_blink()
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self.dither(2)
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class NextVideo(Scene):
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def construct(self):
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title = TextMobject("""
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Next video: Linear transformations in three dimensions
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""")
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title.scale_to_fit_width(2*SPACE_WIDTH - 2)
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title.to_edge(UP)
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rect = Rectangle(width = 16, height = 9, color = BLUE)
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rect.scale_to_fit_height(6)
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rect.next_to(title, DOWN)
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self.add(title)
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self.play(ShowCreation(rect))
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self.dither()
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447
eola/footnote.py
Normal file
447
eola/footnote.py
Normal file
@ -0,0 +1,447 @@
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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 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.numerals 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 mobject.vectorized_mobject import *
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from eola.matrix import *
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from eola.two_d_space import *
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class OpeningQuote(Scene):
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def construct(self):
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words = TextMobject([
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"Lisa:",
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"Well, where's my dad?\\\\ \\\\",
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"Frink:",
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"""Well, it should be obvious to even the most
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dimwitted individual who holds an advanced degree
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in hyperbolic topology that Homer Simpson has stumbled
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into...(dramatic pause)...""",
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"the third dimension."
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])
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words.scale_to_fit_width(2*SPACE_WIDTH - 2)
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words.to_edge(UP)
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words.split()[0].highlight(YELLOW)
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words.split()[2].highlight(YELLOW)
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three_d = words.submobjects.pop()
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three_d.highlight(BLUE)
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self.play(FadeIn(words))
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self.play(Write(three_d))
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self.dither(2)
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class QuickFootnote(TeacherStudentsScene):
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def construct(self):
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self.setup()
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self.teacher_says("Quick footnote here...")
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self.random_blink()
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self.play(
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random.choice(self.get_students()).change_mode, "happy"
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)
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self.random_blink()
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class PeakOutsideFlatland(TeacherStudentsScene):
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def construct(self):
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self.setup()
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self.teacher_says("Peak outside flatland")
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self.dither()
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student = self.get_students()[0]
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self.student_thinks(student_index = 0)
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student.bubble.make_green_screen()
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self.dither()
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class SymbolicThreeDTransform(Scene):
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CONFIG = {
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"input_coords" : [2, 6, -1],
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"output_coords" : [3, 2, 0],
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"title" : "Three-dimensional transformation",
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}
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def construct(self):
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in_vect = Matrix(self.input_coords)
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out_vect = Matrix(self.output_coords)
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in_vect.highlight(BLUE)
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out_vect.highlight(GREEN)
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func = TexMobject("L(\\vec{\\textbf{v}})")
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point = VectorizedPoint(func.get_center())
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in_vect.next_to(func, LEFT, buff = 1)
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out_vect.next_to(func, RIGHT, buff = 1)
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in_words = TextMobject("Input")
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in_words.next_to(in_vect, DOWN)
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in_words.highlight(BLUE_C)
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out_words = TextMobject("Output")
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out_words.next_to(out_vect, DOWN)
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out_words.highlight(GREEN_C)
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title = TextMobject(self.title)
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title.to_edge(UP)
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self.add(title)
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self.play(Write(func))
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self.play(Write(in_vect), Write(in_words))
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self.dither()
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self.add(in_vect.copy())
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self.play(Transform(in_vect, point, submobject_mode = "lagged_start"))
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self.play(Transform(in_vect, out_vect, submobject_mode = "lagged_start"))
