Rename FSF-2020/approximations-and-optimizations/Tangent-Plane-Approximations/file2_Tangent_plane_approximation_visualization.py to FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Tangent-Plane-Approximations/file2_Tangent_plane_approximation_visualization.py

1 files changed, 74 insertions, 0 deletions

diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Tangent-Plane-Approximations/file2_Tangent_plane_approximation_visualization.py b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Tangent-Plane-Approximations/file2_Tangent_plane_approximation_visualization.py
new file mode 100644
index 0000000..d1ecf8c
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Tangent-Plane-Approximations/file2_Tangent_plane_approximation_visualization.py
@@ -0,0 +1,74 @@
+from manimlib.imports import*
+
+#---- tangent plane is parallel to the x-y plane
+class MaximaScene(ThreeDScene):
+    def construct(self):
+
+        axes = ThreeDAxes().scale(1.2)
+        label_x= TextMobject("$x$").shift([5.4,-0.5,0]) #---- x axis
+        label_y= TextMobject("$y$").shift([-0.5,5.2,0]).rotate(-4.5) #---- y axis
+
+        #---- graph of the function 
+        s = ParametricSurface(
+            lambda u, v: np.array([
+                1.5*np.cos(u)*np.cos(v),
+                1.5*np.cos(u)*np.sin(v),
+                1.5*np.sin(u)
+            ]),u_min=0,u_max=PI,v_min=PI,v_max=2*PI,checkerboard_colors=[BLUE_B,BLUE_C,BLUE_D,BLUE_E]).scale(1.5).shift([-0.8,0.5,1.5])
+
+        d1 = Dot([0.2,2.01,2.24],color = '#800000').rotate(1.1,LEFT) #---- point(x_0,y_0)
+        d1_copy = Dot([1.1,2.2,-0.45],color = '#800000') #---- projection of point(x_0,y_0) on x-y plane
+        d1_text = TextMobject("$(x_0,y_0)$",color = "#8B0000").scale(0.4).shift(1.3*RIGHT+1.1*UP)
+
+        d2 = Dot([1.1,2.2,2.7],color = '#800000').rotate(1,LEFT) #---- point(x,y)
+        d2_copy = Dot([0.1,1.95,0.4],color = '#800000') #---- projection of point(x,y) on x-y plane
+        d2_text = TextMobject("$(x,y)$",color = "#8B0000").scale(0.4).shift(0.6*RIGHT+0.8*UP)
+
+        t_plane = Rectangle(color = PURPLE, fill_opacity=0.3).scale(0.4).rotate(1,LEFT).shift([1.1,2.5,2.9]) #---- tangent plane
+
+        t_text= TextMobject("Tangent Plane",color = RED).scale(0.5).shift(0.3*RIGHT+1.3*UP).rotate(math.radians(5),LEFT)
+
+        l1 = Line([1.1,2.2,2.6],[1.1,2.2,-0.45]).fade(0.2)
+        l2 = Line([0.1,1.95,2.05],[0.1,1.95,0.4]).fade(0.2)
+
+        a1 = Line([0.1,1.95,0.4],[1.1,2.2,-0.45],color ="#00FF7F")
+        a_x = Line([0.1,1.95,0.4],[1.7,1.95,0.4],color ="#9400D3")
+        a_y = Line([0.1,1.95,0.4],[0.1,2.75,0.4],color ="#8B4513")
+        a2 = Line([1.7,1.95,0.4],[1.7,2.75,0.4])
+        a3 = Line([0.1,2.75,0.4],[1.7,2.75,0.4])
+        
+        #---- transition of tangent plane
+
+        t2_plane = Rectangle(color = PURPLE, fill_opacity=0.3).scale(0.4).rotate(1,LEFT).shift([1.1,2.5,2]) 
+        t3_plane = Rectangle(color = PURPLE, fill_opacity=0.3).scale(0.4).rotate(math.radians(180),LEFT).shift([1.1,2.5,2])
+        t4_plane = Rectangle(color = PURPLE, fill_opacity=0.3).scale(0.4).rotate(math.radians(180),LEFT).shift([0.9,2.35,0.4])
+
+        #-------------------------------------------
+        self.set_camera_orientation(phi = 50 * DEGREES, theta = 45 * DEGREES)
+        self.wait(1)
+        self.add(axes)
+        self.add(label_x)
+        self.add(label_y)
+        self.play(Write(s))
+        self.wait(1)
+        self.play(Write(d1))
+        self.add_fixed_in_frame_mobjects(d1_text)
+        self.play(ShowCreation(t_plane))
+        self.add_fixed_in_frame_mobjects(t_text)
+        self.wait(1)
+        self.play(FadeOut(t_text),Write(d2))
+        self.add_fixed_in_frame_mobjects(d2_text)        
+        self.wait(1)
+        self.play(Write(l1),Write(l2))
+        self.play(Write(d2_copy),Write(d1_copy))
+        self.wait(1)
+        self.play(Write(a1),Write(a_x),Write(a_y))
+        self.wait(1)
+        self.play(Write(a2),Write(a3))
+        self.wait(1)        
+        self.play(ReplacementTransform(t_plane,t2_plane))
+        self.wait(1)
+        self.play(ReplacementTransform(t2_plane,t3_plane))
+        self.wait(1)
+        self.play(ReplacementTransform(t3_plane,t4_plane))
+        self.wait(1)