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Diffstat (limited to 'FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions')
| -rw-r--r-- | FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file4_vectorvf_sine.py | 114 |
1 files changed, 114 insertions, 0 deletions
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file4_vectorvf_sine.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file4_vectorvf_sine.py new file mode 100644 index 0000000..3c5bb25 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file4_vectorvf_sine.py @@ -0,0 +1,114 @@ +from manimlib.imports import *
+
+class SineVectors(GraphScene):
+ CONFIG = {
+ "x_min": 0,
+ "x_max": 10,
+ "y_min": -5,
+ "y_max": 5,
+ "graph_origin": ORIGIN+4*LEFT,
+ "x_axis_width": 7,
+ "y_axis_height": 7,
+ }
+ def construct(self):
+
+
+
+ XTD = self.x_axis_width/(self.x_max - self.x_min)
+ YTD = self.y_axis_height/(self.y_max - self.y_min)
+
+ self.setup_axes(animate = True)
+
+ sine = self.get_graph(lambda x : np.pi*np.sin(x), x_min = 0, x_max = 6.3, color = GREEN)
+
+
+ dot1 = Dot().rotate(PI/2).set_color(RED_C)
+ alpha1 = ValueTracker(0)
+ vector1 = self.get_vector(alpha1.get_value(),sine)
+ dot1.add_updater(lambda m: m.move_to(vector1.get_end()))
+ self.play(
+ ShowCreation(sine),
+ GrowFromCenter(dot1),
+ GrowArrow(vector1)
+ )
+ vector1.add_updater(
+ lambda m: m.become(
+ self.get_vector(alpha1.get_value()%1,sine)
+ )
+ )
+ self.add(vector1,dot1)
+ self.play(alpha1.increment_value, 1, run_time=5, rate_func=linear)
+
+
+ self.play(FadeOut(vector1), FadeOut(dot1), FadeOut(sine))
+
+ self.wait()
+
+
+ sine1 = self.get_graph(lambda x : np.pi*np.sin(x), x_min = 0, x_max = 1.575, color = GREEN_C)
+
+ point1 = Dot().shift(self.graph_origin+np.pi*YTD*UP + 1.575*XTD*RIGHT)
+ point1_lab = TextMobject(r"$t = (\frac{\pi}{2})$", color = GREY).scale(0.6).next_to(point1, 0.5*UP)
+
+
+ vector1 = Arrow(self.graph_origin, self.graph_origin+np.pi*YTD*UP + 1.575*XTD*RIGHT, buff=0, color = RED_C, tip_length = 0.25)
+ vector1_lab = TextMobject(r"$r(\frac{\pi}{2})$", color = RED).scale(0.7).move_to(self.graph_origin+1.5*XTD*RIGHT+ 1.5*YTD*UP)
+
+ self.play(GrowArrow(vector1),Write(vector1_lab))
+ self.play(ShowCreation(point1), Write(point1_lab))
+ self.play(ShowCreation(sine1))
+ self.wait(1)
+
+
+ sine2 = self.get_graph(lambda x : np.pi*np.sin(x), x_min = 1.575, x_max = 3.15, color = GREEN_C)
+
+ point2 = Dot().shift(self.graph_origin+3.15*XTD*RIGHT)
+ point2_lab = TextMobject(r"$t = (\pi)$", color = GREY).scale(0.6).next_to(point2, 0.5*UP+0.5*RIGHT)
+
+ vector2 = Arrow(self.graph_origin, self.graph_origin+3.15*XTD*RIGHT, buff=0, color = BLUE, tip_length = 0.25)
+ vector2_lab = TextMobject(r"$r(\pi)$", color = BLUE).scale(0.7).move_to(self.graph_origin+1.5*XTD*RIGHT+ 0.4*YTD*UP)
+
+ self.play(GrowArrow(vector2),Write(vector2_lab))
+ self.play(ShowCreation(point2), Write(point2_lab))
+ self.play(ShowCreation(sine2))
+ self.wait(1)
+
+
+ sine3 = self.get_graph(lambda x : np.pi*np.sin(x), x_min = 3.15, x_max = 4.725, color = GREEN_C)
+
+ point3 = Dot().shift(self.graph_origin+np.pi*YTD*DOWN + 4.725*XTD*RIGHT)
+ point3_lab = TextMobject(r"$t = (\frac{3\pi}{2})$", color = GREY).scale(0.6).next_to(point3, 0.5*DOWN)
+
+ vector3 = Arrow(self.graph_origin, self.graph_origin+np.pi*YTD*DOWN + 4.725*XTD*RIGHT, buff=0, color = YELLOW_C, tip_length = 0.25)
+ vector3_lab = TextMobject(r"$r(\frac{3\pi}{2})$", color = YELLOW_C).scale(0.7).move_to(self.graph_origin+2.5*XTD*RIGHT+ 1*YTD*DOWN)
+
+ self.play(GrowArrow(vector3),Write(vector3_lab))
+ self.play(ShowCreation(point3), Write(point3_lab))
+ self.play(ShowCreation(sine3))
+ self.wait(1)
+
+
+ sine4 = self.get_graph(lambda x : np.pi*np.sin(x), x_min = 4.725, x_max = 6.3, color = GREEN_C)
+
+ point4 = Dot().shift(self.graph_origin+6.3*XTD*RIGHT)
+ point4_lab = TextMobject(r"$t = (2\pi)$", color = GREY).scale(0.6).next_to(point4, 0.5*UP+0.5*RIGHT)
+
+ vector4 = Arrow(self.graph_origin, self.graph_origin+6.3*XTD*RIGHT, buff=0, color = PURPLE, tip_length = 0.25)
+ vector4_lab = TextMobject(r"$r(2\pi)$", color = PURPLE).scale(0.7).move_to(self.graph_origin+4.5*XTD*RIGHT+ 0.4*YTD*DOWN)
+
+ self.play(GrowArrow(vector4),Write(vector4_lab))
+ self.play(ShowCreation(point4), Write(point4_lab))
+ self.play(ShowCreation(sine4))
+ self.wait(3)
+
+ self.play(FadeOut(sine1), FadeOut(point1), FadeOut(point1_lab), FadeOut(vector1), FadeOut(vector1_lab),
+ FadeOut(sine2), FadeOut(point2), FadeOut(point2_lab), FadeOut(vector2), FadeOut(vector2_lab),
+ FadeOut(sine3), FadeOut(point3), FadeOut(point3_lab), FadeOut(vector3), FadeOut(vector3_lab),
+ FadeOut(sine4), FadeOut(point4), FadeOut(point4_lab), FadeOut(vector4), FadeOut(vector4_lab))
+
+
+
+ def get_vector(self, proportion, curve):
+ vector = Arrow(np.array([-4,0,0]), curve.point_from_proportion(proportion), color = ORANGE, buff=0, tip_length = 0.25)
+ return vector
+
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