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Rog
er C
raw
fis
Ohi
o St
ate
Uni
vers
ity
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or T
opic
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Oth
er E
xam
ples
Out
line
•R
evie
w–
Tra
nsfo
rmat
ions
–O
penG
L
•Po
lygo
nal m
odel
s an
d m
odel
con
stru
ctio
n
•V
iew
ing
–Pr
ojec
tions
–C
lippi
ng
Out
line
•3D
pol
ygon
al r
ende
ring
–R
aste
riza
tion
–C
lippi
ng
–H
idde
n su
rfac
e de
term
inat
ion
•Sh
adow
s
•T
extu
re M
appi
ng
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❚���FFG�'� � �����"�� ����
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Cou
rse
Top
ics
•T
extu
re M
appi
ng–
Tex
ture
Par
amet
eriz
atio
n:
•M
appi
ng a
n im
age
to a
m
odel
–D
eter
min
ing
the
pixe
l va
lue
duri
ng s
can-
conv
ersi
on–
Avo
idin
g A
liasi
ng in
T
extu
re M
appi
ng
��� ���8--G
J�����8---
Quo
te (
CIS
681
and
782
)
“Now
whe
n I
pain
t, I
am a
ble
to s
ee th
e bi
ts a
nd th
e w
hole
at
the
sam
e tim
e, a
nd c
olor
s an
d sh
apes
pop
out
at m
e m
ore
read
ily. F
or e
xam
ple,
now
, ins
tead
of
seei
ng ju
st a
n ap
ple
insi
de a
bow
l, I
see
an a
pple
cat
chin
g th
e re
flec
tion
from
th
e bo
wl a
nd r
ecip
roca
lly th
e co
lor
of th
e ap
ple
tran
sfer
ring
ont
o th
e ce
ram
ic s
urfa
ce o
f th
e bo
wl.
The
bo
wl m
ust t
hen
have
a r
efle
ctiv
e su
rfac
e ca
ptur
ing
othe
r pa
rts
of th
e st
ill li
fe a
nd it
s sh
adow
on
the
whi
te c
loth
be
low
is n
ot g
ray
but i
s ac
tual
ly a
blu
ish
tinge
with
pur
ple
edge
s, a
nd s
o fo
rth.
”-
Ow
en D
emer
s[d
igit
al]
Tex
turi
ng &
Pai
ntin
g, 2
002
Quo
te
“I a
m in
tere
sted
in th
e ef
fect
s on
an
obje
ct th
at s
peak
of
hum
an in
terv
entio
n. T
his
is a
noth
er f
acto
r th
at y
ou m
ust
take
into
con
side
ratio
n. H
ow m
any
times
has
the
obje
ct
been
pai
nted
? W
ritte
n on
? T
reat
ed?
Bum
ped
into
? Sc
rape
d? T
his
is w
hen
thin
gs g
et e
xciti
ng. I
am
cur
ious
ab
out:
the
wea
ring
aw
ay o
f pa
int o
n st
eps
from
con
tinua
l us
e; s
crap
es m
ade
by a
mov
ing
dolly
alo
ng th
e ba
sebo
ard
of a
wal
l; ac
rylic
pai
nt p
eelin
g aw
ay f
rom
a p
revi
ous
coat
of
an
oil b
ase
pain
t; ci
gare
tte b
urns
on
tile
or w
ood
floo
rs;
chew
ing
gum
–th
e bl
ack
spot
s on
city
sid
ewal
ks; l
over
’s
nam
es a
nd in
itial
s sc
ratc
hed
onto
par
k be
nche
s…”
-O
wen
Dem
ers
[dig
ital]
Tex
turi
ng &
Pai
ntin
g, 2
002
Shad
ows
Ess
enti
al P
roce
ss
Um
bra
Pe
nu
mb
ra
Tex
ture
Map
ping
•W
hy u
se te
xtur
es?
Tex
ture
Map
ping
•M
odel
ing
com
plex
ity
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E�����"�� �������� ��������'5
Mod
elin
g
•T
ypes
: –
Poly
gon
surf
aces
–C
urve
d su
rfac
es
•G
ener
atin
g m
odel
s:
–In
tera
ctiv
e
–Pr
oced
ural
Pol
ygon
Mes
h
•Se
t of
surf
ace
poly
gons
that
en
clos
e an
ob
ject
inte
rior
, po
lygo
n m
esh
•D
e fa
cto:
tr
iang
les,
tr
iang
le m
esh.
