aUCBLogo Demos and Tests / fermisurface2
be fermisurface2
A1=1
G=2
a=360/200
Ef=0
dkz=10
dkx=10 ;when smaller then less gaps, but also slower
dkx_s=2 ;for the surface
dkz_s=2
dkz_s2=dkz_s*1.05 ;because the x-coordinates are different for every z
;so as be compensate some ugly holes in the graphics
dkxfind=1
dkx2min=1
dkx2min_s=1
dmin=50
epsilon=0.001
branches=2
be E kx ky kz
output -A-G*((cos kx*a)+(cos ky*a)+(cos kz*a))
end
be E_solved_to_ky Ef kx kz d f
;output f*sqrt 10000-sqr kx
tmp= -(Ef+A1)/G-(cos kx*a)-(cos kz*a)
ifElse tmp >= -1 and2 tmp <=1
[ output (d+f*ArcCos tmp)/a
][ output 99999999
]
end
be dE_solved_to_ky_dkx Ef kx kz d f
output
( (E_solved_to_ky Ef kx+epsilon kz d f)
- (E_solved_to_ky Ef kx kz d f) ) / epsilon
end
be find_dE_dkx_equal_1 Ef kz d f
l=[]
for [kx -100 100 dkxfind]
[ tmp=abs (abs dE_solved_to_ky_dkx Ef kx kz d f)-1
if tmp < 0.1
[ push "l list tmp kx
]
]
l=mergesort l
l2=[]
repeat branches
[ if l==[] [break]
push "l2 l.(1).(2)
l=butFirst l
]
output l2
end
clearText
setUpdateGraph false
clearScreen
hideTurtle
perspective
setPenSize [2 2]
disableCylinderLines
enableCylinderLines
disableRoundLineEnds
; axes
y=0
ox=-100
oy=0
oz=-100
ok=true
kx=0
ky=0
kz=0
d=0
f=0
dkx2=0
be draw Ef
for [d -360*2 360*2 360]
[ for [f -1 1 2]
[ for [kz -100 100 dkz]
[ l=find_dE_dkx_equal_1 Ef kz d f
while [l != []]
[ ok=true
kx=first l
PenUp
setXYZ kx kz E_solved_to_ky Ef kx kz d f
dkx2=dkx
while [kx <= 100]
[ y=E_solved_to_ky Ef kx kz d f
onePoint
if y == 99999999 [PenUp break]
ifelse dkx2 > 0.001
and2 (abs (y-oy)/dkx2) > dkx2min
and2 (abs y-oy) < 100
[ dkx2=dkx2min*dkx2/(abs y-oy)
][ dkx2=dkx
]
ignore [
(pr dkx2
dkx2 > 0.001
(abs y-oy)/dkx2 > dkx2min
(abs y-oy) < 100
)
]
kx=kx+dkx2
oy=y
]
kx=first l
dkx2=dkx
PenUp
setXYZ kx kz E_solved_to_ky Ef kx kz d f
while [kx >= -100]
[ y=E_solved_to_ky Ef kx kz d f
onePoint
if y == 99999999 [PenUp break]
ifelse dkx2 > 0.001
and2 (abs (y-oy)/dkx2) > dkx2min
and2 (abs y-oy) < 100
[ dkx2=dkx2min*dkx2/(abs y-oy)
][ dkx2=dkx
]
kx=kx-dkx2
oy=y
]
l=butFirst l
]
]
]
]
;ignore [
for [d -360*2 360*2 360]
[ for [f -1 1 2]
[ PenUp
for [kz -100 100 dkz_s]
[ l=find_dE_dkx_equal_1 Ef kz d f
while [l != []]
[ ok=true
kx=first l
dkx2=dkx_s
oy=100
while [kx <= 100]
[ oneQuad
kx=kx+dkx2
]
kx=0
dkx_s=-dkx_s
dkx2=dkx_s
oy=100
while [kx >= -100]
[ oneQuad
kx=kx+dkx2
]
dkx_s=-dkx_s
l=butFirst l
]
]
]
]
;]
end
be onePoint
ifelse y != 99999999
[ if ok
[
PenDown
setPC HSB kz 1 0.7
]
setXYZ kx kz y
PenUp
ok=true
][ ok=false
PenUp
]
end
ignore [
for [d -360 360 360]
[ for [f -1 1 2]
[ for [kz -100 100 dkz_s]
[ for [kx -100 100 dkx_s]
[ oneQuad
]
]
]
]
]
be oneQuad
y1=E_solved_to_ky Ef kx kz d f
ifelse (abs dkx2) > 0.001
and2 (abs (y1-oy)/dkx2) > dkx2min_s
