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Quaternion animations up to Patron draft

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This commit is contained in:
Grant Sanderson 2018-09-02 21:56:10 -07:00
parent 6c590b6de4
commit e967e472f3
1 changed files with 266 additions and 26 deletions
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292
active_projects/quaternions.py
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@ -198,14 +198,15 @@ class PushPin(SVGMobject):
class Hand(SVGMobject):
CONFIG = {
"file_name": "pinch_hand",
"height": 0.4,
"height": 0.5,
"sheen": 0.2,
"fill_color": GREY,
"fill_color": ORANGE,
}
def __init__(self, **kwargs):
SVGMobject.__init__(self, **kwargs)
self.add(VectorizedPoint().next_to(self, UP, buff=0.15))
# self.rotate(30 * DEGREES)
self.add(VectorizedPoint().next_to(self, UP, buff=0.17))
class CheckeredCircle(Circle):
@ -493,14 +494,15 @@ class SpecialThreeDScene(ThreeDScene):
# Animated scenes
class ManyNumberSystems(Scene):
def construct(self):
# Too much dumb manually positioning in here...
title = Title("Number systems")
name_location_color_example_tuples = [
("Reals", [-4, 2, 0], YELLOW, "1.414"),
("Complex numbers", [5, 0, 0], BLUE, "2 + i"),
("Quaternions", [3, 2, 0], PINK, "2 + 7i + 1j + 8k"),
("Complex numbers", [4, 0, 0], BLUE, "2 + i"),
("Quaternions", [0, 2, 0], PINK, "2 + 7i + 1j + 8k"),
("Rationals", [3, -2, 0], RED, "1 \\over 3"),
("p-adic numbers", [-2, -2, 0], GREEN, "\\overline{142857}2"),
("Octonions", [-3, 0, 0], LIGHT_GREY, "3e_1 - 2.3e_2 + \\dots + 1.6e_8"),
@ -528,8 +530,9 @@ class ManyNumberSystems(Scene):
C_example_dot = Dot(plane.coords_to_point(2, 1))
self.add(title)
self.play(FadeInFromLarge(H_label))
self.play(LaggedStart(
FadeInFromLarge, systems,
FadeInFromLarge, VGroup(*it.chain(systems[:2], systems[3:])),
lambda m: (m, 4)
))
self.wait()
@ -560,8 +563,9 @@ class ManyNumberSystems(Scene):
lambda m: (m.shift, 0.5 * FRAME_WIDTH * LEFT),
lag_ratio=0.8,
))
randy = Randolph()
randy = Randolph(height=1.5)
randy.next_to(plane, RIGHT)
randy.to_edge(DOWN)
self.play(
randy.change, "maybe", H_label,
VFadeIn(randy),
@ -606,10 +610,6 @@ class RotationsIn3d(SpecialThreeDScene):
self.wait()
class TODOInsertIntroduceThreeDNumbers(TODOStub):
CONFIG = {"message": "Insert IntroduceThreeDNumbers"}
class IntroduceHamilton(Scene):
def construct(self):
hamilton = ImageMobject("Hamilton", height=6)
@ -709,6 +709,41 @@ class IntroduceHamilton(Scene):
self.wait()
class QuaternionHistory(Scene):
def construct(self):
self.show_dot_product_and_cross_product() # With date
self.teaching_students_quaternions()
self.show_anti_quaternion_quote()
self.mad_hatter()
self.vestiges_in_modern_notation()
def show_dot_product_and_cross_product(self):
date = TexMobject("1843")
date.to_edge(UP)
v1, v2 = [
Matrix([
["{}_{}".format(c, i)]
for c in "xyz"
])
for i in (1, 2)
]
def teaching_students_quaternions(self):
pass
def show_anti_quaternion_quote(self):
pass
