函数
# 预定义
if True:
r = RIGHT;l = LEFT;d = DOWN;u = UP;du = DEGREES;rr = RED;bb = BLUE;gg = GREEN;gg2 = GOLD;pp = PINK;tt = TEAL;h = SVGMobject("D:\manimSVG\constants\h.svg");h2o = SVGMobject("D:\manimSVG\constants\h2o.svg");
# xxp
if type('xxp') == str:
# xxp transform
def xt(names, *args):
def pretrans0(name, i):
if type(i) == int:
back = name + '[' + str(i) + ']'
elif type(i) == str:
m = i.find('.')
n1 = i[0:m]
n2 = i[m+1:]
back = name + '[' + n1 + ':' + n2 + ']'
return back
def pretrans(name, i):
if type(i) == int:
back = name + '[' + str(i) + ']'
elif type(i) == str:
m = i.find('.')
n1 = i[0:m]
n2 = i[m+1:]
back = name + '[' + n1 + ':' + n2 + ']'
elif type(i) == list:
back = 'VGroup('
for j in i:
item = pretrans0(name, j) + ','
back += item
back += ')'
return back
ag = 'AnimationGroup('
# range(0, n-1)是错的
itemli = []
for l in names:
itemli.append(list(range(len(l))))
def countli0(name, i):
if type(i) == int:
name.remove(i)
elif type(i) == str:
m = i.find('.')
n1 = int(i[0:m])
n2 = int(i[m+1:])-1
p1 = name.index(n1)
p2 = name.index(n2)
del name[p1:p2+1]
def countli(name, i):
if type(i) == int:
name.remove(i)
elif type(i) == str:
m = i.find('.')
n1 = int(i[0:m])
n2 = int(i[m+1:])-1
p1 = name.index(n1)
p2 = name.index(n2)
del name[p1:p2+1]
elif type(i) == list:
for j in i:
item = countli0(name, j)
set1 = set()
set2 = set()
for m in range(len(args)):
n = 0
for i in args[m][2]:
n += 1
if n % 2 != 0:
u = pretrans(f'names[args[{str(m)}][0]]', i)
countli(itemli[args[m][0]], i)
set1.add(args[m][0])
else:
v = pretrans(f'names[args[{str(m)}][1]]', i)
item = f'Transform({u}, {v}),'
ag += item
countli(itemli[args[m][1]], i)
set2.add(args[m][1])
for i in set1:
for ii in itemli[i]:
# reverse GrowFromCenter不可用
ag += f'ShrinkToCenter(names[{str(i)}][{str(ii)}]), '
for j in set2:
for jj in itemli[j]:
ag += f'GrowFromCenter(names[{str(j)}][{str(jj)}]), '
ag += ')'
agg = eval(ag)
return agg
# xxp transform 2
def xt2(a, b, c):
def pretrans0(name, i):
if type(i) == int:
back = name + '[' + str(i) + ']'
elif type(i) == str:
m = i.find('.')
n1 = i[0:m]
n2 = i[m+1:]
back = name + '[' + n1 + ':' + n2 + ']'
return back
def pretrans(name, i):
if type(i) == int:
back = name + '[' + str(i) + ']'
elif type(i) == str:
m = i.find('.')
n1 = i[0:m]
n2 = i[m+1:]
back = name + '[' + n1 + ':' + n2 + ']'
elif type(i) == list:
back = 'VGroup('
for j in i:
item = pretrans0(name, j) + ','
back += item
back += ')'
return back
n = 0
ag = 'AnimationGroup('
# range(0, n-1)是错的
for i in c:
n += 1
if n % 2 != 0:
u = pretrans('a', i)
else:
v = pretrans('b', i)
item = f'Transform({u}, {v}),'
ag += item
ag += ')'
agg = eval(ag)
return agg
# xxp transform 3
def xt3(a,b):
x=b.get_center()-a.get_center()
y=b.width/a.width
return AnimationGroup(a.animate.shift(x).scale(y))
# xxp color to hex
def xc2h(c):
return rgb_to_hex(color_to_rgb(c))
# xxp color and opacity init
def xcoi(*args):
for a in args:
# 先缩放再设置透明度（否则会消失不见）
a.set_opacity(1)
for i in a:
if xc2h(i.color) == '#ff0000':
i.set_color(RED).set_sheen(0.1)
elif xc2h(i.color) == '#ffff00':
i.set_color(GOLD).set_sheen(0.1)
elif xc2h(i.color) == '#00ff00':
i.set_color(GREEN).set_sheen(0.1)
elif xc2h(i.color) == '#00ffff':
i.set_color(TEAL).set_sheen(0.1)
elif xc2h(i.color) == '#0000ff':
i.set_color(BLUE).set_sheen(0.1)
elif xc2h(i.color) == '#ff00ff':
i.set_color(PINK).set_sheen(0.1)
# xxp opacity scale
def xos(num, *args):
# 最好让透明度也一样
def premovescale(a, b):
# x = VGroup()
# y = VGroup()
for i in a:
# 设置get_fill_opacity() == 0.5会失效
if i.get_fill_opacity() < 1:
x = i
# x.add(i)
for j in b:
if j.get_fill_opacity() < 1:
y = j
# y.add(j)
scale = y.height/x.height
a.scale(scale)
# 先缩放再移动
vector = y.get_center() - x.get_center()
a.shift(vector)
args[0].scale(num)
for n in range(len(args) - 1):
premovescale(args[n+1], args[n])
xcoi(*args)
# xxp check
def xc(*args):
self.camera.background_color = WHITE
for svg in args:
if type(svg) == list:
self.clear()
for sss in svg:
self.add(sss.set(color = RED))
for sss in svg:
n = 0
for i in sss:
num = Integer(number=n, stroke_width=2).set_color(BLACK).move_to(i)
n += 1
self.add(num)
self.wait()
else:
self.clear()
self.add(svg.set(color = RED))
n = 0
for i in svg:
num = Integer(number=n, stroke_width=2).set_color(BLACK).move_to(i)
