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from manimlib.imports import *
def field_func(coordinate):
x,y = coordinate[:2]
return np.array([
-x,
-y,
0
])
class LineIntegral(MovingCameraScene, Scene):
def setup(self):
MovingCameraScene.setup(self)
Scene.setup(self)
def get_pending(self,path,proportion,dx=0.01):
if proportion < 1:
coord_i = path.point_from_proportion(proportion)
coord_f = path.point_from_proportion(proportion+dx)
else:
coord_i = path.point_from_proportion(proportion-dx)
coord_f = path.point_from_proportion(proportion)
line = Line(coord_i,coord_f)
angle = line.get_angle()
return angle
def construct(self):
# all the text
vec_f = TexMobject(r"\vec F",r" \textit{ is a vector field defined on the plane}").set_color("#EDF2EF")
c = TexMobject(r"C",r" \textit{ is a curve on the plane, oriented counter-clockwise.}").set_color("#EDF2EF")
dr = TexMobject(r"\vec dr", r"\textit{ gives the direction as we move along C}").set_color("#EDF2EF")
intg = TexMobject(r"\oint \vec F \cdot \vec dr", r"\textit{ gives the rotation along the curve}").shift(2.5*DOWN).scale(0.7).set_color("#EDF2EF")
text = VGroup(vec_f, c, dr).scale(0.6).set_stroke(width = 1.5)
text.arrange(DOWN, buff = 0.2)
text.shift(3.2*DOWN)
vec_f[0].set_color("#D1D646")
dr[0].set_color("#D1D646")
intg[0].set_color("#D1D646")
self.camera_frame.save_state()
vec_f_sym = TexMobject(r"\vec F")
c_sym = TexMobject(r"C").move_to(4.8*RIGHT+1.3*UP)
dr_sym = TexMobject(r"\vec dr").next_to(vec_f_sym, DOWN, buff = SMALL_BUFF)
dp_sym = TexMobject(r"\vec F \cdot \vec dr")
intg_sym = TexMobject(r"\oint \vec F \cdot \vec dr")
symbols = VGroup(vec_f_sym, dr_sym, dp_sym, intg_sym).shift(3*UP).set_color("#D1D646")
vector_field = VectorField(field_func, x_min = -15, x_max = 15, y_min = -15, y_max = 15).fade(0.5)
boundary = Ellipse(width = 9, height = 3).set_color("#32908F")
b2 = Ellipse(width = 9, height = 3).set_color(WHITE)
start_angle = self.get_pending(boundary, 0)
pointer = Triangle(fill_opacity = 1).set_height(0.25).set_color(WHITE)
pointer.set_fill(WHITE)
pointer.move_to(boundary.get_start())
pointer.rotate(- PI / 2)
pointer.save_state()
pointer.rotate(start_angle, about_point=pointer.get_center())
dp_sym_1 = TexMobject(r"\vec F \cdot \vec dr").next_to(pointer, RIGHT, buff = SMALL_BUFF).scale(0.5).set_color("#D1D646").add_background_rectangle()
intg_sym_1 = TexMobject(r"\oint \vec F \cdot \vec dr").next_to(pointer, RIGHT, buff = SMALL_BUFF).scale(0.5).set_color("#75485E").add_background_rectangle()
dp = TexMobject(r"\vec F \cdot \vec dr \textit{ measures whether } \vec F \textit{ and } \vec dr", r" \textit{ are oriented the same way }").next_to(dp_sym_1, DOWN, buff = SMALL_BUFF).scale(0.3).set_color("#EDF2EF")
dp[1].next_to(dp[0], DOWN, buff = SMALL_BUFF)
# groups according to animation
#one = VGroup( vec_f, vec_f_sym)
#two = VGroup(boundary, c_sym)
#three = VGroup(dr_sym, pointer)
#four = VGroup(dp, dp_sym) #this is when to zoom in
#five = VGroup(intg, intg_sym)
delete = VGroup(vec_f, vec_f_sym, c, dr, dr_sym)
self.play(ShowCreation(vec_f), ShowCreation(vec_f_sym))
self.wait()
self.play(ShowCreation(vector_field), Indicate(vec_f_sym))
self.wait(2)
self.play(ShowCreation(c))
self.wait()
self.play(ShowCreation(boundary), ShowCreation(c_sym), Indicate(c))
self.wait(2)
self.play(ShowCreation(dr))
self.wait(2)
self.play(ShowCreation(dr_sym), Indicate(dr), ShowCreation(pointer))
self.play(FadeOut(delete))
self.play(
self.camera_frame.scale,.25,
self.camera_frame.move_to,pointer
)
self.play(ShowCreation(dp_sym_1), ShowCreation(dp[0]), ShowCreation(dp[1]))
self.add(dp_sym)
self.wait(3)
self.play(Restore(self.camera_frame))
self.remove(dp[0], dp[1], dp_sym_1)
self.wait()
self.add(boundary, pointer, self.camera_frame)
def update_rotate_move(mob,alpha):
pointer.restore()
angle = self.get_pending(boundary,alpha)
pointer.move_to(boundary.point_from_proportion(alpha))
pointer.rotate(angle, about_point=pointer.get_center())
self.play(
#self.camera_frame.scale,.25,
UpdateFromAlphaFunc(pointer,update_rotate_move),
run_time=3,
)
self.play(Write(b2))
self.play(ReplacementTransform(dp_sym, intg_sym), ShowCreation(intg))
self.play(ReplacementTransform(b2, intg_sym))
self.play(Indicate(intg_sym))
self.wait(2)
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