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from manimlib.imports import *
class fs2(SpecialThreeDScene):
CONFIG = {
"x_min": -2,
"x_max": 2,
"y_min": -6,
"y_max": 6,
"graph_origin": ORIGIN
}
def construct(self):
axes = ThreeDAxes()
# text = TextMobject(r'$\frac{dB}{ds} = -\tau N$ \\ $\frac{dB}{ds}$ gives the direction of N, \\ while $\tau$ gives its magnitude.').scale(0.7).shift(3*UP + 3*LEFT)
self.set_camera_orientation(phi = 75*DEGREES, theta=135*DEGREES)
# self.move_camera(distance=0)
# rprime = np.array([2*np.cos(t), -np.sin(t) - (2*np.sin(2*t)), 0])
# t = rprime / np.sqrt(np.dot(rprime, rprime))
# rpp = np.array([-2*np.sin(t), -np.cos(t) - (4*np.cos(2*t)), 0])
# n = rpp / np.dot(rpp, rpp)
# b = np.cross(rprime, rpp)
text = TextMobject(r'$\frac{dB}{ds}$', r'$= -\tau$', r'$N$').shift(2*UP + 4*LEFT)
text.set_color_by_tex_to_color_map({
r'$\frac{dB}{ds}$': YELLOW,
r'$N$': RED_C
})
dot = Dot().rotate(PI/2)
alpha = ValueTracker(0)
t = alpha.get_value
figure = ParametricFunction(
lambda t: np.array([
np.sinh(t),
np.cosh(t),
2*t
]), t_min = -3, t_max = 3, color=BLUE
).scale(0.5).move_to(ORIGIN)
vector_x = self.get_tangent_vector(t()%1, figure,scale=2)
vector_y = self.get_normal_vector(t(),figure,scale=2)
vector_x.add_updater(
lambda m: m.become(
self.get_tangent_vector(t()%1,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_y.get_start()))
self.add_fixed_in_frame_mobjects(text)
self.play(FadeIn(figure), FadeIn(axes), FadeIn(text))
self.begin_ambient_camera_rotation(rate = 0.1)
self.wait(1)
self.add(vector_x, vector_y,dot)
self.play(alpha.increment_value, 0.999, run_time=20, rate_func=rush_from)
self.wait(1)
self.remove(figure, vector_x, vector_y,dot)
self.play(FadeOut(figure), FadeOut(axes), FadeOut(text))
def get_tangent_vector(self, proportion, curve, dx=0.001, scale=1):
t = proportion.copy()
coord_i = curve.point_from_proportion(proportion)
rprime = np.array([np.cosh(t), np.sinh(t), 2])
T = rprime / np.sqrt(np.dot(rprime, rprime))
rpp = np.array([np.sinh(t), np.cosh(t), 0])
n = rpp / np.dot(rpp, rpp)
# b = (np.cross(T, n)[0] - 0.5, np.cross(T, n)[1], coord_i[2] + 1)
b = np.cross(T, n)
# coord_f = curve.point_from_proportion(proportion + dx)
coord_f = b
reference_line = Line(coord_i,coord_f)
unit_vector = reference_line.get_unit_vector() * 1
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):
coord_i = curve.point_from_proportion(proportion)
coord_f = curve.point_from_proportion(proportion + dx)
t = proportion.copy()/7
rpp = np.array([np.sinh(t), np.cosh(t), 0])
length = np.sqrt(np.dot(rpp, rpp))
length = 1/(1 + np.exp(-length))
reference_line = Line(coord_i,coord_f).rotate(PI/2).set_width(length).scale(2)
unit_vector = reference_line.get_vector() * 0.7
vector = Arrow(coord_i, coord_i + unit_vector, color = RED_C, buff=0)
return vector
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