Update file2_Geometric_Proof.py

1 files changed, 35 insertions, 13 deletions

diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file2_Geometric_Proof.py b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file2_Geometric_Proof.py
index 4374ff7..2c2a9de 100644
--- a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file2_Geometric_Proof.py
+++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file2_Geometric_Proof.py
@@ -1,8 +1,12 @@
 from manimlib.imports import*
 
-class firstScene(ThreeDScene):
+#---- visualization of geometric proof of Lagrange multiplier
+class GeometricProof(ThreeDScene):
     def construct(self):
-        axes = ThreeDAxes().scale(0.7).rotate(math.radians(180))
+        axes = ThreeDAxes().scale(0.7).rotate(math.radians(180))       
+        label_x = TextMobject("$x$").shift(4*RIGHT).fade(0.4)  #---- x axis
+        label_y = TextMobject("$y$").shift(3.2*DOWN+0.2*RIGHT).rotate(math.radians(180)).fade(0.4)  #---- y axis
+
         surface = ParametricSurface(
             lambda u, v: np.array([
                 1*np.sin(u)*np.cos(v),
@@ -11,15 +15,16 @@ class firstScene(ThreeDScene):
             ]),u_min=0,u_max=PI/2,v_min=0,v_max=2*PI,checkerboard_colors=[GREEN_C, GREEN_E]).scale(1).shift([-1.5,-1.5,0])
          
         d = Dot([-2,-2.55,0],color = '#800000')
-        a_df = Arrow(color = '#00FFFF').rotate(-2).shift(3.2*DOWN+2.3*LEFT) #---- f parallel to g
-        a_dg = Arrow(color = '#FF00FF').scale(0.8).shift(3.2*DOWN+2.3*LEFT).rotate(-2) #---- f parallel to g
+        a_df = Arrow(color = '#00FFFF').rotate(-2).shift(3.2*DOWN+2.3*LEFT) #---- f parallel to g at maxima
+        a_dg = Arrow(color = '#FF00FF').scale(0.8).shift(3.2*DOWN+2.3*LEFT).rotate(-2) #---- g parallel to f at maxima
 
-        b_df = Arrow(color = '#00FFFF').rotate(1.1).shift(0.82*LEFT+0.15*UP) #---- f parallel to g
-        b_dg = Arrow(color = '#FF00FF').scale(0.6).rotate(-2).shift(1.43*LEFT+1.1*DOWN) #---- f parallel to g
+        b_dg = Arrow(color = '#00FFFF').rotate(1.1).shift(0.82*LEFT+0.15*UP) #---- g parallel to f at minima
+        b_df = Arrow(color = '#FF00FF').scale(0.6).rotate(-2).shift(1.43*LEFT+1.1*DOWN) #---- f parallel to g at minima
 
 
         qd = Dot(color = '#800000').shift(1.2*LEFT+0.6*DOWN)
 
+        #---- level curves
         l1 = Line([-1,-3.1,0],[-4,-3.1,0],color = PINK).rotate(-0.3).fade(0.6)
         l2 = Line([-0.9,-2.9,0],[-4,-2.9,0],color = PINK).rotate(-0.3).fade(0.6)
         l3= Line([-0.8,-2.7,0],[-4,-2.7,0],color = PINK).rotate(-0.3).fade(0.6)
@@ -36,19 +41,36 @@ class firstScene(ThreeDScene):
         l14= Line([-0,-0.35,0],[-4,-0.35,0],color = PINK).rotate(-0.3).fade(0.6)
         l15= Line([-0.,-0.15,0],[-4,-0.15,0],color = PINK).rotate(-0.3).fade(0.6)
 
