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from manimlib.imports import *
class Helix(ThreeDScene):
def construct(self):
axes = ThreeDAxes() # creates a 3D Axis
helix1=ParametricFunction(
lambda u : np.array([
1.5*np.cos(u),
1.5*np.sin(u),
u/4
]),color=PURPLE,t_min=-TAU,t_max=TAU,
)
helix2=ParametricFunction(
lambda u : np.array([
2*np.cos(u),
2*np.sin(u),
u/2
]),color=GREEN_C,t_min=-TAU,t_max=TAU,
)
function = TexMobject("f(", "r", ",", "\\theta", ")", "=", "[", "r", "\\cos", "\\theta", ",", "r", "\\sin" ,"\\theta", ",", "h" ,"\\theta", "]" ).scale(0.6).to_corner(UL)
function.set_color_by_tex(r"\theta", BLUE_C)
function.set_color_by_tex(r"r", RED_C)
function.set_color_by_tex(r"\cos", GREEN_C)
function.set_color_by_tex(r"\sin", YELLOW_C)
function[0].set_color(ORANGE)
function[4].set_color(ORANGE)
self.add_fixed_in_frame_mobjects(function)
self.set_camera_orientation(phi=60*DEGREES, theta = 45*DEGREES)
self.add(axes)
axis = TextMobject(r"X",r"Y",r"Z")
axis[0].move_to(6*RIGHT)
axis[1].move_to(6*UP)
axis[2].move_to(np.array([0,0,3.7]))
self.add_fixed_orientation_mobjects(axis[2])
self.add_fixed_orientation_mobjects(axis[0])
self.add_fixed_orientation_mobjects(axis[1])
dot1 = Dot().rotate(PI/2).set_color(RED_C)
alpha1 = ValueTracker(0)
vector1 = self.get_vector(alpha1.get_value(),helix1)
dot1.add_updater(lambda m: m.move_to(vector1.get_end()))
self.play(
ShowCreation(helix1),
GrowFromCenter(dot1),
GrowArrow(vector1)
)
vector1.add_updater(
lambda m: m.become(
self.get_vector(alpha1.get_value()%1,helix1)
)
)
self.add(vector1,dot1)
self.play(alpha1.increment_value, 1, run_time=10, rate_func=linear)
self.play(FadeOut(vector1), FadeOut(dot1))
self.play(ReplacementTransform(helix1, helix2))
dot2 = Dot().rotate(PI/2).set_color(RED_C)
alpha2 = ValueTracker(0)
vector2 = self.get_vector(alpha2.get_value(),helix2)
dot2.add_updater(lambda m: m.move_to(vector2.get_end()))
self.play(
ShowCreation(helix2),
GrowFromCenter(dot2),
GrowArrow(vector2)
)
vector2.add_updater(
lambda m: m.become(
self.get_vector(alpha2.get_value()%1,helix2)
)
)
self.add(vector2,dot2)
self.play(alpha2.increment_value, 1, run_time=10, rate_func=linear)
self.wait()
def get_vector(self, proportion, curve):
vector = Line(np.array([0,0,0]), curve.point_from_proportion(proportion), color = YELLOW_C, buff=0)
return vector
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