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from manimlib.imports import *
class SlopeFields(GraphScene):
CONFIG = {
"x_min" : -2,
"x_max" : 2,
"y_min" : -2,
"y_max" : 2,
"graph_origin": ORIGIN+2.5*LEFT,
"x_axis_width": 7,
"y_axis_height": 7,
"x_tick_frequency": 1,
"y_tick_frequency": 1,
"default_slope_field_config": {
"delta_x": .2,
"delta_y": .2,
"opacity": 1,
"color": BLUE_A,
"slope_length_factor": .2,
"line_config": {
"stroke_width":2.5,
},
},
"a":-1.9 ,"b": 2, "c": -1.9 ,"d": 2,
}
def construct(self):
X = RIGHT*self.x_axis_width/(self.x_max- self.x_min)
Y = UP*self.y_axis_height/(self.y_max- self.y_min)
self.X=X ;self.Y=Y
self.setup_axes(animate=False)
slope_field=self.get_slope_field(
lambda x,y:-2.0*(x-self.graph_origin[0])*(y-self.graph_origin[1]),
x_min=self.graph_origin[0]+self.a,
x_max=self.graph_origin[0]+self.b,
y_min=self.graph_origin[1]+self.c,
y_max=self.graph_origin[1]+self.d,
color= GREEN_B
)
self.show_points()
self.wait(.5)
self.show_func_machine()
self.wait(1)
self.produce_slopes(slope_field)
# self.add(slope_field)
self.glimpse_of_solutions()
self.wait(2)
def show_points(self):
dn=1.0/5
x_vals=np.arange(self.a,self.b,dn)
y_vals=np.arange(self.c,self.d,dn)
dots=VGroup()
for x_val in x_vals:
for y_val in y_vals:
dot=Dot(
self.coords_to_point(x_val,y_val),
radius=.04,
color=TEAL,
)
dots.add(dot)
self.play(ShowCreation(dots, run_time=1))
self.dots=dots
def show_func_machine(self):
machine=RoundedRectangle(
height=3,
width=4,
color=PURPLE,
stroke_width=8
).to_edge(RIGHT, buff=.4)
machine_label=TextMobject(
r"Line segment\\ with slope\\"," $y'=-2xy$",
stroke_width=1.2,
color=BLUE
).next_to(machine,IN)
machine_label[1].set_color(GREEN)
machine=VGroup(machine, machine_label)
self.play(FadeIn(machine))
self.func_machine = machine
def produce_slopes(self,slope_field):
count,i=3,0
self.run_time=1
for dot in self.dots:
if i==count:
self.run_time=.05
position=dot.get_center()
line= slope_field.get_slope(position)
self.go_to_machine(dot)
self.take_line_from_machine(line,position)
i+=1
def go_to_machine(self,dot):
if self.run_time>.5:
self.play(ApplyMethod(
dot.next_to,
self.func_machine,4*UP,
),
run_time=self.run_time
)
self.dot=dot
def take_line_from_machine(self,vect,position):
if self.run_time>.5:
vect.next_to(self.func_machine,DOWN,buff=.1)
self.play(
ApplyMethod(
self.dot.shift,DOWN,
run_time=self.run_time
)),
self.play(
FadeOut(self.dot),
run_time=.2
)
self.play(
FadeIn(vect),
run_time=.4
)
self.play(
ApplyMethod(
vect.move_to,position
),
run_time=self.run_time
)
else:
self.remove(self.dot)
self.add(vect)
vect.move_to(position)
def get_slope_field(self,func,**kwargs):
config = dict()
config.update(self.default_slope_field_config)
config.update(kwargs)
slope_field= SlopeField(func,**config)
return slope_field
def glimpse_of_solutions(self):
sol_text= TextMobject(
r"The solution curves\\ seem to be like...",
color= BLUE,
stroke_width=1.2
)
sol_text.to_corner(UR, buff=1)
condition_text= TextMobject(
r"for different\\ initial conditions",
color= GOLD,
stroke_width=1.1
)
condition_text.next_to(sol_text,DOWN,buff=1)
solution1 = self.get_graph(
lambda x : np.exp(-x**2),
x_min = self.a,
x_max = self.b,
color = PINK)
solution2 = self.get_graph(
lambda x : .5*np.exp(-x**2),
x_min = self.a,
x_max = self.b,
color = YELLOW)
solution3 = self.get_graph(
lambda x : 1.5*np.exp(-x**2),
x_min = self.a,
x_max = self.b,
color = BLUE)
solution4 = self.get_graph(
lambda x : -np.exp(-x**2),
x_min = self.a,
x_max = self.b,
color = RED_E)
self.play(FadeOut(self.func_machine))
self.play(Write(sol_text))
self.wait(.6)
self.play(ShowCreation(solution1))
self.play(Write(condition_text))
self.play(ShowCreation(solution2))
self.wait(.5)
self.play(ShowCreation(solution3))
self.wait(.5)
self.play(ShowCreation(solution4))
class SlopeField(VGroup):
CONFIG = {
"delta_x": 0.5,
"delta_y": 0.5,
"x_min": int(np.floor(-FRAME_WIDTH / 2)),
"x_max": int(np.ceil(FRAME_WIDTH / 2)),
"y_min": int(np.floor(-FRAME_HEIGHT / 2)),
"y_max": int(np.ceil(FRAME_HEIGHT / 2)),
"opacity": 1.0,
"color": WHITE,
"slope_length_factor": .25,
"line_config": {},
}
def __init__(self, func, **kwargs):
VGroup.__init__(self, **kwargs)
self.func = func
x_range = np.arange(
self.x_min,
self.x_max + self.delta_x,
self.delta_x
)
y_range = np.arange(
self.y_min,
self.y_max + self.delta_y,
self.delta_y
)
for x, y in it.product(x_range, y_range):
point = x * RIGHT + y * UP
self.add(self.get_slope(point))
self.set_opacity(self.opacity)
def get_slope(self, point, **kwargs):
slope = self.func(*point[:2])
line_config = dict(self.line_config)
line_config.update(kwargs)
line = Line(ORIGIN,self.slope_length_factor*RIGHT, **line_config)
line.move_to(point).rotate(np.arctan(slope/3.2))
line.set_color(self.color)
return line
#uploaded by Somnath Pandit. FSF2020_Vector_fields
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