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self.add(out_words)
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self.dither()
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class ThreeDLinearTransformExample(Scene):
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pass
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class SingleVectorToOutput(Scene):
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pass
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class InputWordOutputWord(Scene):
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def construct(self):
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self.add(TextMobject("Input").scale(2))
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self.dither()
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self.clear()
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self.add(TextMobject("Output").scale(2))
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self.dither()
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class TransformOnlyBasisVectors(Scene):
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pass
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class IHatJHatKHatWritten(Scene):
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def construct(self):
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for char, color in zip(["\\imath", "\\jmath", "k"], [X_COLOR, Y_COLOR, Z_COLOR]):
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sym = TexMobject("{\\hat{%s}}"%char)
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sym.scale(3)
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sym.highlight(color)
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self.play(Write(sym))
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self.dither()
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self.clear()
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class PutTogether3x3Matrix(Scene):
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CONFIG = {
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"col1" : [1, 0, -1],
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"col2" : [1, 1, 0],
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"col3" : [1, 0, 1],
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}
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def construct(self):
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i_to = TexMobject("\\hat{\\imath} \\to").highlight(X_COLOR)
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j_to = TexMobject("\\hat{\\jmath} \\to").highlight(Y_COLOR)
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k_to = TexMobject("\\hat{k} \\to").highlight(Z_COLOR)
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i_array = Matrix(self.col1)
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j_array = Matrix(self.col2)
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k_array = Matrix(self.col3)
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everything = VMobject(
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i_to, i_array, TexMobject("=").highlight(BLACK),
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j_to, j_array, TexMobject("=").highlight(BLACK),
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k_to, k_array, TexMobject("=").highlight(BLACK),
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)
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everything.arrange_submobjects(RIGHT, buff = 0.1)
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everything.scale_to_fit_width(2*SPACE_WIDTH-1)
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everything.to_edge(DOWN)
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i_array.highlight(X_COLOR)
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j_array.highlight(Y_COLOR)
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k_array.highlight(Z_COLOR)
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arrays = [i_array, j_array, k_array]
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matrix = Matrix(reduce(
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lambda a1, a2 : np.append(a1, a2, axis = 1),
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[m.copy().get_mob_matrix() for m in arrays]
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))
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matrix.to_edge(DOWN)
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start_entries = reduce(op.add, map(
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lambda a : a.get_entries().split(),
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arrays
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))
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target_entries = matrix.get_mob_matrix().transpose().flatten()
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start_l_bracket = i_array.get_brackets().split()[0]
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start_r_bracket = k_array.get_brackets().split()[1]
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start_brackets = VMobject(start_l_bracket, start_r_bracket)
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target_bracketes = matrix.get_brackets()
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for mob in everything.split():
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self.play(Write(mob, run_time = 1))
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self.dither()
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self.play(
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FadeOut(everything),
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Transform(VMobject(*start_entries), VMobject(*target_entries)),
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Transform(start_brackets, target_bracketes)
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)
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self.dither()
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class RotateSpaceAboutYAxis(Scene):
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pass
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class RotateOnlyBasisVectorsAboutYAxis(Scene):
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pass
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class PutTogetherRotationMatrix(PutTogether3x3Matrix):
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CONFIG = {
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"col1" : [0, 0, -1],
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"col2" : [0, 1, 0],
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"col3" : [1, 0, 0]
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}
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class ScaleAndAddBeforeTransformation(Scene):
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pass
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class ShowVCoordinateMeaning(Scene):
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CONFIG = {
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"v_str" : "\\vec{\\textbf{v}}",
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"i_str" : "\\hat{\\imath}",
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"j_str" : "\\hat{\\jmath}",
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"k_str" : "\\hat{k}",
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"post_transform" : False,
