Create file 3_Visualization of types of critical points.py

1 files changed, 70 insertions, 0 deletions

diff --git a/FSF-2020/approximations-and-optimizations/Critical-Points/file 3_Visualization of types of critical points.py b/FSF-2020/approximations-and-optimizations/Critical-Points/file 3_Visualization of types of critical points.py
new file mode 100644
index 0000000..f9055e6
--- /dev/null
+++ b/FSF-2020/approximations-and-optimizations/Critical-Points/file 3_Visualization of 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_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)