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Meo yaeoc c ypoe paceo op-aopo.

Ace apaeo peaa eeo Bop Aecee, Caapo Mac Aecapo BMM CO PAH, Hoocpc, Pocc oa ce ee ce e cay ocaoo a oa a x e cae aa a peypye Aomau opae eee ooo cea. oce oo opaoao a opao ce oe pec paec o eo pacea oceeoc oye B ao paoe paccapaec opa oxo oeoo opae. oeo, apea a oeo eoe yaeoc, oo ycop poecc opae oy ocaac oce ao peopao, pacea opae o cpae c accec eoo oao, a ao yoo oe ee ye pacea. oxo ocoa a peapeo opaoe aa e oee ooo cea, x yae oo ce peypco pae oex eeo ce pe oeoy opae ao-o o ex op, oa poe oeoo eea e cae oaco p, apep, ayccoc p c ee ooo cea opae. Ee oo apaepo oe e, ea. Ec aeco ocoeoc eoa ec o, o pace op-aopa aoo opoaoo opae eyoeopeo coc ce y oc ey -a eocaoo eoc (oacoe p oe eea.

xapaepyc e, o o, eoopo cee, peoea apaea peaa papaoaoo eoa, paa opaee), o oo pe peep oopa ooe ycop pace oeoo opae.

a oceo ypoe, .e. pacca opaee cepe oaa, o ocaec ycopee, oee eo ceo ce. eo o papeee oopoe ac eo o ca poeccopo, paa, c coyec a ocoa pep pae ce oeo e 1.

peaaeo eoe. oce oo paccaec ooe ee coa: radiosity, form factor, parallel algorithm, opaee, oopoe ae peopayec opaee subdivision of finite elements.

peyeoo paepa c oo ycpee ae ceo. ycpee oy o pee apaep ayccocoo pa, o cooao 1. BBEEHE ooe ycpeee o aoy-o aoy.

Oo poe, oax p pacee Bepe oxo, coy oee ee c oopeacecx opae oeo-ee paepa e pea paep cea, eoa (eo yaeoc), ec poea peoe paoe [2]. B o paoe paccapac ooe apeao a oeo opae, apa oye oopeacecx opae ce, oycoex peepo py o cpae c cocoe ooo. B epoo, peaaeo papeee oeoo opae eyao paoe [2], oo, oope a oeo opae pa oe eea, oopx coco aa o eee ceo, aac cea. eycoo, coye eo ocea opuponouoau. Ocoo pee paccope o aopo oc ooee opeoc. Hapep, paoe cpaee exoo ecyppoa, coyp pacee op-aopo o eoy oyya [1], ec x pooo. Tecyp acc, o e yacy ep oeoo eea acoe a-o oeo o pacee aaca oceeoc cee, ooy aa, coa cea, o ec oe ee oaaec paccapaeo ao paoe, oxo, ca c e. Toa, cyae pyx oex eeo, e peee ecyp, epe.

o aopaaeo oea ye caea.

B ao paoe paccapaec o apao pya poea eoe yaeoc o oc apaeo peaa ce eo aopo, aa cpoo a oo oee ooo eoa pacea opc peopao ce aaa epa peee aopo. ooo pacea op-aopa eoxoo cce ex ypae acceco eoe c y oc ecoux ap oe, yaeoc. apaea peaa aopo o ae ocooac o pex ocoaec a pee oe MPI [3]. B paoe eoo ce epaa. Bcee y aapyc peya cex cepeo, oc peye epeopa c oex eeo, ec eocppyx peyeca eoca peaaex e coyc ceae eo, ooe eoo, a ae eoc pacapaea.

ye o epeop. Oao, a ae, cee y oc ec eca pyoeo poeypo, copaee oeca ee oo cea ooeo caaec a cpoec.

