Traditional Rendering Radiosity

Transcription

1 Tadtonal Rndng Radost CS 57 all 00 Comput Scnc Conll Unvst Hsto Poblms wth classc a tacng: ot alstc: onl pfct spcula and pfct factv/flcton btwn sufacs Vw-dpndnt Radost 984 Global Illumnaton n dffus scns Dsctz scn Mont Calo Ra Tacng 986 Global Illumnaton fo an nvonmnt

2 Radost dvantags Phscall basd appoach fo dffus nvonmnts Can modl dffus ntactons colo bldng ndct lghtng and pnumba aa lght soucs ounda lmnt fnt lmnt poblm ccounts fo v hgh pcntag of total ng tansf Radost: ssumptons ll sufacs a dffus RD has constant valu fo all dctons Scn has polgons patchs onl ll sufac ponts of a polgon hav th sam adanc valu ll sufac ponts of a polgon hav th sam RD

3 K Ida #: dffus onl Radanc ndpndnt of dcton Sufac looks th sam fom an vwpont o spcula flctons K Ida #: constant polgons Radost soluton s an appomaton du to dsctzaton of scn nto patchs Subdvd scn nto small polgons

4 Constant Radanc Polgons ssumpton: all sufac ponts on a patch hav th sam adanc valu ght-pont tanspot ght-aa tanspot V fst adost pctu

5 Radost: Tpcal Imag Radost algothm Subdvd th scn nto small polgons Comput fo ach polgon a constant llumnaton valu Choos a vwpont and dspla th vsbl polgons

6 Radost algothm Subdvd th scn n small polgons Comput fo ach polgon a constant llumnaton valu Choos a vwpont and dspla th vsbl polgons Choos a nw vwpont. and anoth. and anoth. Radost Equaton Emttd adost slf-mttd adost cvd & flctd adost Radost Radost slf a Radost

7 Radost Equaton Radost quaton fo ach polgon Radost Radost Radost Radost Radost Radost slf slf quatons; unknown vaabls slf a a a Radost Radost Radost Radost algothm Subdvd th scn n small polgons Comput fo ach polgon a constant llumnaton valu Choos a vwpont and dspla th vsbl polgons Choos a nw vwpont. and anoth. and anoth.

8 nt Elmnt Tchnqus omulat th poblm of ndct dffus llumnaton om actos Solvng lna sstms Θ Θ Rndng Equaton Ω f Ψ Θ Ψ dω Ψ Ψ Ψ Ra-castng functon: what s th nast vsbl sufac pont sn fom n dcton Ψ? vp Ψ Ψ vp Ψ Ψ

9 Θ Θ Rndng Equaton Ω f Ψ Θ Ψ dω vp Ψ Ψ Ψ d Ψ vp Ψ Ψ dω Ψ d dω Ψ Rndng Equaton: vsbl sufacs Θ Θ Coodnat tansfom Θ Θ Ω f Ψ Θ Ψ dω f on all sufacs Ψ Θ vp Ψ Intgaton doman vsbl sufac ponts Ψ Intgaton doman tndd to sufac ponts b ncludng vsblt functon Ψ d

10 Ψ Θ d V f K K Rndng Equaton: all sufacs Two foms of th RE Hmsph ntgaton a ntgaton ov polgons fom st Ψ Θ d V f K K Ω Ψ Ψ Θ d f ω K K

11 Radost lgothms asd on aa-fom of th RE ssumptons all lght soucs a dffus mtts all sufacs a dffus flctos so adanc s not dpndnt on dcton ppomaton adanc can b appomatd b pc-ws constant functons ov all sufacs Dffus mtt Dffus sufacs Θ constant ov Θ Dffus flcto f Θ Ψ constant ov Θ and Ψ

12 Dffus sufacs - RE Θ Θ Ψ Θ Ψ V d f f V d Dffus sufacs RD spcal cas: dal dffus ambtan: flctvt [0] Eng d Eng Eng d Eng out n n out 0 Θ Ψ Θ dωθ π d Ψ Ψ dω E d Ψ Θ dω Θ Ψ dω Ψ f E d π E f π f d π

13 Dffus sufacs - RE df - flctanc d V π d V f Sufac lmnts ll sufacs n th scn numb of sufac lmnts.g. polgons sufac lmnts d V π d V π

14 Constant adanc appomaton Radanc s constant ov a sufac lmnt constant ov sufac lmnt : Constant adanc appomaton Radost: π d d d d Θ Ω Θ Θ Ω π ω ω

15 Constant adanc - RE V d π Tansfom to pow b ntgatng on both sds... d Ω dω Θ d Ω dω Θ Constant adanc appomaton V d π Intgatng wth d Ω dω Θ Ω π dω d ωθ d V d π Ω d π V d π π V d d π Θ π

16 D.D.R.E. V π d d V d π d Dffus dsctzd Rndng Equaton D.D.R.E

17 om actos Invaant d d V π d d V π D.D.R.E.Radost Dvd b

18 D.D.R.E. DDRE fo ach polgon : na sstm : pow of patch unknown : msson of patch known I : flctvt of patch known : fom-facto coffcnts of mat Radost Equaton Radost fo ach polgon : na sstm Β : pow of patch unknown Β : msson of patch known I : flctvt of patch known : fom-facto coffcnts of mat

19 na Sstm n n n n n n n n n n n known known unknown na Sstm

20 Radost lgothm Subdvd scn n polgons msh that dtmns fnal soluton Comput om actos tansf of ng btwn polgons Solv lna sstm sults n pow colo p polgon Pck a vwpont and dspla loop Comput om actos V d π d

21 om acto th facton of pow mttd b whch s cvd b om acto a f s small t cvs lss pow Ontaton f facs t cvs mo pow Dstanc f s futh awa t cvs lss pow

22 om actos - how to comput? Closd om naltc Hmcub Mont-Calo om acto naltcal V d π d Equatons fo spcal cass polgons In gnal had poblm Vsblt maks t had

23 om actos - Hmcub Poct patch on hmcub dd hmcub clls to comput fom facto om actos - Hmcub Dpth nfomaton p pl valuats vsblt s fo all polgons n scn Hadwa ndng Z-buff Sv alasng: Small polgons dsappa

24 - Mont Calo Gnat pont on patch Gnat pont on patch Evaluat ntgand Comput avag V 0 k k k V k k p π k k k k om actos Vsblt chcks a most pnsv opaton s a usuall computd whn ndd computatonall pnsv mmo O