Create file4_Tangent plane_at_critical_points.py

Manim code of Video 4 of the lecture note on the subtopic Tangent Plane Approximations

1 files changed, 62 insertions, 0 deletions

diff --git a/FSF-2020/approximations-and-optimizations/Tangent-Plane-Approximations/file4_Tangent plane_at_critical_points.py b/FSF-2020/approximations-and-optimizations/Tangent-Plane-Approximations/file4_Tangent plane_at_critical_points.py
new file mode 100644
index 0000000..d129213
--- /dev/null
+++ b/FSF-2020/approximations-and-optimizations/Tangent-Plane-Approximations/file4_Tangent plane_at_critical_points.py
@@ -0,0 +1,62 @@
+from manimlib.imports import*
+
+class TangenttoSurface(ThreeDScene):
+    def construct(self):
+        axes = ThreeDAxes() 
+        
+        #----graph of first function f(x,y) = -x**2-y**2
+        f = ParametricSurface(
+            lambda u, v: np.array([
+                u,
+                v,
+                -u**2-v**2
+            ]),v_min = -1, v_max = 1, u_min = -1, u_max = 1, checkerboard_colors = [YELLOW_D, YELLOW_E],
+            resolution = (20, 20)).scale(1) 
+        f_text = TextMobject("Tangent plane at relative maxima").to_corner(UL).scale(0.5)
+
+        #----graph of second function f(x,y) = -x**2+y**2   
+        f2 = ParametricSurface(
+            lambda u, v: np.array([
+                u,
+                v,
+                -u**2+v**2
+            ]),v_min = -1, v_max = 1, u_min = -1, u_max = 1, checkerboard_colors = [RED_D, RED_E],
+            resolution = (20, 20)).scale(1)
+        f2_text = TextMobject("Tangent plane at saddle point").to_corner(UL).scale(0.5) 
+        
+        #----graph of third function f(x,y) = x**2+y**2   
+        f3 = ParametricSurface(
+            lambda u, v: np.array([
+                u,
+                v,
+                u**2+v**2
+            ]),v_min = -1, v_max = 1, u_min = -1, u_max = 1, checkerboard_colors = [GREEN_D, GREEN_E],
+            resolution = (20, 20)).scale(1) 
+        f3_text = TextMobject("Tangent plane at relative minima").to_corner(UL).scale(0.5)
+        
+        self.set_camera_orientation(phi = 75 * DEGREES, theta = -45 * DEGREES )
+        d = Dot(np.array([0,0,0]), color = '#800000')        #---- critical point 
+
+        r = Rectangle(height = 2,breadth = 1,color = PURPLE).scale(0.5)
+
+        self.begin_ambient_camera_rotation(rate = 0.3) 
+        self.add(axes)
+        self.play(Write(f),Write(d))
+        self.wait(1)
+        self.add_fixed_in_frame_mobjects(f_text)
+        self.play(ShowCreation(r))
+        self.wait(1)
+        self.play(FadeOut(r),FadeOut(f),FadeOut(d),FadeOut(f_text))
+        self.wait(1)
+        self.play(Write(f2),Write(d))
+        self.wait(1)
+        self.add_fixed_in_frame_mobjects(f2_text)
+        self.play(ShowCreation(r))
+        self.wait(1)
+        self.play(FadeOut(r),FadeOut(f2),FadeOut(d),FadeOut(f2_text))
+        self.wait(1)
+        self.play(Write(f3),Write(d))
+        self.wait(1)
+        self.add_fixed_in_frame_mobjects(f3_text)
+        self.play(ShowCreation(r))
+        self.wait(1)