def mad_hatter(self):
pass
def vestiges_in_modern_notation(self):
pass
class QuaternionRotationOverlay(Scene):
def construct(self):
equations = VGroup(
@ -833,6 +868,8 @@ class HereWeTackle4d(TeacherStudentsScene):
self.play(self.teacher.change, "happy")
self.look_at(self.screen)
self.wait(3)
self.change_student_modes("pondering", "happy", "thinking")
self.wait(4)
class TableOfContents(Scene):
@ -1428,7 +1465,13 @@ class TextbookQuaternionDefinition(TeacherStudentsScene):
self.look_at(equation.get_corner(UL))
self.blink()
self.look_at(equation.get_corner(UR))
self.play(self.teacher.change, "sassy", equation)
self.wait(2)
self.change_all_student_modes("pondering")
self.look_at(equation)
self.wait()
self.play(self.teacher.change, "thinking", equation)
self.wait(8)
class ProblemsWhereComplexNumbersArise(Scene):
@ -1938,9 +1981,12 @@ class OneDegreeOfFreedomForRotation(Scene):
arc.add_updater(lambda m: m.become(get_arc()))
self.add(circle, r_line, angle_label, arc)
angles = np.random.uniform(-TAU, TAU, 10)
angles = IntroduceStereographicProjection.CONFIG.get(
"example_angles"
)
for angle in angles:
self.play(Rotate(circle, angle, run_time=2))
self.play(Rotate(circle, angle, run_time=4))
self.wait()
class StereographicProjectionTitle(Scene):
@ -2184,7 +2230,10 @@ class IntroduceStereographicProjection(MovingCameraScene):
cross = Cross(dot)
cross.scale(2)
label = Integer(value)
label.next_to(dot, UR, SMALL_BUFF)
if value is sample_values[1]:
label.next_to(dot, UL, SMALL_BUFF)
else:
label.next_to(dot, UR, SMALL_BUFF)
self.play(
FadeInFromLarge(dot, 3),
FadeInFromDown(label)
@ -2611,6 +2660,15 @@ class ShowRotationUnderStereographicProjection(IntroduceStereographicProjection)
self.wait()
class WriteITimesW(Scene):
def construct(self):
mob = TexMobject("i", "\\cdot", "w")
mob[0].set_color(GREEN)
mob.scale(3)
self.play(Write(mob))
self.wait()
class IntroduceFelix(PiCreatureScene, SpecialThreeDScene):
def setup(self):
PiCreatureScene.setup(self)
@ -3140,9 +3198,11 @@ class TwoDStereographicProjection(IntroduceFelix):
return line
def get_sphere_dot(sphere_point):
dot = Dot(shade_in_3d=True)
dot = Dot()
dot.rotate(90 * DEGREES)
dot.set_shade_in_3d(True)
dot.set_fill(PINK)
dot.insert_n_anchor_points(12) # Helps with flashing?
dot.shift(OUT)
dot.apply_matrix(
z_to_vector(sphere_point),
about_point=ORIGIN,
@ -3309,7 +3369,7 @@ class TwoDStereographicProjection(IntroduceFelix):
for p in points
])
arrows.set_fill(RED)
arrows.set_stroke(RED, 10)
arrows.set_stroke(RED, 5)
neg_ones = VGroup(*[
TexMobject("-1").next_to(arrow.get_start(), -p)
for p, arrow in zip(points, arrows)
@ -3372,7 +3432,7 @@ class TwoDStereographicProjection(IntroduceFelix):
**self.sphere_config,
)
result.set_fill(opacity=0.2)
result.fade_far_out_submobjects(32)
result.fade_far_out_submobjects(max_r=32)
for submob in result:
if submob.get_center()[1] < -11:
submob.fade(1)
@ -4734,7 +4794,7 @@ class RuleOfQuaternionMultiplicationOverlay(Scene):
}
}
