HAL Id: inria-00073686
https://hal.inria.fr/inria-00073686
Submitted on 24 May 2006
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub-
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non,
Visibility Masks for Solving Complex Radiosity Computations on Multiprocessors
Bruno Arnaldi, Thierry Priol, Luc Renambot, Xavier Pueyo
To cite this version:
Bruno Arnaldi, Thierry Priol, Luc Renambot, Xavier Pueyo. Visibility Masks for Solving Complex Radiosity Computations on Multiprocessors. [Research Report] RR-3008, Inria. 1996. �inria-00073686�
a p p o r t
d e r e c h e r c h e
INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE
Visibility Masks for Solving Complex Radiosity Computations on Multiprocessors
Bruno Arnaldi, Thierry Priol, Luc Renambot, Xavier Pueyo
N ˚ 3008
Octobre 1996
TH `EMES 1 et 3
"$!%'&435 !.6 37 &89:;)<77=>
?0@BA7C7DFE@BC9GIHKJLNMO7P0Q7LSRT@B@VUXWY@BLZD2HKMO9[9A9\^]RTC9GI_a`9DbMOcdGTefLZRT@WYA7RTUgDFh
i;jgk
l ml nYoYl p<q=rts(ul nvlVwyxIz(l p;nv{Tn|p
k
l m8l nXr~}KTpvl w p|
j
m8mlKmw
j
Il
mwyl nBI;ull nV I2wn|nw l n
vBl p;wyIn;l p<Twyml n
s<wyIvp;l|l
j
l |
j
lq(rt p|I|loV5rt02wyl n
! >¡¢B£¤2¥¢¦
}Kp
j
n§wl V¨§lIvl n|l TpwYm8TIª©2l «lvnv¬7p
j
l®ª¯°±²³T´9²³µ³ I l Ip;¨¶l<Tpv|
Ix l ·w+Ivl«xInv¸{IxI¸ n
j
l 02wl B¹ i;j
l§wy¸y¬2x¨¶|ºnfp|l nvwnvp|wp|l {=pv
j
wI¸l
«l v{ mI¸l zYn| l Il n0»m8vl¶p
j
wdo;m8 ¸¸¼Y¬g2wp|
j
l n½¾¬S7w nvpK{0 m8IxIpwypv¹¿¶m2wyvI
p|p
j
l 9wIn|pK{w¸vp
j
mnVBxI7nv¸xIp|=¬ST xInvln§p
j
l<wyI¸ pK{Ypv= m8IxIpvl¶p
j
l;w nvpK{
¸TVw¸l T«T |Im8l Tpvn nvpvlBwdy¬>n|¸«TIp
j
l=IvI¸l mÀ¬Sp
j
l=¨
j
¸ll T«TvIml TpB¹§Á¶{(nvI¸pvp|I
p j
lv¸ lm. Tp|nvxIIv¸ lmnVxIn|I§®ª¯°±²³fêÄB°Ků¼ÆK²BÇ Å·wyId§®È®ªÉ®ª³®°ZÊË0²BÈ Ì ÈB2xI<p|l
j
IÍTxIl0 n
wyI¸lpvwy
j
l«ll pvp|l Y2wpw0¸Bw¸pK{p
j
wydp
j
l <n|pwyI2w|dnv¸xIpvnV¹ i;j
nIv2lvpK{(n<VwyIpw¸
¨ j
lÎxIn|Il p
j
l5w!mTIl |(nvl ÍTxIl Tp|Ïwy¸7 m8IxIpvl;pv|l IxIl2wpw0m«lml Tp9dp
j
lmlm|{
j
l w|
j
{§wYmxI¸pvI|T l nvn||n9pv0ºl lwn¾¸ ¨Ðwn¶2nvn| ¸ l;mmxIVwp| Y2l pK¨¶l l (I|T l nvn||n
¨ j
wypvl «l ;p
j
l< mmxIIVwypv2wywyImÑnBÒfl p
j
l ;mlnvnwyl;2wynvn| ¶n
j
wyvl 8«w|ÏwyI¸l¹}Kp j l
2wy2lV¨§l0Ivlnvl Tpw^ m8I¸l mlpwp|¼8¬;«T n|I¸ pK{m(wnvºTnÓw n|pv| xIpvl Óm8l mv{2wywy¸ ¸l ¸
mIxpvl »Ô}Kp|l ¸
wyw8Õ
9Ö
I½ ¹
×8ØTÙÚÛÜ£Ý7¡¦
w nvpK{T mI¸l z02wypwwnvlnV2ww¸¸l ¸nvmÎB2wypw0¸TVw¸pK{T¹
Þßà
áãâKäVå
à
á¾æçâKèZé ê
ë§ìíVîï íBðñòóªôVîBòvõ ðó îöïí÷Vø õù úûòvîBòü|í2ý þî
ÿ
íòöîûòK÷ í2ý! ñ"ý öü
:;!%'&( )+*)<À/) 9/( 01) 93% :B) % 3&98:;)<77)Y39
Ø ¡ ØÓ¦
wIn l·wyvp| ¸ l2xInIIul n|l TpvInxIIl0«lvnvdmTIª©<ul lYIx4 Il IpYIl n0±¯È<®ª¯
°±BųÈÍTxIl(IxInwB«In= Tp|vTIxIp02wInxIl(IxII¸Vwp|ÓIIul gul Ilp|l¹ lIxpIl(Ip|vl(pvwB«w¸
l n|pIl0 l «xIln|pvwpIullxp|wy p|l YIl nYnv
k
l Il n0pv
k
l n mI¸l zTl n0»I¸xInxIdm¸¸Il
¸{TIl n½+2wxIIl0mXul p
j
TIlYIl0w nvpIul¹
w<wI|p
k
w!µwxIp|vl nYw¸vp
j
m8l n¶IlwInvpIul
Ipv|lnv¸xIp|^2vpvln|xI¸w82nvn| ¸pIul0IlVwy¸ xI¸l Y¸wwInvpIul0nvxI=Il n0nvxnKKl T«|IIlml Tpvn
l pYIdnvx¸w!nv
k
l l2wInnvdl In|l mI¸l¹
