Update file1_Critical_Point_of_a_function.py

1 files changed, 36 insertions, 7 deletions

diff --git a/FSF-2020/approximations-and-optimizations/Critical-Points/file1_Critical_Point_of_a_function.py b/FSF-2020/approximations-and-optimizations/Critical-Points/file1_Critical_Point_of_a_function.py
index 0b15ebf..f3c16d4 100644
--- a/FSF-2020/approximations-and-optimizations/Critical-Points/file1_Critical_Point_of_a_function.py
+++ b/FSF-2020/approximations-and-optimizations/Critical-Points/file1_Critical_Point_of_a_function.py
@@ -6,27 +6,56 @@ class CriticalPoint(ThreeDScene):
     def construct(self):
     
         axes = ThreeDAxes()
-        surface = ParametricSurface(
+        
+        surface = ParametricSurface( #---- partial derivatives of the funtion exists
+            lambda u, v: np.array([
+                u,
+                v,
+                m.exp(-10*u**2-10*v**2)]),u_min=-1,u_max=1, v_min=-1,v_max=1,checkerboard_colors=[TEAL_E,TEAL_D,TEAL_C]).fade(0.6).scale(3.5).shift([0,0,1.5])
+        
+        surface2 = ParametricSurface( #---- partial derivatives of the funtion does not exists
             lambda u, v: np.array([
                 u,
                 v,
-                m.exp(-10*u**2-10*v**2) #---- function equation
-            ]),u_min=-1,u_max=1, v_min=-1,v_max=1,checkerboard_colors=[TEAL_E,TEAL_D,TEAL_C]).fade(0.6).scale(3.5).shift([0,0,1.5])
+                abs(u)+abs(v)]),u_min=-1.5,u_max=1.5, v_min=-1.5,v_max=1.5,checkerboard_colors=[TEAL_E,TEAL_D,TEAL_C,TEAL_B])
         
         l1 = Line([0,0,3.75],[0,0,0],color = '#800000')
         
-        d = Dot([0,0,3.75],color = '#800000')
+        d = Dot([0,0,3.75],color = '#800000') #---- critical point of surface
+        
+        d2 = Dot([0,0,0],color = '#800000') #---- critical point of surface2
+        
+        d_text = TextMobject("$\\frac{\\partial f}{\\partial x}=\\frac{\\partial f}{\\partial y} = 0$").scale(1).to_corner(UL)
+        
+        d2_text = TextMobject("$\\frac{\\partial f}{\\partial x}$ and/or $\\frac{\\partial f}{\\partial y}$ does not exist").scale(0.8).to_corner(UL)
+        
         f_text = TextMobject("Critical Point of a function",color = YELLOW).shift([3,0,3.7]).scale(0.7)
 
-        self.add(axes)
+        g_text = TextMobject("Critical Point of a function",color = YELLOW).shift(1*DOWN).scale(0.5)
+        
         self.set_camera_orientation(phi=75*DEGREES,theta=90*DEGREES) 
-        self.begin_ambient_camera_rotation(rate=0.4)   
+        self.add(axes)        
+        self.begin_ambient_camera_rotation(rate=0.2)   
         self.play(Write(surface))
+        self.add_fixed_in_frame_mobjects(d_text)
         self.wait(1)
         self.play(Write(l1))
         self.play(Write(d))
-        self.wait(2)
+        self.wait(1)
         self.move_camera(phi=0 * DEGREES,theta = 90*DEGREES)
+        self.wait(2)
         self.add_fixed_in_frame_mobjects(f_text)
+        self.play(FadeOut(f_text),FadeOut(surface),FadeOut(axes),FadeOut(d_text),FadeOut(d),FadeOut(l1))
         self.wait(1)
+        self.set_camera_orientation(phi=75*DEGREES,theta=60*DEGREES) 
+        self.add(axes)        
+        self.begin_ambient_camera_rotation(rate=0.3) 
+        self.add_fixed_in_frame_mobjects(d2_text) 
+        self.wait(1) 
+        self.play(Write(surface2))
+        l1.fade(0.4)
+        self.play(Write(l1))
+        self.play(Write(d2))        
+        self.add_fixed_in_frame_mobjects(g_text)
+        self.wait(2)