i_products = VGroup(
TexMobject("i", "\\cdot", "1", "=", "1", **kwargs),
TexMobject("i", "\\cdot", "1", "=", "i", **kwargs),
TexMobject("i", "\\cdot", "i", "=", "-1", **kwargs),
TexMobject("i", "\\cdot", "j", "=", "k", **kwargs),
TexMobject("i", "\\cdot", "k", "=", "-j", **kwargs),
@ -4993,13 +5053,13 @@ class ShowDistributionOfI(TeacherStudentsScene):
}
top_product = TexMobject(
"q", "\\cdot", "\\left(",
"w", "+", "x", "i", "+", "y", "j", "+", "z", "k",
"w", "1", "+", "x", "i", "+", "y", "j", "+", "z", "k",
"\\right)"
)
top_product.to_edge(UP)
self.add(top_product)
bottom_product = TexMobject(
"q", "w",
"w", "q", "\\cdot", "1",
"+", "x", "q", "\\cdot", "i",
"+", "y", "q", "\\cdot", "j",
"+", "z", "q", "\\cdot", "k",
@ -5028,7 +5088,7 @@ class ShowDistributionOfI(TeacherStudentsScene):
bottom_product.get_parts_by_tex(tex, substring=False),
run_time=2
)
for tex in ["w", "x", "i", "y", "j", "z", "k", "+"]
for tex in ["1", "w", "x", "i", "y", "j", "z", "k", "+"]
]
)
self.play(*[
@ -5043,6 +5103,39 @@ class ShowDistributionOfI(TeacherStudentsScene):
self.wait(3)
class ComplexPlane135(Scene):
def construct(self):
plane = ComplexPlane(unit_size=2)
plane.add_coordinates()
for mob in plane.coordinate_labels:
mob.scale(2, about_edge=UR)
angle = 3 * TAU / 8
circle = Circle(radius=2, color=YELLOW)
arc = Arc(angle, radius=0.5)
angle_label = Integer(0, unit="^\\circ")
angle_label.next_to(arc.point_from_proportion(0.5), UR, SMALL_BUFF)
line = Line(ORIGIN, 2 * RIGHT)
point = circle.point_from_proportion(angle / TAU)
dot = Dot(point, color=PINK)
arrow = Vector(DR)
arrow.next_to(dot, UL, SMALL_BUFF)
arrow.match_color(dot)
label = TexMobject("-\\frac{\\sqrt{2}}{2} + \\frac{\\sqrt{2}}{2} i")
label.next_to(arrow.get_start(), UP, SMALL_BUFF)
label.set_background_stroke(width=0)
self.add(plane, circle, line, dot, label, arrow)
self.play(
Rotate(line, angle, about_point=ORIGIN),
ShowCreation(arc),
ChangeDecimalToValue(angle_label, 135),
run_time=3
)
self.wait()
class ShowMultiplicationBy135Example(RuleOfQuaternionMultiplication):
CONFIG = {
"fancy_dot": True,
@ -5176,7 +5269,7 @@ class JMultiplicationChart(Scene):
}
}
j_products = VGroup(
TexMobject("j", "\\cdot", "1", "=", "1", **kwargs),
TexMobject("j", "\\cdot", "1", "=", "j", **kwargs),
TexMobject("j", "\\cdot", "j", "=", "-1", **kwargs),
TexMobject("j", "\\cdot", "i", "=", "-k", **kwargs),
TexMobject("j", "\\cdot", "k", "=", "i", **kwargs),
@ -5240,7 +5333,7 @@ class ShowJMultiplication(ShowMultiplicationBy135Example):
)
def show_multiplication(self):
self.set_camera_orientation(theta=-30 * DEGREES)
self.set_camera_orientation(theta=-80 * DEGREES)
q_tracker = self.q_tracker
m_tracker = self.multiplier_tracker
@ -5270,7 +5363,9 @@ class ShowJMultiplication(ShowMultiplicationBy135Example):
self.wait(2)
# Show ik circle
self.move_camera(theta=-110 * DEGREES)
circle = self.circle_ik.deepcopy()
circle.clear_updaters()
self.play(FadeInFromLarge(circle, remover=True))
m_tracker.set_value([1, 0, 0, 0])
