diff options
| -rw-r--r-- | FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/unfinished_vector_line_integral.py | 151 |
1 files changed, 74 insertions, 77 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 17febce..d5dda1f 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 @@ -8,9 +8,9 @@ class LineIntegrationProcess(GraphScene): "y_min" : -0, "y_max" : 1, "axes_color":WHITE, - "graph_origin": ORIGIN+5*LEFT+3*DOWN, - "x_axis_width": 5, - "y_axis_height": 5, + "graph_origin": ORIGIN+6.5*LEFT+3*DOWN, + "x_axis_width": 6, + "y_axis_height": 6, "x_tick_frequency": 1, "y_tick_frequency": 1, "default_vector_field_config": { @@ -18,8 +18,8 @@ class LineIntegrationProcess(GraphScene): "delta_y": .5, "min_magnitude": 0, "max_magnitude": 15, - "colors": [GREEN,YELLOW,RED], - "length_func": lambda norm : .45*sigmoid(norm), + "colors": [BLUE], + "length_func": lambda norm : norm/35, "opacity": 1.0, "vector_config": { "stroke_width":2 @@ -40,11 +40,12 @@ class LineIntegrationProcess(GraphScene): self.setup_axes(animate=False) fn_text=TexMobject( - r"\vec F = x^2\hat i-xy\hat j" + r"\vec F = x^2\hat i-xy\hat j", + stroke_width=2.5 ).set_color_by_gradient( *self.default_vector_field_config["colors"] ) - fn_text.to_corner(UR,buff=.8).shift(DOWN) + fn_text.to_corner(UR,buff=.8).shift(2*LEFT) origin=self.graph_origin v_field=self.get_vector_field( @@ -53,10 +54,10 @@ class LineIntegrationProcess(GraphScene): -(v[0]-origin[0])*(v[1]-origin[1]), 0, ]), - x_min= 0+origin[0], - x_max= 5+origin[0], + x_min= -.001+origin[0], + x_max= 5.8+origin[0], y_min= -0+origin[1], - y_max= 5+origin[1], + y_max= 6.+origin[1], ) # self.play(Write(surface)) @@ -93,8 +94,8 @@ class LineIntegrationProcess(GraphScene): x_max=0, ) line_of_int.set_style( - stroke_width=5, - stroke_color=BLUE, + stroke_width=3, + stroke_color=PINK, ) # self.play(Write(line_of_int_text)) @@ -105,46 +106,81 @@ class LineIntegrationProcess(GraphScene): self.line_of_int=line_of_int self.line_of_int_text=line_of_int_text - def get_dot_product_values(self): + def get_dot_product_values(self): + t_tracker = ValueTracker(0) + self.t_tracker = t_tracker self.get_vector_and_tangent() + self.get_dot_product_graph() + self.wait(1.5) self.play(ApplyMethod( self.t_tracker.set_value, PI/2, rate_func=linear, - run_time=.5, + run_time=2, ) ) + def get_dot_product_graph(self): + pass + def get_vector_and_tangent(self): - t_tracker = ValueTracker(0) - self.t_tracker = t_tracker - t = t_tracker.get_value - coord = [np.cos(t()), np.sin(t()), 0] - self.show_vector(coord) - self.show_tangent(coord) + self.play(FadeOut(self.axes)) + self.show_vector() + self.show_tangent() - def show_vector(self,coord): - vector = self.vector_field.get_vector(coord) - vector.set_color(ORANGE) + def show_vector(self): + t = self.t_tracker.get_value + vect_label=TextMobject( + "$\\vec F(x_i,y_i)$", + color=YELLOW, + stroke_width=2 + ).scale(.8) - self.add(vector) + vector = always_redraw( lambda: + self.vector_field.get_vector( + self.coords_to_point( + np.cos(t()), np.sin(t()) + ), + stroke_width=6, + 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) - def show_tangent(self,coord): - tangent_sym=TextMobject("$\\vec T(x_i,y_i)$",color="#DC75CD").scale(.8) - angle=self.angle_of_tangent( - coord[0], - self.line_of_int, - dx=0.01 + self.vect_label = vect_label + + def show_tangent(self): + tangent_label=TextMobject("$\\vec T(x_i,y_i)$",color="#DC75CD",stroke_width=2).scale(.8) + + t = self.t_tracker.get_value + + tangent = always_redraw(lambda: + Vector( + color="#DC75CD", + 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 + ), + about_point=self.coords_to_point( + np.cos(t()), np.sin(t()) + ) + ) ) - vect = Vector().rotate(angle,about_point=coord) - vect.set_color("#DC75CD") - tangent=vect.next_to(coord,DR,buff=0) - tangent_sym.next_to(tangent,DOWN,buff=.1) - self.play(Write(VGroup(tangent,tangent_sym))) + tangent_label.next_to(tangent,UP,buff=.1) + self.play(Write(VGroup(tangent,tangent_label))) - self.tangent_sym=tangent_sym + self.tangent_label=tangent_label def dot_product(self): @@ -221,22 +257,9 @@ class LineIntegrationProcess(GraphScene): graph_area ), ] + + def get_area(self): - self.move_camera( - # distance=20, - phi=90 * DEGREES, - theta=-90 * DEGREES, - added_anims=into_graph, - run_time=2 - ) - def get_area(self,graph=False): - axes=self.axes - if graph: - on_surface=self.on_surface_graph - on_base=self.line_graph - else: - on_surface=self.values_on_surface - on_base=self.line_of_int area =Polygon( *[ on_surface.get_point_from_function(t) @@ -253,32 +276,6 @@ class LineIntegrationProcess(GraphScene): return area - 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 - }) - 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 - |