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introduction.py
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import numpy as np
from manim import MovingCameraScene, WHITE, GREEN_B, PURPLE, DARK_GREY, GREY, ORANGE, YELLOW, Circle, Dot, \
FadeIn, Write, Create, RED, BLUE, MathTex, LEFT, ReplacementTransform, DOWN, Group, \
FadeOut, Transform, ImageMobject, Line, RIGHT, Arrow, VGroup, \
VMobject, DecimalNumber, ArcBetweenPoints, GREY_B, BLUE_A, BLUE_E, MoveAlongPath, Rectangle
from animation_constants import OUTER_CIRCLE_STROKE_WIDTH, HEXAGON_STROKE_WIDTH
from euclidean_hexagon import EuclideanHexagon, get_diagonals
from geometry_util import get_intersection_from_angles, get_intersection_in_unit_circle_of_two_tangent_circles, \
polar_to_point, hyperbolic_distance_function, moving_line, moving_circle, hyperbolic_circle_to_euclidean_circle
from hexagon import HexagonAngles, HexagonCircles, HexagonMainDiagonals
from hexagon_util import create_radius_transition
from hyperbolic_polygon import HyperbolicPolygon, HyperbolicArcBetweenPoints
class Rectangles(MovingCameraScene):
def construct(self):
static = False
scaling = .25
rectangle1 = Rectangle(height=9 * scaling, width=16 * scaling).move_to([-4.5, 2, 0])
rectangle2 = Rectangle(height=9 * scaling, width=16 * scaling).move_to([0, 2, 0])
rectangle3 = Rectangle(height=9 * scaling, width=16 * scaling).move_to([4.5, 2, 0])
rectangle4 = Rectangle(height=9 * scaling, width=16 * scaling).move_to([-4.5, -2, 0])
rectangle5 = Rectangle(height=9 * scaling, width=16 * scaling).move_to([0, -2, 0])
rectangle6 = Rectangle(height=9 * scaling, width=16 * scaling).move_to([4.5, -2, 0])
if not static:
self.wait(2)
self.play(Write(rectangle1))
self.wait(2)
self.play(Write(rectangle2))
self.wait(2)
self.play(Write(rectangle3))
self.wait(2)
self.play(Write(rectangle4))
self.wait(2)
self.play(Write(rectangle5))
self.wait(2)
self.play(Write(rectangle6))
self.wait(2)
else:
self.add(rectangle1, rectangle2, rectangle3, rectangle4, rectangle5, rectangle6)
class Scene1(MovingCameraScene):
def construct(self):
self.camera.frame.scale(.3)
OUTER_CIRCLE_COLOR = WHITE
INNER_CIRCLE_COLOR = GREEN_B
INNER_INTERSECTION_COLOR = PURPLE
OUTER_INTERSECTION_COLOR = DARK_GREY
HEXAGON_COLOR = GREY
DIAGONAL_COLOR = ORANGE
DIAGONAL_INTERSECTION_COLOR = YELLOW
circle = Circle(color=OUTER_CIRCLE_COLOR, stroke_width=2)
# keyframe hexagons
phis1 = HexagonAngles(np.array([.3, 1.6, 2.2, 3, 4.3]))
phis2 = HexagonAngles(np.array([.3, 1.2, 2.7, 3.6, 4.2]))
phis3 = HexagonAngles(np.array([.7, 1.4, 2.3, 3.0, 4.1]))
first_circle_radius = 0.4
self.add(circle)
self.add_foreground_mobject(circle)
frame_rate = 60
frame_time = 1 / 60
run_time = 4
frames = run_time * frame_rate
i = 0
phis = np.array([phis1[j] + ((i * (phis2[j] - phis1[j])) / frames) for j in range(5)])
hexagon = EuclideanHexagon(HexagonAngles(np.array(phis)), color=HEXAGON_COLOR, stroke_width=2)
hex_circles = HexagonCircles(hexagon, first_circle_radius, stroke_width=2, color=INNER_CIRCLE_COLOR)
diagonals = get_diagonals(hexagon, color=DIAGONAL_COLOR, stroke_width=2)
diagonal_intersection = Dot(get_intersection_from_angles(phis[0], phis[3], phis[1], phis[4]),