Rep
rese
ntin
g P
olyg
on M
esh
•V
erte
x co
ordi
nate
s lis
t, po
lygo
n ta
ble
and
(may
be)
edge
ta
ble
•A
uxili
ary:
–Pe
r ve
rtex
nor
mal
–N
eigh
borh
ood
info
rmat
ion,
ar
rang
ed w
ith r
egar
d to
ver
tices
and
edg
es
Arr
ivin
g at
a M
esh
•U
se p
atch
es m
odel
as
impl
icit
or p
aram
etri
c su
rfac
es
•B
ezié
rPa
tche
s : c
ontr
ol p
olyh
edro
n w
ith 1
6 po
ints
and
the
resu
lting
bic
ubic
patc
h:
Exa
mpl
e: T
he U
tah
Tea
pot
•32
pat
ches
sing
le s
hade
d pa
tch
wir
efra
me
of th
e co
ntro
l poi
nts
Patc
h ed
ges
Pat
ch R
epre
sent
atio
n vs
. Pol
ygon
Mes
h
•Po
lygo
ns a
re s
impl
e an
d fl
exib
le b
uild
ing
bloc
ks.
•B
ut, a
par
amet
ric
repr
esen
tatio
n ha
s ad
vant
ages
:
–C
onci
sene
ss•
A p
aram
etri
c re
pres
enta
tion
is e
xact
and
ana
lytic
al.
–D
efor
mat
ion
and
shap
e ch
ange
•D
efor
mat
ions
app
ear
smoo
th, w
hich
is n
ot g
ener
ally
th
e ca
se w
ith a
pol
ygon
al o
bjec
t.
Shap
e C
onst
ruct
ion
Ope
rati
ons
•E
xtru
de: a
dd a
hei
ght t
o a
flat
pol
ygon
•R
evol
ve: R
otat
e a
poly
gon
arou
nd a
cer
tain
axi
s
•Sw
eep :
sw
eep
a sh
ape
alon
g a
cert
ain
curv
e (a
ge
nera
lizat
ion
of th
e ab
ove
two)
•L
oft :
sha
pe f
rom
con
tour
s (u
sual
ly in
par
alle
l sl
ices
)
•Se
t ope
ratio
ns (
inte
rsec
tion,
uni
on, d
iffe
renc
e),
CSG
(con
stru
ctiv
e so
lid g
eom
etry
)
Swee
p (R
evol
ve a
nd E
xtru
de)
Con
stru
ctiv
e So
lid
Geo
met
ry
(CSG
)
•T
o co
mbi
ne th
e vo
lum
es o
ccup
ied
by o
verl
appi
ng 3
D
shap
es u
sing
set
ope
ratio
ns.
unio
nin
ters
ectio
ndi
ffer
ence
A C
SG T
ree
Exa
mpl
e M
odel
ing
Pac
kage
: A
lias
Stu
dio
P
P
F
Pin
Hol
e M
odel
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WO
RL
D
OB
JEC
TE
YE
Tra
nsfo
rmat
ions
•M
odel
ing
tran
sfor
mat
ions
•bu
ild c
ompl
ex m
odel
s by
pos
ition
ing
sim
ple
com
pone
nts
•V
iew
ing
tran
sfor
mat
ions
•pl
acin
g vi
rtua
l cam
era
in th
e w
orld
•tr
ansf
orm
atio
n fr
om w
orld
coo
rdin
ates
to
eye
coo
rdin
ates
•Si
de n
ote:
ani
mat
ion:
var
y tr
ansf
orm
atio
ns
over
tim
e to
cre
ate
mot
ion
Vie
win
g P
ipel
ine
•O
bjec
t sp
ace:
coor
dina
te s
pace
whe
re e
ach
com
pone
nt is
def
ined
•W
orld
spa
ce:
all c
ompo
nent
s pu
t tog
ethe
r in
to th
e sa
me
3D s
cene
vi
a af
fine
tran
sfor
mat
ion.
(ca
mer
a, li
ghtin
g de
fine
d in
this
spa
ce)
•E
ye s
pace
:ca
mer
a at
the
orig
in, v
iew
dir
ectio
n co
inci
des
with
the
z ax
is. H
ither
and
Yon
pla
nes
perp
endi
cula
r to
the
z ax
is•
Clip
ping
spa
ce:
do c
lippi
ng h
ere.
All
poin
ts a
re in
hom
ogen
eous
co
ordi
nate
s, i.
e., e
ach
poin
t is
repr
esen
ted
by (
x,y,
z,w
)•
3D im
age
spac
e(C
anon
ical
vie
w v
olum
e): a
par
alle
lpip
ied
shap
e de
fine
d by
(-1
:1,-
1:1,
0,1)
. Obj
ects
in th
is s
pace
are
dis
tort
ed•
Scre
en s
pace
:x
and
y sc
reen
pix
el c
oord
inat
es
Obj
ect
Spac
eW
orld
Sp
ace
Eye
Sp
ace
Clip
ping
Sp
ace
Can
onic
al
view
vol
ume
Scre
en
Spac
e
���
���
���
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���
!� ��
���
:
eye
3.