n += 1
self.add(num)
self.wait()
self.clear()
# xxp find
def xf(a, b):
n1 = str.find(a.text, b)
n2 = n1 + len(b)
return a[n1:n2]
# xxp narrator
def xn(a):
text = Text(a, font='STZhongsong').to_edge(DOWN).scale(0.6)
return text
# xxp narrator 2
def xn2(a):
text = Text(a, font='STFangsong').scale(0.7).to_edge(DOWN)
return text
# xxp upnarrator
def xun(a):
text = Text(a, font='STZhongsong').to_edge(UP).scale(0.8)
return text
# xxp para
def xp(x, y):
a = Text(y, font="STZhongsong").to_edge(DOWN).scale(0.6)
b = Text(x, font="STZhongsong").to_edge(1.8*DOWN).scale(0.6)
return VGroup(a, b)
# xxp scale
def xs(a, n1, b, n2):
scale = b[n2].width/a[n1].width
a.scale(scale)
# xxp move
def xm(a, n1, b, n2):
vect = b[n2].get_center() - a[n1].get_center()
a.shift(vect)
# xxp move and scale
def xms(a, n1, b, n2):
scale = b[n2].width/a[n1].width
a.scale(scale)
vect = b[n2].get_center() - a[n1].get_center()
a.shift(vect)
# xxp choose color
def xcc(a, b):
for i in a:
if rgb_to_hex(color_to_rgb(i.color)) == b:
return i
# xxp narrator wait
def xnw(a):
self.wait(0.1*len(a))
# xxp text flower
def xtf(a):
at = Text(a, font = 'STZhongsong',stroke_width=2).set_color(color = ['#f3e9e0', '#fea8a9'])
# at[0].set_color(color = ['#f3e9e0', '#fea8a9'])
# at[1].set_color(color = ['#f3e9e0', '#fea8a9'])
fl = msm('icon')[8].rotate(PI/2).set_color(color = ['#fea8a9', '#f3e9e0']).scale(1.5)
at.next_to(fl, RIGHT)
vg = VGroup(fl, at)
vg.set(height = 0.6).to_corner(UL)
return vg
# xxp text flower2
def xtf2(judge, a):
if judge == 1:
at = Text(a, font = 'STFangsong',stroke_width=2).set_color(color = ['#f3e9e0', '#b1d85c'])
elif judge == 2:
# 一般不是中文
at = MarkupText(a, stroke_width=2).set_color(color = ['#f3e9e0', '#b1d85c'])
# at[0].set_color(color = ['#f3e9e0', '#fea8a9'])
# at[1].set_color(color = ['#f3e9e0', '#fea8a9'])
fl = msm('icon')[8].rotate(PI/2).set_color(color = ['#b1d85c', '#f3e9e0']).scale(1.5)
at.next_to(fl, RIGHT)
vg = VGroup(fl, at)
vg.set(height = 0.6).to_corner(UL).shift(2*RIGHT)
return vg
# xxp text flower3
def xtf3(a):
at = Text(a, font = 'STZhongsong',stroke_width=2).set_color(color = ['#ccffff', '#afccff'])
# at[0].set_color(color = ['#f3e9e0', '#fea8a9'])
# at[1].set_color(color = ['#f3e9e0', '#fea8a9'])
fl = msm('icon')[8].rotate(PI/2).set_color(color = ['#afccff', '#ccffff']).scale(1.5)
at.next_to(fl, RIGHT)
vg = VGroup(fl, at)
vg.set(height = 0.6).to_corner(UL).shift(2*DOWN)
return vg
# xxp color move and scale
def xcms(a, b):
x = VGroup()
y = VGroup()
for i in a:
if rgb_to_hex(color_to_rgb(i.color)) == '#000000':
x.add(i)
for j in b:
if rgb_to_hex(color_to_rgb(j.color)) == '#000000':
y.add(j)
scale = y.width/x.width
vect = y.get_center() - x.get_center()
a.shift(vect)
a.scale(scale)
# xxp single scale
def xss(a, n):
x = Text('C', font="Times New Roman")
y = a[n]
scale = x.width/y.width
a.scale(scale)
# xxp pre postion
def xpp(a, pos):
d1 = Dot().to_corner(UL)
d2 = Dot().to_edge(UP)
d3 = Dot().to_corner(UR)
d4 = Dot().to_edge(LEFT)
d5 = Dot()
d6 = Dot().to_edge(RIGHT)
d7 = Dot().to_corner(DL)
d8 = Dot().to_edge(DOWN)
d9 = Dot().to_corner(DR)
if pos == 'ul':
a.move_to((d1.get_center() + d5.get_center())/2)
elif pos == 'u':
a.move_to((d2.get_center() + d5.get_center())/2)
elif pos == 'ur':
a.move_to((d3.get_center() + d5.get_center())/2)
elif pos == 'l':
a.move_to((d4.get_center() + d5.get_center())/2)
elif pos == 'o':
a.move_to(d5.get_center())
elif pos == 'r':
a.move_to((d6.get_center() + d5.get_center())/2)
elif pos == 'dl':
a.move_to((d7.get_center() + d5.get_center())/2)
elif pos == 'd':
a.move_to((d8.get_center() + d5.get_center())/2)
elif pos == 'dr':
a.move_to((d9.get_center() + d5.get_center())/2)
# xxp arrange and align
def xaa(mobs, b, d):
vg = VGroup()
for m in mobs:
vg.add(m)
vg.arrange(buff=b)
if d == 'u':
dire = UP
elif d == 'd':
dire = DOWN
for i in mobs:
if i != mobs[0]:
i.align_to(mobs[0], dire)
# xxp add other
def xao(*args):
if len(args) == 2:
sa(args[0].to_corner(UR), args[1].to_corner(DL))
if len(args) == 3:
sa(args[0].to_corner(UR), args[1].to_corner(DL), args[2].to_corner(DR))
# xxp grow from center
def xgf(a, li):
avg = 'AnimationGroup('
def pregrow(name, i):
if type(i) == int:
back = name + '[' + str(i) + ']'
elif type(i) == str:
m = i.find('.')
