diff options
Diffstat (limited to 'FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals')
2 files changed, 208 insertions, 116 deletions
diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/file4_vector_line_integral.py b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/file4_vector_line_integral.py index d5dda1f..6730820 100644 --- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/file4_vector_line_integral.py +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/file4_vector_line_integral.py @@ -8,9 +8,9 @@ class LineIntegrationProcess(GraphScene): "y_min" : -0, "y_max" : 1, "axes_color":WHITE, - "graph_origin": ORIGIN+6.5*LEFT+3*DOWN, - "x_axis_width": 6, - "y_axis_height": 6, + "graph_origin": ORIGIN+6.3*LEFT+3*DOWN, + "x_axis_width": 5.5, + "y_axis_height": 5.5, "x_tick_frequency": 1, "y_tick_frequency": 1, "default_vector_field_config": { @@ -45,7 +45,7 @@ class LineIntegrationProcess(GraphScene): ).set_color_by_gradient( *self.default_vector_field_config["colors"] ) - fn_text.to_corner(UR,buff=.8).shift(2*LEFT) + fn_text.to_edge(TOP,buff=.1).shift(2*LEFT) origin=self.graph_origin v_field=self.get_vector_field( @@ -55,21 +55,19 @@ class LineIntegrationProcess(GraphScene): 0, ]), x_min= -.001+origin[0], - x_max= 5.8+origin[0], + x_max= 5.4+origin[0], y_min= -0+origin[1], - y_max= 6.+origin[1], + y_max= 5.5+origin[1], ) - - # self.play(Write(surface)) - # self.play(Write(v_field),Write(fn_text)) + self.add(v_field, fn_text) + self.play(Write(fn_text)) + self.wait(2) self.get_line_of_int() self.get_dot_product_values() - '''self.get_field_values_on_line() - self.wait(1.5) - - self.remove(surface) - self.trasform_to_graphs()''' + self.wait(2) + self.remove(v_field,fn_text) + self.write_area_as_intgral_value() self.wait(2) @@ -83,9 +81,12 @@ class LineIntegrationProcess(GraphScene): return vector_field def get_line_of_int(self): - line_of_int_text=TextMobject(r"Line of integration is\\","$\\vec r(t)=\cos(t)\hat i+\sin(t)\hat j$") + line_of_int_text=TextMobject( + r"Line of integration is\\", + "$\\vec r(t)=\cos(t)\hat i+\sin(t)\hat j$" + ) line_of_int_text[1].set_color(PINK) - line_of_int_text.to_edge(TOP,buff=SMALL_BUFF) + line_of_int_text.to_corner(UR,buff=.8) line_of_int= self.get_graph( @@ -98,14 +99,15 @@ class LineIntegrationProcess(GraphScene): stroke_color=PINK, ) - # self.play(Write(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=2) + # self.add(line_of_int) self.line_of_int=line_of_int self.line_of_int_text=line_of_int_text - + + def get_dot_product_values(self): t_tracker = ValueTracker(0) self.t_tracker = t_tracker @@ -113,21 +115,37 @@ class LineIntegrationProcess(GraphScene): self.get_dot_product_graph() self.wait(1.5) self.play(ApplyMethod( + self.t_tracker.set_value, PI/6, + rate_func=linear, + run_time=2.5, + ) + ) + self.wait(1) + self.play(ApplyMethod( self.t_tracker.set_value, PI/2, rate_func=linear, - run_time=2, + run_time=4, ) ) + self.dot_prod_graph.suspend_updating() - def get_dot_product_graph(self): - pass - - def get_vector_and_tangent(self): + vect_tangent_text=TextMobject( + "Get the"," vector",r" and\\"," tangent", + " on the"," line" + ) + vect_tangent_text.set_color_by_tex_to_color_map({ + "tangent": ORANGE, "vector": YELLOW, "line":PINK + }) + vect_tangent_text.to_corner(UR,buff=.8) + self.vect_tangent_text= vect_tangent_text + self.play(FadeOut(self.axes)) + self.remove(self.line_of_int_text) + self.play(Write(vect_tangent_text)) self.show_vector() self.show_tangent() - + self.wait(1.3) def