Mod
el->
Eye
Spa
ce
Cli
p an
d Im
age
Spac
es
•C
lip S
pace
•Im
age
Spac
e
1.2.
3.4.
5.6.
2D T
rans
form
atio
n
•T
rans
latio
n
•R
otat
ion
Hom
ogen
eous
Coo
rdin
ates
•M
atri
x/V
ecto
r fo
rmat
for
tran
slat
ion:
Tra
nsla
tion
in H
omog
enou
s C
oord
inat
es
•T
here
exi
sts
an in
vers
e m
appi
ng fo
r ea
ch
func
tion
•T
here
exi
sts
an id
entit
y m
appi
ng
Why
thes
e pr
oper
ties
are
im
port
ant
•w
hen
thes
e co
nditi
ons
are
show
n fo
r an
y cl
ass
of
func
tions
it c
an b
e pr
oven
that
suc
h a
clas
s is
clo
sed
unde
r co
mpo
sitio
n•
i. e.
any
ser
ies
of tr
ansl
atio
ns c
an b
e co
mpo
sed
to a
sing
le tr
ansl
atio
n.
Rot
atio
n in
Hom
ogen
eous
Spa
ce
The
two
prop
ertie
s st
ill a
pply
.
Put
ting
Tra
nsla
tion
and
Rot
atio
n T
oget
her
•O
rder
mat
ters
!!
Aff
ine
Tra
nsfo
rmat
ion
•Pr
oper
ty: p
rese
rvin
g pa
ralle
l lin
es
•T
he c
oord
inat
es o
f th
ree
corr
espo
ndin
g po
ints
uni
quel
y de
term
ine
any
Aff
ine
Tra
nsfo
rm!!
Aff
ine
Tra
nsfo
rmat
ions
•T
rans
latio
n
•R
otat
ion
•Sc
alin
g
•Sh
eari
ng
T
How
to d
eter
min
e an
Aff
ine
2D
Tra
nsfo
rmat
ion?
•W
e se
t up
6 lin
ear
equa
tions
in te
rms
of o
ur 6
un
know
ns. I
n th
is c
ase,
we
know
the
2D c
oord
inat
es
befo
re a
nd a
fter
the
map
ping
, and
we
wis
h to
sol
ve
for
the
6 en
trie
s in
the
affin
e tr
ansf
orm
mat
rix
Aff
ine
Tra
nsfo
rmat
ion
in 3
D
•T
rans
latio
n
•R
otat
e
•Sc
ale
•Sh
ear
Mor
e R
otat
ion
•W
hich
axi
s of
rot
atio
n?
Glo
bal D
efor
mat
ions
•T
aper
•T
wis
t
•B
end
Glo
bal D
efor
mat
ions
•T
aper
ing:
r =
f(z)
x =
r*x
y =
r*y
z =
z
Glo
bal D
efor
mat
ions
•T
wis
ting:
θ=
f(z)
x =
x*c
osθ
-y*
sin
θy
= x
*sin
θ+
y*c
osθ
z =
z
Glo
bal D
efor
mat
ions
•B
endi
ng:
–M
ore
gene
ral,
bend
abo
ut s
ome
axis
.
Vie
win
g
•Pl
acin
g ob
ject
s in
Wor
ld s
pace
: aff
ine
tran
sfor
mat
ions
•W
orld
spa
ce to
Eye
spa
ce: ?
??
•E
ye s
pace
to C
lippi
ng s
pace
: inv
olve
s pr
ojec
tion
and
view
ing
frus
tum
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•D
efin
es v
isib
le r
egio
n of
spa
ce, p
yram
id e
dges
are
clip
ping
pla
nes
•F
rust
um :t
runc
ated
pyr
amid
with
nea
r an
d fa
r cl
ippi
ng p
lane
s
–N
ear
(Hith
er)
plan
e ?
Don
’t c
are
abou
t beh
ind
the
cam
era
–Fa
r (Y
on)
plan
e, d
efin
e fi
eld
of in
tere
st, a
llow
s z
to b
e sc
aled
to a
lim
ited
fixe
d-po
int v
alue
for
z-b
uffe
ring
.
