From 7a741fe759201d54ff29a450e0f70bea96cd6504 Mon Sep 17 00:00:00 2001
From: nishanpoojary
Date: Wed, 1 Jul 2020 11:58:37 +0530
Subject: Added partial-derivatives folder

---
 .../file2_partial_deriv_hill.py                    | 122 +++++++++++++++++++++
 1 file changed, 122 insertions(+)
 create mode 100644 FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file2_partial_deriv_hill.py

(limited to 'FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file2_partial_deriv_hill.py')

diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file2_partial_deriv_hill.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file2_partial_deriv_hill.py
new file mode 100644
index 0000000..bfb7687
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file2_partial_deriv_hill.py
@@ -0,0 +1,122 @@
+from manimlib.imports import *
+
+class Hill(ThreeDScene):
+    def construct(self):
+        axes = ThreeDAxes() 
+
+        function = ParametricSurface(
+            lambda u, v: np.array([
+                1.2*np.sin(u)*np.cos(v),
+                1.2*np.sin(u)*np.sin(v),
+                -1.2*1.2*np.sin(u)*np.sin(u)*(1+0.5*np.sin(v)*np.sin(v))+2
+            ]),u_min=0,u_max=PI/2,v_min=0,v_max=2*PI,checkerboard_colors=[GREEN_C, GREEN_E],
+            resolution=(15, 32)).scale(1)
+
+        func_x =ParametricFunction(
+                lambda u : np.array([
+                u,
+                0,
+                2 - u*u
+            ]),color=RED_E,t_min=-1.2,t_max=1.2,
+            )
+    
+        func_y =ParametricFunction(
+                lambda u : np.array([
+                0,
+                u,
+                2 - 1.5*u*u
+            ]),color=PINK,t_min=-1.2,t_max=1.2,
+            )
+
+        self.set_camera_orientation(phi=60 * DEGREES, theta = 0*DEGREES)
+        #self.set_camera_orientation(phi=45 * DEGREES, theta = -20*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])
+
+        self.play(ShowCreation(function))
+        self.wait()
+
+        self.move_camera(phi=60 * DEGREES, theta = 45*DEGREES)
+        #self.play(ShowCreation(func_x))
+
+        text_x = TextMobject("Slope of the hill along", r"$x$", "axis", color = YELLOW_C).scale(0.6).move_to(2.7*UP + 3.5*RIGHT)
+        text_x[1].set_color(PINK)
+
+
+        slope_text_x = TexMobject("Slope =", "{\\partial", "f", "\\over", "\\partial", "x}").scale(0.6).move_to(2*UP + 3.5*RIGHT)
+        slope_text_x[0].set_color(BLUE_E)
+        slope_text_x.set_color_by_tex("\\partial",YELLOW_C)
+        slope_text_x.set_color_by_tex("f",RED_E)
+        slope_text_x[5].set_color(PINK)
+
+        self.add_fixed_in_frame_mobjects(text_x, slope_text_x)
+
+        dot_x = Dot().rotate(PI/2).set_color(YELLOW_E)
+        alpha_x = ValueTracker(0)
+        vector_x = self.get_tangent_vector(alpha_x.get_value(),func_x,scale=1.5)
+        dot_x.add_updater(lambda m: m.move_to(vector_x.get_center()))
+        self.play(
+            ShowCreation(func_x),
+            GrowFromCenter(dot_x),
+            GrowArrow(vector_x)
+            )
+        vector_x.add_updater(
+            lambda m: m.become(
+                    self.get_tangent_vector(alpha_x.get_value()%1,func_x,scale=1.5)
+                )
+            )
+        
+        self.add(vector_x,dot_x)
+        
+        self.play(alpha_x.increment_value, 1, run_time=10, rate_func=linear)
+
+        #self.move_camera(phi=60 * DEGREES, theta = 0*DEGREES)
+        self.play(FadeOut(vector_x), FadeOut(dot_x), FadeOut(func_x), FadeOut(text_x), FadeOut(slope_text_x))
+
+        text_y = TextMobject("Slope of the hill along", r"$y$", "axis", color = YELLOW_C).scale(0.6).move_to(2.7*UP + 3.5*RIGHT)
+        text_y[1].set_color(RED_C)
+
+
+        slope_text_y = TexMobject("Slope =", "{\\partial", "f", "\\over", "\\partial", "x}").scale(0.6).move_to(2*UP + 3.5*RIGHT)
+        slope_text_y[0].set_color(BLUE_E)
+        slope_text_y.set_color_by_tex("\\partial",YELLOW_C)
+        slope_text_y.set_color_by_tex("f",PINK)
+        slope_text_y[5].set_color(RED_C)
+
+        self.add_fixed_in_frame_mobjects(text_y, slope_text_y)
+
+        dot_y = Dot().rotate(PI/2).set_color(BLUE_E)
+        alpha_y = ValueTracker(0)
+        vector_y = self.get_tangent_vector(alpha_y.get_value(),func_y,scale=1.5)
+        dot_y.add_updater(lambda m: m.move_to(vector_y.get_center()))
+        self.play(
+            ShowCreation(func_y),
+            GrowFromCenter(dot_y),
+            GrowArrow(vector_y)
+            )
+        vector_y.add_updater(
+            lambda m: m.become(
+                    self.get_tangent_vector(alpha_y.get_value()%1,func_y,scale=1.5)
+                )
+            )
+
+        self.add(vector_y,dot_y)
+        self.play(alpha_y.increment_value, 1, run_time=10, rate_func=linear)
+        self.play(FadeOut(vector_y), FadeOut(dot_y), FadeOut(func_y), FadeOut(text_y), FadeOut(slope_text_y))
+        self.wait(2)
+
+    def get_tangent_vector(self, proportion, curve, dx=0.001, scale=1):
+        coord_i = curve.point_from_proportion(proportion)
+        coord_f = curve.point_from_proportion(proportion + dx)
+        reference_line = Line(coord_i,coord_f)
+        unit_vector = reference_line.get_unit_vector() * scale
+        vector = Line(coord_i - unit_vector, coord_i + unit_vector, color = ORANGE, buff=0)
+        return vector       
\ No newline at end of file
-- 
cgit