Update file4_Constraints_g_and_h.py

1 files changed, 30 insertions, 19 deletions

diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file4_Constraints_g_and_h.py b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file4_Constraints_g_and_h.py
index 742d6b5..a1396fc 100644
--- a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file4_Constraints_g_and_h.py
+++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file4_Constraints_g_and_h.py
@@ -1,41 +1,52 @@
 from manimlib.imports import*
 import math as m
 
-class firstScene(ThreeDScene):
+    class Constraints(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)
+       axes = ThreeDAxes().rotate(m.radians(75))
+        label_x = TextMobject("$x$").shift([-5.5,1,0]).fade(0.4)  #---- x axis
+        label_y = TextMobject("$y$").shift([1,5.5,0]).rotate(-4.5).fade(0.4)  #---- y axis
+
         cylinder = ParametricSurface(
             lambda u, v: np.array([
                 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)
+                2 * (1-1.5*v)
+            ]),checkerboard_colors=[YELLOW_C,YELLOW_D,YELLOW_E]).shift([0.5,0.5,-0.13]).scale(1) 
+
         plane =  ParametricSurface(
             lambda u, v: np.array([
                 u,
                 v,
                 u+v
-            ]),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)
+            ]),checkerboard_colors=[TEAL_C,TEAL_D,TEAL_E]).shift([0,0,0]).rotate(m.radians(-40),RIGHT).scale(4).fade(0.3)
+
+        c = Circle(color='#FF00FF',fill_opacity=0.3).shift([0.7,-1.3,0.4]).rotate(2.5,UP).scale(1.32)
+
+        f_text = TextMobject("$f(x,y)=x^2+y^2+z^2$",color = '#FFA074').scale(0.6).to_corner(UL)
+        g_text = TextMobject("$g(x,y)=x^2+y^2+1$",color = '#FFA074').scale(0.6).to_corner(UL)
+        h_text = TextMobject("$h(x,y)=x+y-z=1$",color = '#FFA074').scale(0.6).to_corner(UL)
+
+
+
+        self.set_camera_orientation(phi=65*DEGREES,theta=95*DEGREES)
 
-        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.wait(1) 
+        self.add_fixed_in_frame_mobjects(f_text)    
+        self.play(Write(c))
+        self.wait(1)
+        self.play(FadeOut(f_text))
+        self.wait(1)
+        self.add_fixed_in_frame_mobjects(g_text)
         self.play(Write(cylinder)) 
-        self.play(Write(plane)) 
         self.wait(1)
-        self.begin_ambient_camera_rotation(rate=0.4)    
+        self.play(FadeOut(g_text))
         self.wait(1)
+        self.add_fixed_in_frame_mobjects(h_text)
+        self.play(Write(plane))            
         self.wait(1)
-        self.play(FadeOut(label_x),FadeOut(label_y))
-        self.wait(1)           
+        self.play(FadeOut(h_text))
         self.wait(1)