wyY¸Ïw0 «TnvxdIvI¸
k
l ml=l dnvxInKKI|I¸
k
l m8l nVl
xIp|¸ nwTp§¸l nIp|In¶ÃªÄV°KůªÆN²BÇ Å¶®ª¯ °±Bųµ³Ål p;Il8˲BȱVÅŧ®È®ªÉ®ª³®°ÅIp|vlYnv¸ xpvfTmwIull
k
wYwyxIpv|l n¶pvl
j
IÍTxIl n¶ ¸wn|nvÍTxIl nBwyI2vp|l<xIIlml ¸¸l xI|l9¸Bw¸pIul;Il n¾II;ul l nV¹¶¶l pvp|l<I|I|Vul pIul
l n|plnvnvlp|l ¸¸ l(wB«l ¸ l m8I¸fl n|I2wp|l xI|nnIul ÍTxIl Tpvl ¸n0mTIl |Il nxI=Iul Ix |l¸l nmxI«l1
m8l TpvnYIl0II;ul l n02wInY¸w
j
Vulw|
j
lmXul m8vlTxÎwInxÎ Tpvl zTpvlmx¸ p|IvT l n|nvl xvnxI
m(wTpvl I9¸l n m8mxIIVwypv¼In7l Tpv|lIvT lnvnvlxIvn
k
w0x «lVwx8¸l¸ xn¶¬NwI¸l<n|nvI¸lÍxl ¸Íxl
n|p7¸ l¾mT
k
l ¸l9Il¶ mmxIIVwypvÒ 2w0ul
j
wyIl¶Il¶ml n|nwl n7xw7«w|ÏwyI¸l nfwvpw9ul l nV¹!xIn
IIul nvlp|In02wyIn l p0wvp| ¸lxIlm¸Vulml Tpwypv8Il nm(wn|Íxl nYIl«TnvI¸pIuln|xIxIlm(w
j
Il
2wywy¸ ¸
k
l ¸l
k
w=mXul m8vl;In|pvvIx;ul l»}KTpvl ¸
wwyÕ
9Ö
½ ¹
" Ü¢¡1Ú1¥$#% Ø^¦
wInvpIulTn|
k
l Ilnm¸ lzlnVT2wyw¸¸Bul ¸nvm8l¸TVw¸pIulYIl n;I;ull nV¹
q
< =
f9/43:¶ !
«lp
j
l2wynvppvl d{lVw|nVwyIn| pK{
j
wn<l mlYmvlwm8|lxI¸w;nvIlp
j
npvl
j
IÍTxIl
nwI¸lp|I|TIxI l|lVw¸nvp| = m(wl n;pwyºITpv(w xITpwmIl Tp;¸
j
p;vl?>2l p|l Ó2lpK¨§l lÓT
l pvnYdp
j
lnv lIl¹YTl «lw¸7¨¶|ºn
j
wB«l=2l lÎVwyv| ldxIppvI |lVwn|lp
j
l= |vl p|Il n|n·wyI(p j l
l*@gl p|«l Ilnvn0¬§p
j
lw¸vp
j
mn¶pv8nv¸«lp
j
l0wyIn| pK{8IvI¸l mι;¶I l |IIp
j
ln|2ll IIKxI
y¬wyIn| pK{Ów¸vp
j
mnBfp
j
nvlÍxl Tpvw¸<wyIF2wywy¸ ¸l ¸¶nv¸xIpvn
j
wB«ll l ÐI|nvlf¹ i;j
n
I ¸xIl n;Iv|l nvn| «lYw nvpK{T
j
l w|
j
Bw¸gnv¸xIpvnVTm|pw l;Iv«l wyI( ¸xInvp|l vI¹BA<T
¬Svp|xI2wp|l ¸{IlnvIpvl0TxImlvxn; m8Iv«l mlp|nVTwIn|pK{w¸vp
j
mn¶l l wypvlw
j
xIl0TxIml
y¬ mIxIpwp| In9wI
j
wB«lYw¸wyº0¬72wpw¸TVwy¸ pK{T¹ i;j
n§¸wp|pvl ;wB¨;2wyºm(wºl n7p
j
lYl zTl xpv
y¬wyIn| pK{w¸vp
j
mn7Il*@gl p| «l8l p
j
l;xIIIvT lnvnv;;mxI¸p| vT l n|nv|n§mxIpvl |n§¨;p
j
w! m8I¸l zm8l mv{
j
l wyv
j
{ÎwnnvTÎwyn<p
j
lI|I¸l m.n|Cl»Ôp
j
l0TxIm2l;¬92wp|
j
l n½n
j
xIl¹
i;j
n7I|I¸l m ¨ wynfIpn|Ynvl In|pv«l;¨;p
j
p
j
l 9vlIIl | 5wy¸|p
j
m8ngnvxI
j
wn7n|VwTK¸IlDKIx3@gl
wB{Np|w 2¹5Ep
j
lmÎgw82wpw¸TVw¸pK{(Iv2l |pK{Îlzn|pvnwI^mwyºl np
j
l0l zTl xpvÓy¬§nvxI
j
wy¸ | p
j
mn¾vl ¸wp|«l ¸{l*@gl p| «lT{xIn|Ip
j
lYm8l mv{
j
l wyv
j
{I|l v¸{T¹
i
¸¸xInvp|wypvl;p
j
nBT¸l p n9pwºlp
j
lYwB{Kpvw I0w¸vp
j
m^¹ i;j
l< mIxpwp|0¬fpK¨¶Il
j
| zTl ¸nY¨;¸¸
j
wB«l·w8|lVwpYI|2wyI¸ pK{8pv(lIl wypvl8vx
j
¸{(p
j
l0nwyml02wpwwy l n|n2wypvp|l v
n| lwB{Tn;¨;¸¸gIv2w¸ {lVwynvp;(p
j
lYnwmlYI|l pvf¹9 w0xIIvT l n|nvVp
j
l= m8IxIpwypv
y¬>p
j
ln|l ÎIzTl ¸¨; ¸¸gp
j
xn<xIn|lmnvp;¬9p
j
l2wypw0¸TVwp|l d(Vw
j
lxIlpv8p
j
l= m8IxIpwypv
y¬p
j
lY©2vn|p;IzTl ¸K¹FE¶mxI¸pvI|l nvn|vnBTp
j
l=nwm8l;Iv2lvpK{(Vw82l=xInvl (p|ºl l (¸¨Ðp
j
l=xm
l 0¬;2wpwdw l nvn|l npv(p
j
ln
j
wvlÓml m8v{Ó»Ôl p
j
l =vlVwy¸§«T |pvx2wy¸½ ¹ i;j
n
j
wyn2ll F ¸lVwyv¸{
Ilmnvpvwp|l ({8p
j
lY¨¶|º¬GYvll dl p<wy¸N¹HooI§Á;wxIl ¸l pwy¸K¹Hµ?Iv¹
lYp
j
lTpv|TIxI p| d¬7p
j
l=w nvpK{TIw0¸ p;¬7¨§vºTn
j
wB«lY2l ldVw|vl dxIp<p|Il |lVwn|l
p j
lmxIpwypv(pvm8ll p
j
l T{(pvmC I0p
j
lw¸vp
j
mT{dvlIxI I(p
j
lTxIml ;¦ m!
