Update file4_Types_of_critical_points.py

1 files changed, 99 insertions, 73 deletions

diff --git a/FSF-2020/approximations-and-optimizations/Critical-Points/file4_Types_of_critical_points.py b/FSF-2020/approximations-and-optimizations/Critical-Points/file4_Types_of_critical_points.py
index 42703ba..656fb68 100644
--- a/FSF-2020/approximations-and-optimizations/Critical-Points/file4_Types_of_critical_points.py
+++ b/FSF-2020/approximations-and-optimizations/Critical-Points/file4_Types_of_critical_points.py
@@ -1,108 +1,134 @@
-from manimlib.imports import *
+from manimlib.imports import*
+ 
 
-
-class MaximaScene(ThreeDScene):
+#---- Relative Maxima 
+class firstScene(ThreeDScene):
     def construct(self):
-        axes = ThreeDAxes()
-        
+
         r_text = TextMobject("Relative Maximum at ORIGIN",color ='#87CEFA')
-        f_text = TextMobject("$f(x,y) = -x^2-y^2$").to_corner(UL)
 
-        #----graph of first function f(x,y) = -x**2-y**2
-        f = ParametricSurface(
+        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
+
+        #----graph of the function f(x,y) = -x**2-y**2
+        surface = ParametricSurface(
             lambda u, v: np.array([
                 u,
                 v,
                 -u**2-v**2
-            ]),v_min = -1, v_max = 1, u_min = -1, u_max = 1, checkerboard_colors = [YELLOW_B,YELLOW_C,YELLOW_D, YELLOW_E],
-            resolution = (20, 20)).scale(1.5).shift([0,0,-0.51]).fade(0.3)
-        
-        d = Dot(np.array([0,0,0]), color = '#800000')        #---- critical point 
-        
-        self.set_camera_orientation(phi = 75 * DEGREES, theta = -45 * DEGREES )
+            ]),v_min = -1, v_max = 1, u_min = -1, u_max = 1, checkerboard_colors = [YELLOW_B,YELLOW_C,YELLOW_D, YELLOW_E]).scale(1.5).shift([0,0,-0.51]).fade(0.3)
+
+        f_text = TextMobject("$f(x,y) = -x^2-y^2$").to_corner(UL)
+
+        d = Dot(color = "#800000").shift([0,0,0]) #---- critical point
+
+        self.set_camera_orientation(phi = 75 * DEGREES, theta = 45 * DEGREES)
         self.add_fixed_in_frame_mobjects(r_text)
         self.wait(1)
         self.play(FadeOut(r_text))
+        self.begin_ambient_camera_rotation(rate = 0.1) 
         self.add(axes)
-        self.play(Write(f),Write(d))
+        self.add(label_x)
+        self.add(label_y)
+        self.play(Write(surface),Write(d))
         self.add_fixed_in_frame_mobjects(f_text)
         self.wait(2)
-        self.play(FadeOut(axes),FadeOut(f),FadeOut(f_text),FadeOut(d))
-        
-class SaddlePoint(ThreeDScene):
+        self.play(FadeOut(axes),FadeOut(surface),FadeOut(f_text),FadeOut(d),FadeOut(label_x),FadeOut(label_y))
+
+
+#---- Relative Minima 
+class secondScene(ThreeDScene):
     def construct(self):
 
-        r2_text = TextMobject("Saddle Point",color ='#87CEFA')    
+        r2_text = TextMobject("Relative Minimum at ORIGIN",color ='#87CEFA')
+
         axes = ThreeDAxes()
-        
-        #----graph of third function f(x,y) = -x**2+y**2   
-        f2 = ParametricSurface(
-            lambda u, v: np.array([
-                u,
-                v,
-                -u**2+v**2
-            ]),v_min = -1, v_max = 1, u_min = -1, u_max = 1,checkerboard_colors = [PURPLE_B,PURPLE_C,PURPLE_D,PURPLE_E]).scale(1.5).shift([0,0,0])
-        
-        #---- trace along y axis
-        a = ParametricSurface(
-            lambda u, v: np.array([
-                u,
-                v,
-                v**2
-            ]),v_min = -1, v_max = 1, u_min = -0.2, u_max = 0.2).shift([0,0,0.36]).scale(1.5).set_color(GREEN)
-        
-        #---- trace along x axis
-        b = ParametricSurface(
+        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
+
+        #----graph of the function g(x,y) = x**2+y**2
+        surface = ParametricSurface(
             lambda u, v: np.array([
                 u,
                 v,
-                -u**2
-            ]),v_min = -0.2, v_max = 0.2, u_min = -1, u_max = 1).scale(1.6).shift([0,0,-0.1]).set_color(GREEN)
-        
-        d = Dot(color = '#800000').shift([0,0,0.1]) #---- critical point
-        
-        f2_text = TextMobject("$f(x,y) = -x^2+y^2$").to_corner(UL)
+                u**2+v**2
+            ]),v_min = -1, v_max = 1, u_min = -1, u_max = 1, checkerboard_colors =[TEAL_B,TEAL_C,TEAL_D,TEAL_E]).scale(1.5).shift([0,0,0.55]).fade(0.1)
+
+        d = Dot(color = "#800000").shift([0,0,0]) #---- critical point
         
