diff options
Diffstat (limited to 'FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/unfinished_vector_line_integral.py')
| -rw-r--r-- | FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/unfinished_vector_line_integral.py | 359 |
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 |