Ixpwp|In;§T{xIn|
j
j
l K¬Svm(wI lY mIxpvl |n§n|xI
j
wn¶p
j
nvlYp
j
wp
j
wB«l<nvl«l w¸fC l (y¬
I|T l nvn||nV¹&J¨§l «l V ¬Sl ¨ ¬7p
j
l n|lnv¸xIpvn;IlVw¸p¶¨;p j p j
l= m8Iv«l ml Tp9y¬2wypw0¸TVw¸pK{¹ }K
HµTg$KI7o*Ivnvl «l wy¸9IlVwyn
j
wB«ll l ^Iv2nvl Óp|IlBw¸7¨;p
j
m8I¸l zl T«TvIml TpB¹ i;j
l{ wyvl
m8nvp|¸{2wynvl (ML9®®Å²Ä /N7OIÄ ±Vů7nvp|wypvl lnVÒ9p
j
l<m¸ lzl T«TvIml Tp9n¶nvxII«TIl (p|
n|l «l w¸7¸TVw¸gl T«TvIml Tp|n§¨
j
lvlp
j
lwyIn| pK{mxIpwypvn;wII¸l f¹
}KÐp
j
n2wy2l B<¨¶ldI|n|l wy l ¨.mI|«l m8l Tppvap
j
l^«T |pvx2wy¸;¨ wy¸¸< I l Ip(¨¶l
j
wB«l
wy¸ |lVw{Ó Tp|vTIxI lFnvml{lVw|n·wyPHoQIv¹ i;j
nm8Iv«l ml TpIlVw¸n0¨;p j pj
ll Ilv{apvwInã¬Sl
l pK¨¶l l ÓpK¨¶¸ TVwy¸fl T«TvIml Tp|nV¹SRÓlTpvvTIx lwl ¨ ml
j
wyInvmÀ¨§l=Vw¸¸l PTUV8UXW.UYUXZ\[^]`_V8a
¨ j
j
wm8nwp7|l Ivlnvl TpvIp
j
lS>2¨a¬gl Il |{p
j
wp7n9l zT
j
wIl l pK¨§ll ¸TVw¸l T«|Im8l TpvnV¹
i;j
l§2wy2ln7|wyIC l wynf¬Z¸¸¨;nV¹7E |nvpBnvl pv+Il nvv2ln§n|ml¾p
j
l 7¨§vºTn7¨
j
j
nvl l m
n| m8¸Ïwy9pv0x;pvl
j
IÍTxIl¹¶Tl p|Îq=Ivlnvl TpvnYp
j
lY«|pvx2wy¸g Tp|l K¬Nwy l I l p<¨;p j pj
l^TUV8UXW.UYUXZ\[
]`_V8a3VB¹XTl p| cbÓ«l nw^2wyw¸¸l ¸<wy¸ | p
j
m¨§l(IlnvIlXmwy ¸ { ¬SIn|pvvIxpvl Ðmlm|{
2wywy¸ ¸l ¸¾ m8IxIpvlvnV¹(Tl pvPK(v«TIl nn|ml0l K¬Svm(wI l0mlBwnvxvl m8l TpvnV¹(¶ ¸xInvÓw
l vn|2l pv«lnw|lvl n|l Tpvl ^n|l p| dI¹
b
,.)< Y7)</=
n¨§l0nvpwp|l fp
j
lpwvl py¬§xIY¨¶|ºdnp|(Iv2nvlw^l l TpYwyIn| pK{^w¸vp
j
m.w¸ l0pv
IlBw¸¨; p
j
«l |{m¸ lznv lIl nV¹ i;j
n9Tw¸In§wy
j
l «l T{0mlVwyIn7¬wpvl
j
IÍxl<¨
j
j
l zTI¸pvn
2wypw!¸ TVwy¸ pK{T¹ i;j
n<p|l
j
IÍTxIl0VwdlI|Vl pvl ^Tpv82p
j
nvlÍxl Tpvw¸9wd2ww¸¸l ¸gmwy
j
Il nV¹
T4¨§l0¨;¸ ¸9wy2w¸{Tnvl0Ivl«xIn¨¶vº ¬Svm.pK¨§(Tpvny¬§«T l¨ÒY2ww¸¸l ¸7nv¸xIp|InwfgmwyI¸{
¸TVw¸pK{l
j
wI lml TpV¹
TxIm2l¬2wywy¸ ¸l ¸Yn|¸xIpvIn
j
wB«l^l l Iv2nvl xInvIaI\@¿lvl TpÎwyv
j
pvl pvxI|l nÎw
I\@gl vlppK{T2l n¬72ww¸¸l ¸ n|Invp|wypvl lnV¹¶}K H oBq;Iv7HbIv7HoV;If n| xIn|nvInYw|lIvlnvl TpvlÎn
j
¨;I
p j
l2nvn| ¸ lwyII|w
j
lnY¬SY2wywy¸ ¸l ¸nvIwInvpK{dwpYnvl «l wy¸§¸l «l ¸nV¹ Evm.p
j
lnvl¦p j l
¨¶|º vl n|l Tpvl
j
lvl¨§l4mwB{ÓInvp|IxIn
j
l pK¨¶l l pK¨§aºT In¬nv¸xIpv¹
©2vn|p8¬Nwm8 ¸{
y¬·w¸vp
j
mnw¸¸¨;np
j
lFw lnvndy¬·w¸¸Yp
j
l^I|l nvn|vn^pvÐp
j
lÎlp|vl^2wpw2wynvl¹ i;j
nm(wB{
ldI|Ipvwypvl ÐT{Fn
j
