1 files changed, 93 insertions, 0 deletions
diff --git a/FSF-2020/approximations-and-optimizations/Critical-Points/file2_Traces_and_Tangent.py b/FSF-2020/approximations-and-optimizations/Critical-Points/file2_Traces_and_Tangent.py
new file mode 100644
index 0000000..65b4414
--- /dev/null
+++ b/FSF-2020/approximations-and-optimizations/Critical-Points/file2_Traces_and_Tangent.py
@@ -0,0 +1,93 @@
+from manimlib.imports import*
+import math as m
+
+
+class firstScene(ThreeDScene):
+    def construct(self):
+    
+        axes = ThreeDAxes().scale(1.15)
+        surface = ParametricSurface(
+            lambda u, v: np.array([
+                u,
+                v,
+                m.exp(-10*u**2-10*v**2) #---- f(x,y) 
+            ]),u_min=-2,u_max=1, v_min=-1,v_max=1,checkerboard_colors=[PURPLE_C,PURPLE_D,PURPLE_E,PURPLE_B]).scale(3).shift([1.1,0.48,1.731])
+
+        trace = ParametricSurface(
+            lambda u, v: np.array([
+            m.exp(np.cos(v)+np.sin(v)),
+            v,
+            u/4
+            ]), v_min = -1, v_max= 2).rotate(1.571,DOWN).shift(2.15*LEFT+[0.6,-0.4,1.54]).scale(1).set_color('#800000') 
+
+         
+        
+        d = Dot(color =YELLOW).shift([1.9,0.7,4.1]) #---- critical point
+        tangent_line = Line(color = '#228B22').scale(1).shift([1.9,0.7,4.1]).rotate(4.5) #---- tangent along y axis
+
+        label_x = TextMobject("$x$").shift([5.8,-0.5,0])
+        label_y = TextMobject("$y$").shift([-0.5,5.6,0]).rotate(-4.5)
+
+
+        f_text = TextMobject("Tangent to the trace with $y$ constant at critical point").shift(3*RIGHT+2*UP).scale(0.5).to_corner(UL)
+        
+        self.add(axes)
+        self.set_camera_orientation(phi=60*DEGREES,theta=15*DEGREES)
+        self.add(label_x)
+        self.add(label_y)
+        self.play(Write(surface))  
+        self.wait(1)
+        self.add_fixed_in_frame_mobjects(s_text)
+        self.add(trace)
+        self.wait(1)
+        self.play(Write(tangent_line),Write(d))
+        self.wait(2)
+        
+        
+class secondScene(ThreeDScene):
+    def construct(self):
+    
+        axes = ThreeDAxes().scale(1.15)
+        surface = ParametricSurface(
+            lambda u, v: np.array([
+                u,
+                v,
+                m.exp(-10*u**2-10*v**2) #---- f(x,y) 
+            ]),u_min=-2,u_max=1, v_min=-1,v_max=1,checkerboard_colors=[PURPLE_C,PURPLE_D,PURPLE_E,PURPLE_B]).scale(3).shift([1.1,0.48,1.731])
+
+        trace = ParametricSurface(
+            lambda u, v: np.array([
+            m.exp(np.cos(v)+np.sin(v)),
+            v,
+            u/4
+            ]), v_min = -1, v_max= 2).rotate(1.571,DOWN).shift(2.15*LEFT+[0.6,-0.4,1.54]).scale(1).set_color('#800000') 
+
+         
+        
+        d = Dot(color =YELLOW).shift([1.9,0.7,4.1]) #---- critical point
+
+        label_x = TextMobject("$x$").shift([5.8,-0.5,0])
+        label_y = TextMobject("$y$").shift([-0.5,5.6,0]).rotate(-4.5)
+
+        f_text = TextMobject("Tangent to the trace with $y$ constant at critical point").shift(3*RIGHT+2*UP).scale(0.5).to_corner(UL)
+        
+        tangent_line = Line(color = '#228B22').scale(1).shift([1.9,0.7,4.1]) #---- tangent along x axis
+
+
+        self.add(axes)
+        self.set_camera_orientation(phi=60*DEGREES,theta=15*DEGREES)
+        self.add(label_x)
+        self.add(label_y)
+        self.play(Write(surface))  
+        self.wait(1)       
+        self.add_fixed_in_frame_mobjects(f_text)
+        trace.rotate(-5).shift(0.2*RIGHT+0.8*UP+[0.6,-0.4,0.6])
+        self.add(trace)
+        self.play(Write(tangent_line),Write(d))
+        self.wait(1)
+        
+        
+
+        
+
+