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-rw-r--r--FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/unfinished_vector_line_integral.py359
1 files changed, 82 insertions, 277 deletions
diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/unfinished_vector_line_integral.py b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/unfinished_vector_line_integral.py
index 2a6467d..17febce 100644
--- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/unfinished_vector_line_integral.py
+++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/unfinished_vector_line_integral.py
@@ -1,42 +1,25 @@
from manimlib.imports import *
-class LineIntegrationProcess(SpecialThreeDScene):
+class LineIntegrationProcess(GraphScene):
CONFIG = {
- "axes_config": {
- "x_min": 0,
- "x_max": 4,
- "y_min": 0,
- "y_max": 4,
- "z_min": 0,
- "z_max": 3,
- "a":-3 ,"b": 3, "c":0 , "d":3,
- "axes_shift":IN+2*DL,
- "x_axis_config": {
- "tick_frequency": 1,
- # "include_tip": False,
- },
- "y_axis_config": {
- "tick_frequency": 1,
- # "include_tip": False,
- },
- "z_axis_config": {
- "tick_frequency": 1,
- # "include_tip": False,
- },
- "num_axis_pieces": 20,
- },
+ "x_min" : -0,
+ "x_max" : 1,
+ "y_min" : -0,
+ "y_max" : 1,
+ "axes_color":WHITE,
+ "graph_origin": ORIGIN+5*LEFT+3*DOWN,
+ "x_axis_width": 5,
+ "y_axis_height": 5,
+ "x_tick_frequency": 1,
+ "y_tick_frequency": 1,
"default_vector_field_config": {
"delta_x": .5,
"delta_y": .5,
- "x_min": -3,
- "x_max": 2,
- "y_min": -3,
- "y_max": 2,
"min_magnitude": 0,
- "max_magnitude": 4,
+ "max_magnitude": 15,
"colors": [GREEN,YELLOW,RED],
- "length_func": lambda norm : .4*sigmoid(norm),
+ "length_func": lambda norm : .45*sigmoid(norm),
"opacity": 1.0,
"vector_config": {
"stroke_width":2
@@ -46,21 +29,16 @@ class LineIntegrationProcess(SpecialThreeDScene):
"stroke_width": 2,
"stroke_color": WHITE,
},
-
- "Func": lambda x,y: 1+x**2*y/15
}
def construct(self):
-
- self.setup_axes()
- axes=self.axes
-
- self.set_camera_orientation(distance=10,
- phi=0 * DEGREES,
- theta=-90 * DEGREES,
- )
+ 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)
+
fn_text=TexMobject(
r"\vec F = x^2\hat i-xy\hat j"
).set_color_by_gradient(
@@ -68,42 +46,28 @@ class LineIntegrationProcess(SpecialThreeDScene):
)
fn_text.to_corner(UR,buff=.8).shift(DOWN)
- origin=axes.c2p(0,0,0)
+ origin=self.graph_origin
v_field=self.get_vector_field(
lambda v: np.array([
(v[0]-origin[0])**2,
-(v[0]-origin[0])*(v[1]-origin[1]),
0,
]),
+ x_min= 0+origin[0],
+ x_max= 5+origin[0],
+ y_min= -0+origin[1],
+ y_max= 5+origin[1],
)
- # self.play(Write(surface))
- self.add_fixed_in_frame_mobjects(fn_text)
+ # self.play(Write(surface))
# self.play(Write(v_field),Write(fn_text))
self.add(v_field, fn_text)
self.get_line_of_int()
- # self.begin_ambient_camera_rotation(rate=0.04)
self.get_dot_product_values()
- '''self.get_dot_prod_values_on_line()
+ '''self.get_field_values_on_line()
self.wait(1.5)
- self.area=self.get_area()
- area_text=TextMobject("Line"," Integral in the",r" scalar field\\"," means this" ,"area")
- area_text.set_color_by_tex_to_color_map({
- "Line": PINK, "scalar":BLUE, "area":TEAL_A
- })
- area_text.to_edge(TOP,buff=MED_SMALL_BUFF)
-
- self.remove(self.values_on_line_text)
- self.add_fixed_in_frame_mobjects(area_text)
- self.play(Write(area_text))
- self.play(Write(self.area),run_time=2)
- self.play(FadeOut(VGroup(surface,fn_text)))
- self.wait()
-
- self.stop_ambient_camera_rotation()
- # self.get_lines()
- self.remove(axes,surface)
+ self.remove(surface)
self.trasform_to_graphs()'''
self.wait(2)
@@ -123,19 +87,20 @@ class LineIntegrationProcess(SpecialThreeDScene):
line_of_int_text.to_edge(TOP,buff=SMALL_BUFF)
- line_of_int=(self.get_curve(
- self.Func,on_surface=False