n1 = i[0:m]
n2 = i[m+1:]
back = name + '[' + n1 + ':' + n2 + ']'
return back
for j in li:
partani = pregrow('a', j)
avg += f'GrowFromCenter({partani}), '
avg += ')'
return eval(avg)
# xxp reverse grow from center
def xrgf(a, li):
avg = 'AnimationGroup('
def pregrow(name, i):
if type(i) == int:
back = name + '[' + str(i) + ']'
elif type(i) == str:
m = i.find('.')
n1 = i[0:m]
n2 = i[m+1:]
back = name + '[' + n1 + ':' + n2 + ']'
return back
for j in li:
partani = pregrow('a', j)
avg += f'GrowFromCenter({partani}, reverse_rate_function = True), '
avg += ')'
return eval(avg)
# xxp color and sheen static
def xcss(a, b):
a.set_color(b).set_sheen(0.1)
# xxp place in line
def xpl(*args):
vg = VGroup()
frame = FullScreenRectangle()
wid = frame.width
for i in args:
vg.add(i.copy())
wid -= i.width
mybuff = wid/(len(args)+1)
vg.arrange(buff=mybuff)
for j in range(len(args)):
args[j].match_x(vg[j])
# xxp place in grid
def xpg(*args):
n = 0
full = FullScreenRectangle()
li = ['ul','ur','dl','dr']
for a in args:
if a.width > a.height:
a.set(width = full.width/3)
xpp(a,li[n])
else:
a.set(height = full.height/3)
xpp(a,li[n])
n += 1
# xxp color 1
def xc1(*args):
for a in args:
a.save_state()
a.set_color(WHITE).set_sheen(0)
# xxp color 2
def xc2(*args):
li = []
for a in args:
li.append(Restore(a))
return li
# xxp color 3
def xc3(*args):
li = []
for a in args: # 不可使用animate
li.append(ApplyMethod(a.set_color, WHITE))
return li
# xxp animations list
def xal(t,*argss):
args = []
for i in argss:
args.append(i)
# 不是args = atgs.reverse()
args.reverse()
n = 0
for a in args:
if n == 1:
ag = AnimationGroup(args[1],args[0],lag_ratio=t)
elif n > 1:
ag = AnimationGroup(a,ag,lag_ratio=t)
n += 1
return ag
# xxp sub number
def xsn(*args):
vg = VGroup()
for i in range(len(args)):
n = Integer(i+1).next_to(args[i],0.7*UP)
xcss(n, BLUE)
vg.add(n)
return vg
# xxp get distance
def xgd(a,b):
return b.get_center() - a.get_center()
# xxp get distance by coodrdinate
def xgdc(a,b):
return b - a.get_center()
# xxp text flower list
def xtfl(a,*args):
# for a in args:
vg = VGroup()
li0 = xtf(a)
vg.add(li0)
n = 1
for a in args:
li = xtf2(1,a)
xm(li,0,li0,0);li.shift(n*0.9*DOWN+RIGHT)
vg.add(li)
n += 1
return vg
# xxp text flower list abbr
def xtfla(a,b):
# for a in args:
vg = VGroup()
li0 = xtf(a)
n = 1
li1 = xtf2(1,'');xm(li1,0,li0,0);li1.shift(DOWN+RIGHT)
vg.add(li0,li1)
for i in range(b-1):
li = xtf2(1,'')
xm(li,0,li1,0);li.shift(n*0.2*DOWN)
vg.add(li)
n += 1
return vg
# xxp corner check
def xcc(a,b):
a.to_corner(UL);b.to_corner(DR)
xc([a,b])
# xxp edge check
def xec(a,b):
a.to_edge(UP);b.to_edge(DOWN)
xc([a,b])
# xxp grid check
def xgc(*args):
xpg(*args)
xc([*args])
# xxp orbit color
def xoc(a):
a.set_color([BLUE_C, BLUE_E]).set_sheen(0.3).set_opacity(0.8)
# xxp play
def xxp(*args):
for a in args:
if type(a) == list:
self.wait(0.5)
self.play(*a)
self.wait(0.5)
elif type(a) == set:
self.clear()
self.add(*a)
elif type(a) == tuple:
for i in a:
self.play(i)
else:
self.wait(0.5)
self.play(a)
self.wait(0.5)
# xxp molecule move
def xmm(a,b,c):
return a.animate.shift(xgd(b,c))
# xxp markup text
def xmt(a):
# 最多不能超过三个
for i in range(5):
a = a.replace('_','<sub>',1)
