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from manimlib.imports import *
def field_func(coordinate):
x,y = coordinate[:2]
return np.array([
-y,
x,
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):
vector_field = VectorField(field_func)
vec_field_for_flow = VectorField(field_func, x_min = -1.5, x_max = 1.5, y_min = -1.5, y_max = 1.5)
flow_rep = StreamLines(
field_func,
virtual_time=4,
min_magnitude=0,
max_magnitude=2,
dt = 0.1,
x_min = -1, x_max = 1, y_min = -1, y_max = 1,
).set_color_by_gradient([BLUE_E, TEAL, WHITE])
flow = AnimatedStreamLines(
flow_rep,
line_anim_class=ShowPassingFlashWithThinningStrokeWidth
)
boundary = Circle(radius = 2).set_color("#7FFF00")
start_angle = self.get_pending(boundary, 0)
pointer = Triangle(fill_opacity = 1).set_height(0.25).set_color("#ffff00")
pointer.set_fill("#ffff00")
pointer.move_to(boundary.get_start())
pointer.rotate(- PI / 2)
pointer.save_state()
pointer.rotate(start_angle, about_point=pointer.get_center())
sym_1 = TexMobject(r"\oint \vec F \cdot \vec dr").next_to(pointer, RIGHT, buff = SMALL_BUFF).scale(0.7).set_color("#ffff00").add_background_rectangle()
sym_2 = TexMobject(r"\nabla \times \vec F").scale(0.7).set_color(TEAL).add_background_rectangle()
self.play(ShowCreation(vector_field))
self.wait()
self.add(flow)
self.play(Write(boundary), Write(sym_2))
self.wait(2)
self.play(Write(pointer))
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(sym_1))
self.wait()
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