- ))
+ line_of_int= self.get_graph(
+ lambda x : np.sqrt(1-x**2),
+ x_min=1,
+ x_max=0,
+ )
line_of_int.set_style(
stroke_width=5,
- stroke_color=PINK,
+ stroke_color=BLUE,
)
- self.add_fixed_in_frame_mobjects(line_of_int_text)
# self.play(Write(line_of_int_text))
self.wait(.5)
- self.play(ShowCreation(line_of_int),run_time=1.5)
- # self.add(line_of_int)
+ # self.play(ShowCreation(line_of_int),run_time=1.5)
+ self.add(line_of_int)
self.line_of_int=line_of_int
self.line_of_int_text=line_of_int_text
@@ -143,7 +108,7 @@ class LineIntegrationProcess(SpecialThreeDScene):
def get_dot_product_values(self):
self.get_vector_and_tangent()
self.play(ApplyMethod(
- t_tracker.set_value, PI/2,
+ self.t_tracker.set_value, PI/2,
rate_func=linear,
run_time=.5,
)
@@ -175,7 +140,7 @@ class LineIntegrationProcess(SpecialThreeDScene):
)
vect = Vector().rotate(angle,about_point=coord)
vect.set_color("#DC75CD")
- tangent=vect.next_to(x,DR,buff=0)
+ tangent=vect.next_to(coord,DR,buff=0)
tangent_sym.next_to(tangent,DOWN,buff=.1)
self.play(Write(VGroup(tangent,tangent_sym)))
@@ -198,34 +163,29 @@ class LineIntegrationProcess(SpecialThreeDScene):
))
self.dot_sym=dot_sym
-
- """def get_dot_prod_values_on_line(self):
- self.remove(self.line_of_int_text)
-
- values_on_line_text=TextMobject("Values"," of"," function","on the ","line")
- values_on_line_text.set_color_by_tex_to_color_map({
- "Values":YELLOW, "function":BLUE,"line":PINK
+
+
+
+ def get_curve(self,func,on_surface=False ,**kwargs):
+ config = dict()
+ config.update(self.default_graph_style)
+ config.update({
+ "t_min": 0,
+ "t_max": PI/2,
})
- values_on_line_text.to_edge(TOP,buff=SMALL_BUFF)
-
- values_on_surface=(self.get_curve(
- self.Func,on_surface=True
- ))
- values_on_surface.set_style(
- stroke_width=5,
- stroke_color=YELLOW,
- )
-
- self.add_fixed_in_frame_mobjects(values_on_line_text)
- self.play(Write(values_on_line_text))
- # self.wait()
- self.play(ShowCreation(values_on_surface),run_time=3)
- # self.add(values_on_surface)
-
- self.values_on_surface=values_on_surface
- self.values_on_line_text=values_on_line_text"""
+ config.update(kwargs)
+ r=1
+ curve=ParametricFunction(
+ lambda t: self.coords_to_point(
+ r*np.cos(t),
+ r*np.sin(t),
+ ),
+ **config,
+ )
+ return curve
-
+
+ #-------------------------------------------------------
def trasform_to_graphs(self):
on_surface_graph=(self.get_graph(
self.Func,on_surface=True
@@ -268,8 +228,7 @@ class LineIntegrationProcess(SpecialThreeDScene):
theta=-90 * DEGREES,
added_anims=into_graph,
run_time=2
- )
-
+ )
def get_area(self,graph=False):
axes=self.axes
if graph:
@@ -293,188 +252,34 @@ class LineIntegrationProcess(SpecialThreeDScene):
)
return area
-
- def get_curve(self,func,on_surface=False ,**kwargs):
- config = dict()
- config.update(self.default_graph_style)
- config.update({
- "t_min": 0,
- "t_max": PI/2,
- })
- config.update(kwargs)
- r=abs(self.axes.a)
- curve=ParametricFunction(
- lambda t: self.axes.c2p(
- r*np.cos(t),
- r*np.sin(t),
- func(r*np.cos(t), r*np.sin(t))*bool(on_surface)
- ),
- **config,
- )
- return curve
-
- def get_surface(self, func, **kwargs):
- axes=self.axes
- config = {
- "u_min": axes.a-.2,
- "u_max": axes.b+.2,
- "v_min": axes.c-.1,
- "v_max": axes.d,
- "resolution": (
- 2*(axes.y_max - axes.y_min) // axes.y_axis.tick_frequency,
- (axes.x_max - axes.x_min) // axes.x_axis.tick_frequency,
- ),
- }
-
- config.update(self.default_surface_config)
- config.update(kwargs)
- return ParametricSurface(
- lambda x,y : axes.c2p(
- x, y, func(x, y)
- ),
- **config
- )
-
- def get_graph(self,func,on_surface=False ,**kwargs):
- config = dict()
- config.update(self.default_graph_style)
- config.update({
- "t_min": 0,
- "t_max": PI,
+ def get_field_values_on_line(self):