show_vector(self): t = self.t_tracker.get_value @@ -146,137 +164,211 @@ class LineIntegrationProcess(GraphScene): max_stroke_width_to_length_ratio= 8, ).set_color(YELLOW), ) - vector.set_color(ORANGE) + vect_label.next_to(vector,RIGHT,buff=.1) - self.add(vector,vect_label) - # self.play(Write(vector),run_time=.2) + vector_group= VGroup(vector,vect_label) + + # self.add(vector_group) + self.play(Write(vector_group),run_time=1) + self.wait(.4) self.vect_label = vect_label + self.vector_group= vector_group def show_tangent(self): - tangent_label=TextMobject("$\\vec T(x_i,y_i)$",color="#DC75CD",stroke_width=2).scale(.8) + tangent_label=TextMobject( + "$\\vec T(x_i,y_i)$", + color=ORANGE, + stroke_width=2 + ).scale(.8) t = self.t_tracker.get_value tangent = always_redraw(lambda: Vector( - color="#DC75CD", + color=ORANGE, stroke_width=6, ).scale(1).next_to( self.coords_to_point( np.cos(t()), np.sin(t()) ),DR,buff=-.1 ).rotate( - self.angle_of_tangent( - np.cos(t()), - self.line_of_int, - dx=-0.00001 + self.angle_of_tangent( + np.cos(t()), + self.line_of_int, + dx=-0.00001 ), - about_point=self.coords_to_point( - np.cos(t()), np.sin(t()) + about_point=self.coords_to_point( + np.cos(t()), np.sin(t()) ) ) ) tangent_label.next_to(tangent,UP,buff=.1) - self.play(Write(VGroup(tangent,tangent_label))) + tangent_group=VGroup(tangent,tangent_label) + + # self.add(tangent_group) + self.play(Write(tangent_group)) + self.wait(.6) self.tangent_label=tangent_label - - def dot_product(self): + self.tangent_group=tangent_group - dot_sym=Dot().next_to(self.func_val,RIGHT) + def get_dot_product_graph(self): + t = self.t_tracker.get_value - self.play(FadeOut(VGroup( - self.at_any_points_text, - self.evaluate_text - ))) - self.play(Write(self.dot_prod_text)) - self.play( - FadeIn(dot_sym), - ApplyMethod( - self.tangent_sym.next_to, - dot_sym, RIGHT - )) - - self.dot_sym=dot_sym - - - - 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=1 - curve=ParametricFunction( - lambda t: self.coords_to_point( - r*np.cos(t), - r*np.sin(t), - ), - **config, + self.start_x= 1.3 ; self.end_x=2.3 + + t_axis= self.get_graph( + lambda x : 2.0/5, + x_min= self.start_x, + x_max= self.end_x, + ).set_style( + stroke_width=4, ) - return curve - - #------------------------------------------------------- - def trasform_to_graphs(self): - on_surface_graph=(self.get_graph( - self.Func,on_surface=True + dot_prod_axis= Vector(3*UP).next_to( + t_axis,LEFT,buff=-.1 + ).set_color(GREEN) + dot_prod_label=TexMobject( + "\\vec F","\\cdot","\\vec T", + stroke_width= 1.5, + ).next_to(dot_prod_axis,UP).scale(.8) + dot_prod_label[0].set_color(YELLOW) + dot_prod_label[2].set_color(ORANGE) + + dot_prod_graph_axes= VGroup(t_axis,dot_prod_axis) + + self.write_about_graph() + self.wait(1) + # self.add(dot_prod_graph_axes) + self.play(Write(dot_prod_graph_axes)) + self.show_the_parameter(t,t_axis) + self.wait(.6) + self.play(ReplacementTransform( + self.vect_label,dot_prod_label[0] + )) + self.play(ReplacementTransform( + self.tangent_label,dot_prod_label[1:3] )) - on_surface_graph.set_style( - stroke_width=5, - stroke_color=YELLOW, - ) + self.show_graph_area(t_axis) + + self.dot_prod_graph_axes= dot_prod_graph_axes + self.dot_prod_label= dot_prod_label - line_graph=(self.get_graph( - self.Func,on_surface=False + def write_about_graph(self): + graph_text=TextMobject( + "Graph",r" of