1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
|
from manimlib.imports import *
import numpy as np
# granny smith apple
#misty moss
class Analogue(ThreeDScene):
def construct(self):
axes = ThreeDAxes().set_color("#EBF2FA")
hills_2D = ParametricFunction(
lambda t: np.array([
0,
t,
-((1/1.02)*t**2)
]),t_min= -2.5,t_max=2.5).set_color("#679436")
hills_2D_a = ParametricFunction(
lambda t: np.array([
0,
t,
-((1/1.02)*t**2)
]),t_min= 0,t_max=2.5).set_color("#679436")
hills_3D = ParametricSurface(
lambda u, v: np.array([
u,
v,
-(u**2 + v**2)
]),u_min=-2.5,u_max=2.5, v_min=-2.5,v_max=2.5, checkerboard_colors = ["#679436", "#679436"], stroke_color = "#679436").fade(0.7)
hills_2D_b = ParametricFunction(
lambda t: np.array([
t,
0,
-((1/1.02)*t**2)
]),t_min= 0,t_max=2.5).set_color("#FFCAB1")
hills = VGroup(hills_2D_a, hills_3D, hills_2D_b, hills_2D).move_to(np.array([0,0,-3.8]))
ball = Sphere(radius = 0.08).set_color("#28666E")
path_one = DashedVMobject(hills_2D_a).set_stroke(width = 0.9).set_color("#F0C808")
path_two = DashedVMobject(hills_2D_b).set_stroke(width = 0.9).set_color("#F0C808")
text_a = TexMobject(r"\textit{In the case of a one dimensional hill, }" ,r"\textit{the ball moves along a single path}").set_color("#EBF2FA").scale(0.5).move_to(np.array([-1.5, 2.7, 0]))
text_b = TexMobject(r"\textit{In higher dimensions,}", r"\textit{ there is more than one direction}", r"\textit{the ball can roll in}").set_color("#EBF2FA").scale(0.5).move_to(np.array([-1.5, 2.6, 0]))
text_a[1].next_to(text_a[0], DOWN, buff = SMALL_BUFF)
text_b[1].next_to(text_b[0], DOWN, buff = SMALL_BUFF)
text_b[2].next_to(text_b[1], DOWN, buff = SMALL_BUFF)
text_b[0].set_color("#28666E")
self.set_camera_orientation(phi=90*DEGREES,theta=180*DEGREES,distance=40)
self.add(axes)
self.add_fixed_in_frame_mobjects(text_a)
self.play(ShowCreation(hills_2D), ShowCreation(text_a))
self.play(MoveAlongPath(ball,hills_2D_a),run_time = 2.5)
self.wait()
self.play(FadeIn(hills_3D), FadeOut(hills_2D), FadeOut(text_a))
self.move_camera(phi=45*DEGREES,theta=45*DEGREES)
self.add_fixed_in_frame_mobjects(text_b)
self.begin_ambient_camera_rotation(rate=0.05)
self.play(MoveAlongPath(ball, hills_2D_a), ShowCreation(path_one), run_time = 2.5)
self.wait()
self.play(FadeOut(path_one), MoveAlongPath(ball, hills_2D_b), ShowCreation(path_two), run_time = 2.5)
self.wait()
|