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}
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def construct(self):
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v = TexMobject(self.v_str)
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v.highlight(YELLOW)
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eq = TexMobject("=")
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coords = Matrix(["x", "y", "z"])
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eq2 = eq.copy()
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if self.post_transform:
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L, l_paren, r_paren = map(TexMobject, "L()")
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parens = VMobject(l_paren, r_paren)
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parens.scale(2)
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parens.stretch_to_fit_height(
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coords.get_height()
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)
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VMobject(L, l_paren, coords, r_paren).arrange_submobjects(buff = 0.1)
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coords.submobjects = [L, l_paren] + coords.submobjects + [r_paren]
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lin_comb = VMobject(*map(TexMobject, [
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"x", self.i_str, "+",
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"y", self.j_str, "+",
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"z", self.k_str,
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]))
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lin_comb.arrange_submobjects(
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RIGHT, buff = 0.1,
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aligned_edge = ORIGIN if self.post_transform else DOWN
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)
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lin_comb_parts = np.array(lin_comb.split())
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new_x, new_y, new_z = lin_comb_parts[[0, 3, 6]]
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i, j, k = lin_comb_parts[[1, 4, 7]]
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plusses = lin_comb_parts[[2, 5]]
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i.highlight(X_COLOR)
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j.highlight(Y_COLOR)
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k.highlight(Z_COLOR)
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everything = VMobject(v, eq, coords, eq2, lin_comb)
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everything.arrange_submobjects(buff = 0.2)
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everything.scale_to_fit_width(2*SPACE_WIDTH - 1)
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everything.to_edge(DOWN)
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if not self.post_transform:
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lin_comb.shift(0.35*UP)
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self.play(*map(Write, [v, eq, coords]))
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self.dither()
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self.play(
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Transform(
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coords.get_entries().copy(),
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VMobject(new_x, new_y, new_z),
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path_arc = -np.pi,
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submobject_mode = "lagged_start"
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),
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Write(VMobject(*[eq2, i, j, k] + list(plusses))),
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run_time = 3
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)
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self.dither()
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class ScaleAndAddAfterTransformation(Scene):
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pass
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class ShowVCoordinateMeaningAfterTransform(ShowVCoordinateMeaning):
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CONFIG = {
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"v_str" : "L(\\vec{\\textbf{v}})",
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"i_str" : "L(\\hat{\\imath})",
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"j_str" : "L(\\hat{\\jmath})",
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"k_str" : "L(\\hat{k})",
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"post_transform" : True,
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}
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class ShowMatrixVectorMultiplication(Scene):
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def construct(self):
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matrix = Matrix(np.arange(9).reshape((3, 3)))
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vect = Matrix(list("xyz"))
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vect.scale_to_fit_height(matrix.get_height())
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col1, col2, col3 = columns = [
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Matrix(col)
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for col in matrix.copy().get_mob_matrix().transpose()
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]
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coords = x, y, z = [m.copy() for m in vect.get_entries().split()]
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eq, plus1, plus2 = map(TexMobject, list("=++"))
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everything = VMobject(
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matrix, vect, eq,
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x, col1, plus1,
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y, col2, plus2,
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z, col3
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)
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||||
everything.arrange_submobjects(buff = 0.1)
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||||
everything.scale_to_fit_width(2*SPACE_WIDTH-1)
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result = VMobject(x, col1, plus1, y, col2, plus2, z, col3)
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||||
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||||
trips = [
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(matrix, DOWN, "Transformation"),
|
||||
(vect, UP, "Input vector"),
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(result, DOWN, "Output vector"),
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]
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||||
braces = []
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||||
for mob, direction, text in trips:
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||||
brace = Brace(mob, direction)
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||||
words = TextMobject(text)
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||||
words.next_to(brace, direction)
