14 computer animation - cgl @ ethz · – solve partial differential equation on (regular) grid –...
TRANSCRIPT
1
Intro
du
ction
toC
om
pu
ter An
ima
tion
2
Co
mp
uter A
nim
atio
n 2
Mo
tivatio
n
•A
nim
atio
n fro
m anim
a(la
t.) =
soul, spirit, breath of life•
Brin
g im
ag
es to
life!
•E
xa
mp
les
–C
ha
racte
r an
ima
tion
(h
um
an
s, an
ima
ls)
–S
eco
nd
ary m
otio
n (h
air, clo
th)
–P
hysica
l wo
rld (rig
id b
od
ies, w
ate
r, fire)
3
Co
mp
uter A
nim
atio
n 3
An
ima
tion
Tech
niq
ues
•Fo
r cha
racte
r an
ima
tion
–K
eyfra
min
g
–M
otio
n ca
ptu
ring
/ mo
tion
synth
esis
•Fo
r seco
nd
ary m
otio
n, p
hysica
l effe
cts
–P
roce
du
ral
–S
imu
latio
n (p
hysica
lly ba
sed
an
ima
tion
)
4
Co
mp
uter A
nim
atio
n 4
Keyfra
min
g
•A
rtistd
efin
es ke
y fram
es
•C
om
pu
ter in
terp
ola
tes
5
Co
mp
uter A
nim
atio
n 5
Mo
tion
Ca
ptu
ring
•V
ario
us te
chn
iqu
es (m
ag
ne
tic, me
cha
nica
l, op
tical):
•O
utp
ut: T
raje
ctorie
s of a
set o
f ma
rkers
6
Co
mp
uter A
nim
atio
n 6
Mo
tion
Synth
esis
•C
om
bin
e re
cord
ed
mo
tion
sCo
urte
sy Oka
nA
rikan
•P
rob
lem
s
–N
atu
ral tra
nsitio
ns
–In
tera
ction
with
en
viron
me
nt
(foo
t slidin
g, co
llision
s)
7
Co
mp
uter A
nim
atio
n 7
An
ima
tion
Tech
niq
ues
•Fo
r cha
racte
r an
ima
tion
–K
eyfra
min
g
–M
otio
n ca
ptu
ring
/ mo
tion
synth
esis
•Fo
r seco
nd
ary m
otio
n, p
hysica
l effe
cts
–P
roce
du
ral
–S
imu
latio
n (p
hysica
lly ba
sed
an
ima
tion
)
8
Co
mp
uter A
nim
atio
n 8
Pro
cedu
ral A
nim
atio
n
•O
cea
n su
rface
as su
pe
rpo
sition
of sin
e w
ave
s
Hin
sing
eret. a
l.
•P
lan
t gro
wth
an
ima
ted
with
L-System
s (Gra
mm
ar)
•P
roce
du
re a
nim
ate
s scen
e e
xp
licitly
9
Co
mp
uter A
nim
atio
n 9
Pro
cedu
ral vs. Sim
ula
tion
•P
roce
du
ral a
nim
atio
n
–E
xp
licit de
scriptio
n o
f effe
ct
–S
imp
le to
con
trol
–H
ard
to m
od
el co
mp
lex
effe
cts / inte
ractio
ns
•S
imu
latio
n
–In
teg
ratio
n o
f ph
ysical e
qu
atio
ns (e
.g. N
ew
ton
)
–H
ard
er to
con
trol
–U
nlim
ited
com
ple
xity
(bo
un
d o
nly b
y com
pu
ting
time
)
10
Co
mp
uter A
nim
atio
n 10
Ph
ysical Sim
ula
tion
s
•E
qu
atio
ns kn
ow
n fo
r a lo
ng
time
–M
otio
n (N
ew
ton
, 166
0)
–E
lasticity (H
oo
ke, 16
70)
–Flu
ids (N
avie
r, Sto
kes, 18
22)
•S
imu
latio
n m
ad
e p
ossib
le b
y com
pu
ters
–19
38:
Zu
se1, 0
.2 flop
s,
–20
04
: NE
C's E
arth
Sim
ula
tor
36 te
raflo
ps
fv
=)
(/
mdt
d
Eε
σ=
vg
vv
v2
∇+
+∇
−=
∇⋅+
∂ ∂µ
ρρ
ρk
t
11
Co
mp
uter A
nim
atio
n 11
Aim
of P
hysica
l Simu
latio
ns
•C
om
pu
tatio
na
l Scie
nce
s
–P
erfe
ctre
plica
tion
of th
ere
al w
orld
–S
imu
latio
ns
rep
lace
ex
pe
nsive
ex
pe
rime
nts
–A
ccura
cym
ore
imp
orta
nt
tha
nsp
ee
d
•C
om
pu
ter A
nim
atio
n
–P
lau
sible
be
ha
vior
(use
r/ vie
we
rm
ust
be
con
vince
d)
–C
on
trolla
bility
–S
pe
ed
an
d sta
bility
(for
rea
l-time
use
)
12
Co
mp
uter A
