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from manimlib.imports import *
class sphere(GraphScene, ThreeDScene):
CONFIG = {
'x_min': 0,
'x_max': 10,
'y_min': -3,
'y_max': 3,
'graph_origin': ORIGIN,
"x_axis_width": 10,
"y_axis_height": 10,
"default_graph_style": {
"stroke_width": 2,
"stroke_color": WHITE,
}
}
def construct(self):
XTD = self.x_axis_width/(self.x_max- self.x_min)
YTD = self.y_axis_height/(self.y_max- self.y_min)
text1 = TexMobject(r"y=\frac { 1 }{ x }").move_to(np.array([3,2,0]))
text1a = TexMobject(r"y=\frac { 1 }{ x }, x \ge 1").move_to(np.array([3,2,0]))
text2 = TexMobject(r"y=\frac { 1 }{ x }", r"\text{ is rotated in 3-dimensions}").to_corner(UL)
text3 = TextMobject("For calculating volume, consider a disc as shown").to_corner(UL)
text4 = TextMobject("Imagine the disc to move along the length of the horn").to_corner(UL)
text5 = TextMobject("In this way complete volume is covered").to_corner(UL)
arrow = Vector(np.array([0, np.sin(60*DEGREES), np.cos(60*DEGREES)])).shift(1*RIGHT)
text6 = TexMobject(r"\text{Area of circle is }", r"\pi {r}^{2}").to_corner(UL)
text7 = TextMobject("The disc moves along the length of hyperbolic curve").to_corner(UL)
axes = ThreeDAxes(**self.CONFIG)
self.setup_axes()
graph1 = self.get_graph(lambda x : 1/x, x_min = 1, x_max = 10)
graph2 = self.get_graph(lambda x : 1/x, x_min = 0.1, x_max = 10)
self.play(FadeIn(self.axes))
self.play(ShowCreation(graph2), FadeIn(text1))
self.wait(3)
self.play(Transform(graph2, graph1), ReplacementTransform(text1, text1a))
axes = ThreeDAxes(**self.CONFIG)
self.move_camera(phi = 90*DEGREES, theta=0*DEGREES,distance = 200, run_time=5)
horn2 = ParametricSurface(lambda u, v : np.array([1*u, (1*np.cos(TAU*v))/u,(1*np.sin(TAU*v))/u]), u_min = 1, v_min = 0.001, u_max = 10, fill_opacity = 0.1)
self.play(Transform(graph2, horn2), FadeOut(text1), FadeOut(graph2), ShowCreation(text2), FadeOut(text1a))
self.wait(2)
self.play(FadeOut(text2))
self.add_fixed_in_frame_mobjects(text3)
self.wait(1)
disc = ParametricSurface(lambda u, v : np.array([0, 1*v*np.sin(TAU*u), 1*v*np.cos(TAU*u)]), fill_opacity = 1, fill_color = PINK).shift(1*RIGHT)
self.play(ShowCreation(disc), ShowCreation(arrow))
self.play(FadeOut(text3))
self.add_fixed_in_frame_mobjects(text6)
self.wait(3)
self.play(FadeOut(text6))
self.add_fixed_in_frame_mobjects(text7)
self.wait(2)
self.move_camera(phi = 60*DEGREES, theta= -45*DEGREES, distance = 200, run_time=5)
#self.play(FadeOut(text6))
#self.add_fixed_in_frame_mobjects(text7)
k=0
while k<9:
disc1 = ParametricSurface(lambda u, v : np.array([0, (1/(1+k))*v*np.sin(TAU*u), (1/(1+k))*v*np.cos(TAU*u)]), fill_opacity = 0.5, fill_color = PINK).shift((1+k)*RIGHT)
self.play(FadeIn(disc1), run_time = 0.1)
k = k+0.1
self.play(FadeOut(text7))
self.add_fixed_in_frame_mobjects(text5)
self.wait(2)
self.begin_ambient_camera_rotation(rate = 0.4)
self.wait(10)
self.stop_ambient_camera_rotation()
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