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-rw-r--r--FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file4_cube_surface.py228
1 files changed, 228 insertions, 0 deletions
diff --git a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file4_cube_surface.py b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file4_cube_surface.py
new file mode 100644
index 0000000..9301a00
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file4_cube_surface.py
@@ -0,0 +1,228 @@
+from manimlib.imports import*
+
+
+
+class cuber(ThreeDScene):
+ def construct(self):
+
+ axes=ThreeDAxes()
+ cube=Cube()
+ # cube.scale(1)
+ cube.shift(RIGHT+DOWN+OUT)
+
+
+
+ sq3=Square(color=RED, fill_opacity=0.85)
+ sq3.rotate(PI/2, axis=UP)
+ sq3.shift(DOWN+OUT+2*RIGHT)
+
+ x=TextMobject("x")
+ y=TextMobject("y")
+ z=TextMobject("z")
+
+ x.rotate(PI/2, axis=RIGHT)
+ x.rotate(PI/4,axis=OUT)
+ x.shift(5.8*DOWN)
+
+ y.rotate(PI/2, axis=RIGHT)
+ y.rotate(PI/8,axis=OUT)
+ y.shift(5.8*RIGHT)
+
+ z.rotate(PI/2, axis=RIGHT)
+ z.rotate(PI/5,axis=OUT)
+ z.shift(3.2*OUT+0.4*LEFT)
+ axis_label=VGroup(x,y,z)
+
+ v1=Vector(color=YELLOW,buff=15)
+ v1.rotate(PI/4,axis=RIGHT)
+ v1.shift(2*RIGHT+1*DOWN+1*OUT)
+
+
+ n1=TextMobject(r"$\vec{n}$",color=YELLOW)
+ n1.scale(0.8)
+ n1.rotate(PI/2,axis=RIGHT)
+ n1.shift(3*RIGHT+1.3*OUT+DOWN)
+
+ spaceloc = [[0,0,2],[1,0,2],[-1,0,2],[2,0,2],[-2,0,2],[3,0,2],[-3,0,2],
+ [0,1,2],[1,1,2],[-1,1,2],[2,1,2],[-2,1,2],[3,1,2],[-3,1,2],
+ [0,-1,2],[1,-1,2],[-1,-1,2],[2,-1,2],[-2,-1,2],[3,-1,2],[-3,-1,2],
+ [0,2,2],[1,2,2],[-1,2,2],[2,2,2],[-2,2,2],[3,2,2],[-3,2,2],
+ [0,-2,2],[1,-2,2],[-1,-2,2],[2,-2,2],[-2,-2,2],[3,-2,2],[-3,-2,2],
+ [0,3,2],[1,3,2],[-1,3,2],[2,3,2],[-2,3,2],[3,3,2],[-3,3,2],
+ [0,3,2],[1,3,2],[-1,3,2],[2,3,2],[-2,3,2],[3,3,2],[-3,3,2],
+ [0,4,2],[1,4,2],[-1,4,2],[2,4,2],[-2,4,2],[3,4,2],[-3,4,2],
+ [0,4,2],[1,4,2],[-1,4,2],[2,4,2],[-2,4,2],[3,4,2],[-3,4,2],
+ [0,5,2],[1,5,2],[-1,5,2],[2,5,2],[-2,5,2],[3,5,2],[-3,5,2],
+ [0,5,2],[1,5,2],[-1,5,2],[2,5,2],[-2,5,2],[3,5,2],[-3,5,2],
+ [0,6,2],[1,6,2],[-1,6,2],[2,6,2],[-2,6,2],[3,6,2],[-3,6,2],
+ [0,1.5,2],[1,1.5,2],[-1,1.5,2],[2,1.5,2],[-2,1.5,2],[3,1.5,2],[-3,1.5,2],
+ [0,3,2],[1,3,2],[-1,3,2],[2,3,2],[-2,3,2],[3,3,2],[-3,3,2]]
+
+
+ veclist1=[Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),
+ Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),
+ Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),
+ Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),
+ Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),
+ Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),
+ Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),
+ Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),
+ Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),
+ Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),
+ Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),
+ Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),
+ Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),
+ Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E)]
+
+
+
+
+
+ [veclist1[i].rotate(PI/4,axis=RIGHT) for i in range(10,30,1)]
+ [veclist1[i].rotate(PI/4,axis=RIGHT) for i in range(40,80,2)]
+ [veclist1[i].rotate(PI/6,axis=OUT) for i in range(98)]
+ [veclist1[i].rotate(PI/8,axis=DOWN) for i in range(98)]
+ vectorfield1=VGroup(*veclist1)
+ [veclist1[i].shift(spaceloc[i]) for i in range(98)]
+
+
+
+
+ veclist2=[Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),
+ Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),
+ Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),
+ Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),
+ Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),
+ Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),
+ Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),
+ Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),
+ Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),
+ Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),
+ Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),
+ Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),
+ Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),
+ Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E)]
+
+
+
+
+
+ [veclist2[i].rotate(PI/4,axis=RIGHT) for i in range(10,30,1)]
+ [veclist2[i].rotate(PI/4,axis=RIGHT) for i in range(40,80,2)]
+ [veclist2[i].rotate(PI/6,axis=OUT) for i in range(98)]
