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from manimlib.imports import *
class PartialDeriv(ThreeDScene):
def construct(self):
axes = ThreeDAxes()
paraboloid = ParametricSurface(
lambda u, v: np.array([
2*np.sin(u)*np.cos(v),
2*np.sin(u)*np.sin(v),
-2*2*np.sin(u)*np.sin(u)+2
]),u_min=0,u_max=PI/2,v_min=0,v_max=2*PI,checkerboard_colors=[PINK, PURPLE],
resolution=(15, 32)).scale(1)
paraboloid_copy1 = paraboloid.copy()
paraboloid_copy2 = paraboloid.copy()
paraboloid_x = ParametricSurface(
lambda u, v: np.array([
2*np.sin(u)*np.cos(v),
2*np.sin(u)*np.sin(v),
-2*2*np.sin(u)*np.sin(u)+2
]),u_min=0,u_max=PI/2,v_min=PI,v_max=2*PI,checkerboard_colors=[PINK, PURPLE],
resolution=(15, 32)).scale(1)
paraboloid_x_copy = paraboloid_x.copy()
paraboloid_y = ParametricSurface(
lambda u, v: np.array([
2*np.sin(u)*np.cos(v),
2*np.sin(u)*np.sin(v),
-2*2*np.sin(u)*np.sin(u)+2
]),u_min=0,u_max=PI/2,v_min=PI/2,v_max=3*PI/2,checkerboard_colors=[PINK, PURPLE],
resolution=(15, 32)).scale(1)
parabola1 =ParametricFunction(
lambda u : np.array([
u,
0,
-(u*u) + 2
]),color="#006400",t_min=-2,t_max=2,
)
parabola2 =ParametricFunction(
lambda u : np.array([
0,
u,
-(u*u) + 2
]),color=BLUE_C,t_min=-2,t_max=2,
)
plane1 = Polygon(np.array([-2.2,0,-2.5]),np.array([2.2,0,-2.5]),np.array([2.2,0,2.5]),np.array([-2.2,0,2.5]),np.array([-2.2,0,-2.5]), color = GREEN, fill_color = GREEN, fill_opacity = 0.2)
plane1_text = TextMobject(r"$y = 0$", color = GREEN_C).move_to(2*UP + 3.3*RIGHT)
plane2 = Polygon(np.array([0,-2.2,-2.5]),np.array([0,2.2,-2.5]),np.array([0,2.2,2.5]),np.array([0,-2.2,2.5]),np.array([0,-2.2,-2.5]), color = BLUE, fill_color = BLUE, fill_opacity = 0.2)
plane2_text = TextMobject(r"$x = 0$", color = BLUE_C).move_to(2*UP + 3.2*RIGHT)
surface_eqn = TextMobject("Surface", r"$z = f(x,y) = 2 - x^2 - y^2$", color = YELLOW_C).scale(0.6).move_to(np.array([3*LEFT +3*UP]))
surface_eqn[0].set_color(PINK)
dot1 =Sphere(radius=0.08).move_to(np.array([-1,0,1]))
dot1.set_fill(RED)
line1 = Line(np.array([-1.55, 0,0]), np.array([-0.4, 0,2.2]), color = RED)
lab_x = TextMobject(r"$f(x_0,y_0)$", color = RED).scale(0.7)
para_lab_x = TextMobject(r"$f(x,y_0)$", color = "#006400").scale(0.7)
tangent_line_x = TextMobject("Tangent Line", color = RED_C, buff = 0.4).scale(0.6).move_to(np.array([1.7*RIGHT +1.8*UP]))
text1 = TextMobject(r"$\frac{\partial f}{\partial x}\vert_{(x_0,y_0)} = \frac{d}{dx}$", r"$f(x,y_0)$", r"$\vert_{x=x_0}$").scale(0.6)
brace1 = Brace(text1[1], DOWN, buff = SMALL_BUFF, color = GREEN)
t1 = brace1.get_text("Just depends on x")
t1.scale(0.6)
t1.set_color(GREEN)
dot2 =Sphere(radius=0.08).move_to(np.array([0,1,1]))
dot2.set_fill(RED)
line2 = Line(np.array([0, 1.55,0]), np.array([0, 0.4,2.2]), color = RED)
lab_y = TextMobject(r"$f(x_0,y_0)$", color = RED).scale(0.7)
para_lab_y = TextMobject(r"$f(x_0,y)$", color = BLUE_C).scale(0.7)
tangent_line_y = TextMobject("Tangent Line", color = RED_C, buff = 0.4).scale(0.6).move_to(np.array([1.7*RIGHT +1.8*UP]))
text2 = TextMobject(r"$\frac{\partial f}{\partial y}\vert_{(x_0,y_0)} = \frac{d}{dy}$", r"$f(x_0,y)$", r"$\vert_{y=y_0}$").scale(0.6)
brace2 = Brace(text2[1], DOWN, buff = SMALL_BUFF, color = GREEN)
t2 = brace2.get_text("Just depends on y")
t2.scale(0.6)
t2.set_color(GREEN)
text3 = TextMobject(r"$= \lim_{h \to 0} \frac{f(x_0+h,y_0) - f(x_0,y_0)}{h}$").scale(0.6)
dot3 =Sphere(radius=0.08).move_to(np.array([-1.22,0,0.5]))
dot3.set_fill(YELLOW_C)
line3 = Line(np.array([-1.44,0,0]), np.array([-0.6,0,2.2]), color = YELLOW_C)
lab_line3 = TextMobject(r"$f(x_0+h,y_0)$", color = YELLOW_C).scale(0.7)
self.set_camera_orientation(phi=80 * DEGREES, theta = 0*DEGREES)