a = a.replace('_','</sub>',1)
a = a.replace('^','<sup>',1)
a = a.replace('^','</sup>',1)
return MarkupText(a)
# xxp move along arc
def xmaa(a,b,c,s):
arc = ArcBetweenPoints(b.get_center(), c.get_center(), angle = s*120*DEGREES)
return MoveAlongPath(a, arc)
# xxp dot group
def xdg(num,r1,r2):
vg = VGroup()
for i in range(num):
r = np.random.rand()*(r2-r1) + r1
t = np.random.rand()*2*PI
vg.add(Circle(radius=0.02, color=BLUE_B, fill_opacity=1).shift(r*np.cos(t)*RIGHT+r*np.sin(t)*UP))
return vg
# manim CE
if type('manim CE') == str:
# self.play()
def sp(*args, **kwargs):
return self.play(*args, **kwargs)
# self.wait()
def sw(*args, **kwargs):
return self.wait(*args, **kwargs)
# self.add()
def sa(*args, **kwargs):
return self.add(*args, **kwargs)
# self.clear()
def sc(*args, **kwargs):
return self.clear(*args, **kwargs)
# self.remove()
def sr(*args, **kwargs):
return self.remove(*args, **kwargs)
# Animation Transform()
def at(a, b, *args, **kwargs):
return ReplacementTransform(a, b, *args, **kwargs)
# Animation Transform()
def at0(a, b, *args, **kwargs):
return Transform(a, b, *args, **kwargs)
# Animation ReplacementTransform()
def art(a, b, *args, **kwargs):
return ReplacementTransform(a, b, *args, **kwargs)
# Animation TransformMatchingShapes()
def atm(a, b, *args, **kwargs):
return TransformMatchingShapes(a, b, *args, **kwargs)
# Animation ClockwiseTransform()
def act(a, b, *args, **kwargs):
return ClockwiseTransform(a, b, *args, **kwargs)
# Animation CounterclockwiseTransform()
def acct(a, b, *args, **kwargs):
return CounterclockwiseTransform(a, b, *args, **kwargs)
# Animation Write()
def aw(a, *args, **kwargs):
return Write(a, *args, **kwargs)
# Animation LaggedStart()
def als(a, *args, **kwargs):
return LaggedStart(a, *args, **kwargs)
# Animation Unwrite()
def auw(a, *args, **kwargs):
return Unwrite(a, *args, **kwargs)
# Animation FadeOut()
def afo(a, *args, **kwargs):
return FadeOut(a, *args, **kwargs)
# Animation FadeIn()
def afi(a, *args, **kwargs):
return FadeIn(a, *args, **kwargs)
# Animation FadeOut()
def afoo(a, *args, **kwargs):
return FadeOut(a, *args, shift=DOWN, **kwargs)
# Animation FadeIn()
def afii(a, *args, **kwargs):
return FadeIn(a, *args, shift=DOWN, **kwargs)
# Animation Restore()
def are(a, *args, **kwargs):
return Restore(a, *args, **kwargs)
# Animation Rotate()
def aro(a, b, *args, **kwargs):
return Rotate(a, about_point = b.get_center(), *args, **kwargs)
# Animation DrawBorderThenFill()
def adb(a, *args, **kwargs):
return DrawBorderThenFill(a, *args, **kwargs)
# Animation DrawBorderThenFill() reverse
def adbr(a, *args, **kwargs):
return DrawBorderThenFill(a, *args, **kwargs, reverse_rate_function = True)
# Animation GrowFromCenter()
def agf(a, *args, **kwargs):
return GrowFromCenter(a, *args, **kwargs)
# Animation MoveAlongPath()
def ama(a, b, *args, **kwargs):
return MoveAlongPath(a, b, *args, **kwargs)
# Animation SpinInFromNothing
def asi(a, *args, **kwargs):
return SpinInFromNothing(a, angle=2 * PI, *args, **kwargs)
# Animation SpinInFromNothing reverse
def asir(a, *args, **kwargs):
return SpinInFromNothing(a, angle=2 * PI, *args, **kwargs, reverse_rate_function = True)