w|l m8l mv{^nv{Tnvp|l mnT{FInvp|vIxIp|l Xm8l mv{^nv{Tnvp|l mn8¨
j
l vl4p j l
2wypwy2wn|lnxII¸Vwp|l wyplVwy
j
¸TVw¸¶ml m8|{ Hµq IãSHoV;Iv&HoK;Iv¹^}KÓp
j
l(|lVw0Vwn|l¶nv lIl nnvC l
n«lv{F¸mp|l f¹ i;j
l(nvl IЬKwm¸{dy¬5w¸vp
j
mnYn nvpvp|xIpvl {Óp
j
l(pvl
j
ÍTxIln2wynvl
n|pv| xIpvl (m8l mv{n|{n|pvl m8n;¨
j
l |lp
j
lY2wypwy2wn|ln¶Invp|vIxIp|l dwmIp
j
lYI\@¿l |l Tp<¸TVw¸
m8l mvl nwy¸¸ ¨;I8p
j
lwyII¸Vwp|dy¬ p j
lwy¸ | p
j
m.pv(Il n| l Iln HT¾oVIT7TTfq Iã¹
T¸xIpvn§2wynvl 4(Invp|vIxIp| p
j
lYl T«|Im8l Tp wymp
j
lY¸TVw¸gm8l mvl n§wyvlY¬Zpvl (2wynvl
wy(l zTI¸ p;<m¸ p7nvx2I«Tnv(y¬>p
j
lYl T«T |Im8l Tp;|Il pvBwIpwy¸CldwT{pK{T2l
y¬§2wpw¸TVw¸pK{pv8vl xI lp
j
ll zT
j
wyIly¬§T¬Svmwypvl pK¨¶l l ÓI|T l nvn||nV¹
i
p
j
l·wyxIp
j
vn
ºTI¨;¸l Il¶Ily¬p
j
l n|lÎm8l p
j
nl zTI¸ p|n2wpw^¸Bw¸pK{Î2wynvl Ð2p
j
Ò4mIm¼n|I(p j l
wymxp7y¬¿T¬Svm(wpvpvwIn|mpvl 0l pK¨§ll (IvT l n|nvvnwyIpwyºT 5wyI«wTpwl¶¬fp
j
l<«TnvI¸pK{
T¬Svm(wpvm¸ p98p
j
lYl T«Tvml Tp n¶Il mn| p|f¹
i;j
l lVw(¬; InvIl |IÎn|xITKl T«T |Im8l Tpvn»¸TVwy¸9l T«T |Im8l Tpvn½
j
wnl l ÐxIn|l Ó¬S|m
I\@gl vlp0TpvnY¬<«Tl ¨g^vl p|(vl Ix l mIxpwp|2wy¸nvp= ^wyIn| pK{^w¸vp
j
m8n¶¬S
mI¸l z(l T«TvIml Tp|nV¹ i;j
l=©2vn|pY Tpv|IxIpvÎdp
j
n |l p| d¨;wnYIv2nvl ÓPHµ;Iã¹ i;j
n
m8l p
j
Td «TIl n;l«TvImlp;Tpv8¸Bw¸fl«TvImlp|n<wI4 m8IxIpvln;¬SvmZ¬Nwy pvvn¶ 4lVw
j
y¬
p j l mι
¬Spvlv¨;wvnV¾¬S|mZ¬Nwpv|nl pK¨¶l l Xwpv
j
lnÐIl
j
xI| θTVw¸;l«TvImlp|n·wyvl
mIxpvl 8¬S|mI|l «TxIn|¸ {8 m8IxIp|l (¸ TVwy¸¬S|mZ¬Nwpv|nV¹7Tm¸w9wIvTw
j
l n¨§l |lI|l nvl Tp|l
HµK;IfwI/Ho*Iv¹7Il |{0 n¶w xmxI¸wpvl·wyp9p
j
l2xII2wyvl n¶¬gIl
j
xI|IY¸ TVwy¸2l«TvImlp|n
»ÔVw¸¸l Ó«Tvpvxw¸9¨;w¸¸n½wIFw¬Spvl |¨ wyvIn=pvwyInK¬Zl vl ¹}KIn|pvlVwyFy¬ I«TIIp
j
ll T«Tvml TpYp|
n|mw¸¸l ¶IlnVBHobIfI|nvlnp||xI(Il
j
xvI2wypv
j
l nB¹ i;j
l nvl0|xIIn;|l l «l·wyI(n
j
Tp
l l v{ wyn;IlYn| ¸lYl TpvpK{¹RÓlYmwB{0Vw¸¸gp
j
l mÀ«|pvx2wy¸gnvxIã¬Nw lnV¹
G5vxInfy¬ n|xIK¬Kw l n¶wvl¾xInvl 0|Il pv<n|mI¸ª¬S{;l Ilv{Yl zT
j
wyIl¶ m8I¸l z<l«TvImlp|n
T{m8lVwIn7y¬2nvm¸ ª¬S{TI¶p
j
l;l m8l pv|{Y¬gp
j
l¶l T«T |Im8l Tp7 0wq
vxIIIYwII|wy
j
HoB;Iã
Hµ;IvBHµ;I§w HµIoQIv¹RÓlxIIl vn|pwÓ{dq
vxIII2p
j
l=¬Nw pp
j
wypYp
j
l n|lml p
j
TIn<l©2IlqB
¸xIn|pvl |nλÔ02zTl n½0 nvpvlBwFy¬vxIny¬2wypv
j
l n¨;p
j
