1 files changed, 92 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..fc151ac
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file5_vectorvf_helix.py
@@ -0,0 +1,92 @@
+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
+\ No newline at end of file