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
78
|
from manimlib.imports import *
class GR(GraphScene):
CONFIG = {
"x_axis_label": "",
"y_axis_label": "",
"x_min": -4,
"x_max": 6,
"y_min": -6,
"y_max": 10,
"graph_origin": ORIGIN,
'x_tick_frequency': 20,
'y_tick_frequency': 20
}
def construct(self):
self.setup_axes()
def curve(x):
return 3 - (3653*x**2)/5292 + (2477*x**3)/31752 + (13*x**4)/784 - (17*x**5)/5292 + (17*x**6)/63504
graph = FunctionGraph(curve, x_min=-3, x_max=6, stroke_width = 2, color = BLUE)
tracker = ValueTracker(-3)
text = TextMobject(r'$\because R_{1} > R_{2}$, the curvature at \\ point $P_{1}$ is less than that \\ at point $P_{2}$ as $\kappa = \frac{1}{R}$').shift(3.2*RIGHT+3*UP).scale(0.6)
dot1 = Dot((0,3,0), color = YELLOW)
dot1label = TextMobject(r'$P_{1}$').next_to(dot1, UP+RIGHT, buff = 0.1)
dot2 = Dot((4,-1, 0), color = YELLOW)
dot2label = TextMobject(r'$P_{2}$').next_to(dot2, DOWN, buff = 0.1)
dots = VGroup(*[dot1, dot2, dot1label, dot2label])
def get_tangent_line():
line = Line(
ORIGIN, 2 * RIGHT,
color=RED,
stroke_width=4,
)
dx = 0.0001
x = tracker.get_value()
p0 = np.array([x-dx,curve(x-dx),0])
p1 = np.array([x, curve(x), 0])
p2 = np.array([x + dx, curve(x + dx), 0])
angle = angle_of_vector(p2 - p1)
line.rotate(angle)
line.move_to(p0)
return line
circle1 = Circle(radius = 0.8, color = GREY, opacity = 0.2).shift(2.2*UP)
tgt1 = Line((-2,3,0), (2,3,0), color = GREY, opacity = 0.2).scale(0.4)
r1 = Line(circle1.get_center(), circle1.get_center() + np.array([0,0.8,0]), color=GREEN_SCREEN)
r1label = TextMobject(r'$R_{1}$',color=WHITE).next_to(r1, RIGHT, buff = 0.1).scale(0.6)
curvature1 = VGroup(*[circle1, tgt1, r1, r1label])
circle2 = Circle(radius = 0.6, color = GREY, opacity = 0.2).shift(0.4*DOWN + 4*RIGHT)
tgt2 = Line((4,-2,0), (6, -2, 0), color = GREY, opacity = 0.2).scale(0.5).shift(LEFT + UP)
r2 = Line(circle2.get_center(), circle2.get_center() + np.array([0,-0.6,0]), color=GREEN_SCREEN)
r2label = TextMobject(r'$R_{2}$', color=WHITE).next_to(r2, 0.9*RIGHT, buff = 0).scale(0.6)
curvature2 = VGroup(*[circle2, tgt2, r2, r2label])
line = always_redraw(get_tangent_line)
self.add(graph,line, dots, text)
self.wait(1.2)
self.play(tracker.set_value, 0, rate_func=smooth, run_time=5)
self.play(FadeIn(curvature1))
self.play(tracker.set_value, 4, rate_func=smooth, run_time=5)
self.play(FadeIn(curvature2))
self.play(tracker.set_value, 6, rate_func=smooth, run_time=3)
self.play(FadeOut(VGroup(*[curvature1, curvature2, graph, self.axes, line, dots, text])))
self.wait()
|
