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Diffstat (limited to 'FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file5_vectorvf_helix.py')
| -rw-r--r-- | FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file5_vectorvf_helix.py | 99 |
1 files changed, 99 insertions, 0 deletions
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file5_vectorvf_helix.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file5_vectorvf_helix.py new file mode 100644 index 0000000..c02f540 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file5_vectorvf_helix.py @@ -0,0 +1,99 @@ +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", ")", "=", "{ \\begin{bmatrix} r \\cos\\theta \\\ r \\sin \\theta \\\ h \\theta \\end{bmatrix}}" ).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)
+
+
+
+ slope_text = TextMobject(r"$\theta = $").move_to(3*UP+3*RIGHT)
+ number = DecimalNumber(0,unit=r" rad", color=RED_C).next_to(slope_text, RIGHT)
+
+
+ self.add_fixed_in_frame_mobjects(function,slope_text, number)
+
+ 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()))
+ number.add_updater(lambda m: m.set_value(alpha1.get_value()*4*np.pi))
+ number.add_updater(lambda m: self.add_fixed_in_frame_mobjects(m))
+
+
+ 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), FadeOut(number))
+
+ self.move_camera(phi=0* DEGREES,theta=90*DEGREES)
+
+ alpha1 = ValueTracker(0)
+
+ self.add(vector1,dot1)
+
+
+ self.play(alpha1.increment_value, 1, run_time=10, rate_func=linear)
+
+
+
+ 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
\ No newline at end of file |