Rename FSF-2020/approximations-and-optimizations/The-Second-Derivative-Test/file4_Contour_Diagram.py to FSF-2020/calculus-of-several-variables/approximations-and-optimizations/The-Second-Derivative-Test/file4_Contour_Diagram.py

1 files changed, 120 insertions, 0 deletions

diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/The-Second-Derivative-Test/file4_Contour_Diagram.py b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/The-Second-Derivative-Test/file4_Contour_Diagram.py
new file mode 100644
index 0000000..d3084e2
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/The-Second-Derivative-Test/file4_Contour_Diagram.py
@@ -0,0 +1,120 @@
+from manimlib.imports import*
+
+#---- contour diagram animation
+class ContourDiagram(ThreeDScene):
+    def construct(self):
+
+        heading = TextMobject("CONTOUR DIAGRAM", color = YELLOW).scale(1) 
+
+        axes = ThreeDAxes()  
+        label_x = TextMobject("$x$").shift([5.5,-0.5,0]) #---- x axis
+        label_y = TextMobject("$y$").shift([-0.5,5.5,0]).rotate(-4.5) #---- y axis    
+
+        #---- surface of a paraboloid 
+        surface = ParametricSurface(
+            lambda u, v: np.array([
+                np.cos(v)*u,
+                np.sin(v)*u,
+                u**2
+            ]),v_min = -2, v_max = 2, u_min = -2, u_max = 2, checkerboard_colors = [GREEN_B,GREEN_C,GREEN_D,GREEN_E]).shift([0,0,0]).scale(0.5)
+        
+        #---- first contour projection
+        contour1 = ParametricSurface(
+            lambda u, v: np.array([
+                np.cos(TAU * v),
+                np.sin(TAU * v),
+                2*(1 - 2.5*u)
+            ])).fade(0.5).scale(0.21).shift([0,0,1.01])
+        
+        #---- first contour line
+        c_1 = Circle(color = BLUE).scale(0.21).shift([0,0,0]).rotate(0.1,DOWN)
+
+        #-------------------------------------------------
+
+        #---- second contour projection
+        contour2 = ParametricSurface(
+            lambda u, v: np.array([
+                np.cos(TAU * v),
+                np.sin(TAU * v),
+                2*(1 - 1.6*u)
+            ])).fade(0.5).scale(0.41).shift([0,0,0.3]).set_color(RED)
+
+        #---- second contour line
+        c_2 = Circle(color = RED).scale(0.41).shift([0,0,0]).rotate(0.1,DOWN)
+
+        #-------------------------------------------------
+        
+        #---- third contour projection
+        contour3 = ParametricSurface(
+            lambda u, v: np.array([
+                np.cos(TAU * v),
+                np.sin(TAU * v),
+                2*(1 - 1.5*u)
+            ])).fade(0.5).scale(0.61).shift([0,0,0.4]).set_color(YELLOW)
+        
+        #---- third contour line
+        c_3 = Circle(color = YELLOW).scale(0.61).shift([0,0,0])
+
+        #-------------------------------------------------
+
+        #---- fourth contour projection
+        contour4 = ParametricSurface(
+            lambda u, v: np.array([
+                np.cos(TAU * v),
+                np.sin(TAU * v),
+                2*(1 - 1.5*u)
+            ])).fade(0.7).scale(0.81).shift([0,0,0.7]).set_color(PINK)
+
+        #---- fourth contour line
+        c_4 = Circle(color = PINK).scale(0.81).shift([0,0,0])
+
+        #-------------------------------------------------
+        
+        #---- fifth contour projection
+        contour5 = ParametricSurface(
+            lambda u, v: np.array([
+                np.cos(TAU * v),
+                np.sin(TAU * v),
+                2*(1 - 1.5*u)
+            ])).fade(0.7).scale(1.01).shift([0,0,1]).set_color(PURPLE)
+        
+        #---- fifth contour line
+        c_5 = Circle(color = PURPLE).scale(1.01).shift([0,0,0])
+
+        c_text= TextMobject("Contour Lines").scale(0.5).shift(2*DOWN)
+        s = Square().scale(1.3)
+        
+        self.set_camera_orientation(phi = 75 * DEGREES, theta = 10 * DEGREES)  
+        self.add_fixed_in_frame_mobjects(heading)
+        self.wait(1)
+        self.play(FadeOut(heading))
+        self.wait(1)
+        self.add(axes)
+        self.add(label_x)
+        self.add(label_y)
+        self.play(Write(surface))
+        self.wait(1)
+        self.add(contour1)
+        self.wait(1)
+        self.play(Write(c_1))
+        self.play(ReplacementTransform(contour1,contour2))
+        self.wait(1)
+        self.play(Write(c_2))
+        self.play(ReplacementTransform(contour2,contour3))
+        self.wait(1)
+        self.play(Write(c_3))
+        self.play(ReplacementTransform(contour3,contour4))
+        self.wait(1)
+        self.play(Write(c_4))
+        self.play(ReplacementTransform(contour4,contour5))
+        self.wait(1)
+        self.play(Write(c_5))
+        self.wait(1)
+        self.play(FadeOut(contour5),FadeOut(axes),FadeOut(label_x),FadeOut(label_y),FadeOut(surface),FadeOut(contour5),FadeOut(contour4),FadeOut(contour3),FadeOut(contour2),FadeOut(contour1))
+        self.wait(1)
+        self.move_camera(phi=0 * DEGREES,theta= 90*DEGREES)
+        self.wait(1)
+        self.add_fixed_in_frame_mobjects(c_text)  
+        self.wait(1)
+        self.play(ShowCreation(s),FadeOut(c_text))      
+        self.wait(1)