q_tracker.set_value([0, 1, 0, 0])
self.wait()
@ -5342,7 +5437,7 @@ class ShowArbitraryMultiplication(ShowMultiplicationBy135Example):
circle1, circle2 = self.circle1, self.circle2
for circle in [circle1, circle2]:
circle.tucked_away_updaters = circle1.updaters
circle.tucked_away_updaters = circle.updaters
circle.clear_updaters()
self.remove(circle)
@ -5518,3 +5613,148 @@ class RotationsOfCube(SpecialThreeDScene):
FadeInFrom(label2[1], IN),
)
self.wait(5)
class QuaternionEndscreen(PatreonEndScreen):
CONFIG = {
"specific_patrons": [
"Juan Benet",
"Matt Russell",
"soekul",
"Desmos",
"Burt Humburg",
"Dinesh Dharme",
"Scott Walter",
"Brice Gower",
"Peter Mcinerney",
"brian tiger chow",
"Joseph Kelly",
"Roy Larson",
"Andrew Sachs",
"Hoàng Tùng Lâm",
"Devin Scott",
"Akash Kumar",
"Arthur Zey",
"David Kedmey",
"Ali Yahya",
"Mayank M. Mehrotra",
"Lukas Biewald",
"Yana Chernobilsky",
"Kaustuv DeBiswas",
"Yu Jun",
"dave nicponski",
"Jordan Scales",
"Markus Persson",
"Lukáš Nový",
"Fela",
"Randy C. Will",
"Britt Selvitelle",
"Jonathan Wilson",
"Ryan Atallah",
"Joseph John Cox",
"Luc Ritchie",
"Ryan Williams",
"Michael Hardel",
"Federico Lebron",
"L0j1k",
"Ayan Doss",
"Dylan Houlihan",
"Steven Soloway",
"Art Ianuzzi",
"Nate Heckmann",
"Michael Faust",
"Richard Comish",
"Nero Li",
"Valeriy Skobelev",
"Adrian Robinson",
"Solara570",
"Peter Ehrnstrom",
"Kai Siang Ang",
"Alexis Olson",
"Ludwig Schubert",
"Omar Zrien",
"Sindre Reino Trosterud",
"Jeff Straathof",
"Matt Langford",
"Matt Roveto",
"Magister Mugit",
"Stevie Metke",
"Cooper Jones",
"James Hughes",
"John V Wertheim",
"Song Gao",
"Richard Burgmann",
"John Griffith",
"Chris Connett",
"Steven Tomlinson",
"Jameel Syed",
"Bong Choung",
"Zhilong Yang",
"Giovanni Filippi",
"Eric Younge",
"Prasant Jagannath",
"Cody Brocious",
"James H. Park",
"Norton Wang",
"Kevin Le",
"Oliver Steele",
"Yaw Etse",
"Dave B",
"Delton Ding",
"Thomas Tarler",
"1st",
"Jacob Magnuson",
"Clark Gaebel",
"Mathias Jansson",
"David Clark",
"Michael Gardner",
"Mads Elvheim",
"Awoo",
"Dr David G. Stork",
"Ted Suzman",
"Linh Tran",
"Andrew Busey",
"John Haley",
"Ankalagon",
"Eric Lavault",
"Boris Veselinovich",
"Julian Pulgarin",
"Jeff Linse",
"Robert Teed",
"Jason Hise",
"Bernd Sing",
"James Thornton",
"Mustafa Mahdi",
"Mathew Bramson",
"Jerry Ling",
"Rish Kundalia",
"Achille Brighton",
"Ripta Pasay",
],
}
class Thumbnail(RuleOfQuaternionMultiplication):
CONFIG = {
"three_d_axes_config": {
"num_axis_pieces": 20,
}
}
def construct(self):
self.setup_all_trackers()
quat = normalize([-0.5, 0.5, -0.5, 0.5])
self.multiplier_tracker.set_value(quat)
self.q_tracker.set_value(quat)
sphere = self.get_projected_sphere(0, solid=False)
# self.specially_color_sphere(sphere)
# sphere.set_fill(opacity=0.5)
sphere.set_fill_by_checkerboard(BLUE_E, BLUE, opacity=0.8)
for face in sphere:
face.points = face.points[::-1]
self.set_camera_orientation(
phi=70 * DEGREES,
theta=-110 * DEGREES,
)
self.add(sphere)