nim
atio
n 12
Rea
l-Tim
e P
hysica
lly Ba
sed A
nim
atio
n
•T
rad
e a
ccura
cy for sp
ee
d“Cheat as m
uch as you can without getting caught”•
Un
con
ditio
na
l stab
ility
•A
pp
licatio
ns:
Fligh
t/car S
imu
lato
rs3D
Ga
me
sS
urg
ery train
ers
13
Co
mp
uter A
nim
atio
n 13
Exa
mp
les
Brittle
De
form
ab
leLiq
uid
14
Co
mp
uter A
nim
atio
n 14
Tech
niq
ues
•P
article
system
s–
Fire, sm
oke
, wa
ter
•M
ass-sp
ring
system
s–
De
form
ab
le o
bje
cts
•R
igid
bo
dy sim
ula
tion
–C
ars, a
irpla
ne
s, furn
iture
,…
•G
rid b
ase
d m
eth
od
s–
Wa
ter, sm
oke
, airflo
w
•O
the
rs, e.g
. Finite
Ele
me
nts, …
15
Co
mp
uter A
nim
atio
n 15
Pa
rticle Systems
Wa
ter Fire
Sn
ow
, du
st, san
dS
mo
ke
16
Co
mp
uter A
nim
atio
n 16
Pa
rticle Systems
•C
olle
ction
of m
an
y sm
all sim
ple
pa
rticles
•P
article
mo
tion
in
flue
nce
d b
y force
s
•G
en
era
ted
by e
mitte
rs
•D
ele
ted
wh
en
lifetim
e
rea
che
d o
r ou
t of sce
ne
mi
vi
ge
ne
rato
r
fi
17
Co
mp
uter A
nim
atio
n 17
Pa
rticle System A
nim
atio
n
•N
ew
ton
’s seco
nd
law
of m
otio
n
)(
1)
(
)(
)(
tm
tdt d
tt
dt d
ii
i
ii
fv
vx
= =
•S
imp
le u
pd
ate
rule
(inte
gra
tion
me
tho
d)
ii
i
ii
ii
tm t
vx
x
fv
v
⋅∆
+←
∆+
←1
18
Co
mp
uter A
nim
atio
n 18
Force C
om
pu
tatio
n
•M
ultip
le in
flue
nce
s:
⋅−
=
i
i
mg 0 0
gravityf
ii
dvf
−=
damping
),
(external
ti
ix
ff
=∑ =j
ji
i)
,(
interactx
xf
finteractexternal
damping
gravityi
ii
ii
ff
ff
f+
++
=
•A
dd
ition
of in
flue
nce
s:
19
Co
mp
uter A
nim
atio
n 19
Tech
niq
ues
•P
article
system
s–
Fire, sm
oke
, wa
ter
•M
ass-sp
ring
system
s–
De
form
ab
le o
bje
cts
•R
igid
bo
dy sim
ula
tion
–C
ars, a
irpla
ne
s, furn
iture
,…
•G
rid b
ase
d m
eth
od
s–
Wa
ter, sm
oke
, airflo
w
20
Co
mp
uter A
nim
atio
n
20
Ma
ss-Sprin
g System
s
•P
article
system
p
lus sp
ring
s
•S
pe
cial in
tera
ction
force
{} (
)0
i
0i
0i
xx
xx
xx
f− −
−−
=∑∈
iii
iL
k3,2,
1|
interact0
0x
3x
2x
1x
11 ,k
L
22 ,k
L
33 ,k
L
stiffness
rest le
ng
th
21
Co
mp
uter A
nim
atio
n 21
Ap
plica
tion
s
Facia
l an
ima
tion
Stra
sser
Ku
eh
na
pfe
lT
ha
lma
nn
Clo
th sim
ula
tion
Su
rge
ry simu
latio
n
22
Co
mp
uter A
nim
atio
n 22
Issues
•W
he
re to
pu
t sprin
gs
•C
ho
ice o
f stiffne
sses
•C
ollisio
n d
ete
ction
•C
ollisio
n re
spo
nse
•S
tab
ility (time
step o
r stiffne
ss too
hig
h)
ii
i
ii
ii
tm t
vx
x
fv
v
⋅∆
+←
∆+
←1
rest co
nfig
ura
tion
ove
rcorre
ction
23
Co
mp
uter A
nim
atio
n 23
Tech
niq
ues
•P
article
system
s–
Fire, sm
oke
, wa
ter
•M
ass-sp
ring
system
s–
De
form
ab
le o
bje
cts
•R
igid
bo
dy sim
ula
tion
–C
ars, a
irpla
ne
s, furn
iture
,…
•G
rid b
ase
d m
eth
od
s–
Wa
ter, sm
oke
, airflo
w
24
Co
mp
uter A
nim
atio
n 24
Rig
id B
od
y Simu
latio
n
•D
efo
rma
ble
ob
jects h
ave
m
an
y de
gre
es o
f free
do
m
•E
ach
verte
x is sim
ula
ted
sep
ara
tely
•A
rigid
bo
dy o
nly h
as
6 d
eg
ree