-        level_Curve = VGroup(l1,l2,l3,l4,l5,l6,l7,l8,l9,l10,l11,l12,l13,l14,l15)
-
         rel_text = TextMobject("$\\nabla f = \\lambda \\nabla g$",color = TEAL).shift([3,3.2,0]).scale(0.5)
 
         f_text = TextMobject("$\\nabla f$",color = '#800000').shift([1,1,0]).scale(0.5)
         g_text = TextMobject("$\\nabla g$").shift([1.2,-0.8,0]).scale(0.5)
 
         p_text= TextMobject("$P$").shift([1.8,2.6,0]).scale(0.5)
-        
 
-        
-        self.add(axes)
+        #---- labelling of level curves
+        l1_text = TextMobject("$w=$ 17").rotate(math.radians(180)).scale(0.4).shift(2.7*DOWN+4.36*LEFT)
+        l2_text = TextMobject("$w=$ 16").rotate(math.radians(180)).scale(0.4).shift(2.46*DOWN+4.36*LEFT)
+        l3_text = TextMobject("$w=$ 15").rotate(math.radians(180)).scale(0.4).shift(2.2*DOWN+4.36*LEFT)
+        l4_text = TextMobject("$w=$ 14").rotate(math.radians(180)).scale(0.4).shift(1.97*DOWN+4.36*LEFT)
+        l5_text = TextMobject("$w=$ 13").rotate(math.radians(180)).scale(0.4).shift(1.74*DOWN+4.36*LEFT)
+        l6_text = TextMobject("$w=$ 12").rotate(math.radians(180)).scale(0.4).shift(1.5*DOWN+4.36*LEFT)
+        l7_text = TextMobject("$w=$ 11").rotate(math.radians(180)).scale(0.4).shift(1.26*DOWN+4.36*LEFT)
+        l8_text = TextMobject("$w=$ 10").rotate(math.radians(180)).scale(0.4).shift(1.05*DOWN+4.36*LEFT)
+        l9_text = TextMobject("$w=$ 9").rotate(math.radians(180)).scale(0.4).shift(0.8*DOWN+4.32*LEFT)
+        l10_text = TextMobject("$w=$ 8").rotate(math.radians(180)).scale(0.4).shift(0.6*DOWN+4.32*LEFT)
+        l11_text = TextMobject("$w=$ 7").rotate(math.radians(180)).scale(0.4).shift(0.4*DOWN+4.32*LEFT)
+        l12_text = TextMobject("$w=$ 6").rotate(math.radians(180)).scale(0.4).shift(0.2*DOWN+4.32*LEFT)
+        l13_text = TextMobject("$w=$ 5").rotate(math.radians(180)).scale(0.4).shift(-0.02*DOWN+4.32*LEFT)
+        l14_text = TextMobject("$w=$ 4").rotate(math.radians(180)).scale(0.4).shift(-0.23*DOWN+4.32*LEFT)
+        l15_text = TextMobject("$w=$ 3").rotate(math.radians(180)).scale(0.4).shift(-0.44*DOWN+4.32*LEFT)
+
+        level_Curve = VGroup(l1,l1_text,l2,l2_text,l3,l3_text,l4,l4_text,l5,l5_text,l6,l6_text,l7,l7_text,l8,l8_text,l9,l9_text,l10,l10_text,l11,l11_text,l12,l12_text,l13,l13_text,l14,l14_text,l15,l15_text)
+
         self.set_camera_orientation(phi=0 * DEGREES, theta = 90*DEGREES)
+        self.add(axes)
+        self.add(label_x)
+        self.add(label_y)      
         self.play(Write(surface))
         self.wait(1)
         self.play(ShowCreation(level_Curve))
@@ -61,8 +83,8 @@ class firstScene(ThreeDScene):
         self.play(Write(qd)) 
         self.wait(1)        
         self.play(ShowCreation(b_df))
-        self.play(ShowCreation(b_dg))        
-        self.wait(1)
         self.add_fixed_in_frame_mobjects(f_text)
+        self.wait(1)
+        self.play(ShowCreation(b_dg))              
         self.add_fixed_in_frame_mobjects(g_text)
         self.wait(1)