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path: root/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file4_cube_surface.py
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-rw-r--r--FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file4_cube_surface.py174
1 files changed, 71 insertions, 103 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
index 9301a00..146d955 100644
--- 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
@@ -1,7 +1,4 @@
from manimlib.imports import*
-
-
-
class cuber(ThreeDScene):
def construct(self):
@@ -41,6 +38,7 @@ class cuber(ThreeDScene):
n1=TextMobject(r"$\vec{n}$",color=YELLOW)
n1.scale(0.8)
n1.rotate(PI/2,axis=RIGHT)
+ n1.rotate(PI,axis=OUT)
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],
@@ -59,158 +57,128 @@ class cuber(ThreeDScene):
[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=[Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),
+ Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),
+ Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),
+ Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),
+ Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),
+ Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY)]
- [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)]
+ [veclist1[i].rotate(PI/4,axis=RIGHT) for i in range(42)]
+ [veclist1[i].rotate(PI/6,axis=OUT) for i in range(42)]
+ [veclist1[i].rotate(PI/8,axis=DOWN) for i in range(42)]
vectorfield1=VGroup(*veclist1)
- [veclist1[i].shift(spaceloc[i]) for i in range(98)]
+ [veclist1[i].shift(spaceloc[i]) for i in range(42)]
- 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=[Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),
+ Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),
+ Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),
+ Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),
+ Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),
+ Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY)]
- [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)]
+ [veclist2[i].rotate(PI/4,axis=RIGHT) for i in range(42)]
+ [veclist2[i].rotate(PI/4,axis=RIGHT) for i in range(42)]
+ [veclist2[i].rotate(PI/6,axis=OUT) for i in range(42)]
+ [veclist2[i].rotate(PI/8,axis=DOWN) for i in range(42)]
vectorfield2=VGroup(*veclist2)
- [veclist2[i].shift(spaceloc[i]) for i in range(98)]
+ [veclist2[i].shift(spaceloc[i]) for i in range(42)]
- 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=[Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),
+ Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),
+ Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),
+ Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),
+ Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),
+ Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY)]
- [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)]
+ [veclist3[i].rotate(PI/4,axis=RIGHT) for i in range(42)]
+ [veclist3[i].rotate(PI/4,axis=RIGHT) for i in range(42)]
+ [veclist3[i].rotate(PI/6,axis=OUT) for i in range(42)]
+ [veclist3[i].rotate(PI/8,axis=DOWN) for i in range(42)]
vectorfield3=VGroup(*veclist3)
- [veclist3[i].shift(spaceloc[i]) for i in range(98)]
+ [veclist3[i].shift(spaceloc[i]) for i in range(42)]
- 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=[Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),
+ Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),
+ Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),
+ Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),
+ Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),
+ Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY)]
- [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)]
+ [veclist4[i].rotate(PI/4,axis=RIGHT) for i in range(42)]
+ [veclist4[i].rotate(PI/4,axis=RIGHT) for i in range(42)]
+ [veclist4[i].rotate(PI/6,axis=OUT) for i in range(42)]
+ [veclist4[i].rotate(PI/8,axis=DOWN) for i in range(42)]
vectorfield4=VGroup(*veclist4)
- [veclist4[i].shift(spaceloc[i]) for i in range(98)]
+ [veclist4[i].shift(spaceloc[i]) for i in range(42)]
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)
+ vectorfield4.shift(3*IN+1.5*DOWN)
+
vectors=[vectorfield1,vectorfield2,vectorfield3,vectorfield4]
vectorfield=VGroup(*vectors)
- vectorfield.scale(1.25)
+ vectorfield.scale(1.3)
+
- 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),
+ fv=[Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),
+ Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),
+ Vector(color=GREY)
]
- 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)]
+ spaceloc2 = [[1.5,0.5,0.5],[1.5,1,0.5],[1.5,1.5,0.5],
+ [1.5,0.5,1],[1.5,1,1],[1.5,1.5,1],
+ [1.5,0.5,1.5],[1.5,1,1.5],[1.5,1.5,1.5]
+ ]
+ [fv[i].rotate(PI/4,axis=RIGHT) for i in range(9)]
+ [fv[i].rotate(PI/6,axis=OUT) for i in range(9)]
+ [fv[i].rotate(PI/8,axis=DOWN) for i in range(9)]
+ [fv[i].shift(spaceloc2[i]) for i in range(9)]
fvfield=VGroup(*fv)
- fvfield.shift(0.5*IN+2*DOWN)
+ fvfield.shift(2*DOWN)
+ fvfield.scale(1.3)
- flux=TextMobject("Flux through one side of the cube").set_color(ORANGE)
- flux.shift(3*UP+1.5*LEFT)
+ flux=TextMobject("Flux through one side of the cube").set_color(GOLD)
+ flux.shift(3.5*UP+0.5*LEFT)
+ alll=[vectorfield1,vectorfield2,vectorfield3,vectorfield4,fvfield]
+ alllvectors=VGroup(*alll)
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.begin_ambient_camera_rotation(rate=0.2)
+ self.play(ShowCreation(alllvectors))
+ # self.add(fvfield)
self.play(ShowCreation(cube, run_time=1))
@@ -223,6 +191,6 @@ class cuber(ThreeDScene):
# self.play(ShowCreation(flux))
self.wait(1)
self.play(ShowCreation(v1),ShowCreation(n1))
- self.wait(6)
- # self.stop_ambient_camera_rotation()
-
+ self.wait(5)
+ self.stop_ambient_camera_rotation()
+ self.wait(1)
generated by cgit (git 2.34.1) at 2024-12-20 11:09:23 +0000