diff options
Diffstat (limited to 'FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file7_div-formula.py')
| -rw-r--r-- | FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file7_div-formula.py | 225 |
1 files changed, 225 insertions, 0 deletions
diff --git a/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file7_div-formula.py b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file7_div-formula.py new file mode 100644 index 0000000..4e1eab2 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file7_div-formula.py @@ -0,0 +1,225 @@ +from manimlib.imports import * +import numpy as np + +def div(coordinate): + x,y = coordinate[:2] + return np.array([ + x, + y, + 0 + ]) + + + + +class Grid(VMobject): + CONFIG = { + "height": 6.0, + "width": 6.0, + } + + def __init__(self, rows, columns, **kwargs): + digest_config(self, kwargs, locals()) + VMobject.__init__(self, **kwargs) + + def generate_points(self): + x_step = self.width / self.columns + y_step = self.height / self.rows + + for x in np.arange(0, self.width + x_step, x_step): + self.add(Line( + [x - self.width / 2., -self.height / 2., 0], + [x - self.width / 2., self.height / 2., 0], + )) + for y in np.arange(0, self.height + y_step, y_step): + self.add(Line( + [-self.width / 2., y - self.height / 2., 0], + [self.width / 2., y - self.height / 2., 0] + )) + + +class ScreenGrid(VGroup): + CONFIG = { + "rows":8, + "columns":14, + "height": FRAME_Y_RADIUS*2, + "width": 14, + "grid_stroke":0.5, + "grid_color":WHITE, + "axis_color":RED, + "axis_stroke":2, + "show_points":False, + "point_radius":0, + "labels_scale":0.5, + "labels_buff":0, + "number_decimals":2 + } + + def __init__(self,**kwargs): + VGroup.__init__(self,**kwargs) + rows=self.rows + columns=self.columns + grilla=Grid(width=self.width,height=self.height,rows=rows,columns=columns).set_stroke(self.grid_color,self.grid_stroke) + + vector_ii=ORIGIN+np.array((-self.width/2,-self.height/2,0)) + vector_id=ORIGIN+np.array((self.width/2,-self.height/2,0)) + vector_si=ORIGIN+np.array((-self.width/2,self.height/2,0)) + vector_sd=ORIGIN+np.array((self.width/2,self.height/2,0)) + + ejes_x=Line(LEFT*self.width/2,RIGHT*self.width/2) + ejes_y=Line(DOWN*self.height/2,UP*self.height/2) + + ejes=VGroup(ejes_x,ejes_y).set_stroke(self.axis_color,self.axis_stroke) + + divisiones_x=self.width/columns + divisiones_y=self.height/rows + + direcciones_buff_x=[UP,DOWN] + direcciones_buff_y=[RIGHT,LEFT] + dd_buff=[direcciones_buff_x,direcciones_buff_y] + vectores_inicio_x=[vector_ii,vector_si] + vectores_inicio_y=[vector_si,vector_sd] + vectores_inicio=[vectores_inicio_x,vectores_inicio_y] + tam_buff=[0,0] + divisiones=[divisiones_x,divisiones_y] + orientaciones=[RIGHT,DOWN] + puntos=VGroup() + leyendas=VGroup() + + + for tipo,division,orientacion,coordenada,vi_c,d_buff in zip([columns,rows],divisiones,orientaciones,[0,1],vectores_inicio,dd_buff): + for i in range(1,tipo): + for v_i,direcciones_buff in zip(vi_c,d_buff): + ubicacion=v_i+orientacion*division*i + punto=Dot(ubicacion,radius=self.point_radius) + coord=round(punto.get_center()[coordenada],self.number_decimals) + leyenda=TextMobject("%s"%coord).scale(self.labels_scale) + leyenda.next_to(punto,direcciones_buff,buff=self.labels_buff) + puntos.add(punto) + leyendas.add(leyenda) + + self.add(grilla,ejes,leyendas) + if self.show_points==True: + self.add(puntos) + + + + + + +class ExpDiv(Scene): + def construct(self): + + #all the text + field_text = TexMobject(r"\vec F = P\hat i + Q\hat j").shift(3*UP+5*RIGHT) + field_text_2 = TexMobject(r"\vec F = 2x\hat i + 2y\hat j").shift(3*UP+5*RIGHT) + p = TexMobject(r"P = 2x").scale(0.8) + q = TexMobject(r"Q = 2y").next_to(p, RIGHT).scale(0.8) + pq = VGroup(p, q) + pq.next_to(field_text_2, DOWN, buff = SMALL_BUFF) + dpq = TexMobject(r"\frac{\partial P}{\partial x}", r" \frac{\partial Q}{\partial y}").scale(0.8).next_to(pq, DOWN, buff = LARGE_BUFF) + + + dp_dq = TexMobject(r"\frac{\partial P}{\partial x} + \frac{\partial Q}{\partial y}", r" = \textrm{div} \vec F").scale(0.8).next_to(pq, DOWN, buff = LARGE_BUFF) + #dp_dq1 = TexMobject(r" = \textrm{div} \vec F").scale(0.8) + #dp_dq1.next_to(dp_dq[0], DOWN, buff = SMALL_BUFF) + dp_text = TexMobject(r"\frac{\partial P}{\partial x}\textit{: the rate of change of the horizontal component as x increases}").shift(3*DOWN).scale(0.8) + dq_text = TexMobject(r"\frac{\partial Q}{\partial y}\textit{: the rate of change of the vertical component as y increases}").shift(3*DOWN).scale(0.8) + + + vector_field = VectorField(div, x_min = -4, x_max = 4, y_min = -4, y_max = 4).shift(1.5*LEFT) + + x_comps=VGroup() + y_comps=VGroup() + for vector in vector_field: + x = Vector(RIGHT, color = BLUE_E) + y = Vector(UP, color= YELLOW_E) + x.put_start_and_end_on(vector.points[0], np.array([vector.get_end()[0],vector.points[0][1],0])) + y.put_start_and_end_on(vector.points[0], np.array([vector.points[0][0],vector.get_end()[1],0])) + x_comps.add(x) + y_comps.add(y) + + line1 = Arrow(4*LEFT, 4*RIGHT).shift(3.5*DOWN+1.5*LEFT) + line2 = Arrow(4*DOWN, 4*UP).shift(3*RIGHT) + + + + + # f(x) = x**2 + fx = lambda x: x.get_value()/10 + # ValueTrackers definition + x_value = ValueTracker(-4) + fx_value = ValueTracker(fx(x_value)) + # DecimalNumber definition + x_tex = DecimalNumber(x_value.get_value()).add_updater(lambda v: v.set_value(x_value.get_value())) + fx_tex = DecimalNumber(fx_value.get_value()).add_updater(lambda v: v.set_value(fx(x_value))) + # TeX labels definition + x_label = TexMobject("x = ") + fx_label = TexMobject("P = ") + # Grouping of labels and numbers + group = VGroup(x_tex,fx_tex,x_label,fx_label).scale(0.8) + VGroup(x_tex, fx_tex).arrange_submobjects(DOWN,buff=0.3) + # Align labels and numbers + x_label.next_to(x_tex,LEFT, buff=0.1,aligned_edge=x_label.get_bottom()) + fx_label.next_to(fx_tex,LEFT, buff=0.1,aligned_edge=fx_label.get_bottom()) + + + fy = lambda y: y.get_value()/10 + # ValueTrackers definition + y_value = ValueTracker(-4) + fy_value = ValueTracker(fy(y_value)) + # DecimalNumber definition + y_tex = DecimalNumber(y_value.get_value()).add_updater(lambda v: v.set_value(y_value.get_value())) + fy_tex = DecimalNumber(fy_value.get_value()).add_updater(lambda v: v.set_value(fy(y_value))) + # Tey labels definition + y_label = TexMobject("y = ") + fy_label = TexMobject("Q = ") + # Grouping of labels and numbers + group_2 = VGroup(y_tex,fy_tex,y_label,fy_label).scale(0.8) + VGroup(y_tex, fy_tex).arrange_submobjects(DOWN,buff=0.3) + # Align labels and numbers + y_label.next_to(y_tex,LEFT, buff=0.1,aligned_edge=y_label.get_bottom()) + fy_label.next_to(fy_tex,LEFT, buff=0.1,aligned_edge=fy_label.get_bottom()) + + + self.play(ShowCreation(field_text)) + self.wait() + self.play(ShowCreation(vector_field), ReplacementTransform(field_text, field_text_2)) + self.wait() + self.play(ShowCreation(p), ShowCreation(q), FadeOut(vector_field)) + self.wait() + self.play(ShowCreation(dpq[0]), ShowCreation(x_comps)) + self.play(Indicate(dpq[0])) + self.wait() + self.play(ShowCreation(dp_text)) + self.wait() + self.play(Uncreate(dp_text)) + + self.add(group.move_to(5*RIGHT+3*DOWN)) + self.play(Write(line1), + x_value.set_value,4, + rate_func=linear, + run_time=3 + ) + self.wait(2) + self.play(FadeOut(group), FadeOut(line1), ApplyFunction(lambda a:a.fade(), x_comps)) + + self.play(ShowCreation(dpq[1]), ShowCreation(y_comps)) + self.play(Indicate(dpq[1])) + self.wait(2) + self.play(ShowCreation(dq_text)) + self.wait() + self.play(Uncreate(dq_text)) + + self.add(group_2.move_to(5*RIGHT+3*DOWN)) + self.play(Write(line2), + y_value.set_value,4, + rate_func=linear, + run_time=3 + ) + self.wait(2) + self.play(ReplacementTransform(dpq, dp_dq), FadeOut(line2), ReplacementTransform(x_comps, vector_field), ReplacementTransform(y_comps, vector_field), FadeOut(group_2)) + + self.play(Indicate(dp_dq)) + self.wait() + |