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from manimlib.imports import *
class SurfacesAnimation(ThreeDScene):
CONFIG = {
"axes_config": {
"x_min": 0,
"x_max": 4,
"y_min": 0,
"y_max": 4,
"z_min": -2,
"z_max": 4,
"a":0 ,"b": 4, "c":0 , "d":4,
"axes_shift":IN+2*LEFT+2*DOWN,
"x_axis_config": {
"tick_frequency": 1,
"include_tip": False,
},
"y_axis_config": {
"tick_frequency": 1,
"include_tip": False,
},
"z_axis_config": {
"tick_frequency": 1,
# "include_tip": False,
},
"num_axis_pieces": 1,
},
"default_graph_style": {
"stroke_width": 2,
"stroke_color": WHITE,
},
"default_surface_config": {
"fill_opacity": 0.5,
"checkerboard_colors": [LIGHT_GREY],
"stroke_width": 0.5,
"stroke_color": WHITE,
"stroke_opacity": 0.5,
},
"Func": lambda x,y: x*y/4
}
def construct(self):
self.setup_axes()
self.set_camera_orientation(
distance=30,
phi=75 * DEGREES,
theta=20 * DEGREES,
)
fn_text=TextMobject("$z=xy$").set_color(BLUE).scale(1.5)
fn_text.to_corner(UR,buff=2)
self.add_fixed_in_frame_mobjects(fn_text)
#get the surface
surface= self.get_surface(
self.axes, lambda x , y:
self.Func(x,y)
)
surface.set_style(
fill_opacity=.5,
fill_color=BLUE_E,
stroke_width=0.4,
stroke_color=WHITE,
)
#get boundary curves
c1=self.get_curve(
self.axes, lambda x: x**2/4
)
c1_label=TextMobject("$y=x^2$").next_to(c1,IN+OUT).shift(DOWN+RIGHT)
c1_label.rotate(PI)
c1_group=VGroup(c1,c1_label).set_color(ORANGE)
c2=self.get_curve(
self.axes, lambda x: x
).set_color(PINK)
c2_label=TextMobject("$y=x$").next_to(c2,IN+OUT)
c2_label.rotate(PI/2,about_point=(c2_label.get_corner(UL)))
c2_group=VGroup(c2,c2_label).set_color(YELLOW_E)
self.add(c1,c2,c1_label,c2_label)
self.begin_ambient_camera_rotation(rate=0.24)
self.get_region(self.axes,c1,c2)
self.play(Write(surface))
self.get_lines()
self.wait(3.5)
self.stop_ambient_camera_rotation()
self.wait(.5)
self.move_camera(
distance=20,
phi=10 * DEGREES,
theta=80 * DEGREES,
run_time=3
)
self.wait(2)
def get_curve(self,axes, func, **kwargs):
config = {
"t_min": axes.x_min,
"t_max": axes.x_max,
}
config.update(kwargs)
return ParametricFunction(
lambda x : axes.c2p(
x, func(x),0
),
**config
)
def get_region(self,axes,curve1,curve2,**kwargs):
x_vals=np.arange(axes.x_min,axes.x_max,.1)
c1_points=[curve1.get_point_from_function(x) for x in x_vals]
c2_points=[curve2.get_point_from_function(x) for x in x_vals]
c2_points.reverse()
points=c1_points+c2_points
region=Polygon(*points,
stroke_width=0,
fill_color=PINK,
fill_opacity=.5
)
R=TextMobject("R").set_color(PINK).scale(2).rotate(180*DEGREES , OUT)
R.move_to(region,IN+RIGHT)
self.play(ShowCreation(region))
self.add(R)
def get_surface(self,axes, func, **kwargs):
config = {
"u_min": axes.x_max,
"u_max": axes.x_min,
"v_min": axes.y_max,
"v_max": axes.y_min,
"resolution": (10,10),
}
config.update(self.default_surface_config)
config.update(kwargs)
return ParametricSurface(
lambda x,y : axes.c2p(
x, y, func(x, y)
),
**config
)
def get_lines(self):
axes = self.axes
labels=[axes.x_axis.n2p(axes.a), axes.x_axis.n2p(axes.b), axes.y_axis.n2p(axes.c),
axes.y_axis.n2p(axes.d)]
surface_corners=[]
for x,y,z in self.region_corners:
surface_corners.append([x,y,self.Func(x,y)])
lines=VGroup()
for start , end in zip(surface_corners,
self.region_corners):
lines.add(self.draw_lines(start,end,"YELLOW"))
for start , end in zip(labels,
self.region_corners):
# lines.add(self.draw_lines(start,end,"BLUE"))
# print (start,end)
pass
self.play(ShowCreation(lines))
def draw_lines(self,start,end,color):
start=self.axes.c2p(*start)
end=self.axes.c2p(*end)
line=DashedLine(start,end,color=color)
return line
#customize 3D axes
def get_three_d_axes(self, include_labels=True, include_numbers=True, **kwargs):
config = dict(self.axes_config)
config.update(kwargs)
axes = ThreeDAxes(**config)
axes.set_stroke(width=2)
if include_numbers:
self.add_axes_numbers(axes)
if include_labels:
self.add_axes_labels(axes)
# Adjust axis orientation
axes.x_axis.rotate(
90 * DEGREES, LEFT,
about_point=axes.c2p(0, 0, 0),
)
axes.y_axis.rotate(
90 * DEGREES, UP,
about_point=axes.c2p(0, 0, 0),
)
# Add xy-plane
input_plane = self.get_surface(
axes, lambda x, t: 0
)
input_plane.set_style(
fill_opacity=0.3,
fill_color=PINK,
stroke_width=.2,
stroke_color=WHITE,
)
axes.input_plane = input_plane
self.region_corners=[
input_plane.get_corner(pos) for pos in (DL,DR,UR,UL)]
return axes
def setup_axes(self):
axes = self.get_three_d_axes(include_labels=True)
# axes.add(axes.input_plane)
axes.scale(1)
# axes.center()
axes.shift(axes.axes_shift)
self.add(axes)
self.axes = axes
def add_axes_numbers(self, axes):
x_axis = axes.x_axis
y_axis = axes.y_axis
tex_vals_x = [
("1", axes.b),
]
tex_vals_y=[
("1", axes.d)
]
x_labels = VGroup()
y_labels = VGroup()
for tex, val in tex_vals_x:
label = TexMobject(tex)
label.scale(1)
label.next_to(x_axis.n2p(val), DOWN)
label.rotate(180 * DEGREES)
x_labels.add(label)
x_axis.add(x_labels)
x_axis.numbers = x_labels
for tex, val in tex_vals_y:
label = TexMobject(tex)
label.scale(1)
label.next_to(y_axis.n2p(val), LEFT)
label.rotate(90 * DEGREES)
y_labels.add(label)
y_axis.add(y_labels)
y_axis.numbers = y_labels
return axes
def add_axes_labels(self, axes):
x_label = TexMobject("x")
x_label.next_to(axes.x_axis.get_end(), RIGHT)
axes.x_axis.label = x_label
y_label = TextMobject("y")
y_label.rotate(90 * DEGREES, OUT)
y_label.next_to(axes.y_axis.get_end(), UP)
axes.y_axis.label = y_label
z_label = TextMobject("z")
z_label.rotate(90 * DEGREES, LEFT)
z_label.next_to(axes.z_axis.get_zenith(), LEFT)
axes.z_axis.label = z_label
for axis in axes:
axis.add(axis.label)
return axes
#uploaded by Somnath Pandit.FSF2020_Fubini's_Theorem
|