Vie
w V
olum
eD
iffi
cult
y
•It
is d
iffi
cult
to d
o cl
ippi
ng d
irec
tly in
the
view
ing
frus
tum
Can
onic
al V
iew
Vol
ume
•N
orm
aliz
e th
e vi
ewin
g fr
ustu
m to
a c
ube,
can
onic
al v
iew
vo
lum
e
•C
onve
rts
pers
pect
ive
frus
tum
to o
rtho
grap
hic
frus
tum
–pe
rspe
ctiv
e tr
ansf
orm
atio
n
Per
spec
tive
Tra
nsfo
rm
•T
he e
quat
ions
alph
a =
hith
er/(
yon-
hith
er)
beta
= y
on*h
ither
/(hi
ther
-yo
n)
s: s
ize
of w
indo
w o
n th
e im
age
plan
e
z
z’
1al
pha
yon
hith
er
Abo
ut P
ersp
ecti
ve T
rans
form
•So
me
prop
ertie
s
Abo
ut P
ersp
ecti
ve T
rans
form
•C
lippi
ng c
an b
e pe
rfor
med
aga
inst
the
rect
iline
ar b
ox
•Pl
anar
ity a
nd li
near
ity a
re p
rese
rved
•A
ngle
s an
d di
stan
ces
are
not p
rese
rved
•Si
de e
ffec
ts: o
bjec
ts b
ehin
d th
e ob
serv
er a
re
map
ped
to th
e fr
ont.
Per
spec
tive
+ P
roje
ctio
n M
atri
x
•A
R: a
spec
t rat
io c
orre
ctio
n, R
esX
/Res
Y
•s=
Res
X,
•T
heta
: hal
f vi
ew a
ngle
, tan
(the
ta)
= s
/d
10
00
00
0
00
tan
tan
00
tan
0
AR
Pα
θθ
βθ
=
eye
coi
ρ
hith
eryo
n
Cam
era
Con
trol
and
Vie
win
g
•Fo
cal l
engt
h (d
), im
age
size
/sha
pe a
nd c
lippi
ng p
lane
s in
clud
ed
in p
ersp
ectiv
e tr
ansf
orm
atio
n
–ρ
-A
ngle
or
Fiel
d of
vie
w (
FOV
) –
AR
-A
spec
t Rat
io o
f vi
ew-p
ort
–H
ither
, Yon
-N
eare
st a
nd f
arth
est v
isio
n lim
its (
WS)
.–
Loo
kat –
CO
I–
Loo
kfro
m –
Eye
poi
nt–
Vie
w a
ngle
–Fi
eld-
of-v
iew
Com
plet
e P
ersp
ecti
ve
•Sp
ecif
y ne
ar a
nd f
ar c
lippi
ng p
lane
s -
tran
sfor
m z
betw
een
znea
ran
dzf
aron
to a
fi
xed
rang
e•
Spec
ify
fiel
d-of
-vie
w (
fov)
ang
le•
Ope
nGL
’s g
lFru
stum
and
gluP
ersp
ecti
vedo
th
ese
Mor
e V
iew
ing
Par
amet
ers
Cam
era,
Eye
or
Obs
erve
r:lo
okfr
om:
loca
tion
of f
ocal
poi
nt o
r ca
mer
alo
okat
:po
int t
o be
cen
tere
d in
imag
e
Cam
era
orie
ntat
ion
abou
t the
look
at-l
ookf
rom
axis
vup:
a ve
ctor
that
is p
oint
ing
stra
ight
up
in
the
imag
e. T
his
is li
ke a
n or
ient
atio
n.
Impl
emen
tati
on …
Ful
l Blo
wn
•T
rans
late
by
-loo
kfro
m, b
ring
foc
al p
oint
to o
rigi
n•
Rot
ate
look
at-l
ookf
rom
to th
e z -
axis
with
mat
rix
R:
•v
= (
look
at-l
ookf
rom
) (n
orm
aliz
ed)
and
z=
[0,
0,1]
•ro
tatio
n ax
is:
a=
(vx
z)/| v
xz|
•ro
tatio
n an
gle:
cos θ
= a
• zan
d si
n θ =
| rxz
|
•O
penG
L: g
lRot
ate(
θ, a
x, a
y,a z
)•
Rot
ate
abou
t z- a
xis
to g
etvu
ppa
ralle
l to
the
y-ax
is
Vie
wpo
rt m
appi
ng
•C
hang
e fr
om th
e im
age
coor
dina
te s
yste
m (
x,y,
z)
to th
e sc
reen
coo
rdin
ate
syst
em (
X,Y
).
•Sc
reen
coo
rdin
ates
are
alw
ays
non-
nega
tive
inte
gers
.