# Animation ShrinkToCenter
def ast(a, *args, **kwargs):
return ShrinkToCenter(a, *args, **kwargs)
# Animation Circumscribe
def ac(a, *args, **kwargs):
return Circumscribe(a, *args, **kwargs)
# Animation Indicate
def ai(a, *args, **kwargs):
return Indicate(a, *args, **kwargs)
# Animation Restore
def ar(a, *args, **kwargs):
return Restore(a, *args, **kwargs)
# Group sheen
def gs(*args):
li = []
for i in args:
li.append(i.animate.set_sheen(0.1))
return AnimationGroup(*li, run_time=0.5)
# Group color
def gc(*args):
li = []
for i in range(len(args)):
if i % 2 == 0:
li.append(args[i].animate.set_color(args[i+1]))
return AnimationGroup(*li)
# mobject Text
def mt(text, *args, **kwargs):
return Text(text, *args, **kwargs)
# mobject SVGMobject
def msm(name, *args, **kwargs):
sm = SVGMobject(f'D:\\manimSVG\\{name}.svg')
return sm
# mobject MathTex
def mmt(text, *args, **kwargs):
return MathTex(text, *args, **kwargs)
# mobject VGroup
def mvg(*args, **kwargs):
return VGroup(*args, **kwargs)
# mobject ArcBetweenPoints
def mab(a, b, *args, **kwargs):
return ArcBetweenPoints(a.get_center(), b.get_center(), angle = 120*DEGREES, *args, **kwargs)
# mobject DashedLine
def mdl(a, b, *args, **kwargs):
return DashedLine(a, b, *args, **kwargs)
# other function
if type('other function') == str:
# shift
def sh(*args):
i = 1
for a in args:
if i % 2 != 0:
a.shift(args[i])
i += 1
# scale
def sc(*args):
i = 1
for a in args:
if i % 2 != 0:
a.scale(args[i])
i += 1
# coloring
def c(*args):
i = 1
for a in args:
if i % 2 != 0:
xcss(a, args[i])
i += 1
# Wait
def w(*args):
return Wait(*args)
# refresh
def refresh(*args, **kwargs):
self.clear()
sa(*args, **kwargs)
# color refresh
def crefresh(*args, **kwargs):
sc()
for i in args:
xcoi(i)
sa(*args, **kwargs)
# execute narrator
def ext(a):
for i in a:
globals()[f't{str(i)}']=xn(a[i])
# execute narrator 2
def exn(a):
for i in a:
globals()[f't{str(i)}']=xn2(a[i])
# execute mobject
def exm(name, num):
for i in range(num):
globals()[name + str(i+1)]=msm(name + str(i+1))
# ApplyMethod Shift
def lsh(a, b):
return ApplyMethod(a.shift,b)
# ApplyMethod Scale
def lsc(a, b):
return ApplyMethod(a.scale,b)
# temporary
if type('temporary') == str:
def dotflash(a):
self.play(afi(a[0]))
n = len(a)
for i in range(n-1):
if i <= 5:
self.play(xal(0.5,afo(a[i]),afi(a[i+1])),run_time=1/(i+1))
elif i >= n-5:
self.play(xal(0.5,afo(a[i]),afi(a[i+1])),run_time=2/(n-i+1))
else:
self.play(xal(0.5,afo(a[i]),afi(a[i+1])),run_time=1/6)
def orbitname(a,b):
t1 = mmt(a).scale(1.2)
t2 = mmt(b).scale(0.8).next_to(t1,d)
vg = mvg(t1,t2)
return vg
def myan(a,b,c):
r = (b-a)/c
vg = mvg()
for i in range(c):
vg.add(Annulus(inner_radius=a+i*r,outer_radius=a+(i+1)*r))
return vg
View Code
scene
def playscene1():
title = Text('单电子原子结构', font='STZhongsong')
ext({1:'1913年，丹麦物理学家 Bohr 提出了原子结构模型',2:'氢原子的电子沿着以原子核为中心的圆形轨道上运动',3:'符合要求的圆形轨道的半径是不连续的',4:'电子在轨道中跃迁时会相应地放出或吸收能量',
5:'但是 Bohr 理论也有很大的局限性',6:'这只适用于单电子的类氢离子体系',7:'对于多电子原子，Bohr 理论忽略了电子间的相互作用',8:'更本质的原因是电子的运动并不遵循经典的力学定律',
9:'实际上,电子在某一时刻的位置无法确定',10:'因此必须从电子的本性及其运动规律入手，建立新的理论'})
