Update file3_Optimizing_function_w.r.t_one_constraint.py

1 files changed, 26 insertions, 14 deletions

diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file3_Optimizing_function_w.r.t_one_constraint.py b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file3_Optimizing_function_w.r.t_one_constraint.py
index bf75dd8..742d6b5 100644
--- a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file3_Optimizing_function_w.r.t_one_constraint.py
+++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file3_Optimizing_function_w.r.t_one_constraint.py
@@ -1,29 +1,41 @@
 from manimlib.imports import*
+import math as m
 
 class firstScene(ThreeDScene):
     def construct(self):
         axes = ThreeDAxes()
+        label_x = TextMobject("$x$").shift([5.5,-0.5,0]).fade(0.4)  #---- x axis
+        label_y = TextMobject("$y$").shift([-0.5,5.5,0]).rotate(-4.5).fade(0.4)  #---- y axis
+        
+        #---- constraint g(x,y)
         cylinder = ParametricSurface(
             lambda u, v: np.array([
-                np.cos(TAU * v),
-                np.sin(TAU * v),
-                2 * (u)
-            ]),checkerboard_colors=[YELLOW_C,YELLOW_D,YELLOW_E]
-        ).fade(0.4) #Resolution of the surfaces
-
+                np.cos(TAU * u),
+                np.sin(TAU * u),
+                2 * (v)
+            ]),checkerboard_colors=[YELLOW_C,YELLOW_D,YELLOW_E]).rotate(m.radians(-40),RIGHT).shift([0.5,0.5,0]).scale(0.8)
+        
+        #---- constraint h(x,y)
         plane =  ParametricSurface(
             lambda u, v: np.array([
                 u,
                 v,
                 u+v
-            ]),checkerboard_colors=[TEAL_C,TEAL_D,TEAL_E]
-        ).scale(2.5)
-        self.add(axes)
-        self.set_camera_orientation(phi=75*DEGREES,theta=45*DEGREES)
+            ]),checkerboard_colors=[TEAL_C,TEAL_D,TEAL_E]).shift([0,0,0]).rotate(m.radians(-40),RIGHT).scale(2).fade(0.3)
+        
+        figure = VGroup(cylinder,plane).rotate(m.radians(-45),DOWN).scale(1.5)
+
+        self.set_camera_orientation(phi=65*DEGREES,theta=45*DEGREES)
+        self.add(axes)        
+        self.add(label_x) 
+        self.add(label_y)
+        self.wait(1)       
         self.play(Write(cylinder)) 
         self.play(Write(plane)) 
         self.wait(1)
-        self.begin_ambient_camera_rotation(rate=0.7)          
-        self.wait(5)
-        self.move_camera(phi=35*DEGREES,theta=-45*DEGREES)
-        self.wait(2)
+        self.begin_ambient_camera_rotation(rate=0.4)    
+        self.wait(1)
+        self.wait(1)
+        self.play(FadeOut(label_x),FadeOut(label_y))
+        self.wait(1)           
+        self.wait(1)