nvm8 ¸wyvl TpwypvFwynaIIl8
HobIv¹ i;j
l l Ilv{Ðl zT
j
wyIl^pwyºl n8I¸w ldl pK¨¶l l ¸xInvp|l vnB¹ i;j
lÎw¸vp
j
mnm(wB{Óm(wB{
Ip;I ¸xIIlw
j
l wv
j
Vwy¸fn|pvwypvl {¹9¶¸xIn|pvl |In<w¸nv0xInvldMHo;I7¨
j
l vl=p
j
lYl T«Tvml Tp¶ n
m(wIl p|<p
j
l§¨;w¸¸ng¬p
j
l¶ ¸xInvp|l V¹ i;j
n7m(w<n7xIn|l I¸{¬Snvl I2wyv{wB{n7¨
j
¸l9I|mw|{
wB{n¶IYIp9xInvlp
j
l ¸xInvp|l vnB¹ i;j
lp|l vlnvp¶¬g2ww¸¸l ¸ n|IYp
j
l<wy¸ | p
j
mÑn9TpvlxIp9/Ho;I
l VwyxInvly¬p
j
lY¸ TVwy¸ pK{0vlnvxI¸pvI=¬S|m p j
lYm(wIIIYIxp;p
j
n¶¸ TVwy¸ pK{0n§I¸{lz¸ pvl 8IxIvI
K
Virtual Interface Source
Object
Local Environment 2 Local Environment 1
No Light Energy
EfxIvloÒvpvxw¸g}KTpvl ã¬Nwl»¬Svm8l vpvxw¸7RFw¸¸½ ¹
p j
l|l IIlvIn|pvl ¹
¸¸fp
j
l n|lm8l p
j
TIn;Tpv|TIxI lwyII|zm(wpvIn7¬S;l zTI¸pvI¸TVw¸pK{IxIp
xIp
j
l <l?@¿l pvnY|Il pv0ºl l 4p
j
lYvlÍx |l Îwy xIw {T¹
}K/Hµ.bI2n7I|nvlw<n|{TnvpvlmpvYl zTI¸p7¸TVw¸pK{Y =vl §p|YmImC l7p
j
l;p|wnK¬Sl |n9l pK¨§ll
In|ºwI0mwym8l mv{T¹ i;j
n7nv{Tn|pvl m n7Il nvIl pvY mIxpvl9wIn|pK{l l Tpv¸{«l v{=¸Ïwyvl
l T«TvIml Tp|n¨
j
l vl8p
j
l0«T n|I¸ pK{(vl¸Ïwypvn
j
Inw|l¸Bw¸¸{l InvlxIp¸2w¸¸{n|2w|nvl¹8}KpY n
2wynvl (w
j
l wyv
j
Vw¸fwyII|w
j ¹ i
¨¶2wynv<IlBwn<w|l<l zTI¸ p|l fÒ72wyvp| p|IIw|Il | 2¹
w|pvpvIIYmlVwyIn9Il Tpvª¬S{TIYnvxInvl p|n<y¬¿p
j
lY2wpw2wynvl;lVwy
j
m82nvl T{p
j
l< ¸xIn|pvl |n;¨
j
j
Tpvl w p8¨;p
j
w^«l »Ôvl l «l ½( ¸xInvp|l V¹ i;j
l4Il©2Ip| Ьp
j
lnvl^nvxIIn|l pvn(n2wynvl XÐp j l
n| l Il8nvpv|xI p|xIvl(wIÓw8«n| ¸pK{I|l m8IxIpwpvd2lpK¨§l lF ¸xIn|pvl |nV¹vIl |IdmI¸l n;pwºTI
p j
lYnvxIIn|l pvnw8|Il ;¨
j
j
m8 mC lnp
j
lYI\@¿lvl Il2lpK¨§l ldpK¨§=nvxI l nvn| «ln|xIIn|l pvnB¹ i;j
l
|l nvxI¸p|n HbI<n
j
¨Àp
j
wpV¾¬Sp
j
ldn|2l ¼©dpK{T2l(¬l T«TvIml Tpl nv |2l w«l9p
j
ld2lnvp
l lI {^¨ wyn<pwIld¨;p
j
l¸ ¸¾vl V¹ i;j
lnvl l ¸¸nwyvl0Il©2l ÓT{ w!¨ wy¸¸¼vw¸l Á;
Kpv|l l
n|2wp|Ïwy¸gnvxII«Tnvf¹
793
=
7);9:;)
|pvx2wy¸§TpvlK¬Nwy lnw^mI|«l m8l Tp<¬;p
j
l«|pvx2wy¸9¨ wy¸¸9 l Ip0¨§l0©vnvp0TpvvTIx l Ó HoQIã¹
i;j
l=2wn| = lVw0¬9p
j
n;¨¶|º¨;wn;p|©2Idw0¨;wB{p|nvxII«T l5w! m8I¸l zl T«Tvml Tp¶ (¸TVw¸
l T«TvIml Tp|n;xInvI0I¸wIln;¨§lYVwy¸ ¸l TUZ3_Y _YYVV¹
i;j
l«Tvp|x2w¸g¨;w¸¸n<w0ml
j
wyInvm ¨ j
j
wymn9p|wp
j
l <wyI(pvnvBwpvp|l <p
j
lYl Il |{(¸lVwB«TI
l Tpvl |Idw¸TVwy¸9l T«T |Im8l TpV¹ J<¨¶l «l Bfp
