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from manimlib.imports import *
class fs1(GraphScene):
CONFIG = {
"x_min": -2,
"x_max": 2,
"y_min": -6,
"y_max": 6,
"graph_origin": ORIGIN
}
def construct(self):
text = TextMobject(r'$\frac{dT}{ds} = \kappa N$ \\ $\frac{dT}{ds}$ gives the direction of N, \\ while $\kappa$ gives its magnitude.').scale(0.7).shift(3*UP + 3*LEFT)
self.setup_axes()
def curve_(x):
return x**3 - 2*x
def nm(x):
return abs(6 * x / ((9*(x**4) - 6*(x**2) + 5)**1.5))
figure = self.get_graph(curve_)
dot = Dot().rotate(PI/2)
alpha = ValueTracker(0)
t2_ = ValueTracker(-2)
t2 = t2_.get_value
t = alpha.get_value
vector_x = self.get_tangent_vector(t(),figure,scale=2)
vector_y = self.get_normal_vector(t(),figure,scale=2)
kappa = TextMobject(r'$\kappa = $').scale(0.7).shift(3*DOWN + 3*RIGHT)
t_text = always_redraw(
lambda: DecimalNumber(
nm(t2()),
color=WHITE,
).scale(0.7).next_to(kappa)
).scale(0.6)
self.play(
ShowCreation(figure),
GrowFromCenter(dot),
GrowArrow(vector_x),
GrowArrow(vector_y)
)
vector_x.add_updater(
lambda m: m.become(
self.get_tangent_vector(t(),figure,scale=2)
)
)
vector_y.add_updater(
lambda m: m.become(
self.get_normal_vector(t(),figure,scale=2)
)
)
dot.add_updater(lambda m: m.move_to(vector_x.get_start()))
circle = Circle(radius = 2, color = GREEN_SCREEN). shift(2.63*RIGHT + 2.8*UP)
dot2 = Dot(np.array([2, curve_(2), 0]), color = WHITE).shift(2*DOWN + 2.5*RIGHT)
self.add(vector_x, vector_y,dot, t_text, kappa, text)
self.play(t2_.set_value, 2, alpha.set_value, 1, run_time=18, rate_func=smooth)
self.play(FadeIn(dot2), FadeIn(circle))
self.wait(2)
self.play(FadeOut(VGroup(*[self.axes, dot2, figure, circle, text, kappa, t_text])))
def get_tangent_vector(self, proportion, curve, dx=0.001, scale=0.5):
coord_i = curve.point_from_proportion(proportion)
coord_f = curve.point_from_proportion(proportion + dx)
reference_line = Line(coord_i,coord_f)
unit_vector = reference_line.get_unit_vector() * 0.7
vector = Arrow(coord_i , coord_i + unit_vector, color = YELLOW, buff=0)
return vector
def get_normal_vector(self, proportion, curve, dx=0.001, scale=1):
t = proportion.copy()/6
coord_i = curve.point_from_proportion(proportion)
coord_f = curve.point_from_proportion(proportion + dx)
length = 6 * t / ((9*(t**4) - 6*(t**2) + 5)**1.5)
if coord_i[0] <= 0 and coord_i[0] > -0.5:
reference_line = Line(coord_i,coord_f).rotate(PI/2).set_width(0).scale(2)
elif coord_i[0] > 0 and (coord_i[0] < 0.5 or coord_i[0] > 2.7):
reference_line = Line(coord_i,coord_f).rotate(PI/2).set_width(0).scale(2)
elif coord_i[0] > 0:
reference_line = Line(coord_i,coord_f).rotate(PI/2).set_width(length).scale(2)
else:
reference_line = Line(coord_i,coord_f).rotate(-PI/2).set_width(length).scale(2)
unit_vector = reference_line.get_vector() * scale
vector = Arrow(coord_i , coord_i + unit_vector, color = RED_C, buff=0)
return vector
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