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from manimlib.imports import*
import math as m
class DegenerateHessian(ThreeDScene):
def construct(self):
heading = TextMobject("Degenerate Hessian Matrix",color = BLUE)
h_text = TextMobject("For $det \\hspace{1mm} H = 0$, the surface of the function at the critical point would be flat.").scale(0.7)
axes = ThreeDAxes()
label_x = TextMobject("$x$").shift([5.5,-0.3,0]) #---- x axis
label_y = TextMobject("$y$").shift([-0.3,5.5,0]).rotate(-4.5) #---- y axis
#---- function f(x,y)
f_surface = ParametricSurface(
lambda u, v: np.array([
u,
v,
-4*u**3-v**3
]),u_min = -0.8, u_max = 0.8, v_min = -0.8, v_max = 0.8).set_color(TEAL).shift([0,1,0]).scale(1.3)
#---- function f(x,y)
zoom_surface = ParametricSurface(
lambda u, v: np.array([
u,
v,
-4*u**3-v**3
]),u_min = -0.8, u_max = 0.8, v_min = -0.8, v_max = 0.8).set_color(TEAL).shift([0,1,0]).scale(2.5)
f_text= TextMobject("surface of the function").to_corner(UL).scale(0.5)
d = Dot(color = "#800000").shift([0,1,0]) #---- critical point
d2 = Dot(color = "#800000").shift([0,0.7,0]) #---- critical point
plane = Rectangle(color = YELLOW,fill_opacity= 0.3).shift([0,0.6,0]).rotate(m.radians(90)).scale(0.4)
self.set_camera_orientation(phi = 70*DEGREES, theta = 45*DEGREES)
self.add_fixed_in_frame_mobjects(heading)
self.wait(1)
self.play(FadeOut(heading))
self.add_fixed_in_frame_mobjects(h_text)
self.wait(2)
self.play(FadeOut(h_text))
self.wait(1)
self.add(axes)
self.add(label_x)
self.add(label_y)
self.play(Write(f_surface))
self.add_fixed_in_frame_mobjects(f_text)
self.wait(1)
self.play(Write(d))
self.wait(1)
self.play(ReplacementTransform(f_surface,zoom_surface),ReplacementTransform(d,d2))
self.wait(2)
self.play(Write(plane))
self.wait(1)
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