color=DIAGONAL_INTERSECTION_COLOR, radius=.05)
self.add(*hex_circles.circles, *diagonals, diagonal_intersection)
for i in range(1, frames):
prev_hex_circles = hex_circles
prev_diagonals = diagonals
prev_diagonal_intersection = diagonal_intersection
phis = np.array([phis1[j] + ((i * (phis2[j] - phis1[j])) / frames) for j in range(5)])
hexagon = EuclideanHexagon(HexagonAngles(np.array(phis)), color=HEXAGON_COLOR, stroke_width=2)
hex_circles = HexagonCircles(hexagon, first_circle_radius, stroke_width=2, color=INNER_CIRCLE_COLOR)
diagonals = get_diagonals(hexagon, color=DIAGONAL_COLOR, stroke_width=2)
diagonal_intersection = Dot(get_intersection_from_angles(phis[0], phis[3], phis[1], phis[4]),
color=DIAGONAL_INTERSECTION_COLOR, radius=.05)
self.play(Transform(prev_hex_circles[0], hex_circles[0]),
Transform(prev_hex_circles[1], hex_circles[1]),
Transform(prev_hex_circles[2], hex_circles[2]),
Transform(prev_hex_circles[3], hex_circles[3]),
Transform(prev_hex_circles[4], hex_circles[4]),
Transform(prev_hex_circles[5], hex_circles[5]),
Transform(prev_diagonals[0], diagonals[0]),
Transform(prev_diagonals[1], diagonals[1]),
Transform(prev_diagonals[2], diagonals[2]),
Transform(prev_diagonal_intersection, diagonal_intersection),
run_time=frame_time
)
self.remove(*prev_hex_circles, *prev_diagonals, prev_diagonal_intersection)
for i in range(frames):
prev_hex_circles = hex_circles
prev_diagonals = diagonals
prev_diagonal_intersection = diagonal_intersection
phis = np.array([phis2[j] + ((i * (phis3[j] - phis2[j])) / frames) for j in range(5)])
hexagon = EuclideanHexagon(HexagonAngles(np.array(phis)), color=HEXAGON_COLOR, stroke_width=2)
hex_circles = HexagonCircles(hexagon, first_circle_radius, stroke_width=2, color=INNER_CIRCLE_COLOR)
diagonals = get_diagonals(hexagon, color=DIAGONAL_COLOR, stroke_width=2)
diagonal_intersection = Dot(get_intersection_from_angles(phis[0], phis[3], phis[1], phis[4]),
color=DIAGONAL_INTERSECTION_COLOR, radius=.05)
self.play(Transform(prev_hex_circles[0], hex_circles[0]),
Transform(prev_hex_circles[1], hex_circles[1]),
Transform(prev_hex_circles[2], hex_circles[2]),
Transform(prev_hex_circles[3], hex_circles[3]),
Transform(prev_hex_circles[4], hex_circles[4]),
Transform(prev_hex_circles[5], hex_circles[5]),
Transform(prev_diagonals[0], diagonals[0]),
Transform(prev_diagonals[1], diagonals[1]),
Transform(prev_diagonals[2], diagonals[2]),
Transform(prev_diagonal_intersection, diagonal_intersection),
run_time=frame_time
)
self.remove(*prev_hex_circles, *prev_diagonals, prev_diagonal_intersection)
for i in range(frames):
prev_hex_circles = hex_circles
prev_diagonals = diagonals
prev_diagonal_intersection = diagonal_intersection
phis = np.array([phis3[j] + ((i * (phis1[j] - phis3[j])) / frames) for j in range(5)])
hexagon = EuclideanHexagon(HexagonAngles(np.array(phis)), color=HEXAGON_COLOR, stroke_width=2)
hex_circles = HexagonCircles(hexagon, first_circle_radius, stroke_width=2, color=INNER_CIRCLE_COLOR)
diagonals = get_diagonals(hexagon, color=DIAGONAL_COLOR, stroke_width=2)
diagonal_intersection = Dot(get_intersection_from_angles(phis[0], phis[3], phis[1], phis[4]),
color=DIAGONAL_INTERSECTION_COLOR, radius=.05)