nu = Circle(radius=0.3, color=BLUE_B, fill_opacity=1);el = Circle(radius=0.15, color=RED_B, fill_opacity=1).shift(0.8*r);orb1 = Circle(radius=0.8, color=BLUE_B);orb2 = Circle(radius=1.5, color=BLUE_B);orb3 = Circle(radius=2.8, color=BLUE_B)
el2=Circle(radius=0.15, color=RED_B, fill_opacity=1);el3=el2.copy();sh(el2,1.5*d,el3,2.8*l)
p1 = ImageMobject(r"C:\Users\86158\Music\p1.png").scale(0.3).shift(3.5*l+0.8*u);name=xn('Niels Henrik David Bohr').next_to(p1,DOWN);name2=xn('(1885-10-7—1962-11-18)').scale(0.8).next_to(name,DOWN);p11=Group(p1,name,name2)
y1 = mmt(r'r=\frac{n^2h^2\varepsilon _0}{\pi me^2}').scale(1.2);y2 = mmt('(n=1,2,3…)').scale(0.9).next_to(y1,DOWN);y0=mvg(y1,y2).next_to(orb3,2*r).shift(2*u)
cr = msm('cross').scale(1.5)
c(nu,BLUE,el,RED,cr,GREEN)
z1 = mvg(xdg(1,0.8,0.8),xdg(1,1.5,1.5),xdg(1,2.8,2.8));z2 = xdg(30,0.8,2.8);l1=mdl(z1[0],z1[1]);l2=mdl(z1[1],z1[2]);l3=mdl(z1[2],z1[0]);
nu.save_state();el.save_state();sc(nu,3.5,el,1.5);sh(nu,3*r+0.6*d);el.next_to(nu,3*u);x2=xn('+e').scale(1.5).move_to(nu);x3=xn('Z=1').next_to(nu,d);x1=xn('-e').scale(1.5).next_to(el,UP);
xxp(adb(title),afo(title),[afi(t1),afii(p11)],[agf(nu),agf(el)],xal(0.3,afii(x1),afii(x2),afii(x3)),[at(t1,t2),afo(p11),afo(x1),afo(x2),afo(x3),ar(nu),ar(el)],xal(0.5,agf(orb1),agf(orb2),agf(orb3)))
xxp(ama(el,orb1,run_time=2),at(t1,t3),aw(y0),xal(0.5,ai(orb1,color=PINK),ai(orb2,color=PINK),ai(orb3,color=PINK)),afo(y0),at(t1,t4),xmaa(el,el,el3,1),xmaa(el,el3,el2,1),at(t1,t5),w(0.5),at(t1,t6),w(0.5),at(t1,t7),w(0.5),at(el,z1),xal(0.3,agf(l1),agf(l2),agf(l3)))
xxp(at(t1,t8),w(0.5),xal(0.3,ast(l3),ast(l2),ast(l1),ast(orb1),ast(orb2),ast(orb3)),xal(0.5,aro(el[0],nu,angle=2*PI,run_time=2),aro(el[1],nu,angle=2*PI,run_time=2),aro(el[2],nu,angle=2*PI,run_time=2)),at(t1,t9),w(0.5),afo(el));dotflash(z2);xxp(at(t1,t10),w(),afo(t1,z2[-1],nu))
def playscene2():
p2=ImageMobject(r"C:\Users\86158\Music\p2.png");f1=mmt(r'\left [ -\frac{h^2}{8\pi ^2m} \nabla ^2 + V \right ] \psi =E\psi');f2=mmt(r'\psi (x,y,z)');f3=mmt(r'\psi (r,\theta ,\phi )');f4=mmt(r'\psi (r,\theta ,\phi ) = R(r)\cdot \Theta (\theta )\cdot\Phi (\phi )')
f5=mmt(r'\frac{\sin^2 \theta }{R} \frac{d}{dr} \left ( r^2\frac{dR}{dr} \right ) + \frac{8\pi ^2\mu r^2\sin^2 \theta}{h^2}\left ( E+\frac{Ze^2}{4\pi\varepsilon _0r} \right ) +\frac{\sin \theta}{\Theta }\frac{d}{d\theta} \left (\sin \theta \frac{d\Theta}{d\theta}\right )','+', r'\frac{1}{\Phi } \frac{d^2\Phi}{d\phi ^2}','=0 ')
f6=mmt(r'\frac{1}{\Phi } \frac{d^2\Phi}{d\phi ^2}','=-m^2');f7=mmt(r'\frac{1}{R} \frac{d}{dr} \left ( r^2\frac{dR}{dr} \right ) + \frac{8\pi ^2\mu r^2}{h^2}\left ( E+\frac{Ze^2}{4\pi\varepsilon _0r} \right )',' +',r'\frac{1}{\Theta \sin \theta}\frac{d}{d\theta} \left (\sin \theta \frac{d\Theta}{d\theta}\right )-\frac{m^2}{\sin^2 \theta} ','=0')
f8=mmt(r'\frac{1}{R} \frac{d}{dr} \left ( r^2\frac{dR}{dr} \right ) + \frac{8\pi ^2\mu r^2}{h^2}\left ( E+\frac{Ze^2}{4\pi\varepsilon _0r} \right )',r'=\beta ')
f9=mmt(r'\frac{1}{\Theta \sin \theta}\frac{d}{d\theta} \left (\sin \theta \frac{d\Theta}{d\theta}\right )-\frac{m^2}{\sin^2 \theta} ',r'=-\beta')
v1=mmt(r'\Phi',r' =\left ( \frac{1}{\sqrt{2\pi } } \right ) e^{im\phi }');
v2=mmt(r'\Theta',r' =\left ( -1 \right ) ^m\left [ \frac{(2l+1)}{2}\frac{(l-\lvert m \rvert)!}{(l+\lvert m \rvert)!} \right ] ^{\frac{1}{2} }P^{\lvert m \rvert}_l(\cos \theta )')