+ self.remove(self.line_of_int_text)
+
+ values_on_line_text=TextMobject("Values"," of"," function","on the ","line")
+ values_on_line_text.set_color_by_tex_to_color_map({
+ "Values":YELLOW, "function":BLUE,"line":PINK
})
- config.update(kwargs)
- slice_curve=ParametricFunction(
- lambda t: self.axes.c2p(
- 4*np.cos(t),
- 0,
- 2+func(3*np.cos(t), 3*np.sin(t))*bool(on_surface)
- ),
- **config,
- )
- return slice_curve
-
- def get_lines(self):
- pass
- axes = self.axes
- labels=[axes.x_axis.n2p(axes.a), axes.x_axis.n2p(axes.b), axes.y_axis.n2p(axes.c),
- axes.y_axis.n2p(axes.d)]
-
-
- surface_corners=[]
- for x,y,z in self.region_corners:
- surface_corners.append([x,y,self.Func(x,y)])
-
- lines=VGroup()
- for start , end in zip(surface_corners,
- self.region_corners):
- lines.add(self.draw_lines(start,end,"PINK"))
-
- for start , end in zip(labels,
- self.region_corners):
- # lines.add(self.draw_lines(start,end,"BLUE"))
- # print (start,end)
- pass
- # self.play(ShowCreation(lines))
- self.add(lines)
-
-
- def draw_lines(self,start,end,color):
- start=self.axes.c2p(*start)
- end=self.axes.c2p(*end)
- line=DashedLine(start,end,color=color)
-
- return line
-
-#-------------------------------------------------------
- #customize 3D axes
- def get_three_d_axes(self, include_labels=True, include_numbers=True, **kwargs):
- config = dict(self.axes_config)
- config.update(kwargs)
- axes = ThreeDAxes(**config)
- axes.set_stroke(width=2)
- self.axes=axes
-
- if include_numbers:
- self.add_axes_numbers(axes)
-
- if include_labels:
- self.add_axes_labels(axes)
-
- # Adjust axis orientation
- '''axes.x_axis.rotate(
- -90 * DEGREES, LEFT,
- about_point=axes.c2p(0, 0, 0),
- )
- axes.y_axis.rotate(
- 90 * DEGREES, UP,
- about_point=axes.c2p(0, 0, 0),
- )'''
-
- return axes
-
+ values_on_line_text.to_edge(TOP,buff=SMALL_BUFF)
- def setup_axes(self):
- axes = self.get_three_d_axes(include_labels=True)
- axes.scale(1)
- # axes.center()
- axes.shift(axes.axes_shift)
-
- self.add(axes)
- self.axes = axes
+ values_on_surface=(self.get_curve(
+ self.Func,on_surface=True
+ ))
+ values_on_surface.set_style(
+ stroke_width=5,
+ stroke_color=YELLOW,
+ )
- def add_axes_numbers(self, axes):
- x_axis = axes.x_axis
- y_axis = axes.y_axis
- tex_vals_x = [
-
- ("1", axes.b),
- ]
- tex_vals_y=[
-
- ("1", axes.d)
- ]
- x_labels = VGroup()
- y_labels = VGroup()
- for tex, val in tex_vals_x:
- label = TexMobject(tex)
- label.scale(1)
- label.next_to(x_axis.n2p(val), DOWN)
- # label.rotate(180 * DEGREES)
- x_labels.add(label)
- x_axis.add(x_labels)
- x_axis.numbers = x_labels
-
- for tex, val in tex_vals_y:
- label = TexMobject(tex)
- label.scale(1)
- label.next_to(y_axis.n2p(val), LEFT)
- label.rotate(90 * DEGREES)
- y_labels.add(label)
-
- y_axis.add(y_labels)
- y_axis.numbers = y_labels
+ self.add_fixed_in_frame_mobjects(values_on_line_text)
+ self.play(Write(values_on_line_text))
+ # self.wait()
+ self.play(ShowCreation(values_on_surface),run_time=3)
+ # self.add(values_on_surface)
- return axes
+ self.values_on_surface=values_on_surface
+ self.values_on_line_text=values_on_line_text
+
+
- def add_axes_labels(self, axes):
- x_label = TexMobject("x")
- x_label.next_to(axes.x_axis.get_end(), RIGHT)
- axes.x_axis.label = x_label
-
- y_label = TextMobject("y")
- y_label.rotate(90 * DEGREES, OUT)
- y_label.next_to(axes.y_axis.get_end(), UP)
- axes.y_axis.label = y_label
-
- z_label = TexMobject("")
- z_label.rotate(90 * DEGREES, RIGHT)
- z_label.next_to(axes.z_axis.get_zenith(), LEFT)
- axes.z_axis.label = z_label
- for axis in axes:
- axis.add(axis.label)
- return axes
-
-
-
+
#uploaded by Somnath Pandit.FSF2020_Line_Integrals
generated by cgit (git 2.34.1) at 2025-01-10 11:49:23 +0000