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from manimlib.imports import *
class Continuity(ThreeDScene):
def construct(self):
axes = ThreeDAxes()
text3d = TextMobject(r"$f(x,y) = \frac{3x^2y}{x^2 + y^2}$")
self.add_fixed_in_frame_mobjects(text3d)
text3d.to_corner(UL)
text3d.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)
self.play(Write(text3d))
self.wait(1)
continuity_func = ParametricSurface(
lambda u, v: np.array([
3*np.sin(u)*np.cos(v),
3*np.sin(u)*np.sin(v),
9*np.sin(u)*np.cos(v)*np.cos(v)*np.sin(v)
]),u_min=0,u_max=PI,v_min=0,v_max=2*PI,checkerboard_colors=[YELLOW_C, YELLOW_E],
resolution=(15, 32)).scale(1)
continuity_func_copy1 = continuity_func.copy()
continuity_func_copy2 = continuity_func.copy()
continuity_func_x = ParametricSurface(
lambda u, v: np.array([
3*np.sin(u)*np.cos(v),
3*np.sin(u)*np.sin(v),
9*np.sin(u)*np.cos(v)*np.cos(v)*np.sin(v)
]),u_min=0,u_max=PI,v_min=PI,v_max=2*PI,checkerboard_colors=[YELLOW_C, YELLOW_E],
resolution=(15, 32)).scale(1)
continuity_func_y = ParametricSurface(
lambda u, v: np.array([
3*np.sin(u)*np.cos(v),
3*np.sin(u)*np.sin(v),
9*np.sin(u)*np.cos(v)*np.cos(v)*np.sin(v)
]),u_min=0,u_max=PI,v_min=PI/2,v_max=3*PI/2,checkerboard_colors=[YELLOW_C, YELLOW_E],
resolution=(15, 32)).scale(1)
continuity_x =ParametricFunction(
lambda u : np.array([
u,
0,
0
]),color="#006400",t_min=-3,t_max=3,
)
continuity_y =ParametricFunction(
lambda u : np.array([
0,
u,
0
]),color="#000080",t_min=-3,t_max=3,
)
plane_x = Polygon(np.array([-3,0,-3]),np.array([3,0,-3]),np.array([3,0,3]),np.array([-3,0,3]),np.array([-3,0,-3]), color = GREEN, fill_color = GREEN, fill_opacity = 0.2)
plane_x_text = TextMobject(r"$y = 0$", color = GREEN_C).move_to(1.7*UP + 3.8*RIGHT)
plane_y = Polygon(np.array([0,-3,-3]),np.array([0,3,-3]),np.array([0,3,3]),np.array([0,-3,3]),np.array([0,-3,-3]), color = BLUE, fill_color = BLUE, fill_opacity = 0.2)
plane_y_text = TextMobject(r"$x = 0$", color = BLUE_C).move_to(1.7*UP + 3.8*RIGHT)
origin_x = Polygon(*[np.array([0.05*np.cos(i*DEGREES),0,0.05*np.sin(i*DEGREES)]) for i in range(361)], color = "#000080", fill_color = "#000080", fill_opacity = 1).move_to(np.array([0,0,0]))
origin_x_text = TextMobject(r"$(0,0,0)$", color = RED_C).scale(0.7).move_to(np.array([-0.6,0,-0.5]))
origin_y = Polygon(*[np.array([0,0.05*np.cos(i*DEGREES),0.05*np.sin(i*DEGREES)]) for i in range(361)], color = "#006400", fill_color = "#006400", fill_opacity = 1).move_to(np.array([0,0,0]))
origin_y_text = TextMobject(r"$(0,0,0)$", color = RED_C).scale(0.7).move_to(np.array([0,-0.6,-0.5]))
self.set_camera_orientation(phi=80 * DEGREES, theta = 0*DEGREES)
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(3.7*UP)
self.add_fixed_in_frame_mobjects(axis[2])
self.add_fixed_orientation_mobjects(axis[0])
self.add_fixed_orientation_mobjects(axis[1])
self.play(ShowCreation(continuity_func))
self.move_camera(phi=80* DEGREES,theta=105*DEGREES)
self.play(ShowCreation(plane_x))
self.add_fixed_in_frame_mobjects(plane_x_text)
self.wait()
self.play(ReplacementTransform(continuity_func, continuity_func_x))
self.play(FadeOut(plane_x), FadeOut(plane_x_text))
self.play(ShowCreation(continuity_x), ShowCreation(origin_x))
self.add_fixed_orientation_mobjects(origin_x_text)
self.move_camera(phi=80* DEGREES,theta=15*DEGREES)
self.wait(3)
self.play(FadeOut(origin_x), FadeOut(origin_x_text), FadeOut(continuity_x), ReplacementTransform(continuity_func_x, continuity_func_copy1))
self.play(ShowCreation(plane_y))
self.add_fixed_in_frame_mobjects(plane_y_text)
self.wait()
self.play(ReplacementTransform(continuity_func_copy1, continuity_func_y))
self.play(FadeOut(plane_y), FadeOut(plane_y_text))
self.play(ShowCreation(continuity_y), ShowCreation(origin_y))
self.add_fixed_orientation_mobjects(origin_y_text)
self.move_camera(phi=80* DEGREES,theta=75*DEGREES)
self.wait(3)
self.play(FadeOut(origin_y), FadeOut(origin_y_text), FadeOut(continuity_y), ReplacementTransform(continuity_func_y, continuity_func_copy2))
self.wait(2)
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