v3=mmt(r'R',r'=-\left [ (\frac{2Z}{na_0} ) ^3\frac{(n-l-1)!}{2n\left [ (n+l)! \right ]^3 } \right ] ^{\frac{1}{2} }e^{-\frac{\rho }{2} }\rho^lL^{2l+1}_{n+l}(\rho)')
z1=mmt(r'\Phi _m');z2=mmt(r'\Theta _{l,m}');z3=mmt(r'R_{n,l}')
sc(p2,1.6,f2,1.3,f3,1.3,f4,1.3,f5,0.7,z1,1.5,z2,1.5,z3,1.5,f7,0.8);sh(p2,3.5*l+u,f1,2.6*r,f2,3.5*r,f3,3.5*r,f6,2*u,f8,2*d,v1,2*u,v3,2*d,z1,4*l,z3,4*r)
f00=mmt('-m^2').scale(0.7).move_to(f5[2])
name=xn('Erwin Schrödinger').next_to(p2,DOWN);name2=xn('(1887-8-12—1961-1-4)').scale(0.8).next_to(name,DOWN);pic=Group(p2,name,name2)
c1=msm('coord1').scale(3);c2=msm('coord2').scale(3);sh(c1,3*l+0.3*u,c2,3*l+0.3*u)
ext({1:'1926年，奥地利物理学家 Schrödinger 提出用波动力学来描述电子的运动',2:'对于氢原子，采用球坐标系更容易求解',3:'随后采取变数分离法，设ψ为三个一元函数的乘积',4:'代入 Schrödinger 方程并化简',
5:'固定r和θ，改变φ，原式恒成立',6:'这说明含φ的式子为常数，为了后续计算方便，设为-m²',7:'化简后同理可知，含r和θ的式子也为常数，设为β',8:'在解函数的过程中发现，β只有等于l(l+1)，且l为自然数时函数才有意义',9:'三个方程解的形式为：',
10:'这就产生了三个量子数n,l,m',11:'也就是说，一组n,l,m决定一个波函数ψ'})
xxp([afii(pic),afi(t1),afii(f1)],w(),[afo(pic),at0(t1,t2),f1.animate.to_edge(UP)],afii(c1),afii(f2));xxp([xt2(c1,c2,[3,9,2,10,5,7,4,5,6,6]),agf(c2[3]),agf(c2[4]),agf(c2[2])],at(f2,f3));refresh(t1,f1,c2,f3)
xxp(afoo(c2),[f3.animate.move_to(ORIGIN),f1.animate.move_to([0,2,0])],at0(t1,t3),at(f3,f4),at0(t1,t4),at(mvg(f1,f4),f5),at0(t1,t5));refresh(t1,f5);sp(f5[2].animate.set_color(BLUE),run_time=2)
xxp(at0(t1,t6),w(),[at(f5[2].copy(),f6[0]),afi(f6[1])],at0(f5[1:3],f00),at0(t1,t7),at(f5,f7));refresh(t1,f6,f7);sp(f7[0].animate.set_color(GOLD),f7[2].animate.set_color(GREEN),run_time=2)
xxp([at(f7[0],f8[0]),at(f7[2],f9[0]),afo(f7[1],f7[3])],afi(f8[1],f9[1]));refresh(t1,f6,f8,f9);xxp(at0(t1,t8),w(1.5),at0(t1,t9),xal(0.3,afoo(f6),afii(v1),afoo(f9),afii(v2),afoo(f8),afii(v3)))
xxp(at0(t1,t10),w(0.5),at0(t1,t11),[at(v1[0],z1),at(v2[0],z2),at(v3[0],z3),afo(v1[1],v2[1],v3[1])])
def playscene3():
# config.disable_caching=True
z1=mmt(r'\Phi _m');z2=mmt(r'\Theta _{l,m}');z3=mmt(r'R_{n,l}');z4=mmt(r'Y_{l,m}')
sc(z1,1.5,z2,1.5,z3,1.5,z4,1.5);sh(z1,4*l,z3,4*r,z4,2*l)
p0=ImageMobject(r"C:\Users\86158\Music\0.png");p1=ImageMobject(r"C:\Users\86158\Music\1.png");p2=ImageMobject(r"C:\Users\86158\Music\2.png");p3=ImageMobject(r"C:\Users\86158\Music\3.png")
ext({1:'也就是说，一组n,l,m决定一个波函数ψ',2:'Θ与Φ的乘积称为球谐函数，它决定了电子波函数的角度特性',3:'我们常常利用球谐函数来作图'})
s=orbitname('s','(l=0,m=0)');px=orbitname('p_x','(l=1,m=1)');py=orbitname('p_y','(l=1,m=-1)');pz=orbitname('p_z','(l=1,m=0)');
dz2=orbitname('d_{z^2}','(l=2,m=0)');dxz=orbitname('d_{xz}','(l=2,m=1)');dyz=orbitname('d_{yz}','(l=2,m=-1)');dx2y2=orbitname('d_{x^2-y^2}','(l=2,m=2)');dxy=orbitname('d_{xy}','(l=2,m=-2)');
f1=orbitname('f_{z^3}','(l=3,m=0)').scale(0.8);f2=orbitname('f_{xz^2}','(l=3,m=1)').scale(0.8);f3=orbitname('f_{yz^2}','(l=3,m=-1)').scale(0.8);f4=orbitname('f_{xyz}','(l=3,m=2)').scale(0.8);f5=orbitname('f_{z(x^2-y^2)}','(l=3,m=-2)').scale(0.8);f6=orbitname('f_{x(x^2-3y^2)}','(l=3,m=3)').scale(0.8);f7=orbitname('f_{y(3x^2-y^2)}','(l=3,m=-3)').scale(0.8);
sc(dz2,0.8,dxz,0.8,dyz,0.8,dx2y2,0.8,dxy,0.8)