self.play(Transform(prev_hex_circles[0], hex_circles[0]),
Transform(prev_hex_circles[1], hex_circles[1]),
Transform(prev_hex_circles[2], hex_circles[2]),
Transform(prev_hex_circles[3], hex_circles[3]),
Transform(prev_hex_circles[4], hex_circles[4]),
Transform(prev_hex_circles[5], hex_circles[5]),
Transform(prev_diagonals[0], diagonals[0]),
Transform(prev_diagonals[1], diagonals[1]),
Transform(prev_diagonals[2], diagonals[2]),
Transform(prev_diagonal_intersection, diagonal_intersection),
run_time=frame_time
)
self.remove(*prev_hex_circles, *prev_diagonals, prev_diagonal_intersection)
self.add(*hex_circles, *diagonals, diagonal_intersection)
class Scene2(MovingCameraScene):
def construct(self):
self.camera.frame.width = 4.1
self.camera.frame.move_to([1, 0, 0])
outer_circle = Circle(color=WHITE, stroke_width=2)
self.add(outer_circle)
konvergenz = MathTex(r'P_n \xrightarrow{n \rightarrow \infty}P_\infty', font_size=30).move_to(
[2, 0, 0])
radius = np.array([0.7, 0.6, .75, .56, .65, .53])
phis = [0.47654, 2.065432, 2.876, 3.87623, 5.024, 5.673]
# circle_radius = np.array([.2, .25, .16, .29, .18, .12]) # radius for disks
circle_radius = np.array([.8, .8, .8, .8, .5, .4]) # radius for disks
self.add(konvergenz)
self.add_foreground_mobjects(outer_circle)
hex_n_ideal = HyperbolicPolygon.from_polar(phis, radius, dot_radius=0.01, stroke_width=2)
disks = []
euclidean_centers = []
euclidean_radii = []
for k in range(0, 6): # creating disks
hyperbolic_center = hex_n_ideal.polygon_points[k]
hyperbolic_radius = circle_radius[k]
eucl_center, eucl_radius = hyperbolic_circle_to_euclidean_circle(hyperbolic_center, hyperbolic_radius)
euclidean_centers.append(eucl_center)
euclidean_radii.append(eucl_radius)
circle = Circle(arc_center=eucl_center, radius=eucl_radius, color=GREEN_B, fill_opacity=0.5, stroke_width=2)
disks.append(circle)
self.add_foreground_mobjects(circle)
self.add(circle)
euclidean_centers = np.array(euclidean_centers)
euclidean_radii = np.array(euclidean_radii)
dynamic_arcs = []
for k in range(0, 6): # creating S_k tilde
point1 = euclidean_centers[k]
radius1 = euclidean_radii[k]
point2 = euclidean_centers[(k + 1) % 6]
radius2 = euclidean_radii[(k + 1) % 6]
arc = hex_n_ideal.arcs[k]
intersection1 = get_intersection_in_unit_circle_of_two_tangent_circles(arc.circle_center, arc.radius,
point1, radius1)
intersection2 = get_intersection_in_unit_circle_of_two_tangent_circles(point2,
radius2,
arc.circle_center, arc.radius)
arc_new = ArcBetweenPoints(intersection2, intersection1, color=ORANGE,
radius=arc.radius, stroke_width=2).reverse_direction()
dynamic_arcs.append(arc_new)
# transforming into ideal hexagon
disks_group = VGroup(disks[0], disks[1], disks[2], disks[3], disks[4], disks[5])
arc_group = VGroup(dynamic_arcs[0], dynamic_arcs[1], dynamic_arcs[2], dynamic_arcs[3], dynamic_arcs[4],
dynamic_arcs[5])
step_size = 50
new_disk_group = VGroup()
new_arc_group = VGroup()
transition = create_radius_transition(start_point=radius, step_size=step_size)
disk_transition = create_radius_transition(start_point=np.linalg.norm(euclidean_centers, axis=1),
step_size=step_size, end_point=1 - euclidean_radii)
for t in range(1, step_size):
