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from manimlib.imports import*
#---- contour diagram animation
class ContourDiagram(ThreeDScene):
def construct(self):
heading = TextMobject("CONTOUR DIAGRAM", color = YELLOW).scale(1)
axes = ThreeDAxes()
label_x = TextMobject("$x$").shift([5.5,-0.5,0]) #---- x axis
label_y = TextMobject("$y$").shift([-0.5,5.5,0]).rotate(-4.5) #---- y axis
#---- surface of a paraboloid
surface = ParametricSurface(
lambda u, v: np.array([
np.cos(v)*u,
np.sin(v)*u,
u**2
]),v_min = -2, v_max = 2, u_min = -2, u_max = 2, checkerboard_colors = [GREEN_B,GREEN_C,GREEN_D,GREEN_E]).shift([0,0,0]).scale(0.5)
#---- first contour projection
contour1 = ParametricSurface(
lambda u, v: np.array([
np.cos(TAU * v),
np.sin(TAU * v),
2*(1 - 2.5*u)
])).fade(0.5).scale(0.21).shift([0,0,1.01])
#---- first contour line
c_1 = Circle(color = BLUE).scale(0.21).shift([0,0,0]).rotate(0.1,DOWN)
#-------------------------------------------------
#---- second contour projection
contour2 = ParametricSurface(
lambda u, v: np.array([
np.cos(TAU * v),
np.sin(TAU * v),
2*(1 - 1.6*u)
])).fade(0.5).scale(0.41).shift([0,0,0.3]).set_color(RED)
#---- second contour line
c_2 = Circle(color = RED).scale(0.41).shift([0,0,0]).rotate(0.1,DOWN)
#-------------------------------------------------
#---- third contour projection
contour3 = ParametricSurface(
lambda u, v: np.array([
np.cos(TAU * v),
np.sin(TAU * v),
2*(1 - 1.5*u)
])).fade(0.5).scale(0.61).shift([0,0,0.4]).set_color(YELLOW)
#---- third contour line
c_3 = Circle(color = YELLOW).scale(0.61).shift([0,0,0])
#-------------------------------------------------
#---- fourth contour projection
contour4 = ParametricSurface(
lambda u, v: np.array([
np.cos(TAU * v),
np.sin(TAU * v),
2*(1 - 1.5*u)
])).fade(0.7).scale(0.81).shift([0,0,0.7]).set_color(PINK)
#---- fourth contour line
c_4 = Circle(color = PINK).scale(0.81).shift([0,0,0])
#-------------------------------------------------
#---- fifth contour projection
contour5 = ParametricSurface(
lambda u, v: np.array([
np.cos(TAU * v),
np.sin(TAU * v),
2*(1 - 1.5*u)
])).fade(0.7).scale(1.01).shift([0,0,1]).set_color(PURPLE)
#---- fifth contour line
c_5 = Circle(color = PURPLE).scale(1.01).shift([0,0,0])
c_text= TextMobject("Contour Lines").scale(0.5).shift(2*DOWN)
s = Square().scale(1.3)
self.set_camera_orientation(phi = 75 * DEGREES, theta = 10 * DEGREES)
self.add_fixed_in_frame_mobjects(heading)
self.wait(1)
self.play(FadeOut(heading))
self.wait(1)
self.add(axes)
self.add(label_x)
self.add(label_y)
self.play(Write(surface))
self.wait(1)
self.add(contour1)
self.wait(1)
self.play(Write(c_1))
self.play(ReplacementTransform(contour1,contour2))
self.wait(1)
self.play(Write(c_2))
self.play(ReplacementTransform(contour2,contour3))
self.wait(1)
self.play(Write(c_3))
self.play(ReplacementTransform(contour3,contour4))
self.wait(1)
self.play(Write(c_4))
self.play(ReplacementTransform(contour4,contour5))
self.wait(1)
self.play(Write(c_5))
self.wait(1)
self.play(FadeOut(contour5),FadeOut(axes),FadeOut(label_x),FadeOut(label_y),FadeOut(surface),FadeOut(contour5),FadeOut(contour4),FadeOut(contour3),FadeOut(contour2),FadeOut(contour1))
self.wait(1)
self.move_camera(phi=0 * DEGREES,theta= 90*DEGREES)
self.wait(1)
self.add_fixed_in_frame_mobjects(c_text)
self.wait(1)
self.play(ShowCreation(s),FadeOut(c_text))
self.wait(1)
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