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authorVaishnavi2020-07-19 20:51:24 +0530
committerGitHub2020-07-19 20:51:24 +0530
commitfbc57951a3d9154e9a1fb979491308d378e139da (patch)
tree91773c83ef1cbc20419e4c86993fb06f39371e5a /FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/vector-fields/file4_slope_field.py
parent8fcbefa74a25ace1dd68831797898dfaf2fab512 (diff)
parenta15447d7f518153438894928f960329cc32b1053 (diff)
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Merge pull request #6 from FOSSEE/master
Update fork repo. DONE
Diffstat (limited to 'FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/vector-fields/file4_slope_field.py')
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diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/vector-fields/file4_slope_field.py b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/vector-fields/file4_slope_field.py
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index 0000000..8ebb6f5
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/vector-fields/file4_slope_field.py
@@ -0,0 +1,247 @@
+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
+
+
+