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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 + (277*x**3)/31752 + (13*x**4)/784 - (17*x**5)/5292 + (170*x**6)/63504
graph = FunctionGraph(curve, x_min=-2, x_max=6, stroke_width = 2, color = BLUE)
tracker = ValueTracker(-2)
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*LEFT+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((2.9,-0.47, 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 = 0.2, color = GREY, opacity = 0.2).shift(0.3*DOWN + 2.9*RIGHT)
tgt2 = Line((4,-2,0), (6, -2, 0), color = GREY, opacity = 0.2).scale(0.5).shift(2.1*LEFT + 1.5*UP)
r2 = Line(circle2.get_center(), circle2.get_center() - np.array([0,0.2,0]), color=GREEN_SCREEN)
r2label = TextMobject(r'$R_{2}$', color=WHITE).next_to(r2.get_start(), np.array([0,0,0]), buff = 0).scale(0.4)
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, 4, rate_func=smooth, run_time=10)
self.play(FadeIn(curvature1), FadeIn(curvature2))
self.wait(2)
self.play(FadeOut(VGroup(*[curvature1, curvature2, graph, self.axes, line, dots, text])))
self.wait()
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