hexagon_new = HyperbolicPolygon.from_polar(phis, transition[t], dot_radius=0.01, stroke_width=2)
for i in range(0, 6):
circle = Circle(radius=euclidean_radii[i], arc_center=polar_to_point(phis[i], disk_transition[t][i]),
color=GREEN_B, fill_opacity=.5, stroke_width=2)
new_disk_group.add(circle)
# transforming orange s_k
moving_arc = HyperbolicArcBetweenPoints(polar_to_point(phis[i], transition[t][i]),
polar_to_point(phis[(i + 1) % 6],
transition[t][(i + 1) % 6]))
moving_intersection1 = get_intersection_in_unit_circle_of_two_tangent_circles(
moving_arc.circle_center, moving_arc.radius,
polar_to_point(phis[i], disk_transition[t][i]),
euclidean_radii[i])
intersection1 = get_intersection_in_unit_circle_of_two_tangent_circles(
polar_to_point(phis[(i + 1) % 6], disk_transition[t][(i + 1) % 6]),
euclidean_radii[(i + 1) % 6], moving_arc.circle_center, moving_arc.radius)
arc_new = ArcBetweenPoints(intersection1, moving_intersection1, color=ORANGE,
radius=moving_arc.radius, stroke_width=2).reverse_direction()
new_arc_group.add(arc_new)
self.play(Transform(hex_n_ideal, hexagon_new), Transform(disks_group, new_disk_group),
Transform(arc_group, new_arc_group), run_time=.05, rate_func=lambda a: a)
new_disk_group = VGroup() # nochmal leeren
new_arc_group = VGroup()
self.wait(2)
class Scene3(MovingCameraScene):
def construct(self):
self.camera.frame.width = 4
OUTER_CIRCLE_COLOR = WHITE
INNER_CIRCLE_COLOR = GREEN_B
INNER_INTERSECTION_COLOR = PURPLE
OUTER_INTERSECTION_COLOR = DARK_GREY
HEXAGON_COLOR = GREY
DIAGONAL_COLOR = ORANGE
DIAGONAL_INTERSECTION_COLOR = YELLOW
circle = Circle(color=OUTER_CIRCLE_COLOR, stroke_width=OUTER_CIRCLE_STROKE_WIDTH)
phis = HexagonAngles(np.array([.3, 1.6, 2.2, 3, 4.3]))
hexagon = HyperbolicPolygon.from_polar(phis, color=HEXAGON_COLOR, add_dots=False,
stroke_width=HEXAGON_STROKE_WIDTH)
inner_circles = HexagonCircles(hexagon, first_circle_radius=.4, color=GREEN_B,
stroke_width=HEXAGON_STROKE_WIDTH)
diagonals = HexagonMainDiagonals(hexagon, color=ORANGE, stroke_width=HEXAGON_STROKE_WIDTH)
intersection = get_intersection_in_unit_circle_of_two_tangent_circles(diagonals.arc1.circle_center,
diagonals.arc1.radius,
diagonals.arc2.circle_center,
diagonals.arc2.radius)
intersection_dot = Dot(intersection, color=YELLOW, radius=.03)
self.add(circle, hexagon, inner_circles, diagonals, intersection_dot)
self.add_foreground_mobject(circle)
self.add_foreground_mobjects(hexagon, diagonals, intersection_dot, circle)
self.wait(1)
# transform hyperbolic hexagon to euclidean hexagon
euclidean_hexagon = EuclideanHexagon(phis, color=GREY, stroke_width=2)
euclidean_diagonals = get_diagonals(hexagon, color=ORANGE, stroke_width=2)
euclidean_intersection_dot = Dot(get_intersection_from_angles(phis[0], phis[3], phis[1], phis[4]), color=YELLOW,
radius=.03)
self.add_foreground_mobjects(hexagon, diagonals, intersection_dot, circle)
self.play(*[ReplacementTransform(hexagon.arcs[i], euclidean_hexagon.edges[i]) for i in range(6)],
ReplacementTransform(diagonals.arc1, euclidean_diagonals[0].reverse_direction()),
ReplacementTransform(diagonals.arc2, euclidean_diagonals[1].reverse_direction()),