sh(s,2.5*d,px,2.5*d+4.5*r,py,2.5*d+4.5*l,pz,2.5*d,dz2,0.3*u+4.2*r+0.5*u,dx2y2,3*d+0.2*u,dyz,0.3*u+0.5*u,dxz,3*d+3.8*l+0.2*u,dxy,0.3*u+3.8*l+0.5*u,p2,0.3*u)
sh(p3,0.3*u,f1,4.6*r+0.8*u,f2,2.9*d+4.2*l,f3,1.8*r+0.8*u,f4,1.3*l+0.8*u,f5,2.9*d+1.3*l,f6,4.2*l+0.8*u,f7,1.8*r+2.9*d)
sa(z1,z2,z3,t1);xxp(at(t1,t2),w(0.5),[at(mvg(z1,z2),z4),z3.animate.shift(2*l)],at(t2,t3),w(0.5),afo(t3,z4,z3))
xxp(afii(p0),afii(s),[afoo(p0),afoo(s)],afii(p1),xal(0.3,afii(py),afii(pz),afii(px)),w(),[afoo(p1),afoo(py),afoo(pz),afoo(px)],afii(p2),xal(0.3,afii(dxy),afii(dyz),afii(dz2),afii(dxz),afii(dx2y2)),w(2))
xxp([afoo(p2),afoo(dxy),afoo(dyz),afoo(dz2),afoo(dxz),afoo(dx2y2)],afii(p3),xal(0.3,afii(f6),afii(f4),afii(f3),afii(f1),afii(f2),afii(f5),afii(f7)),w(2),[afoo(p3),afoo(f6),afoo(f4),afoo(f3),afoo(f1),afoo(f2),afoo(f5),afoo(f7)])
def playscene4():
pic=ImageMobject(r"C:\Users\86158\Music\xxx.png");pp=ImageMobject(r"C:\Users\86158\Music\1part.png");ss=ImageMobject(r"C:\Users\86158\Music\0part.png").scale(0.8);
sss=ss.copy().scale(1.5);sh(ss,3.5*l+u,sss,3.5*r+u)
s=orbitname('s','(l=0,m=0)');p=orbitname('p_z','(l=1,m=0)');d=orbitname('d_{z^2}','(l=2,m=0)');f=orbitname('f_{z^3}','(l=3,m=0)')
px=orbitname('p_x','(l=1,m=1)');py=orbitname('p_y','(l=1,m=-1)');pz=orbitname('p_z','(l=1,m=0)');
o1=orbitname('1s','(n=1,l=0,m=0)');o2=orbitname('2s','(n=2,l=0,m=0)');
sh(pic,u,f,1.2*DOWN+4.7*r,s,1.2*DOWN+4.2*l,p,1.2*DOWN+1.3*l,d,1.2*DOWN+1.8*r,px,2.5*DOWN+4.5*r,py,2.5*DOWN+4.5*l,pz,2.5*DOWN)
sh(o1,3.6*l+1.7*DOWN,o2,3.6*r+1.7*DOWN)
ext({1:'l为角量子数，决定原子轨道的形状',2:'m为磁量子数，决定原子轨道在空间的取向',3:'n为主量子数，决定轨道的能量，也大体上决定轨道的大小'})
sh(pp,1.2*u,px,1.2*u,py,1.2*u,pz,1.2*u)
xxp([afii(pic),afi(t1)],xal(0.3,afii(s),afii(p),afii(d),afii(f)),w(),[at(t1,t2),afoo(pic,s,p,d,f)],afii(pp),xal(0.3,afii(py),afii(pz),afii(px)),w())
xxp([at(t2,t3),afoo(pp,px,py,pz)],[afii(ss),afii(sss)],xal(0.3,afii(o1),afii(o2)),w(),[afoo(ss,sss,o1,o2),afo(t3)])
def playscene5():
z1=mmt(r'R_{n,l}');z2=mmt(r'Y_{l,m}')
sc(z1,1.5,z2,1.5);sh(z1,2*r,z2,2*l)
n1=mmt(r'a_0^{3/2}R');n2=mmt(r'r/a_0')
ext({1:'R为径向函数，它决定了电子波函数的径向特性',2:'例如，2s轨道截面的电子几率密度如图所示',3:'实际上电子出现的几率密度由|ψ²|决定',4:'|ψ²|在空间的分布称为电子云'})
graph=msm('graph');c1=myan(0,0.7,15);c2=myan(0.7,2.7,30)
d1=xdg(100,0,0.4);d2=xdg(100,0.4,0.6);d3=xdg(300,0.8,2);d4=xdg(100,2,2.7)
sc(graph,2.5,n1,0.8,n2,0.8);sh(graph,1.55*r+0.35*u,n1,0.7*l+2.6*u,n2,0.5*d+2.8*r)
xxp(afi(z1,z2,t1),w(),[afo(z1,z2),at(t1,t2)],[adb(c1),adb(c2)],[c1.animate.set_color_by_gradient(BLUE,BLACK),c2.animate.set_color_by_gradient(BLACK,BLUE,BLACK)])
xxp(Write(graph[1:9]),[Write(n1),Write(n2)],Write(graph[0],run_time=2),at(t2,t3),afo(graph,n1,n2),at(t3,t4),[at(c1,mvg(d1,d2)),at(c2,mvg(d3,d4))],w(),afo(t4,d1,d2,d3,d4))
def playscene0():
title = mt('本期视频BGM及推荐者',font='YouYuan').scale(0.8).to_edge(UP)
m1 = ImageMobject(r"C:\Users\86158\Downloads\111.png").scale(2);n1=xn('孟欣不会画画').set_color_by_gradient(['#FFE4B5','#F5FFFA']).scale(1.1).next_to(m1);v1=Group(m1,n1);xpp(v1,'r')
t1 = mt('Undertale',font='STFangsong').scale(0.6).scale(1.3);xpp(t1,'l')
sw(0.5);sp(adb(title));sp(agf(m1));sp(agf(n1));sp(afi(t1));sw(2);sp(afo(title,v1,t1));sw(0.5)
View Code
标签：xxp,return,color,args,electron,Single,structure,kwargs,def From： https://www.cnblogs.com/daxiangcai/p/16723854.html