•L
et (
v r,v
t) be
the
uppe
r-ri
ght c
orne
r an
d (v
l,vb)
be
the
low
er-l
eft c
orne
r.
•X
= x
* (
v r-v
l) /2
+ (v
r+v l
)/2
•Y
= y
* (
v t-v
b)/2
+ (v
t+v b
)/2
Tru
e O
r F
alse
•In
per
spec
tive
tran
sfor
mat
ion
para
llelis
m is
no
t pre
serv
ed.
–Pa
ralle
l lin
es c
onve
rge
–O
bjec
t siz
e is
red
uced
by
incr
easi
ng d
ista
nce
from
cen
ter
of
proj
ectio
n–
Non
-uni
form
for
esho
rten
ing
of li
nes
in th
e ob
ject
as
a fu
nctio
n of
ori
enta
tion
and
dist
ance
fro
m c
ente
r of
pro
ject
ion
–A
id th
e de
pth
perc
eptio
n of
hum
an v
isio
n, b
ut s
hape
is n
ot
pres
erve
d
Tru
e O
r F
alse
•A
ffin
e tr
ansf
orm
atio
n is
a c
ombi
natio
n of
lin
ear
tran
sfor
mat
ions
•T
he la
st c
olum
n/ro
w in
the
gene
ral 4
x4
affi
ne tr
ansf
orm
atio
n m
atri
x is
[0
0 0
1]T.
•A
fter
aff
ine
tran
sfor
m, t
he h
omog
eneo
us
coor
dina
te w
mai
ntai
ns u
nity
.
Intr
oduc
tion
to O
penG
L
Rog
er C
raw
fis
Thi
s se
t of
slid
es a
re f
rom
Jia
nH
uang
and
are
bas
ed u
pon
the
slid
es f
rom
th
e In
tera
ctiv
e O
penG
L P
rogr
amm
ing
cour
se g
iven
by
Dav
e Sh
rein
e, E
d A
ngel
and
Vic
ki S
hrei
ner
on S
IGG
RA
PH
200
1.
Ope
nGL
an G
LUT
Ove
rvie
w
•W
hat i
s O
penG
L &
wha
t can
it d
o fo
r m
e?•
Ope
nGL
in w
indo
win
g sy
stem
s•
Why
GLU
T•
GLU
T p
rogr
am te
mpl
ate
Wha
t Is
Ope
nGL?
•G
raph
ics
rend
erin
g A
PI
–hi
gh-q
ualit
y co
lor
imag
es c
ompo
sed
of
geom
etric
and
imag
e pr
imiti
ves
–w
indo
w s
yste
m in
depe
nden
t
–op
erat
ing
syst
em in
depe
nden
t
Ope
nGL
Arc
hite
ctur
e
Ope
nGL
as a
Ren
dere
r
•G
eom
etric
prim
itive
s–
poin
ts, l
ines
and
pol
ygon
s–
Imag
e P
rimiti
ves
–im
ages
and
bitm
aps
•se
para
te p
ipel
ine
for
imag
es a
nd g
eom
etry
–lin
ked
thro
ugh
text
ure
map
ping
•R
ende
ring
depe
nds
on s
tate
–co
lors
, mat
eria
ls, l
ight
sou
rces
, etc
.
Rel
ated
AP
Is
•A
GL,
GLX
, WG
L–
glue
bet
wee
n O
penG
L a
nd w
indo
win
g sy
stem
s
•G
LU (
Ope
nGL
Util
ity L
ibra
ry)
–pa
rt o
f Ope
nGL
–N
UR
BS
,tes
sella
tors
, qua
dric
sha
pes,
etc
•G
LUT
(O
penG
L U
tility
Too
lkit)
–po
rtab
le w
indo
win
g A
PI
–no
t offi
cial
ly p
art o
f Ope
nGL
Ope
nGL
and
Rel
ated
AP
IsP
relim
inar
ies
•H
eade
r F
iles
–#i
nclu
de <
GL
gl.h
>–
#inc
lude
<G
Lgl
u.h>
–#i
nclu
de <
GL
glut
.h>
•Li
brar
ies
•E
num
erat
edty
pes
•O
penG
L de
fines
num
erou
s ty
pes
for
com
patib
ility
–G
Lflo
at,G
Lint
,GLe
num
, etc
.
GLU
T B
asic
s
•A
pplic
atio
n S
truc
ture
•C
onfig
ure
and
open
win
dow
•In
itial
ize
Ope
nGL
stat
e
•R
egis
ter
inpu
t cal
lbac
k fu
nctio
ns–
rend
er–
resi
ze–
inpu
t: ke
yboa
rd, m
ouse
, etc
.