B peaaeo paoe peaaec oxo pee x poe. Paccapae eo ocoa a peopaoe ce o aaa ce. aao cpyc apaep aep, a ae co pye ee ce epao paac a oee ee o ex op, International Conference Graphicon 2002, Nizhny Novgorod, Russia, http://www.graphicon.ru/ 2. METO ATEHOCT k(x) cos(x - y, n ) cos (x - y, ny) x, V (x, y) x - y K (x, y) =, 2.1. Bo ocox ypae ec x y 0, ae yc cea S pooa ycoo-aa oepxoc, e yu uuocmu a L(x, ) - yu pocmu, o ec ooc cea, yaeoo o x S apae.

1, ec op opeo (x, y) aepo ye aa yopoe aop V(x, y) = e epeceaec c S, apaepo (r, x, y, z, Nx, N,d), e y 0, ae r R3 ep aep, o ec aao cce oopa aep;

k(x) ouuem pacceuau oe x.

(x, y, z) opooppoa ac cce Tao y pa cooecye opae o aoy oopa aep, x, y, z R3 ;

aepa (yoy opae) [1], p oopo (Nx, Ny ) papeeue aep, o ec apa ex yee ao oe oepxoc e ac o apae a aae. B x peooex ce, ooaax oeco cee o ypaee yaa accecoo eoa opoa o epa opae, yaeoc acaec ceye e:

oyaeo c oo o aep;

L(x) = K(x, y) L(y)d + Le(x) (2) d oycoe paccmoue aep, paccoe o yS S epa aep o ee oyca F ;

opaeue ye aa paoepy yepy Cyecye ae opa ypae (2) ycopox (Nx, Ny ) peey nuceo. ce o ee oepxoce [6]. B ycopoe eoe, oe o opae, xpa oo eeceoe aee v 0,1. accecoo eoa yaeoc, peepea acoc y poc L o apae e M ye paccapa opae paax ooc, a ceye cce: ao o cepoo, ocoy paax ae oe eoe x oepxoc ce ca, o e cex opaee o ceo p eacx opae apae aa a ae y poc paax cepoo (pac, ee oyo aa), oo apae, cocax ocp yo c py coa paccapaeo oe oceeoc, apaee opa o oe, pyoe aoece cea pax aco eee aco cocax yo yo. Ta opao, ycopoe cea oce opae o oepxoc e yac.

eoe yaeoc eco y L(x, ) B paax eex ooae oee ypaeue uyauauu (rendering equation, [1]) acaec e paccapaec y L(x,i), e i pae ae ceyeo epaoo coooe:

1 acoc o oo, c ao copo oepxoc epec aee y poc.

L(x, ) = K(x,, y, ) L( y, )dyS d (1) S 2.2. cpea ypae + Le(x, ) yaa accecoo eoa e ea cepa, K(x,, y, ) y pa, a yaeoc Le(x, ) cocmeoe uyeue (cc) ce.

ceoo pee ypae (2) ye cooa o apao emoa oex eemo emo o ypaee coaae c oo op ecoo aepua [7].

ypae epeoca ye (c., apep, [4]).

B accueco emoe uyameocmu [1] yc L pocpaco cypyex c apao 2(S) paccapac ye ce, .e. ce, oepxoc y, aax a ycoo-ao oepxoc S.

oopx pacceae ce o ce copo paoepo.

Bepe oe opooppoa L aop ooy o eoe ooc peepea 2(S) acoc yuu pocmu L o apae, .e. eco N aucx y i. ye ca pe y L(x, ) paccapa y L(x). i = Cooeceo y pa K(x,, y, ) ye ace eeco y e eo oa x o yx epeex ye e K(x, y). acx y:

Oe, o cyecy oa eoa N L(x) = L (x) (3) yaeoc, oope paoa epaoj j j = yx oepxoce, c., apep, [5]. B x eoax oo caaa paccaec aac ep c oo ooo eoa yaeoc, a oo ooeo oca pecaee (3) ypaee (2) ae paccac e epaoc. p o oee capo ( L ) yoa ypaee a k e a 2(S) ypaee yaa e (1) e coyec.

y K(x, y) oo c o opye:

International Conference Graphicon 2002, Nizhny Novgorod, Russia, http://www.graphicon.ru/ oepxocoo epaa. oo coyec ecoo oa oeoo eea mes(Si), oy ceyy ocox eoo:

ccey ex ypae ooceo eecx Li :

