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from manimlib.imports import *
class GeomRepresen(ThreeDScene):
def construct(self):
axes = ThreeDAxes()
paraboloid = ParametricSurface(
lambda u, v: np.array([
3*np.sin(u)*np.cos(v),
3*np.sin(u)*np.sin(v),
-0.25*3*3*np.sin(u)*np.sin(u)+2
]),u_min=0,u_max=PI/4,v_min=0,v_max=2*PI, color = BLUE_C, fill_color = BLUE_C, fill_opacity = 0.7,
resolution=(15, 32)).scale(1)
parabola_curve = ParametricFunction(
lambda u : np.array([
u,
-u,
-0.5*(u*u)+2
]),color=PINK,t_min=-1.5,t_max=1.5,
)
circle = Circle(radius = 2.22 , color = BLACK, fill_color = BLUE_C, fill_opacity= 0.3, stroke_width=0.1)
plane = Polygon(np.array([2.5,-2.5,0]),np.array([-2.5,2.5,0]),np.array([-2.5,2.5,2.5]),np.array([2.5,-2.5,2.5]),np.array([2.5,-2.5,0]), color = BLACK, fill_color = PINK, fill_opacity= 0.2, stroke_width=0.1)
line = DashedLine(np.array([1,-1,0]), np.array([1,-1,1.5]), color = YELLOW_C)
tangent_line = Line(np.array([1.5,-1.5,1]), np.array([0.5,-0.5,2]), color = RED_C)
vector = Arrow(np.array([1,-1,0]), np.array([0.5,-0.5,0]), buff=0.01, color = GREEN_C)
dot1 =Sphere(radius=0.08).move_to(np.array([1,-1,0])).set_fill(YELLOW_C)
dot2 =Sphere(radius=0.08).move_to(np.array([1,-1,1.5])).set_fill(YELLOW_C)
dot1_lab = TextMobject(r"$P_0$").scale(0.6).move_to(np.array([1,-1,1.8])).set_color(RED_C)
dot2_lab = TextMobject(r"$(x_0,y_0)$").scale(0.6).move_to(np.array([1.6,-1,0])).set_color(PURPLE)
vector_lab = TextMobject(r"$\hat{u}$").scale(0.8).move_to(np.array([1.2,-0.5,0])).set_color(GREEN_C)
domain_lab = TextMobject(r"$D$").scale(0.6).move_to(np.array([1,1,0])).set_color(GREEN_C)
func_lab = TextMobject(r"$z = f(x,y)$").scale(0.6).move_to(1*UP + 2.8*RIGHT).set_color(BLUE_C)
directional_deriv_lab = TextMobject(r"Slope = $D_{\hat{u}}f(x_0,y_0)$").scale(0.6).move_to(2.2*UP + 1.5*RIGHT).set_color(YELLOW_C)
self.add(axes)
axis = TextMobject(r"X",r"Y",r"Z")
axis[0].move_to(6*RIGHT)
axis[1].move_to(6*UP)
axis[2].move_to(np.array([0,0,3.7]))
self.add_fixed_orientation_mobjects(axis[2])
self.add_fixed_orientation_mobjects(axis[0])
self.add_fixed_orientation_mobjects(axis[1])
self.set_camera_orientation(phi=65 * DEGREES, theta = 20*DEGREES)
self.play(ShowCreation(paraboloid))
self.add_fixed_in_frame_mobjects(func_lab)
self.wait()
#self.play(ShowCreation(circle))
self.bring_to_front(circle)
self.wait()
self.add_fixed_orientation_mobjects(domain_lab)
self.wait()
self.play(ShowCreation(plane), ShowCreation(parabola_curve))
self.play(ShowCreation(dot1), GrowArrow(line), ShowCreation(dot2))
self.add_fixed_orientation_mobjects(dot1_lab)
self.wait()
self.add_fixed_orientation_mobjects(dot2_lab)
self.wait()
self.play(ShowCreation(tangent_line))
self.add_fixed_in_frame_mobjects(directional_deriv_lab)
self.wait()
self.play(GrowArrow(vector))
self.add_fixed_orientation_mobjects(vector_lab)
self.wait()
self.begin_ambient_camera_rotation(rate=0.1)
self.wait(3)
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