+        g_text = TextMobject("$f(x,y) = x^2+y^2$").to_corner(UL)   
+
+        self.set_camera_orientation(phi = 75 * DEGREES, theta = 45 * DEGREES)
         self.add_fixed_in_frame_mobjects(r2_text)
         self.wait(1)
-        self.set_camera_orientation(phi=75*DEGREES,theta=10*DEGREES)
         self.play(FadeOut(r2_text))
-        self.add(axes)        
-        self.begin_ambient_camera_rotation(rate=0.4) 
-        self.add_fixed_in_frame_mobjects(f2_text)
-        self.play(Write(f2))         
-        self.add(b)
-        self.wait(1)
-        self.add(a)
-        self.wait(3)
-        self.add(d)          
+        self.begin_ambient_camera_rotation(rate = 0.1) 
+        self.add(axes)
+        self.add(label_x)
+        self.add(label_y)
+        self.play(Write(surface),Write(d))
+        self.add_fixed_in_frame_mobjects(g_text)
         self.wait(2)
-      
-    
-class MinimaScene(ThreeDScene):
+        self.play(FadeOut(axes),FadeOut(surface),FadeOut(g_text),FadeOut(d),FadeOut(label_x),FadeOut(label_y))
+
+
+
+#---- Saddle Point
+class thirdScene(ThreeDScene):
     def construct(self):
-        
-        r3_text = TextMobject("Relative Minimum at ORIGIN",color ='#87CEFA')
+
+        r3_text = TextMobject("Saddle Point", color = '#87CEFA')
+    
         axes = ThreeDAxes()
-        
-        f3_text = TextMobject("$f(x,y) = x^2+y^2$").to_corner(UL)         
-        
-        #----graph of third function f(x,y) = x**2+y**2   
-        f3 = ParametricSurface(
+        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     
+
+        #---- graph of function h(x,y) = -x^2 + y^2   
+        surface = ParametricSurface(
             lambda u, v: np.array([
                 u,
                 v,
-                u**2+v**2
-            ]),v_min = -1, v_max = 1, u_min = -1, u_max = 1, checkerboard_colors =[TEAL_B,TEAL_C,TEAL_D,TEAL_E],
-            resolution = (20, 20)).scale(1.5).shift([0,0,0.55]).fade(0.1) 
+                -u**2+v**2
+            ]),v_min = -1, v_max = 1, u_min = -1, u_max = 1,checkerboard_colors = [PURPLE_B,PURPLE_C,PURPLE_D,PURPLE_E]).scale(1.5).shift([0,0,0])
         
-        self.set_camera_orientation(phi = 75 * DEGREES, theta = -45 * DEGREES )
-        d = Dot(np.array([0,0,0]), color = '#800000')        #---- critical point  
+        #---- curve(trace) along x axis
+        curve_x = ParametricSurface(
+            lambda u, v: np.array([
+                u*0.4,
+                v,
+                v**2
+            ]),v_min = -1, v_max = 1, u_min = -0.2, u_max = 0.2).shift([0,0,0.34]).scale(1.5).set_color("#800000")
+
+        #---- curve(trace) along y axis
+        curve_y = ParametricSurface(
+            lambda u, v: np.array([
+                u,
+                v*0.4,
+                -u**2
+            ]),v_min = -0.2, v_max = 0.2, u_min = -1, u_max = 1).scale(1.6).shift([0,0,-0.1]).set_color("#800000")
         
+        d = Dot(color = GREEN).shift([0,0,0.1]) #---- critical point
+
+        h_text = TextMobject("$f(x,y) = -x^2+y^2$").to_corner(UL)
+
         self.add_fixed_in_frame_mobjects(r3_text)
         self.wait(1)
+        self.set_camera_orientation(phi = 50 * DEGREES,theta = 45 * DEGREES)
         self.play(FadeOut(r3_text))
-        self.add(axes)
-        self.play(Write(f3),Write(d))
-        self.add_fixed_in_frame_mobjects(f3_text)
-        self.wait(2)
+        self.add(axes)    
+        self.add(label_x)
+        self.add(label_y)    
+        self.begin_ambient_camera_rotation(rate = 0.3) 
+        self.add_fixed_in_frame_mobjects(h_text)
+        self.play(Write(surface))
+        self.wait(1)               
+        self.add(curve_y)
+        self.add(d)
+        self.wait(1)
+        self.play(FadeOut(curve_y))
+        self.wait(1)
+        self.add(curve_x)
+        self.wait(1)
+        self.add(d)  
+        self.wait(1)