1. npoe. B o eoe peoe aee opaopa oeaec o ooy yy ey y oa N j Li = Fij L + Le, (4) a oex eeax Si S, apep, ey x j i j = epa, o ceye opye:

< nx, x - y >< ny, x - y > j e Fij = mes(S )k V (x, y) (6) j x - y Fij = K(x, y) i(x) (y)dxSd (5) j yS mes(Si ) SS j e x y o, paeae Si S, cooeceo.

aa ape op-amopo, ape Fij Heocao oo eoa ec ooee eoempuecux ouuemo op. B epaype apeao p ope co pyx oex ocaoo aco paec ecoo oe opeeee:

eeo Si. Oao eec cepeoe peyeco 1 ' Fij = K (x, y) i (x) (y)dxSd y oc cec oa.

j yS mes(Si) aeaue: ecea oepa (6), oopa peye SSk(x) aex cex apa, o cee ' Oe aaec o, o Fij ac o y oc. ooy ee cc apaee oca xpa a ae y eoep ce, e ac o oea paccea, oc, a op-aop oya oe pee oop oycaaec ec xapaepca cce ex ypae (4) a ey. o ooe ce. Oao ao paoe a ye yoee aeo coo a, e aee y cooa opeeee (5).

oc aae o , a eeceoe aee ec op-aop Fij pecae coo o oo ooc 64 a.

2. o ecou moa. Bpae a ao oeo ceoo ep, aae a i- oe ee, eee aoe-o oeco oe ( cyae poyox oopa, yy opaea o eo, oaae a j- oe oex eeo oo pa o paoepo ee. Oca, acoc, ceye, o opa ap ce). yc a oeo eee Si pa op-aopo, ocaa a acy paoepx op cpo, ee e.

N M o xk, a a S yl. Toa op-aop Fij k = 1 j l = Oo eoe yaeoc coyec ycooocooe ocoee, o ec aece acx oo oe c oo ceyeo pe:

pac ycoo-ocoe y. B o cyae c N M< nx, xk - yl >< ny, xk - yl > cea S paaec a oee eem Si a, o j Fij = mes(S )k V (xk, yl ) j j k = 1l = S = Si Si S =, ec i j. xk - yl i Bapao oo eoa ce op-aopo oe B aece acx y epyc eo Moe-apo [8], pee ce 1, ec x Si eepoo epaa.

i (x) =.

Hyo ae, o ecop a o, o paccapaea opya p ox cax M N ae ooo xopoee 0, ec x Si pee, eca cepe eocao oo eoa Bee ee oo ypoee: ye ca, o ec o, o p yee ooc co oe paccea k(x) ae ec ycooyeac cee apa a ce oco, o ec oopaoo ocea y oc.

k(x) = k x S.

j j Cyecy pye, oee ceae, eo B o cyae oo pec oee opey opyy ce op-aopo [1], apep, emo noyya, oao, paax ao pao o e paccapac.

ce eeo ap op-aopo Fij :

3. METO ATEHOCT C Fij = k j mes(Si ) POEHHM PACETOM OPMATOPOB < nx, x - y >< ny, x - y > V (x, y) d dxS yS 3.1. ocaoa aa j x - y Si S a paee, ye paccapa cey S ycooay oepxoc c aa a e a y o co, o ca co oeo ce opoea pacce cc. yc cea aopo ec ce oce eepoo pecaea e oeoo oeca ax International Conference Graphicon 2002, Nizhny Novgorod, Russia, http://www.graphicon.ru/ ye aa a peypye opae e oee eepeceaxc oepxoce Si, oope ye ooo ce.

aa oeu eemau ():

N 3.2. Ocae aopa S = Si, Si S = p i j.

j i = 1 aee ee ye peoaa, o (Sij ) o ocoo pep pae. oo pep oe acpye ocae . 2.1 apaep aep ocpo ocaoo e aop pee (r, x, y, z, Nx, N,d).

y ocaeo aa. o aop ocaec cey cpoa ceooa:

Paueue ce ye aa oeco oex eeo Sij 1 < i < N, yoeopee cey 1 < j < M i yco:

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