the "," vector",r" $-$\\ ", + r"tangent",r" dot product\\", + " with the parameter ","$t$" + ) + graph_text.set_color_by_tex_to_color_map({ + "Graph":GREEN, "vector": YELLOW, + "tangent":ORANGE, "$t$":RED + }) + graph_text.to_corner(UR,buff=.5) + self.graph_text=graph_text + + self.remove(self.vect_tangent_text) + self.play(Write(graph_text),run_time=4) + + def show_the_parameter(self,t,t_axis): + t_dot=Dot(color=RED).next_to(t_axis,LEFT,buff=0) + t_dot.add_updater(lambda obj : + obj.move_to(self.c2g([t(),0]) )) - line_graph.set_style( - stroke_width=5, - stroke_color=PINK, + t_text=TextMobject("$t$=").next_to(t_dot,UP,buff=.25) + t_val=always_redraw( + lambda: DecimalNumber( + t()/PI, + color=GOLD + ).next_to(t_text,RIGHT,buff=0).scale(.8) ) + t_label=VGroup( + t_text,t_val + ).set_color(RED) - self.on_surface_graph=on_surface_graph - self.line_graph=line_graph - graph_area=self.get_area(graph=True) - into_graph=[ - ReplacementTransform( - self.values_on_surface, - on_surface_graph - ), - ReplacementTransform( - self.line_of_int, - line_graph - ), - ReplacementTransform( - self.area, - graph_area - ), - ] - - def get_area(self): + pi = TexMobject( + "\\pi ", + color=GOLD, + ).next_to(t_val,RIGHT,buff=0.05) + t_label.add(pi) + + t_label.add_updater(lambda label : + label.next_to(t_dot,UP) + ) + + t_group=VGroup(t_dot,t_label) + + # self.add(t_group) + self.play(Write(t_group)) - area =Polygon( + self.t_group= t_group + + + def show_graph_area(self,t_axis): + t = self.t_tracker.get_value + dot_prod_graph= always_redraw(lambda: Polygon( *[ - on_surface.get_point_from_function(t) - for t in np.arange(0,PI,0.01) + self.c2g([t,-2*np.cos(t)**2*np.sin(t)]) + for t in np.arange(0,t(),0.01) ], *[ - on_base.get_point_from_function(t) - for t in np.arange(PI,0,-0.01) + self.c2g([t,0]) + for t in [ t(),0 ] ], - stroke_width=0, - fill_color=TEAL_A, + stroke_width=2.5, + fill_color=TEAL_D, fill_opacity=.6, + )) + + self.add(dot_prod_graph) + + self.dot_prod_graph=dot_prod_graph + + def c2g(self,coord): + """ get points for the dot product graph + from its coordinates""" + + return self.coords_to_point( + self.start_x+coord[0]/(PI/2), + 2.0/5+coord[1]/2, ) - return area - - + def write_area_as_intgral_value(self): + area_text=TextMobject( + "Value of the "," line"," integral in the", + r"Vector field\\", + "is equal to this ","area" + ) + area_text.set_color_by_tex_to_color_map({ + "Vector field": BLUE, "line":PINK, "area":TEAL_C + }) + area_text.to_edge(TOP,buff=MED_SMALL_BUFF) + + + self.play(FadeOut(VGroup( + self.line_of_int, + self.vector_group, + self.tangent_group, + self.t_group, + self.dot_prod_graph_axes, + self.dot_prod_label, + self.graph_text + ) + )) + area= self.dot_prod_graph.copy().scale(1.3) + area.next_to(area_text,DOWN,buff=1.5) + + # self.add(area_text) + self.play(Write(area_text),run_time=4) + self.play(ReplacementTransform( + self.dot_prod_graph, + area + )) + self.wait(.5) #uploaded by Somnath Pandit.FSF2020_Line_Integrals + + diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/gifs/file4_vector_line_integral.gif b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/gifs/file4_vector_line_integral.gif Binary files differindex 8c63d36..1be7e1e 100644 --- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/gifs/file4_vector_line_integral.gif +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/gifs/file4_vector_line_integral.gif |