•E
nter
eve
nt p
roce
ssin
g lo
op
Sam
ple
Pro
gram
void
mai
n(in
t ar
gc, c
har*
*ar
gv)
{gl
utIn
itD
ispl
ayM
ode(
GL
UT
_RG
B |
GL
UT
_DO
UB
LE
);
glut
Cre
ateW
indo
w(
“Sim
ple
Ope
nGL
Pro
gram
” );
my_
init
();
// in
itia
te O
penG
L s
tate
s, p
rogr
am v
aria
bles
glut
Dis
play
Fun
c( m
y_di
spla
y );
// r
egis
ter
callb
ack
rout
ines
glut
Res
hape
Fun
c( m
y_re
size
);
glut
Key
boar
dFun
c( m
y_ke
y_ev
ents
);gl
utId
leF
unc(
my_
idle
_fun
c);
glut
Mai
nLoo
p();
// e
nter
the
eve
nt-d
rive
n lo
op
}
Ope
nGL
Initi
aliz
atio
n
•S
et u
p w
hate
ver
stat
eyo
u’re
goi
ng to
use
void
my_
init
( vo
id )
{gl
Cle
arC
olor
( 0.
0, 0
.0, 0
.0, 1
.0 );
glC
lear
Dep
th(
1.0
);gl
Ena
ble(
GL
_LIG
HT
0 );
glE
nabl
e( G
L_L
IGH
TIN
G );
glE
nabl
e( G
L_D
EP
TH
_TE
ST )
;
}
GLU
T C
allb
ack
Fun
ctio
ns
•R
outin
e to
cal
l whe
n so
met
hing
hap
pens
–w
indo
w r
esiz
e or
red
raw
–us
er in
put
–an
imat
ion
•“R
egis
ter”
cal
lbac
ks w
ith G
LU–
glut
Dis
play
Fun
c( m
y_di
spla
y );
–gl
utId
leF
unc(
my_
idle
_fun
c);
–gl
utK
eybo
ardF
unc(
my_
key_
even
ts )
;
Ren
derin
g C
allb
ack
•D
o al
l of
our
draw
ing
here
glut
Dis
play
Fun
c( m
y_di
spla
y );
void
my_
disp
lay(
voi
d )
{gl
Cle
ar(
GL
_CO
LO
R_B
UF
FE
R_B
IT )
;gl
Beg
in( G
L_T
RIA
NG
LE
);gl
Ver
tex3
fv(
v[0]
);
glV
erte
x3fv
( v[
1] )
;gl
Ver
tex3
fv(
v[2]
);
glE
nd()
;gl
utSw
apB
uffe
rs()
;
}
Idle
Cal
lbac
ks
•U
sed
for
anim
atio
n, g
ame
AI a
nd o
ther
co
ntin
uous
upd
ates
glut
Idle
Fun
c( m
y_id
le_f
unc
);
void
my_
idle
_fun
c(
void
)
{if
( ro
tate
) t
heta
+=d
t;gl
utP
ostR
edis
play
();
}
Use
r In
put C
allb
acks
•P
roce
ss u
ser
inpu
tgl
utK
eybo
ardF
unc(
my_
key_
even
ts )
;vo
id m
y_ke
y_ev
ents
( c
har
key,
int
x,in
ty
){
swit
ch(
key
) {
case
‘q’
: c
ase
‘Q’
:ex
it(
EX
IT_S
UC
CE
SS )
;br
eak;
case
‘r’
: c
ase
‘R’
:ro
tate
= G
L_T
RU
E;
brea
k;}
}
Ele
men
tary
Ren
derin
g
•G
eom
etric
Prim
itive
s•
Man
agin
g O
penG
L S
tate
•O
penG
L B
uffe
rs
Ope
nGL
Geo
met
ric P
rimiti
ves
•A
ll ge
omet
ric p
rimiti
ves
are
spec
ified
by
vert
ices
Sim
ple
Exa
mpl
e
void
dra
wR
hom
bus(
GL
floa
tco
lor[
] )
{gl
Beg
in(
GL
_QU
AD
S );
glC
olor
3fv(
col
or );
glV
erte
x2f(
0.0
, 0.0
);gl
Ver
tex2
f( 1
.0, 0
.0 );
glV
erte
x2f(
1.5
, 1.1
18 )
;gl
Ver
tex2
f( 0
.5, 1
.118
);
glE
nd()
;
}
Ope
nGL
Com
man
d F
orm
ats
Spe
cify
ing
Geo
met
ric
Prim
itive
s
•P
rimiti
ves
are
spec
ified
usi
nggl
Beg
in(
prim
Typ
e);
glE
nd()
;
•pr
imT
ype
dete
rmin
es h
owve
rtic
es a
