Update file2_Traces_and_Tangent.py

1 files changed, 50 insertions, 55 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
index 6be4c6a..95c3af9 100644
--- 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
@@ -1,93 +1,88 @@
 from manimlib.imports import*
 import math as m
 
-
+#---- tangent to the trace with x constant
 class firstScene(ThreeDScene):
     def construct(self):
     
-        axes = ThreeDAxes().scale(1.15)
+        axes = ThreeDAxes().scale(1)
+        label_x= TextMobject("$x$").shift([5.8,-0.5,0])
+        label_y= TextMobject("$y$").shift([-0.5,-5.6,0]).rotate(-4.5)
+        
+        #---- graph of f(x,y) = -x^2-y^2
         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(
+                -u**2-v**2
+            ]),u_min=-1,u_max=1, v_min=-1,v_max=1,checkerboard_colors=[PURPLE_C,PURPLE_D,PURPLE_E,PURPLE_B]).scale(1.5).shift([0,0,2]).rotate(0.2)
+        
+        #---- curve(trace) along y axis
+        curve = 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') 
+                u*0.4,
+                v,
+                -v**2
+            ]),v_min =-1 , v_max =1 , u_min = -0.1, u_max = 0.1).scale(1.6).shift([0.02,0.1,2.3]).set_color("#800000").rotate(0.1)
 
-         
-        
-        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
+        d = Dot(color =YELLOW).shift([-0.05,-0.2,2.3]) #---- 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)
+        x_text = TextMobject("Tangent to the trace with $x$ constant at critical point").shift(3*RIGHT+2*UP).scale(0.5).to_corner(UL)
 
+        tangent_line = Line([-0.05,-1.5,2.3],[-0.05,1.5,2.3],color = '#228B22')
 
-        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.set_camera_orientation(phi = 40 * DEGREES, theta = 55 * DEGREES)
+        self.begin_ambient_camera_rotation(rate = 0.1) 
         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.add_fixed_in_frame_mobjects(x_text)
+        self.add(curve)
         self.wait(1)
         self.play(Write(tangent_line),Write(d))
-        self.wait(2)
-        
-        
+        self.wait(1)  
+
+
+
+#---- tangent to the trace with y constant
 class secondScene(ThreeDScene):
     def construct(self):
     
-        axes = ThreeDAxes().scale(1.15)
+        axes = ThreeDAxes().scale(1)
+        label_x= TextMobject("$x$").shift([5.8,-0.5,0])
+        label_y= TextMobject("$y$").shift([-0.5,-5.6,0]).rotate(-4.5)
+        
+        #---- graph of f(x,y) = -x^2-y^2
         surface = ParametricSurface(
             lambda u, v: np.array([
                 u,
                 v,
-                m.exp(-10*u**2-10*v**2) #---- f(x,y) 
-            ]),u_min=-1,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])
+                -u**2-v**2
+            ]),u_min = -1, u_max = 1, v_min = -1, v_max = 1, checkerboard_colors = [PURPLE_B,PURPLE_C,PURPLE_D,PURPLE_E]).scale(1.5).shift([0,0,2]).rotate(0.2)
 
-        trace = ParametricSurface(
+        #---- curve(trace) along x axis
+        curve = 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') 
-
-         
+                u,
+                v*0.4,
+                -u**2
+            ]),v_min = -0.1, v_max = 0.1, u_min = -1, u_max = 1).scale(1.6).shift([0.07,0.1,2.3]).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)
+        d = Dot(color = YELLOW).shift([0,-0.2,2.3]) #---- critical point
         
-        tangent_line = Line(color = '#228B22').scale(1).shift([1.9,0.7,4.1]) #---- tangent along x axis
-
+        tangent_line = Line(color = '#228B22').scale(1).shift([0,-0.2,2.3]).rotate(m.radians(190),LEFT)
+        
+        y_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.set_camera_orientation(phi = 40 * DEGREES, theta = 55 * DEGREES)
         self.add(label_x)
         self.add(label_y)
+        self.begin_ambient_camera_rotation(rate = 0.1) 
         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.add_fixed_in_frame_mobjects(y_text)
+        self.add(curve)
+        self.wait(1.5)
         self.play(Write(tangent_line),Write(d))
-        self.wait(1)
-        
-        
-
-        
-
-        
+        self.wait(0.5)