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from manimlib.imports import *
class ElementaryArea(GraphScene):
CONFIG = {
"x_min" : 0,
"x_max" : 2,
"y_min" : 0,
"y_max" : 2,
"x_tick_frequency" : 1,
"y_tick_frequency" : 1,
# "x_labeled_nums": list(np.arange(0,3)),
# "y_labeled_nums": list(np.arange(0 ,3)),
"x_axis_width": 6,
"y_axis_height": 6,
"graph_origin": ORIGIN+3.5*LEFT+3.5*DOWN,
}
def construct(self):
X = self.x_axis_width/(self.x_max- self.x_min)
Y = self.y_axis_height/(self.y_max- self.y_min)
self.X=X ;self.Y=Y
self.setup_axes(animate=False)
caption=TextMobject("The elementary area in ").to_edge(UP)
rect_text=TextMobject("Cartesian Coordinates").next_to(caption,DOWN,)
polar_text=TextMobject("Polar Coordinates").next_to(caption,DOWN,)
self.add(caption)
self.play(Write(rect_text))
self.get_rect_element()
# self.play(Write(polar_text))
self.play(ReplacementTransform(rect_text,polar_text),
FadeOut(VGroup(self.dydx,self.rect_brace_gr)))
self.get_polar_element()
def get_rect_element(self):
rect=Rectangle(
height=2, width=3,fill_color=BLUE_D,
fill_opacity=1, color=BLUE_D
).scale(.75).move_to(
self.graph_origin+(RIGHT*self.X+UP*self.Y)
)
dx_brace=Brace(rect, DOWN, buff = SMALL_BUFF)
dx_label=dx_brace.get_text("$dx$", buff = SMALL_BUFF)
dx_brace_gr=VGroup(dx_brace,dx_label)
dy_brace=Brace(rect,RIGHT, buff = SMALL_BUFF)
dy_label=dy_brace.get_text("$dy$", buff = SMALL_BUFF)
dy_brace_gr=VGroup(dy_brace,dy_label)
brace_gr=VGroup(dx_brace_gr,dy_brace_gr)
dydx=TextMobject("$dxdy$",color=BLACK).next_to(rect,IN)
self.play(FadeIn(rect))
self.play(GrowFromCenter(brace_gr))
self.play(GrowFromCenter(dydx))
self.rect=rect
self.rect_brace_gr=brace_gr
self.dydx=dydx
self.wait(2)
def get_polar_element(self):
X=self.X ;Y=self.Y
theta1=25*DEGREES
dtheta=TAU/12
r_in=1.3*X ; r_out=1.9*X
arc=AnnularSector(
arc_center=self.graph_origin,
inner_radius=r_in,
outer_radius=r_out ,
angle= dtheta,
start_angle= theta1,
fill_opacity= 1,
stroke_width= 0,
color= BLUE_D,
)
# # #getting braces
r_in_theta1=self.graph_origin+r_in*(np.cos(theta1)*RIGHT+np.sin(theta1)*UP)
dr_line=Line(r_in_theta1,r_in_theta1+RIGHT*(r_out-r_in))
dr_brace=Brace(dr_line, DOWN, buff = SMALL_BUFF
).rotate(theta1, about_point=r_in_theta1
)
dr_label=dr_brace.get_text("$dr$", buff = SMALL_BUFF)
dr_brace_gr=VGroup(dr_brace,dr_label)
theta2=theta1+dtheta
r_out_theta2=self.graph_origin+r_out*(
np.cos(theta2)*RIGHT+np.sin(theta2)*UP
)
rdt_line=Line(r_out_theta2,r_out_theta2
+DOWN*(r_out*dtheta)
)
rdt_brace=Brace(rdt_line, RIGHT,
buff = MED_SMALL_BUFF).rotate(
theta2-(dtheta/2), about_point=r_out_theta2
)
rdt_label=rdt_brace.get_text("$rd\\theta$",buff = SMALL_BUFF)
rdt_brace_gr=VGroup(rdt_brace,rdt_label)
#getting label r and dtheta
r1=DashedLine(self.graph_origin,r_in_theta1).set_color(RED)
r2=DashedLine(self.graph_origin,r_out_theta2).set_color(RED)
r_brace=Brace(r1, DOWN, buff = SMALL_BUFF).rotate(theta1, about_point=self.graph_origin)
r_label=r_brace.get_text("$r$", buff = SMALL_BUFF)
r_brace_gr=VGroup(r_brace,r_label)
dtheta_arc=Arc(
arc_center=self.graph_origin,
radius=.5*X,
angle= dtheta,
start_angle= theta1,
)
dtheta_arc_label=TextMobject("$d\\theta$").move_to(.99*dtheta_arc.get_corner(UR))
dtheta_label=VGroup(dtheta_arc,dtheta_arc_label)
rdrdt=TextMobject("$rdrd\\theta$",color=BLACK).next_to(arc,IN)
self.play(ReplacementTransform(self.rect,arc))
self.wait()
self.play(ShowCreation(r1),
ShowCreation(r2)
)
self.play(ShowCreation(r_brace_gr),
Write(dtheta_label)
)
self.wait()
self.play(GrowFromCenter(rdt_brace_gr))
self.wait(.5)
self.play(GrowFromCenter(dr_brace_gr))
self.wait(.5)
self.play(GrowFromCenter(rdrdt))
self.wait(2)
#uploaded by Somnath Pandit.FSF2020_Double_Integral
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