ReplacementTransform(diagonals.arc3, euclidean_diagonals[2].reverse_direction()),
ReplacementTransform(intersection_dot, euclidean_intersection_dot),
run_time=3)
self.wait(2)
# quick fix such that hexagon gets transformed into old shape
hexagon = HyperbolicPolygon.from_polar(phis, color=HEXAGON_COLOR, add_dots=False,
stroke_width=HEXAGON_STROKE_WIDTH)
diagonals = HexagonMainDiagonals(hexagon, color=ORANGE, stroke_width=HEXAGON_STROKE_WIDTH)
intersection = get_intersection_in_unit_circle_of_two_tangent_circles(diagonals.arc1.circle_center,
diagonals.arc1.radius,
diagonals.arc2.circle_center,
diagonals.arc2.radius)
intersection_dot = Dot(intersection, color=YELLOW, radius=.03)
self.play(*[ReplacementTransform(euclidean_hexagon.edges[i], hexagon.arcs[i]) for i in range(6)],
ReplacementTransform(euclidean_diagonals[0], diagonals.arc1),
ReplacementTransform(euclidean_diagonals[1], diagonals.arc2),
ReplacementTransform(euclidean_diagonals[2], diagonals.arc3),
ReplacementTransform(euclidean_intersection_dot, intersection_dot),
run_time=3)
self.wait(1)
class Scene4(MovingCameraScene):
def construct(self):
center = np.array([0, 0, 0])
klein_origin = np.array([2, 0, 0])
poincare_origin = np.array([-2, 0, 0])
MY_BLUE = "#22c1dd"
klein_model = ImageMobject("tessellation_klein.png").scale(1.0).move_to(klein_origin)
poincare_model = ImageMobject("tessellation_poincare.png").scale(1.0).move_to(poincare_origin)
scale_back = 3.57
phis = [[0.4, 2], [3.3, 5.2]]
kcircle = Circle(color=MY_BLUE, stroke_width=1).scale(scale_back).move_to(klein_origin)
pcircle = Circle(color=MY_BLUE, stroke_width=1).scale(scale_back).move_to(poincare_origin)
p_geodesics_raw = [HyperbolicArcBetweenPoints(polar_to_point(x), polar_to_point(y)) for [x, y] in phis]
p_geodesics = [geo.scale(scale_back).move_to(geo.get_center() * scale_back).shift(poincare_origin) for geo in
p_geodesics_raw]
k_geodesics_raw = [Line(polar_to_point(x), polar_to_point(y)) for [x, y] in phis]
k_geodesics = [geo.scale(scale_back).move_to(geo.get_center() * scale_back).shift(klein_origin) for geo in
k_geodesics_raw]
arrow_lr = Arrow(start=LEFT, end=RIGHT, stroke_width=4, max_tip_length_to_length_ratio=.5)
arrow_rl = Arrow(start=RIGHT, end=LEFT, stroke_width=4, max_tip_length_to_length_ratio=.5)
arrow_group = VGroup(arrow_lr, arrow_rl).arrange(DOWN)
p_geo0 = p_geodesics[0].copy()
p_geo0 = p_geo0.shift(-poincare_origin).scale(0.7).move_to(p_geo0.get_center() * 0.7).shift(
poincare_origin + 1.5 * LEFT)
p_geo0_copy = p_geo0.copy()
p_geo1 = p_geodesics[1].copy()
p_geo1 = p_geo1.shift(-poincare_origin).scale(0.7).move_to(p_geo1.get_center() * 0.7).shift(
poincare_origin + 1.5 * LEFT)
k_geo0 = k_geodesics[0].copy()
k_geo0 = k_geo0.shift(-klein_origin).scale(0.7).move_to(k_geo0.get_center() * 0.7).shift(
klein_origin + 1.5 * RIGHT)
k_geo1 = k_geodesics[1].copy()
k_geo1 = k_geo1.shift(-klein_origin).scale(0.7).move_to(k_geo1.get_center() * 0.7).shift(
klein_origin + 1.5 * RIGHT)
k_geo1_copy = k_geo1.copy()
# todo here
poincare_model.scale(0.7).shift(1.5 * LEFT)
klein_model.scale(0.7).shift(1.5 * RIGHT)
self.add(poincare_model, klein_model, arrow_group)
self.add(pcircle.scale(0.7).shift(1.5 * LEFT), kcircle.scale(0.7).shift(1.5 * RIGHT))
