Update file4_Types_of_critical_points.py

1 files changed, 63 insertions, 25 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 f9c1ef0..42703ba 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
@@ -1,6 +1,7 @@
 from manimlib.imports import *
 
-class TypescpAnimation(ThreeDScene):
+
+class MaximaScene(ThreeDScene):
     def construct(self):
         axes = ThreeDAxes()
         
@@ -16,19 +17,74 @@ class TypescpAnimation(ThreeDScene):
             ]),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)
         
-        r2_text = TextMobject("Saddle Point at ORIGIN",color ='#87CEFA')
-        f2_text = TextMobject("$f(x,y) = -x^2+y^2$").to_corner(UL)
+        d = Dot(np.array([0,0,0]), color = '#800000')        #---- 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.add(axes)
+        self.play(Write(f),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):
+    def construct(self):
 
-        #----graph of second function f(x,y) = -x**2+y**2   
+        r2_text = TextMobject("Saddle Point",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 = [RED_B,RED_C,RED_D, RED_E],
-            resolution = (20, 20)).scale(1.5).shift([0,0.2,0]).fade(0.3)
+            ]),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(
+            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)
+        
+        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.wait(2)
+      
+    
+class MinimaScene(ThreeDScene):
+    def construct(self):
         
         r3_text = TextMobject("Relative Minimum at ORIGIN",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   
@@ -42,25 +98,7 @@ class TypescpAnimation(ThreeDScene):
         
         self.set_camera_orientation(phi = 75 * DEGREES, theta = -45 * DEGREES )
         d = Dot(np.array([0,0,0]), color = '#800000')        #---- critical point  
-
-        self.add_fixed_in_frame_mobjects(r_text)
-        self.wait(1)
-        self.play(FadeOut(r_text))
-        self.add(axes)
-        self.play(Write(f),Write(d))
-        self.add_fixed_in_frame_mobjects(f_text)
-        self.wait(2)
-        self.play(FadeOut(axes),FadeOut(f),FadeOut(f_text),FadeOut(d))
-
-        self.add_fixed_in_frame_mobjects(r2_text)
-        self.wait(1)
-        self.play(FadeOut(r2_text))
-        self.add(axes)
-        self.play(Write(f2),Write(d))
-        self.add_fixed_in_frame_mobjects(f2_text)
-        self.wait(2)
-        self.play(FadeOut(axes),FadeOut(f2),FadeOut(f2_text),FadeOut(d))
-
+        
         self.add_fixed_in_frame_mobjects(r3_text)
         self.wait(1)
         self.play(FadeOut(r3_text))