Create file1_Extrema_over_g(x,y)=k.py

1 files changed, 53 insertions, 0 deletions

diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file1_Extrema_over_g(x,y)=k.py b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file1_Extrema_over_g(x,y)=k.py
new file mode 100644
index 0000000..17f31ac
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file1_Extrema_over_g(x,y)=k.py
@@ -0,0 +1,53 @@
+from manimlib.imports import*
+
+class firstScene(ThreeDScene):
+    def construct(self):
+        axes = ThreeDAxes()
+        surface = ParametricSurface(
+            lambda u, v: np.array([
+                u,
+                v,
+                u**2+v**2+u**3-v**3
+            ]),u_min=-0.5,u_max=0.5, v_min=-0.5,v_max=0.5).scale(5).shift([0,1,2.5]).set_color('#F0FFFF').fade(0.4)
+        
+        c = Circle().set_color('#FF00FF').shift([-0.4,0,1.5]).rotate(1.9,UP).scale(0.7)
+
+        minima = Dot(color = '#4169E1').shift([-0.5,0.5,1]).rotate(1.571,UP)
+        maxima  = Dot(color = '#4169E1').shift([0.1,0,2.2]).rotate(1.571,UP)
+
+        l1 = DashedLine([-0.5,0.5,0.9],[-0.5,0.5,0],color = '#F08080')
+        l2 = DashedLine([0.1,0,2.1],[0.1,0,0],color = '#F08080')
+
+        c2 = Circle(fill_opacity= 0.5).shift([-0.3,0.2,0]).scale(0.4)
+
+        minima_refl = Dot(color = '#4682B4').shift([-0.5,0.5,0]).rotate(1.571,UP)
+        maxima_refl  = Dot(color = '#4682B4').shift([0.1,0,0]).rotate(1.571,UP)
+
+        max_text = TextMobject("maximum over $g(x,y)=k$",color = '#FFA074').shift([-1.7,0,0]).scale(0.5).shift(2.2*UP)
+        min_text = TextMobject("minimum over $g(x,y)=k$",color = '#FFA074').shift([2.5,0.5,1]).scale(0.5).shift(0.5*UP)
+        label_f = TextMobject("$z=f(x,y)$",color = '#8A2BE2').scale(0.5).shift(3*UP+3*RIGHT)
+        label_g = TextMobject("$g(x,y)=k$",color = '#8A2BE2').scale(0.5).shift(2*RIGHT)      
+       
+
+        self.add(axes)
+        self.set_camera_orientation(phi=75*DEGREES,theta=45*DEGREES)
+        self.play(Write(surface)) 
+        self.add_fixed_in_frame_mobjects(label_f)
+        self.wait(2)
+        self.play(Write(c)) 
+        self.wait(1)
+        self.play(Write(maxima))
+        self.add_fixed_in_frame_mobjects(max_text)
+        self.wait(1)
+        self.play(Write(minima)) 
+        self.add_fixed_in_frame_mobjects(min_text)
+        self.wait(1)
+        self.play(ShowCreation(l1),ShowCreation(l2))
+        self.play(Write(c2))                       
+        self.add_fixed_in_frame_mobjects(label_g)
+        self.wait(1)
+        self.play(Write(maxima_refl))
+        self.play(Write(minima_refl))
+        self.wait(1)
+
+