Nomo dil kolor-modelo devenas de nomo Internacionala Komisiono pri Lumizo (France Commission Internationale de l’Eclairage ) e faktori "L", "u" e "v". La lineigo per CIELUV propozesis en 1960, e korektesis en 1976.
La kolor-modelo CIELUV es strikte relatat a kolor-spaco CIEXYZ , qua anke kreesis da la sama komisiono.
Kolor-parametri CIE 1976 L*u*v* recevesis de CIE XYZ per sequa equacioni (
u
′
,
v
′
{\displaystyle u',v'}
L
∗
=
116
(
Y
/
Y
n
)
1
/
3
−
16
,
{\displaystyle L^{*}=116(Y/Y_{n})^{1/3}-16,}
u
∗
=
13
L
∗
(
u
′
−
u
n
′
)
,
{\displaystyle u^{*}=13L^{*}(u'-u_{n}'),}
v
∗
=
13
L
∗
(
v
′
−
v
n
′
)
.
{\displaystyle v^{*}=13L^{*}(v'-v_{n}').}
Faktori
u
n
′
,
{\displaystyle u_{n}',}
v
n
′
{\displaystyle v_{n}'}
Y
n
{\displaystyle Y_{n}}
blanko di lum -fonto. Por tipala mezur-geometrio di observanto 2° e lumizo C, ke to es:
u
n
′
=
0,200
9
{\displaystyle u_{n}'=0{,}2009}
v
n
′
=
0,461
0
,
{\displaystyle v_{n}'=0{,}4610,}
e por blanka lumo en temperaturo 6500 K
Y
n
=
0,331
00.
{\displaystyle Y_{n}=0{,}33100.}
Equacioni por
u
′
{\displaystyle u'}
v
′
{\displaystyle v'}
u
′
=
4
X
/
(
X
+
15
Y
+
3
Z
)
=
4
x
/
(
−
2
x
+
12
y
+
3
)
,
{\displaystyle u'=4X/(X+15Y+3Z)=4x/(-2x+12y+3),}
v
′
=
9
Y
/
(
X
+
15
Y
+
3
Z
)
=
9
y
/
(
−
2
x
+
12
y
+
3
)
.
{\displaystyle v'=9Y/(X+15Y+3Z)=9y/(-2x+12y+3).}
En transformado inversa uzesis dependaji
(
u
′
,
v
′
)
{\displaystyle (u',v')}
(
x
,
y
)
{\displaystyle (x,y)}
x
=
27
u
′
/
(
18
u
′
−
48
v
′
+
36
)
,
{\displaystyle x=27u'/(18u'-48v'+36),}
y
=
12
v
′
/
(
18
u
′
−
48
v
′
+
36
)
.
{\displaystyle y=12v'/(18u'-48v'+36).}
Transformo CIELUV a XYZ deskriptata es per:
u
′
=
u
∗
/
(
13
L
∗
)
+
u
n
,
{\displaystyle u'=u^{*}/(13L^{*})+u_{n},}
v
′
=
v
∗
/
(
13
L
∗
)
+
v
n
,
{\displaystyle v'=v^{*}/(13L^{*})+v_{n},}
Y
=
Y
n
(
(
L
∗
+
16
)
/
116
)
3
,
{\displaystyle Y=Y_{n}((L^{*}+16)/116)^{3},}
X
=
−
9
Y
u
′
/
(
(
u
′
−
4
)
v
′
−
u
′
v
′
)
,
{\displaystyle X=-9Yu'/((u'-4)v'-u'v'),}
Z
=
(
9
Y
−
15
v
′
Y
−
v
′
X
)
/
3
v
′
.
{\displaystyle Z=(9Y-15v'Y-v'X)/3v'.}
