1 files changed, 41 insertions, 0 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
new file mode 100644
index 0000000..742d6b5
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file4_Constraints_g_and_h.py
@@ -0,0 +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 * 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]).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=0.4)    
+        self.wait(1)
+        self.wait(1)
+        self.play(FadeOut(label_x),FadeOut(label_y))
+        self.wait(1)           
+        self.wait(1)