self.wait(1)
self.play(Create(p_geo0), FadeOut(poincare_model))
self.add(p_geo0_copy)
self.wait(1)
self.play(Transform(p_geo0, k_geo0), FadeOut(klein_model))
self.wait(1)
self.play(Create(k_geo1))
self.add(k_geo1_copy)
self.wait(1)
self.play(Transform(k_geo1, p_geo1))
self.wait(1)
class Scene5(MovingCameraScene):
def construct(self):
self.camera.frame.move_to([1, 0, 0])
self.camera.frame.width = 6
radius_disks = [.5, .4]
circle = Circle(color=WHITE, stroke_width=HEXAGON_STROKE_WIDTH)
phis = [0.47654, 2.065432, 2.876, 3.87623, 5.024, 5.673]
hexagon = HyperbolicPolygon.from_polar(phis, add_dots=False, color=GREY_B, stroke_width=2)
arc_colored = HyperbolicPolygon.from_polar(phis, add_dots=False, color=ORANGE, stroke_width=2).arcs[0]
point1 = hexagon.polygon_points[0]
point2 = hexagon.polygon_points[1]
arc = hexagon.arcs[0]
distance_text = MathTex(r'\mathrm{dist_h}(a,b) =', font_size=27).move_to([1.2, 0, 0],
aligned_edge=LEFT) # partially new
infinity = MathTex(r'\infty', font_size=27).next_to(distance_text, buff=.05)
s_0 = Dot(hexagon.polygon_points[0], radius=.02, color=ORANGE)
s_1 = Dot(hexagon.polygon_points[1], radius=.02, color=ORANGE)
self.add(hexagon, circle, arc_colored, s_0, s_1, distance_text, infinity)
self.add_foreground_mobjects(circle)
self.wait(1)
distance_number = DecimalNumber(6343.242564,
num_decimal_places=2, show_ellipsis=True, group_with_commas=False,
font_size=27).next_to(distance_text, buff=.05)
self.remove(infinity)
# self.add(distance_number, s_0, s_1)
label = VGroup(distance_text, distance_number)
step_size = 450
for t in range(1, step_size):
if t < step_size / 2:
transition = 2 * t / step_size
else:
transition = (1 - t / step_size) * 2
interp_point1 = get_intersection_in_unit_circle_of_two_tangent_circles(arc.circle_center, arc.radius,
point1,
transition * radius_disks[0])
interp_point2 = get_intersection_in_unit_circle_of_two_tangent_circles(point2,
transition * radius_disks[1],
arc.circle_center, arc.radius)
new_arc = ArcBetweenPoints(interp_point2, interp_point1, color=ORANGE,
radius=arc.radius, stroke_width=2).reverse_direction()
distance = np.exp(
hyperbolic_distance_function(interp_point2, interp_point1))
distance_number.font_size = 27
label.arrange(buff=.05)
label.move_to([1.2, 0, 0], aligned_edge=LEFT)
if t == step_size - 1:
self.play(Transform(arc_colored, new_arc),
Transform(s_0, Dot(interp_point1, radius=.02, color=ORANGE)),
Transform(s_1, Dot(interp_point2, radius=.02, color=ORANGE)),
Transform(distance_number, infinity),
run_time=1 / 60, rate_func=lambda a: a)
else:
self.play(Transform(arc_colored, new_arc),
Transform(s_0, Dot(interp_point1, radius=.02, color=ORANGE)),
Transform(s_1, Dot(interp_point2, radius=.02, color=ORANGE)),
distance_number.animate.set_value(distance), run_time=1 / 60,
rate_func=lambda a: a)
self.remove(s_0, s_1)
self.wait(2)
everything = VGroup(*filter(lambda x: isinstance(x, VMobject), self.mobjects))
class Scene6(MovingCameraScene):
def construct(self):
self.camera.frame.width = 4
center = [0, 0, 0]
start_points = np.array([center, center, center, center])
length = [1 / 2, 1 / 2, -3 / 2] # 1 is 1 unit to the left, -3 is 3 units to the right, way of circles moving