re c
ombi
ned
GL
floa
tre
d, g
reed
, blu
e;G
lflo
at c
oord
s[3]
;gl
Beg
in(
prim
Typ
e);
for
( i =
0; i
<nV
erts
; i+
+ )
{gl
Col
or3f
( re
d, g
reen
, blu
e );
glV
erte
x3fv
(co
ords
);}
glE
nd()
;
Ope
nGL
Col
or M
odel
•B
oth
RG
BA
(tr
ue c
olor
) an
d C
olor
Ind
ex
Con
trol
ling
Ren
derin
g
•A
ppea
ranc
e•
Fro
mW
irefr
ame
to T
extu
re m
appe
d
Ope
nGL’
s S
tate
Mac
hine
•A
ll re
nder
ing
attr
ibut
es a
re
enca
psul
ated
in th
e O
penG
L S
tate
–re
nder
ing
styl
es
–sh
adin
g–
light
ing
–te
xtur
e m
appi
ng
Man
ipul
atin
g O
penG
L S
tate
•A
ppea
ranc
e is
con
trol
led
by c
urre
nt s
tate
for
each
( p
rimiti
ve to
ren
der
) {
up
dat
e O
pen
GL
sta
tere
nd
er p
rim
itiv
e
}
•m
anip
ulat
ing
vert
ex a
ttrib
utes
is m
ost
com
mon
way
to m
anip
ulat
e st
ate
–gl
Col
or*(
) /g
lInd
ex*(
)–
glN
orm
al*(
)–
glT
exC
oord
*()
Con
trol
ling
curr
ent s
tate
•S
ettin
g S
tate
glP
oint
Size
( si
ze )
;
glL
ineS
tipp
le(
repe
at, p
atte
rn )
;
glSh
adeM
odel
( G
L_
SMO
OT
H )
;
•E
nabl
ing
Fea
ture
sgl
Ena
ble(
GL
_ L
IGH
TIN
G )
;
glD
isab
le(
GL
_TE
XT
UR
E_2
D )
;
Tra
nsfo
rmat
ions
in O
penG
L
•M
odel
ing
•V
iew
ing
–or
ient
cam
era
–pr
ojec
tion
•A
nim
atio
n•
Map
to s
cree
n
Coo
rdin
ate
Sys
tem
s an
d
Tra
nsfo
rmat
ions
•S
teps
in F
orm
ing
an Im
age
–sp
ecify
geo
met
ry (
wor
ld c
oord
inat
es)
–sp
ecify
cam
era
(cam
era
coor
dina
tes)
–pr
ojec
t (w
indo
w c
oord
inat
es)
–m
ap to
view
port
(scr
een
coor
dina
tes)
•E
ach
step
use
s tr
ansf
orm
atio
ns•
Eve
ry tr
ansf
orm
atio
n is
equ
ival
ent t
o a
chan
ge in
coo
rdin
ate
syst
ems
3D T
rans
form
atio
ns
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Spe
cify
ing
Tra
nsfo
rmat
ions
•P
rogr
amm
er h
as tw
o st
yles
of s
peci
fyin
g tr
ansf
orm
atio
ns–
spec
ify m
atric
es g
lLoa
dMat
rix,
glM
ultM
atri
x–
spec
ify o
pera
tions
glR
otat
e, g
lOrt
h o
•P
rogr
amm
er d
oes
not h
ave
to r
emem
ber
the
ex
act m
atric
es
•C
heck
App
endi
x of
the
Red
Boo
k
Pro
gram
min
g T
rans
form
atio
ns
•P
rior
to r
ende
ring,
vie
w, l
ocat
e, a
nd o
rient
:–
eye/
cam
era
posi
tion
–3D
geo
met
ry
•M
anag
e th
e m
atric
es–
incl
udin
g m
atrix
sta
ck
•C
ombi
ne (
com
posi
te)
tran
sfor
mat
ions
•T
rans
form
atio
n m
atri
ces
are
part
of
the
stat
e, th
ey m
ust b
e de
fine
d pr
ior
to a
ny v
ertic
es to
whi
ch th
ey a
re to
app
ly.
•O
penG
L p
rovi
des
mat
rix
stac
ks f
or e
ach
type
of
supp
orte
d m
atri
x (M
odel
Vie
w, p
roje
ctio
n, te
xtur
e) to
sto
re m
atri
ces.