j
lxIn|l¬§«Tvp|x2w¸9¨;w¸¸n
j
wnYnvml0Inw«wTpwyl
n| l( p=vl ÍTxIvlnwIpv2wy¸9 mIxIpwp| InwIaml m8|{¹
n=¬S=p
j
l(1l p0¬p
j
ln| l Il w
«Tvp|x2w¸I¨;w¸¸
j
wyn9pvl;Il mn|l TpvY2wp|
j
l n7¬S9¨
j
j p j
l;l Ilv{Ip
j
|xI
jj
wn9p|Y2l
n|pv|l f¹Ys;l vl n|l TpvI(p
j
l0l Ilv{(¸lVwB«TIwwpv
j
¬Zvm.w«Tvp|x2w¸¨ wy¸¸gvl ÍTxIvlnp
j
l0nvpvvIy¬
n|l «l w¸gT¬Svm(wpvnvxI
j
wn9p
j
l<n|2wp|Ïwy¸2 n|pv| xIpv0¬fp
j
l<lIl v{¹ vl«l BTp
j
lnvxII«T n|
y¬5w4«|pvx2wy¸§¨;w¸¸
j
wnp|Îl(IIl8Fnvx
j
w4¨ wB{Óp
j
wp0p
j
wn0¬Sl ¨ m82wpap
j
l(ÍTx2w¸pK{dy¬
p j
l(vl Il vI¹
i
d«l vmlp
j
l n|lv¸ lmnV7¨¶lTpv|TIxI l(wdIl¨pvl
j
ÍTxIl8Vw¸¸l a§®ª¯ °±²³
êÄV°KÅy¯¼ÆN²BÇŨ
j
j
n;Ilnv | l ^p
j
l<¬Z¸¸¨; 2www
j
nV¹
R p j p j
n7Il¨Fpvl
j
IÍxlw+«T |pvx2wy¸T Tp|l K¬Nwy l¶ n7Imvl§w+nvl p9y¬22wypv
j
l nB¹7}KInvp|lVwy¬
j
wB«TI
p j
l nvlY2wypv
j
l n¶pv=vl I|l nvlp;p
j
l<lz
j
wyIl¬gl Il |{l pK¨¶l l (¸Bw¸Il T«TvIml Tp|nV¨¶l<xIn|lwIl ¨
m8l
j
wIn|mÎTVwy¸ ¸l (§®È®ªÉ®ª³®°ZʲBÈ Ìpvp|wyInK¬Sl¸
j
p;l l v{l pK¨¶l l ^¸Bw¸fl«TvImlp|nV¹ i;j
l
wy m ¬2p
j
n9ml
j
wInvm n7pv0w¸¸¨ wY¸TVwy¸mxIpwypvy¬¿p
j
l;wyIn| pK{Yw<¸TVwy¸Il T«T |Im8l Tp
(|Il ;pvm8Iv«l;p
j
lwpw=¸TVw¸pK{w l nvnB¹
! "#$%&!'(
i;j
l0©vnvp0I| I¸ly¬ p j
l«T |pvx2wy¸9Tpvl ã¬Nw lwyII|l nvn|l np
j
llIl v{Îp|wyInK¬Sll pK¨¶l l F¸TVwy¸9l T
«TvIml Tp|nV¹Y}KIn|pvlVwyÓ¬ wy xImxI¸wypvIp
j
ll Il |{4¬Svm.I\@¿l |l TpnvxIvl nTp| w`TUZ 3_Y _YY
l¬Svln|l III(pYpvÎwyIp
j
l vT l n|nvB7p
j l TUZ3_Y U*)7Z,+ -X_/.0+0pvl
j
IÍxlw¸¸¨;np
j
lmwy2wl
m8l Tp9¬9wYnvxIv l=nvl 2wywypvl ¸{0¬S|mp
j
l ¶nvxIvl n<p
j
lnwm8l;¸ TVwy¸2l«TvImlpB¹
n§n|Twyn w
n|xI| l
j
wn;l m8 p|pvl 8pvn;l Ilv{TTp;n;nvl Tp;pvp
j
lIlzp;vT l n|nvB¹
i;j
lnvl IÓI|I I¸l¬9p
j
l«Tvp|x2w¸7Tpvl ã¬Nwl l vnp
j
l0¨;wB{p|pwºl= Tp|w xITpp j l
n|xI| l<p|wnK¬Sl ¶l pK¨§ll ¸TVw¸Tl T«TvIml Tp|nV¹}KIIl l n|l IIIp
j
l;lmlpvv{0wI0pvn9l m8nvnv«TpK{
p|p
j
lIl zTp;l T«Tvml Tp<wB¬Zpvl <w0¸TVw¸IvT lnvnvI8mI¸{0pvw w!Il ¨ nvp|vxI p|xIvlgVw¸¸l 21(3
¡ 3Ú
3#3
¢ Ù Ó¤2¡&4
gpv(p
j
lnvxIv ld»Ï©2xvl(oV½ ¹ i;j
l«TnvI¸ pK{m(wn|ºn|pvvl nBfdp
j
lnvxIv ln|pv|xI pvxvl
wy¸ ¸gp
j
lT ¸xIn|In;l xITp|l vl ^IxI|Ip
j
lI|T l nvn|IlBw
j
¸TVw¸gl T«TvIml TpB¹
i;j
ll zTp;nvl p|InIl nvv2lnm8|l<Il lI¸{p
j
lYpK¨§0I| I¸l nV¹
65 789%: ;/<>=>!9?
