Update and rename file4_f(x,y)=(y-x)(1-2x-3y).py to file4_Types_of_critical_points.py

2 files changed, 70 insertions, 32 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
new file mode 100644
index 0000000..f9c1ef0
--- /dev/null
+++ b/FSF-2020/approximations-and-optimizations/Critical-Points/file4_Types_of_critical_points.py
@@ -0,0 +1,70 @@
+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_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)
+
+        #----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_B,RED_C,RED_D, RED_E],
+            resolution = (20, 20)).scale(1.5).shift([0,0.2,0]).fade(0.3)
+        
+        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 =[TEAL_B,TEAL_C,TEAL_D,TEAL_E],
+            resolution = (20, 20)).scale(1.5).shift([0,0,0.55]).fade(0.1) 
+        
+        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)
diff --git a/FSF-2020/approximations-and-optimizations/Critical-Points/file4_f(x,y)=(y-x)(1-2x-3y).py b/FSF-2020/approximations-and-optimizations/Critical-Points/file4_f(x,y)=(y-x)(1-2x-3y).py
deleted file mode 100644
index 72c93b1..0000000
--- a/FSF-2020/approximations-and-optimizations/Critical-Points/file4_f(x,y)=(y-x)(1-2x-3y).py
+++ /dev/null
@@ -1,32 +0,0 @@
-from manimlib.imports import*
-
-class ExampleAnimation(ThreeDScene):
-    def construct(self):
-        axes = ThreeDAxes()
-
-        f_text = TextMobject("$f(x,y) = (y-x)(1-2x-3y)$").to_corner(UL)        
-        d = Dot(np.array([0,0,0]), color = '#800000')   #---- Critical Point
-        d_text = TextMobject("$(0.2,0.2)$",color = '#DC143C').scale(0.5).shift(0.2*UP)  #----x = 0.2, y = 0.2
-        r_text=TextMobject("Critical Point",color = '#00FFFF').shift(0.3*DOWN).scale(0.6)
-
-        #----f(x,y) = (y-x)(1-2x-3y)
-        f = ParametricSurface(
-            lambda u, v: np.array([
-                u,
-                v,
-                (v-u)*(1-2*u-3*v)
-            ]),v_min = -1, v_max = 1, u_min = -1, u_max = 1, checkerboard_colors = [PURPLE_D, PURPLE_E],
-            resolution=(20, 20)).scale(1)       
-        
-        self.set_camera_orientation(phi = 75 * DEGREES)
-        self.begin_ambient_camera_rotation(rate=0.5)
-
-        self.add_fixed_in_frame_mobjects(f_text)
-        self.wait(1) 
-        self.add(axes)
-        self.play(Write(f),Write(d))
-        self.wait(1)
-        self.add_fixed_in_frame_mobjects(d_text)
-        self.wait(1)
-        self.add_fixed_in_frame_mobjects(r_text)
-        self.wait(3)