and2 (abs y1-oy) < 100
[ dkx2=dkx2min_s*dkx2/(abs y1-oy)
][ dkx2=dkx_s
]
y2=E_solved_to_ky Ef kx+dkx2 kz d f
y3=E_solved_to_ky Ef kx+dkx2 kz+dkz_s d f
y4=E_solved_to_ky Ef kx kz+dkz_s d f
PenUp
setPC HSBA kz 1 0.7 1
ignore [
setXYZ kx kz y1
PolyStart
PenDown
setXYZ kx+dkx2 kz y2
setXYZ kx+dkx2 kz+dkz_s y3
setXYZ kx kz+dkz_s y4
setXYZ kx kz y1
PenUp
PolyEnd
]
;ignore[
if y1 == 99999999
and2 y2 == 99999999
and2 y3 == 99999999
and2 y4 == 99999999 [stop]
rim = y1 == 99999999
or2 y2 == 99999999
or2 y3 == 99999999
or2 y4 == 99999999
ifelse (mod round abs oy/100 2) == 0
[ yh=d/a
][ yh=d/a+f*100
]
if y1 == 99999999 [y1=yh]
if y2 == 99999999 [y2=yh]
if y3 == 99999999 [y3=yh]
if y4 == 99999999 [y4=yh]
PolyStart
PenDown
setXYZ kx kz y1
setXYZ kx+dkx2 kz y2
setXYZ kx+dkx2 kz+dkz_s2 y3
setXYZ kx kz y1
PenUp
PolyEnd
PolyStart
PenDown
setXYZ kx kz y1
setXYZ kx+dkx2 kz+dkz_s2 y3
setXYZ kx kz+dkz_s2 y4
setXYZ kx kz y1
PenUp
PolyEnd
;]
oy=y1
end
; setEye {0 -500 0}{0 0 0}{0 0 1}
; redraw
drawEs
; drawit
be drawEs
video=false
; video=true
if video
[ (VideoStart "fermisurface.divx 25)
]
for [Ef -4 4 1/50]
[ clearScreen
draw Ef
updateGraph
if video [VideoFrame]
]
if video [VideoEnd]
end
end
to drawit
video=false
; video=true
if video
[ (VideoStart "fermisurface.divx 25)
]
rotatescene3 video
if video [VideoEnd]
end
be rotatescene3 video [dphi 0.3][phi 0][dtheta 1][r 500]
local [eye r dr ddphi theta center upvector]
singleshot=Name? "framenr
if singleshot [phi=framenr*10]
eye=array 3
light=array 3
r=500
l=r ;200
dr=1.1
p={0 0 0}
dx={10 0 0}
theta=30
center={0 0 0}
upvector={0 1 0}
upv=upvector
ddphi=dphi/3
pr [left, right changes rotation speed, up down set pitch, ESC exits]
dispatchMessages
forever
[ eye.1=r*(cos theta)*sin phi
eye.2=r* sin theta
eye.3=r*(cos theta)*cos phi
upv.1=(cos 90-theta)*sin phi+180
upv.2= sin 90-theta
upv.3=(cos 90-theta)*cos phi+180
setEye eye+center-p center-p upv
light.1=l*(cos theta)*sin phi
light.2=l* sin theta
light.3=l*(cos theta)*cos phi
setLightPos light
redraw
if video [VideoFrame]
if singleshot [break]
phi=phi+dphi
if key?
[ local [ch]
ch=readChar
ifelse ch==char 255
[ ch=readCharExt
ifElse (BitAnd MouseButtons 16)==16
[ dx=cross eye-center upvector
dx=(dx/Norm dx)*10
dy=cross dx eye-center
dy=(dy/Norm dy)*10
dz=eye-center
dz=(dz/Norm dz)*10
if ch==wxk_right [p=p+dx]
if ch==wxk_left [p=p-dx]
if ch==wxk_up [p=p+dy]
if ch==wxk_down [p=p-dy]
if ch==wxk_prior [p=p+dz]
if ch==wxk_next [p=p-dz]
][
if ch==wxk_right [dphi=dphi+ddphi]
if ch==wxk_left [dphi=dphi-ddphi]
if ch==wxk_up [theta=theta+dtheta]
if ch==wxk_down [theta=theta-dtheta]
if ch==wxk_prior [r=r/dr]
if ch==wxk_next [r=r*dr]
]
][
if ch==char 27 [stop]
if ch=="+ [r=r-dr]
if ch=="- [r=r+dr]
]
]
]
end