#self.set_camera_orientation(phi=80 * DEGREES, theta = 20*DEGREES)
#self.begin_ambient_camera_rotation(rate=0.3)
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[2])
self.play(Write(paraboloid))
self.add_fixed_in_frame_mobjects(surface_eqn)
#self.move_camera(phi=80* DEGREES,theta=110*DEGREES)
self.move_camera(phi=80* DEGREES,theta=45*DEGREES)
self.add_fixed_orientation_mobjects(axis[0])
self.add_fixed_orientation_mobjects(axis[1])
self.play(ShowCreation(plane1))
self.add_fixed_in_frame_mobjects(plane1_text)
self.wait()
self.play(ReplacementTransform(paraboloid, paraboloid_x))
lab_x.move_to(np.array([1.8*RIGHT +1.15*UP]))
para_lab_x.move_to(np.array([1.3*LEFT +1.6*UP]))
self.wait()
self.play(FadeOut(plane1), FadeOut(plane1_text))
self.play(ShowCreation(parabola1))
self.add_fixed_in_frame_mobjects(para_lab_x)
self.play(ShowCreation(dot1))
self.add_fixed_in_frame_mobjects(lab_x)
#self.play(ShowCreation(dot1))
self.wait()
self.play(ShowCreation(line1))
self.add_fixed_in_frame_mobjects(tangent_line_x)
self.wait()
self.add_fixed_in_frame_mobjects(text1, brace1, t1)
grp1 = VGroup(text1, brace1, t1)
grp1.move_to(3*UP+3*RIGHT)
self.play(Write(text1),GrowFromCenter(brace1), FadeIn(t1))
self.wait()
self.play(FadeOut(parabola1), FadeOut(line1), FadeOut(lab_x), FadeOut(para_lab_x), FadeOut(dot1), FadeOut(tangent_line_x),FadeOut(grp1))
#self.move_camera(phi=80* DEGREES,theta=20*DEGREES)
self.play(ReplacementTransform(paraboloid_x, paraboloid_copy1))
self.wait()
self.play(ShowCreation(plane2))
self.add_fixed_in_frame_mobjects(plane2_text)
self.wait()
self.play(ReplacementTransform(paraboloid_copy1, paraboloid_y))
lab_y.move_to(np.array([1.8*RIGHT +1.15*UP]))
para_lab_y.move_to(np.array([1.3*LEFT +1.6*UP]))
self.wait()
self.play(FadeOut(plane2), FadeOut(plane2_text))
self.play(ShowCreation(parabola2))
self.add_fixed_in_frame_mobjects(para_lab_y)
self.play(ShowCreation(dot2))
self.add_fixed_in_frame_mobjects(lab_y)
self.wait()
self.play(ShowCreation(line2))
self.add_fixed_in_frame_mobjects(tangent_line_y)
self.wait()
self.add_fixed_in_frame_mobjects(text2, brace2, t2)
grp2 = VGroup(text2, brace2, t2)
grp2.move_to(3*UP+3*RIGHT)
self.play(Write(text2),GrowFromCenter(brace2), FadeIn(t2))
self.wait()
self.play(FadeOut(parabola2), FadeOut(line2), FadeOut(lab_y), FadeOut(para_lab_y), FadeOut(dot2), FadeOut(tangent_line_y), FadeOut(grp2))
self.wait()
#self.move_camera(phi=80* DEGREES,theta=105*DEGREES)
self.play(ReplacementTransform(paraboloid_y, paraboloid_copy2))
self.wait()
self.play(ShowCreation(plane1))
self.add_fixed_in_frame_mobjects(plane1_text)
self.wait()
self.play(ReplacementTransform(paraboloid_copy2, paraboloid_x_copy))
lab_x.move_to(np.array([1.8*RIGHT +1.15*UP]))
para_lab_x.move_to(np.array([1.3*LEFT +1.6*UP]))
lab_line3.move_to(np.array([2.4*RIGHT +0.5*UP]))
self.wait()
self.play(FadeOut(plane1), FadeOut(plane1_text))
self.play(ShowCreation(parabola1))
self.add_fixed_in_frame_mobjects(para_lab_x)
self.play(ShowCreation(dot1))
self.add_fixed_in_frame_mobjects(lab_x)
self.play(ShowCreation(dot3))
self.add_fixed_in_frame_mobjects(lab_line3)
self.wait()
self.play(ShowCreation(line1))
self.add_fixed_in_frame_mobjects(tangent_line_x)
self.play(ShowCreation(line3))
self.wait()
self.add_fixed_in_frame_mobjects(text1,text3)
text1.move_to(3*UP+3*RIGHT)
text3.next_to(text1, DOWN)
self.play(Write(text1),Write(text3))
self.wait()
self.play(FadeOut(parabola1), FadeOut(line1), FadeOut(lab_x), FadeOut(line3), FadeOut(lab_line3), FadeOut(para_lab_x), FadeOut(dot1), FadeOut(dot3), FadeOut(tangent_line_x), FadeOut(text1), FadeOut(text3))
self.wait()
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