s of fre
ed
om
•Fa
ster sim
ula
tion
po
ssible
orie
nta
tion
po
sition
25
Co
mp
uter A
nim
atio
n 25
States o
f a R
igid
Bo
dy
•S
tatic sta
tes
–P
ositio
n x
–O
rien
tatio
n R
•D
yna
mic sta
tes
–Lin
ea
r velo
city v–
An
gu
lar ve
locity ω
Rx
v
ω
26
Co
mp
uter A
nim
atio
n 26
Simu
latio
n o
f Rig
id B
od
ies
•N
ew
ton
’s law
of m
otio
n
⋅
=
)()(
)(
)( ~
)(
)(
)(
)( )( )(
t tt
tt
tt
tM
t t
dt d
τ FR
ωv
ωIv R x
•U
se in
teg
ratio
n m
eth
od
to
up
da
te sta
tes
27
Co
mp
uter A
nim
atio
n 27
Issues
•C
ollisio
n d
ete
ction
•C
ollisio
n re
spo
nse
for
com
ple
x co
nfig
ura
tion
s
•C
on
strain
ts (join
ts)
28
Co
mp
uter A
nim
atio
n 28
Ap
plica
tion
s
•R
ob
otic sim
ula
tion
s
•3D
com
pu
ter g
am
es
Ha
lf Life
29
Co
mp
uter A
nim
atio
n 29
Tech
niq
ues
•P
article
system
s–
Fire, sm
oke
, wa
ter
•M
ass-sp
ring
system
s–
De
form
ab
le o
bje
cts
•R
igid
bo
dy sim
ula
tion
–C
ars, a
irpla
ne
s, furn
iture
,…
•G
rid b
ase
d m
eth
od
s–
Wa
ter, sm
oke
, airflo
w
30
Co
mp
uter A
nim
atio
n
30
Grid
Ba
sed M
etho
ds
•B
asic id
ea
:
–S
olve
pa
rtial d
iffere
ntia
l eq
ua
tion
o
n (re
gu
lar) g
rid
–R
ep
lace
diffe
ren
tials b
y finite
diffe
ren
ces
31
Co
mp
uter A
nim
atio
n 31
Exa
mp
le: Wa
ter Surfa
ce
•W
ate
r surfa
ce d
efin
ed
as h
eig
ht u(x,y,t)
at lo
catio
n x,y
at tim
e t)
(2 2
2 22
2 2
uy
ux
cu
t∂ ∂
+∂ ∂
=∂ ∂
u(x,y,t)(x,y)•
Dyn
am
ics give
n b
y 2D
wa
ve e
qu
atio
n:
32
Co
mp
uter A
nim
atio
n 32
Discretiza
tion
•R
ep
lace
con
tinu
ou
s u(x,y,t)b
y discre
te a
rray
ut[i,j]
(grid
spa
cing
h)
•R
ep
lace
de
rivative
s by fin
ite d
iffere
nce
s, e.g
. ∂u/∂
x = (u
t[i+1,j]-u
t[i,j])/h•
Sim
ple
up
da
te sch
em
e (w
ith co
ol re
sults!)
22
1]
,[4
]1,[
]1,[
],1
[]
,1[
],[
],[
hct
ji
vj
iv
ji
tuj
itu
ji
tuj
itu
ji
tut
t−
−+
++
−+
+∆
+=
+
],[
],[
],[
11
ji
vtj
iu
ji
ut
tt
++
∆+
=
33
Co
mp
uter A
nim
atio
n 33
Bo
un
da
ry Co
nd
ition
s
•A
ssum
ing
i∈(1,..,n)
•P
erio
dic:
ut[0,j]=
ut[n,j], u
t[n+1,j]=
ut[1,j]
•M
irror:
ut[0,j]=
ut[1,j], u
t[n+1,j]=
ut[n,j]
•A
na
log
for j
34
Co
mp
uter A
nim
atio
n 34
Ad
vertisemen
t
•S
om
me
rsem
este
r 200
5251-0
546
-00
: Ph
ysikalisch
-ba
sierte
S
imu
latio
n in
de
r Co
mp
ute
r Gra
ph
ik
•2V
1U
•Ü
bu
ng
= 1 S
em
este
rpro
jekt
in G
rup
pe
n
http://graphics.ethz.ch/~mattm
uel/teaching/projects2004/
35
Co
mp
uter A
nim
atio
n 35
Prü
fun
gsth
emen
0.
Intro
du
ction
wird
nich
tg
eprü
ft1.
Gra
ph
ics AP
Is2.
Co
lors
3.T
ran
sform
atio
ns
4.
Pro
jectio
ns
5.Lig
htin
g &
Sh
ad
ing
6.
Ra
ytracin
g7.
Te
xtu
re M
ap
pin
g8
.A
nti A
liasin
g9
.C
lipp
ing
Alg
orith
ms
10.S
can
Co
nve
rsion
11.G
rap
hics H
ard
wa
rekein
eP
rod
uktd
etails, ke
ine
Sh
ad
erbe
fehle
12.R
eal-tim
e Ren
derin
gP
ipelin
e op
timiza
tion
wird
nich
tg
ep
rüft
13.T
erra
in R
en
de
ring
wird
nich
tg
ep
rüft
14.
Co
mp
uter A
nim
atio
nw
irdn
icht
gep
rüft