angles = [0, np.pi / 4, 4 * np.pi / 3]
outer_circle = Circle(color=WHITE, radius=1, stroke_width=HEXAGON_STROKE_WIDTH).move_to(center)
self.add_foreground_mobjects(outer_circle)
circle = [Dot(color=WHITE, radius=0.04), Circle(color=BLUE_A, radius=0.25, stroke_width=2),
Circle(color=BLUE, radius=.5, stroke_width=2), Circle(color=BLUE_E, radius=0.75, stroke_width=2)]
# circle[0] is dot, circle[1] is smallest circle, circle[2] is middle circle, circle[3] is biggest circle
Group(circle[0], circle[1], circle[2], circle[3]).move_to(center)
# todo from here on
self.add(outer_circle, circle[0])
self.add_foreground_mobjects(circle[0])
# self.wait(2)
self.play(Create(circle[1]), Create(circle[2]), Create(circle[3]))
# self.wait(2)
# circles moving along a line 3 times
for t in range(3):
end_points = np.array([start_points[0] - [1 * length[t], 0, 0],
start_points[1] - [0.75 * length[t], 0, 0],
start_points[2] - [0.5 * length[t], 0, 0],
start_points[3] - [0.25 * length[t], 0, 0]])
lines = moving_line(start_points, end_points)
self.play(MoveAlongPath(circle[0], lines[0]), MoveAlongPath(circle[3], lines[3]), # hyperbolic
MoveAlongPath(circle[2], lines[2]), MoveAlongPath(circle[1], lines[1]))
# self.wait(1)
start_points = end_points
# circles moving along part circle twice
for t in range(2):
arcs = moving_circle(angles[t], angles[t + 1], center)
self.play(MoveAlongPath(circle[0], arcs[0]), MoveAlongPath(circle[3], arcs[1]),
MoveAlongPath(circle[2], arcs[2]), MoveAlongPath(circle[1], arcs[3]))
# self.wait(1)
self.wait(1)
class Scene6Unused(MovingCameraScene):
def construct(self):
# Labels
s_1 = MathTex('S_1', color=BLUE, font_size=15).move_to([0.15, .5, 0])
s_2 = MathTex('S_2', color=BLUE, font_size=15).move_to([-.6, .45, 0])
s_2_red = MathTex('S_2', color=RED, font_size=15).move_to([-.6, .45, 0])
s_3 = MathTex('S_3', color=BLUE, font_size=15).move_to([-.7, -0.1, 0])
s_4 = MathTex('S_4', color=BLUE, font_size=15).move_to([-.1, -0.6, 0])
s_4_red = MathTex('S_4', color=RED, font_size=15).move_to([-.1, -0.6, 0])
s_5 = MathTex('S_5', color=BLUE, font_size=15).move_to([0.4, -.55, 0])
s_6 = MathTex('S_6', color=BLUE, font_size=15).move_to([.6, 0, 0])
s_6_red = MathTex('S_6', color=RED, font_size=15).move_to([.6, 0, 0])
s_k = [s_1, s_2, s_3, s_4, s_5, s_6]
s_k_colored = [s_1, s_2_red, s_3, s_4_red, s_5, s_6_red]
formula_size = 15
self.camera.frame.width = 6
circle = Circle(color=WHITE, stroke_width=HEXAGON_STROKE_WIDTH)
self.wait(1)
# creating our nonideal hexagon
radius = [0.5, 0.7, 0.6, 0.7, 0.5, 0.6]
phis = [0.47654, 2.065432, 2.876, 3.87623, 5.024, 5.673]
hexagon = HyperbolicPolygon.from_polar(phis, radius, dot_radius=0.01, stroke_width=2)
hex_name = MathTex('P', font_size=15).move_to([0.6, 0.4, 0])
self.play(FadeIn(circle, hexagon), Write(hex_name))
self.wait(2)
arc = HyperbolicPolygon.from_polar(phis, radius, dot_radius=0.01, color=BLUE, stroke_width=2).arcs
dots = hexagon.dots
# Kantenbeschriftung
dots[-1].set_color(BLUE)
for i in range(0, 6):
dots[i].set_color(BLUE)
self.play(Create(arc[i]), Write(s_k[i], stroke_width=.5),
rate_func=lambda a: a, run_time=1)
self.wait(2)
self.play(FadeOut(*self.mobjects))