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||||
brace.add(words)
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||||
braces.append(brace)
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||||
matrix_brace, vect_brace, result_brace = braces
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||||
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||||
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||||
self.play(*map(Write, [matrix, vect]), run_time = 2)
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||||
self.play(Write(matrix_brace, run_time = 1))
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||||
self.play(Write(vect_brace, run_time = 1))
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||||
sexts = zip(
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matrix.get_mob_matrix().transpose(),
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||||
columns,
|
||||
vect.get_entries().split(),
|
||||
coords,
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||||
[eq, plus1, plus2],
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||||
[X_COLOR, Y_COLOR, Z_COLOR]
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||||
)
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||||
for o_col, col, start_coord, coord, sym, color in sexts:
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||||
o_col = VMobject(*o_col)
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||||
self.play(
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||||
start_coord.highlight, YELLOW,
|
||||
o_col.highlight, color
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||||
)
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||||
coord.highlight(YELLOW)
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||||
col.highlight(color)
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||||
self.play(
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||||
Write(col.get_brackets()),
|
||||
Transform(
|
||||
o_col.copy(), col.get_entries(),
|
||||
path_arc = -np.pi
|
||||
),
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||||
Transform(
|
||||
start_coord.copy(), coord,
|
||||
path_arc = -np.pi
|
||||
),
|
||||
Write(sym)
|
||||
)
|
||||
self.dither()
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||||
self.play(Write(result_brace, run_time = 1))
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||||
self.dither()
|
||||
|
||||
class ShowMatrixMultiplication(Scene):
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||||
def construct(self):
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||||
right = Matrix(np.arange(9).reshape((3, 3)))
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||||
left = Matrix(np.random.random_integers(-5, 5, (3, 3)))
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||||
VMobject(left, right).arrange_submobjects(buff = 0.1)
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||||
right.highlight_columns(X_COLOR, Y_COLOR, Z_COLOR)
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||||
left.highlight(PINK)
|
||||
|
||||
trips = [
|
||||
(right, DOWN, "First transformation"),
|
||||
(left, UP, "Second transformation"),
|
||||
]
|
||||
braces = []
|
||||
for mob, direction, text in trips:
|
||||
brace = Brace(mob, direction)
|
||||
words = TextMobject(text)
|
||||
words.next_to(brace, direction)
|
||||
brace.add(words)
|
||||
braces.append(brace)
|
||||
right_brace, left_brace = braces
|
||||
|
||||
VMobject(*self.get_mobjects()).scale_to_fit_width(2*SPACE_WIDTH-1)
|
||||
|
||||
self.add(right, left)
|
||||
self.play(Write(right_brace))
|
||||
self.play(Write(left_brace))
|
||||
self.dither()
|
||||
|
||||
class ApplyTwoSuccessiveTransforms(Scene):
|
||||
pass
|
||||
|
||||
class ThreeDRotation(Scene):
|
||||
pass
|
||||
|
||||
class ThreeDRotationBrokenUp(Scene):
|
||||
pass
|
||||
|
||||
class SymbolicTwoDToThreeDTransform(SymbolicThreeDTransform):
|
||||
CONFIG = {
|
||||
"input_coords" : [2, 6],
|
||||
"output_coords" : [3, 2, 0],
|
||||
"title" : "Two dimensions to three dimensions",
|
||||
}
|
||||
|
||||
class SymbolicThreeDToTwoDTransform(SymbolicThreeDTransform):
|
||||
CONFIG = {
|
||||
"input_coords" : [4, -3, 1],
|
||||
"output_coords" : [8, 4],
|
||||
"title" : "Three dimensions to two dimensions",
|
||||
}
|
||||
|
||||
class QuestionsToPonder(Scene):
|
||||
def construct(self):
|
||||
title = TextMobject("Questions to ponder")
|
||||
title.highlight(YELLOW).to_edge(UP)
|
||||
self.add(title)
|
||||
questions = map(TextMobject, [
|
||||
"Can you visualize these transformations?",
|
||||
"Can you represent them with matrices?",
|
||||
"How many rows and columns?",
|
||||
"When does it make sense to multiply these matrices?",
|
||||
])
|
||||
nums = VMobject(*[
|
||||
TexMobject("%d."%(num+1))
|
||||
for num in range(len(questions))
|
||||
])
|
||||
nums.arrange_submobjects(DOWN, buff = 1, aligned_edge = LEFT)
|
||||
nums.to_edge(LEFT)
|
||||
for num, question in zip(nums.split(), questions):
|
||||
question.scale(0.8)
|
||||
question.next_to(num)
|
||||
self.play(Write(num), FadeIn(question))
|
||||
self.dither()
|
||||
|
||||
class NextVideo(Scene):
|
||||
def construct(self):
|
||||
title = TextMobject("""
|
||||
Next video: The determinant
|
||||
""")
|
||||
title.scale_to_fit_width(2*SPACE_WIDTH - 2)
|
||||
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()
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
@ -145,7 +145,6 @@ class NumericalMatrixMultiplication(Scene):
|
||||
)
|
||||
|
||||
self.organize_matrices(left, right, result)
|
||||
# self.add_lines(left, right)
|
||||
self.animate_product(left, right, result)
|
||||
|
||||
|
||||
|
||||
@ -207,9 +207,9 @@ class Bubble(SVGMobject):
|
||||
self.direction = -np.array(self.direction)
|
||||
return self
|
||||
|
||||
def pin_to(self, mobject):
|
||||
def pin_to(self, mobject, allow_flipping = True):
|
||||
mob_center = mobject.get_center()
|
||||
if (mob_center[0] > 0) != (self.direction[0] > 0):
|
||||
if np.sign(mob_center[0]) != np.sign(self.direction[0]) and allow_flipping:
|
||||
self.flip()
|
||||
boundary_point = mobject.get_critical_point(UP-self.direction)
|
||||
vector_from_center = 1.0*(boundary_point-mob_center)
|
||||
@ -338,21 +338,21 @@ class TeacherStudentsScene(Scene):
|
||||
self.play(*anims)
|
||||
return pi_creature.bubble
|
||||
|
||||
def teacher_says(self, content, **kwargs):
|
||||
def teacher_says(self, content = "", **kwargs):
|
||||
return self.introduce_bubble(
|
||||
content, "speech", self.get_teacher(), **kwargs
|
||||
)
|
||||
|
||||
def student_says(self, content, student_index = 1, **kwargs):
|
||||
def student_says(self, content = "", student_index = 1, **kwargs):
|
||||
student = self.get_students()[student_index]
|
||||
return self.introduce_bubble(content, "speech", student, **kwargs)
|
||||
|
||||
def teacher_thinks(self, content, **kwargs):
|
||||
def teacher_thinks(self, content = "", **kwargs):
|
||||
return self.introduce_bubble(
|
||||
content, "thought", self.get_teacher(), **kwargs
|
||||
)
|
||||
|
||||
def student_thinks(self, content, student_index = 1, **kwargs):
|
||||
def student_thinks(self, content = "", student_index = 1, **kwargs):
|
||||
student = self.get_students()[student_index]
|
||||
return self.introduce_bubble(content, "thought", student, **kwargs)
|
||||
|
||||
|
||||
Reference in New Issue
Block a user