Update and rename file3_Visualization_of_types_of_critical_points.py to file3_Tangent_plane_at_extrema_of_a_function.py

modified code for gif 3

2 files changed, 53 insertions, 70 deletions

diff --git a/FSF-2020/approximations-and-optimizations/Critical-Points/file3_Tangent_plane_at_extrema_of_a_function.py b/FSF-2020/approximations-and-optimizations/Critical-Points/file3_Tangent_plane_at_extrema_of_a_function.py
new file mode 100644
index 0000000..a9b29f3
--- /dev/null
+++ b/FSF-2020/approximations-and-optimizations/Critical-Points/file3_Tangent_plane_at_extrema_of_a_function.py
@@ -0,0 +1,53 @@
+from manimlib.imports import*  
+
+class TheoremAnimation(ThreeDScene):
+    def construct(self):
+
+        axes = ThreeDAxes()
+
+        #----parabola: x**2+y**2
+        parabola1 = 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=[GREEN_E,GREEN_D,GREEN_C,GREEN_B],
+            resolution=(20, 20)).scale(1)     
+        
+        #----parabola: -x**2-y**2
+        parabola2 = 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=[BLUE_E,BLUE_D,BLUE_C,BLUE_B],
+            resolution=(20, 20)).scale(1)
+               
+        self.set_camera_orientation(phi=75 * DEGREES)  
+        self.begin_ambient_camera_rotation(rate=0.2)  
+
+        d = Dot(np.array([0,0,0]), color = '#800000')           #---- critical point     
+        r = Rectangle(fill_color= '#C0C0C0',fill_opacity = 0.3).move_to(ORIGIN).fade(0.7)   #----tangent plane         
+
+        parabola1_text = TextMobject("Maximum with horizontal tangent plane").scale(0.7).to_corner(UL)    
+     
+        parabola2_text = TextMobject("Minimum with horizontal tangent plane").scale(0.7).to_corner(UL)        
+
+        self.add(axes)
+        self.add_fixed_in_frame_mobjects(parabola2_text)
+        self.wait(1) 
+        self.play(Write(parabola1))
+        self.play(ShowCreation(d))
+        self.wait(1)
+        self.play(ShowCreation(r))     
+        self.wait(2)
+        self.play(FadeOut(parabola2_text),FadeOut(parabola1),FadeOut(r),FadeOut(d))  
+        
+        self.wait(1)
+        self.add_fixed_in_frame_mobjects(parabola1_text)
+        self.wait(1)
+        self.play(Write(parabola2))
+        self.play(ShowCreation(d))
+        self.wait(1)
+        self.play(ShowCreation(r))     
+        self.wait(1)
diff --git a/FSF-2020/approximations-and-optimizations/Critical-Points/file3_Visualization_of_types_of_critical_points.py b/FSF-2020/approximations-and-optimizations/Critical-Points/file3_Visualization_of_types_of_critical_points.py
deleted file mode 100644
index f9055e6..0000000
--- a/FSF-2020/approximations-and-optimizations/Critical-Points/file3_Visualization_of_types_of_critical_points.py
+++ /dev/null
@@ -1,70 +0,0 @@
-from manimlib.imports import *
-
-class TypescpAnimation(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(
-            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_D, YELLOW_E],
-            resolution = (20, 20)).scale(1) 
-        
-        r2_text = TextMobject("Saddle Point at ORIGIN",color ='#87CEFA')
-        f2_text = TextMobject("$f(x,y) = -x^2+y^2$").to_corner(UL)
-
-        #----graph of second 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_D, RED_E],
-            resolution = (20, 20)).scale(1)
-        
-        r3_text = TextMobject("Relative Minimum at ORIGIN",color ='#87CEFA')
-        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(
-            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 = [GREEN_D, GREEN_E],
-            resolution = (20, 20)).scale(1) 
-        
-        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))
-        self.add(axes)
-        self.play(Write(f3),Write(d))
-        self.add_fixed_in_frame_mobjects(f3_text)
-        self.wait(2)