i
Fl nv |2l^mvl(Il l ¸ { xI8pvl
j
IÍTxIl¨¶ld¨;¸ ¸pwyºldp
j
lÎwn|nvxIm8Ipv p j
wp(wÓI|vl n|nv«l
wIn|pK{p|l
j
IÍTxIln<xIn|l Tp|¸ {8¨;p j w j
l m8nv
j
lvl0pvmxIpvlY¬ZvmÀ¬Kw p|vnB¹,RXp
j
nvxI
j
p|l
j
IÍTxIlIw2wp|
j ¨ j
j0j
wynp
j
l;mnvp7xIIn
j
p7l l v{ n7n|l ¸l pvlwpvn¾l Il |{0 n7In|pvvIxpvl
p|Îp
j
l wpv
j
ln ap
j
l8nv lIlÎw |IIÎp| w ¬Svm ¬Nwpv0 mIxIpwp| f¹ R p
j
xI«Tvp|x2w¸
Tpvl ã¬Nwl< I l IpBTp
j
ll Il |{0¬flVwy
j
nvl ¸l p|l (2wp|
j
¨¶l;Vwy¸ ¸ p¶w<n|xI| lTn7©2|nvp¶Invp|vIxIp|l
p j
l<¸TVw¸l T«Tvml Tp7¨
j
j
p9n9Tpwy l f¹ i;j
l T p|n9l Ilv{n9vwwypvl 8pvp
j
l§¸TVw¸
l T«TvIml Tp|nV¹J<¨¶l «l Bp|I|2wywp|l;l l Tpv¸{0p
j
l;lIl v{¬fwY«l wpv
j
pvwIp
j
l§¸TVw¸
l T«TvIml TpBp9n9Il lnvnwyv{(pv=Il pvlvmIl;p
j
l<«TnvI¸pK{Y¬fp
j
l<2wypv
j
w v pv0p
j
l;xIv|l Tp
¸TVw¸¶l T«Tvml TpVÒ=pm(wB{dl zTnvpwyÓl pw¸ w «l ^Ivl pva¨
j
jÓj
Il n0p
j
l8nvxv l
»Ï©2xI|l½¹SRÓlTpv|TIxI l 4p
j
l®È®ªÉ®ª³®°SÊ ²BÈ Ì<¨
j
j
n<w0nvxInwymI¸l
j
l m8nv
j
lvlYIl TpvVwy¸fpv
p j
l§Il¶ T«¸«l YYp
j
l¶ mIxIpwp| Y¬Ip
j
l¾¬Svm ¬Nw p||nV¹ 9wy
j
Izl¸y¬Ip j l j
l m8 n|
j
l |lp
j
wp n
xIn|l ¬Z7p
j
l¶¬Zvm ¬Nwpv7 mIxpwp|InBVv|l nvIn;pvw2T¸ lBw0«w¸xIl¶ 0p
j
l;«n| ¸pK{Ymwynvºg¹
«w¸xIl= nnvl pYp|ÆN²³È|Ū¬9p
j
l0 vvlnvIII(wB{Ip
j
|xI
j p j
l0Izl¸f¬¶p j l j
l m8 n|
j
l |l
j
p|n5wyd1l pY w!Ivl«xInY¸ TVwy¸fl T«TvIml TpB¹!<pvl0p
j
wyp<x<pvl
j
IÍxlVwyÎlwyII¸l dpv
j
lm xIlT(p
j
wyp;Vwn|lp
j
l«TnvI¸pK{mwynvº0¨; ¸¸glw
j
l m8 xI2lYwn;¨¶l ¸¸K¹@(vl «l Vp§Vwy(2l
lVwynv¸{(l zTpvl Il Ópv8pwºlTpv(w xITp<wvp| 2wp| mlIwI¹;}KIn|pvlVwyÎy¬§xIn| ¸lVwd«wy¸xIl nV
wyTpvll ;«wy¸ xlxI¸|l I|l nvl TpYp
j
l2lv l Tpwl0¬9wIn||Ipvdwy¸ Iw0 «l |l p| f¹
Source
Object Local Environment 1
True
False
True Visibility mask
EfxIvlIÒ7}K p|w¸nwp|0¬9p
j
lY«TnvI¸pK{m(wnvº=¬S<w¸TVw¸gn|xI| l¹
Virtual Interface Local Environment 2
No Light Energy Source
False True True Visibility mask
None
None
ExI|l5qÒBA<n|l¬7p
j
lY«TnvI¸ pK{0mwynvº0¬S w0 n|pwyp¶nvxIvl¹
, '($99# 29: 6/< =>!9?9
i;j
l=«n| ¸pK{m(wnvºwy¸¸ ¨;n¾p
j
l n|pv| xIpv8¬7l Il |{(pv¸TVw¸gl«TvImlp¶w=nvp|l dT{n|pvl
2wynvnV¹
i
¨¶ÎVwynvl n8mwB{Ów| n|l¹a}Z¬p
j
ln|xI| ldl ¸Inpv^p
j
l(¸TVw¸;l«TvImlpB9wd«TnvI¸pK{
m(wnvºn¶ vlBwpvlÎwI(w¸¸gpvn¶2T¸ lBw«wy¸xIl<n;nvlp;pv0°¯S±BÅp
j
l v¨;n|lp
j
lY«TnvI¸pK{mwynvºw¸vlVwyI{
l zTnvp|nwyI(¨; ¸¸glxI2wp|l dIxvI0p
j
lvT l n|nvIy¬9p
j
ln|xI| l¹&Evm ¬Nw p||nw|lY m8IxIpvl
¨;p j p j
ldwpv
j
lnl ¸I ÓpvÓp
j
ld¸Bw¸<l«TvImlp0T{FVwynvp| FwB{Tn!¬Svm p j
l4 l Tpvl (y¬
p j
ln|xI| lp
j
vxI
j p j l j
lmnv
j
l vl¹(}Z¬w wB{
j
p|n·wyÓl pÓp
j
l8¸ TVwy¸9l T«Tvml TpV pj l
v|l nvI «wy¸xIlY 8p
j
l0«TnvI¸ pK{0mwynvºn;nvlp<pv!ÆN²³ÈvÅYp
j
l |¨;nvlp
j
l vl0n;Im8TIª©2Vwp|f¹
i;j
lfw nvpvl n;y¬9¸ TVwy¸g2wp|
j
l nwyvlx22wypvl 4xInvIIlpvl wp| (¬>w0vvl n|nv«l0wyIn| pK{
wy¸ | p
j
mι E2w¸¸{Tfp
j
ldnvxIvlÎwIapvn«TnvI¸ pK{4mwn|º wyvldn|l TppvÓp
j
l(Il
j
xI| θTVw¸