Tra
nsfo
rmat
ion
Pip
elin
eM
atrix
Ope
ratio
ns
•S
peci
fy C
urre
nt M
atrix
Sta
ck–
glM
atri
xMod
e( G
L_M
OD
EL
VIE
W o
r G
L_P
RO
JEC
TIO
N )
•O
ther
Mat
rix o
r S
tack
Ope
ratio
n–
glL
oadI
dent
ity(
)gl
Pus
hMat
rix(
)gl
Pop
Mat
rix(
)
•V
iew
port
–us
ually
sam
e as
win
dow
siz
e–
view
port
aspe
ct r
atio
sho
uld
be
sam
e as
pr
ojec
tion
tran
sfor
mat
ion
or r
esul
ting
imag
e m
ay
be d
isto
rted
–gl
Vie
wpo
rt(
x, y
, wid
th, h
eigh
t )
Pro
ject
ion
Tra
nsfo
rmat
ion
•P
ersp
ectiv
e pr
ojec
tion
–gl
uPer
spec
tive
(fo
vy, a
spec
t,zN
ear,
zFar
)–
glF
rust
um(
left
, rig
ht, b
otto
m, t
op,z
Nea
r,zF
ar)
(ver
y ra
rely
use
d)
•O
rtho
grap
hic
para
llel p
roje
ctio
n–
glO
rtho
( le
ft, r
ight
, bot
tom
, top
,zN
ear,
zFar
)–
gluO
rtho
2D(
left
, rig
ht, b
otto
m, t
op )
–ca
lls g
lOrt
how
ith z
val
ues
near
zer
o
•W
arni
ng:
forgluPerspective()
orglFrustum(
), d
on’t
use
zer
o fo
r zNea
r!
App
lyin
g P
roje
ctio
n
•T
rans
form
atio
ns•
Typ
ical
use
( o
rtho
grap
hic
proj
ectio
n)gl
Mat
rixM
ode(
GL
_PR
OJE
CT
ION
);gl
Loa
dIde
ntit
y();
glO
rtho
( le
ft, r
ight
, bot
tom
, top
,zN
ear,
zFar
);
Vie
win
g T
rans
form
atio
ns
•P
ositi
on th
e ca
mea
/eye
in th
e sc
ene
•T
o “f
ly th
roug
h” a
sce
ne•
chan
ge v
iew
ing
tran
sfor
mat
ion
and
redr
aw
scen
egl
uLoo
kAt(
eye
x ,e
ye y
,eye
z ,
aim
x ,a
im y
,aim
z ,
up x
,up
y ,u
p z
)
•up
vec
tor
dete
rmin
es u
niqu
e or
ient
atio
n•
care
ful o
f deg
ener
ate
posi
tions
Mod
elin
g T
rans
form
atio
ns
•M
ove
obje
ct–
glT
rans
late
{fd}
( x,
y, z
)
•R
otat
e ob
ject
aro
ndar
bitr
ary
axis
–gl
Rot
ate{
fd}(
ang
le, x
, y, z
)
–an
gle
is in
deg
rees
•D
ilate
(st
retc
h or
shr
ink)
obj
ect
–gl
Scal
e{fd
}( x
, y, z
)
Pro
ject
ion
is le
ft ha
nded
•P
roje
ctio
n tr
ansf
orm
atio
n (
gluP
ersp
ecti
ve,
glO
rth o
) ar
e le
ft ha
nded
–th
ink
of
zNea
ran
d z
Far
as d
ista
nce
from
vie
w
poin
t
•E
very
thin
g el
se is
rig
ht h
ande
d, in
clud
ing
the
vert
exes
to
be r
ende
red
Com
mon
Tra
nsfo
rmat
ion
Usa
ge
•E
xam
ple
of r
esiz
e()
rout
ine
–re
stat
e pr
ojec
tion
& v
iew
ing
tran
sfor
mat
ions
•U
sual
ly c
alle
d w
hen
win
dow
res
ized
•R
egis
tere
d a
cal
lbac
k fo
rgl
utR
esha
peF
unc(
)
resi
ze()
: P
ersp
ecti
ve &
Loo
kAt
void
res
ize(
int
w,i
nth
){
glV
iew
port
( 0,
0, (
GL
size
i) w
, (G
Lsi
zei)
h )
;gl
Mat
rixM
ode(
GL
_PR
OJE
CT
ION
);gl
Loa
dIde
ntit
y();
gluP
ersp
ecti
ve(
65.0
, (G
Lfl
oat)
w /
h,1.
0, 1
00.0
);
glM
atri
xMod
e( G
L_M
OD
EL
VIE
W )
;gl
Loa
dIde
ntit
y();
gluL
ookA
t( 0
.0, 0
.0, 5
.0,
0.0,
0.0
, 0.0
,0.
0, 1
.0, 0
.0 )
;
}