+ [veclist2[i].rotate(PI/8,axis=DOWN) for i in range(98)]
+ vectorfield2=VGroup(*veclist2)
+ [veclist2[i].shift(spaceloc[i]) for i in range(98)]
+
+
+
+ veclist3=[Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(),
+ Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(),
+ Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(),
+ Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(),
+ Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(),
+ Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(),
+ Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(),
+ Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(),
+ Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(),
+ Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(),
+ Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(),
+ Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(),
+ Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(),
+ Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector()]
+
+
+
+
+
+ [veclist3[i].rotate(PI/4,axis=RIGHT) for i in range(10,30,1)]
+ [veclist3[i].rotate(PI/4,axis=RIGHT) for i in range(40,80,2)]
+ [veclist3[i].rotate(PI/6,axis=OUT) for i in range(98)]
+ [veclist3[i].rotate(PI/8,axis=DOWN) for i in range(98)]
+ vectorfield3=VGroup(*veclist3)
+ [veclist3[i].shift(spaceloc[i]) for i in range(98)]
+
+
+
+
+ veclist4=[Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(),
+ Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(),
+ Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(),
+ Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(),
+ Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(),
+ Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(),
+ Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(),
+ Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(),
+ Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(),
+ Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(),
+ Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(),
+ Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(),
+ Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(),
+ Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector()]
+
+
+
+
+
+ [veclist4[i].rotate(PI/4,axis=RIGHT) for i in range(10,30,1)]
+ [veclist4[i].rotate(PI/4,axis=RIGHT) for i in range(40,80,2)]
+ [veclist4[i].rotate(PI/6,axis=OUT) for i in range(98)]
+ [veclist4[i].rotate(PI/8,axis=DOWN) for i in range(98)]
+ vectorfield4=VGroup(*veclist4)
+ [veclist4[i].shift(spaceloc[i]) for i in range(98)]
+
+
+ vectorfield1.shift(1.5*DOWN)
+ vectorfield2.shift(IN+1.5*DOWN)
+ vectorfield3.shift(2*IN+1.5*DOWN)
+ vectorfield4.shift(3*IN+1.5*DOWN)
+
+ vectors=[vectorfield1,vectorfield2,vectorfield3,vectorfield4]
+ vectorfield=VGroup(*vectors)
+ vectorfield.scale(1.25)
+
+ fv=[Vector(color=ORANGE),Vector(color=ORANGE),Vector(color=ORANGE),Vector(color=ORANGE),
+ Vector(color=ORANGE),Vector(color=ORANGE),Vector(color=ORANGE),Vector(color=ORANGE),
+ Vector(color=ORANGE),Vector(color=ORANGE),Vector(color=ORANGE),Vector(color=ORANGE),
+ Vector(color=ORANGE),Vector(color=ORANGE),Vector(color=ORANGE),Vector(color=ORANGE),
+ ]
+
+ spaceloc2 = [[1.5,0.5,0.5],[1.5,1,0.5],[1.5,1.5,0.5],[1.5,2,0.5],
+ [1.5,0.5,1],[1.5,1,1],[1.5,1.5,1],[1.5,2,1],
+ [1.5,0.5,1.5],[1.5,1,1.5],[1.5,1.5,1.5],[1.5,2,1.5],
+ [1.5,0.5,2],[1.5,1,2],[1.5,1.5,2],[1.5,2,2]]
+
+ [fv[i].rotate(PI/4,axis=RIGHT) for i in range(1)]
+ [fv[i].rotate(PI/6,axis=OUT) for i in range(16)]
+ [fv[i].rotate(PI/8,axis=DOWN) for i in range(16)]
+ [fv[i].shift(spaceloc2[i]) for i in range(16)]
+ fvfield=VGroup(*fv)
+ fvfield.shift(0.5*IN+2*DOWN)
+
+ flux=TextMobject("Flux through one side of the cube").set_color(ORANGE)
+ flux.shift(3*UP+1.5*LEFT)
+
+
+
+
+
+ self.set_camera_orientation(phi=70 * DEGREES,theta=-75*DEGREES)
+ self.play(ShowCreation(axes),ShowCreation(axis_label))
+ self.play(ShowCreation(vectorfield))
+ self.add(fvfield)
+ self.begin_ambient_camera_rotation(rate=0.01)
+
+ self.play(ShowCreation(cube, run_time=1))
+
+ self.wait(1)
+ self.play(ShowCreation(sq3))
+ self.wait(1)
+ self.play(FadeOut(cube))
+ self.play(FadeOut(vectorfield))
+ self.add_fixed_in_frame_mobjects(flux)
+ # self.play(ShowCreation(flux))
+ self.wait(1)
+ self.play(ShowCreation(v1),ShowCreation(n1))
+ self.wait(6)
+ # self.stop_ambient_camera_rotation()
+
generated by cgit (git 2.34.1) at 2024-12-21 17:19:41 +0000