l T«TvIml Tp|n;pv02lvT l n|nvl ^¸wpvl»©2xIvlq½ ¹
!'( 9: ;9%# 6 ! #$%&!'(9
Ildy¬p
j
l(mwyÓI xI¸pK{Ó xnvI^«|pvx2wy¸<Tpvl ã¬Nw lnnp|^©2IXw^mwyIIIdy¬«Tvp|x2w¸;T
p|l K¬Nwy l n0dp
j
lm¸ lzl«TvImlpB¹
xIlp|(p
j
l0 m8IxIpwpvd¤p
j
l0«n| ¸pK{m(wn|ºnBp j l
I|T l nvn|I¬wYn|xI| lYVwIp¶2lVw|vl 8xIp¶wT{vIlV¹7}KIIll fIwY«TnvI¸pK{mwynvº TpwIn
«TnvI¸pK{T¬Svm(wpv¬S|m wy¸¸gp
j
l ;¸Bw¸gl T«Tvml Tpvn¶l pK¨§ll Îp
j
lYnvxIv l0wI(p
j
lxIv|l Tp
¸TVw¸7l T«TvIml TpB¹,EfxIvl bn
j
¨;nY2p
j
wÎo
wIÓw
n|2wlnvxII«T n|f¹s+l wyvII8p j l
o
Vwynvl7l¬Svl8IvT l n|nvIFw8nvxIvl p
j
wnp|dlI|l nvn|l X·wyI w
n|l ÍTxIl Tpvw¸mwyIIl B¹g}Z¬p
j
lYpw|l p¶ mIxIp|l
j
wn¶nvl «l wy¸fI|T l nvn||nVp
j
lvlYn§I0¨;wB{pv0l zTI¸p
p j
l m.nvmxI¸pwIl xInv¸{(p
j
l=IvT l n|nvI(¬9IlYnvxv l0¨
j
j
nvxI
j
n|2wln|xI2 «Tnvf¹RXp j w
Il mn| p|fp
j
lIvT l n|nvI^¬<w8nvxv l
j
wnYpv(lIlxInvIdw8¨ wB«l¬S|TpYpvl
j
IÍTxIl
wy¸ ¸¨;I(p
j
l mIxIpwp| Îy¬p
j
ln|xI| l( a2ww¸¸l ¸K¹gTVwy¸;l T«|Im8l Tpvnl ¸IIdpv4p j l
t1 t2 t3 t4
LE1 LE2 LE3 LE4
Source
t1 t2 t3 t4
t5 t6
LE1,3
LE1,2
LE1,1
LE2,3
LE2,2
LE2,1
LE3,3
LE3,2
LE3,1
LE4,3
LE4,2
LE4,1
Source
ExI|l b2Ò;o
wyId
n|2w l=nvxII«T n|¨;p
j
«Tvp|x2w¸gTpvlK¬Nwy l n
nwml¨;wB«l1¬Svp^Vwa2l8p
j
xInl «wy¸ xwpvlFÓ2ww¸¸l ¸K¹ i;j
n0Iv2lvpK{FBwFl(l zTpvl Il a¬S
w(q
n|xI2 «TnvÎy¬§p
j
lIp|Ïwy¸fl T«TvIml TpB¹TxI
j
wpw8Il2l Il I l nB7Îp
j
lvT l n|nvIdy¬
n|xI| l nV7xI¸^2l|l Ivlnvl Tpvl wpvxw¸¸{(T{dmlVwy(¬;ml n|nwl nY w82wyw¸¸l ¸ m8I¸l mlpwp|
y¬>p
j l TUZ 3_Y7U)2Z,+ -_ .0+YI lIpV¹
f9 43·7)</ %')5%'=7 %'&( )Y% )Y7Y !
i;j
l=Il nvd¬§wwwy¸¸ l¸fw¸vp
j m ¬SInvpv|IxIpvldml m8|{2wywy¸ ¸l ¸gmxIpvl |n<|l ÍTxIvl n©2|nvp
wyIЬSvl m8nvpw^2wypw^ImwÓIl m82nvpva vIlpvÓ n|pv| xIpvldwpwawm8Idp
j
ld¸TVw¸
m8l mvl nV¹ i;j
nY©2|nvpn|pvl Ónp
j
l ^¬S¸ ¸¨¶l dT{Îw8Invp|vIxIp|^¬; m8IxIpwypvnw |IIdpv
2wypw4Invp|vIxIp| f¹F¶mIxIpwp| Inwyvldwn|nvIlFpvÓw^I|l nvn|p
j
wp0¨;In0p
j
l(2wypw4Il l l
p|Ó2l ã¬S|ml ap
j
lmιÐTxI
j
pvl
j
IÍxl
j
wnl l X¨;Il ¸{ÓxIn|l f;p0nº¨; wnwpw4|l Tpvl
2wywy¸ ¸l ¸nwypv¹ i;j
lΫTvp|x2w¸ Tp|l K¬Nwy l^ Il IpVY¨¶ldIl«l ¸l Xp
j
n82wl VYw¸¸¨;nxIn(pv
wyII¸{Îp
j
nwpw4|l Tpvl a2ww¸¸l ¸ nwp| În|
j
l ml8pvdp
j
l(wyInvpK{^ m8IxIpwpvf¹ i;j
lIp|Ïwy¸
l T«TvIml Tp7n7nvI¸pvl TpvYn|l «l w¸¸Bw¸Il T«TvIml Tp|n¨
j
j
Vwl;mwyIl p
j
l<wB«w¸w¸ l
I|T l nvn||nV¹
nvxIIn|l p¶¬gp
j
l n|l<¸TVw¸l T«|Im8l Tpvn7n>wynvn| Il p|wIvT l n|nvV¹
IvT l n|nv§n7
j
wyvl¬g2lK¬SvmIYp
j
l< mIxpwp||l ¸wpvlpvpvn¾¨;2wpwI¹}Kp9 nvnvp|n§p
j
l;Invpv|IxIpv
y¬>p
j
ll l v{y¬2wypv
j
l np
j
wyp<l ¸I0pvp|n<¸TVw¸gl T«TvIml Tp|n wyn;¨§l ¸¸7wn;p
j
lInvp|vIxIp| y¬
l l v{mI5¬SvmIl
j
xI|I¸TVwy¸gl T«|Im8l TpvnV¹
Á¶l¬SvlITpv0Il pw¸nV¨§lYIl n| vlI| l?>2{p
j
lIl zTp;nvl pv4p j l j
wyvI¨;w|l5wyI(nvy¬SpK
¨;w|ldl T«T |Im8l Tp¨§ldwyvldxIn|IÓ¬Sl zT2lvml Tp| ÓxI2wywy¸ ¸l ¸;wInvpK{ wy¸ | p
j
mι i;j
l
Ilnv | pvdy¬xI;nv¸ xpv8 n;«l 8 (n|l pv b¹µI¹