Rendering Equation. Linear equation Spatial homogeneous Both ray tracing and radiosity can be considered special case of this general eq.
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1 Rederg quto Ler equto Sptl homogeeous oth ry trcg d rdosty c be cosdered specl cse of ths geerl eq.
2 Relty ctul photogrph Rdosty Mus Rdosty Rederg quls the dfferece or error mge
3
4 Comprso Ry trcg Rdosty Vew pot depedet Speculr Vew pot depedet Dffuse
5 Rdosty Therml het trsfer Lght trsport: trsfer of eergy from thermlly excted surfce Rdosty: rte t whch eerge leves surfce mtted + reflected lce equlbrum determe the blce of comg d outgog flux
6 Rdosty the mout of lght eergy tht leves surfce, cludg self-emttg eergy source reflected d/or trsmtted eergy rdosty = emsso + b-drectol reflecto b-drectol reflecto couts both reflecto d trsmsso trsport of both speculr d dffuse compoets b-drectol reflecto s fucto of rdostes of ll other obects the evromet how much receved by the prtculr obect
7 Mthemtclly ptch from eergy totl pth from ptch t receved eergy totl tme re eergy fctor form rdosty reflectvty emsso rdosty : / :, _
8
9 Implemetto Detls Reflectvty d emsso my be fuctos of wvelegth, hece, the equto my represet fmly of equtos e.g., for red, gree, d blue chels the form fctors deped oly o geometry
10 I geerl Implemetto Detls the mtrx c be very bg e.g., wth 000 ptches the mtrx s 000x000 or wth oe mllo etres t s usully ot sprse or tr-dgol, or bded lmted, etc. etc. tertve soluto e.g., Guss-Sedl
11 ,,, Itlly, ll s c be pproxmted by s Order ptches wth sources frst Ptches dcet to sources lt up, the they lght up other ptches Iterte utl the umbers stblze
12 Stdrd rdosty methods Compute the form fctors Solve the rdosty mtrx equto usg Guss-Sedl method Rederg select vewg drecto determe vsble surfces terpolte rdosty vlues e b e b e b e
13 orm ctors Wthout beg mthemtclly rgorous, form fctors re ffected by dstce betwee two ptches gles betwee two ptches N r N d H d d 0 H vsble ot cos cos r d
14 d d d d d d d dd r H d d d r H d d r H d r H cos cos cos cos cos cos cos cos
15 Grphcl terpretto r re of the proecto form fctor re of the bse crcle proecto proecto cos oto the hemsphere r dow o the the bse cos dvded by the re of the bse
16 urther smplfcto s log s the sme proecto s produced, ll these surfces hve the sme form fctor
17 Smplfcto Isted of proectg oto hemsphere, we c proect oto hemcube wth plr surfces wth trdtol vsble surfce determto lgorthm The hemcube c be dscretzed d pxel rdostes tbulted dvce The ust cout how my pxels prtculr ptch covers d dd up dvdul rdosty vlues
18 Smplfcto
19 xmple r x y z y x y x y x r cos cos ot vsble H r H d d 0 cos cos
20 More xmple r x y z z y z y z y z y r cos cos
21 My Possble Geerlztos Substructurg Sptl refemet Progressve rdosty ster updte Icremetl rdosty Temporl refemet
22 Substructurg t plces wth lrge rdosty chges Need smller ptches for better pproxmto re oe ptch to m sub ptches troduce m more rdosty vlues the rdosty mtrx becomes O+m^
23 Isted compute sub-ptch form fctors updte form fctor of ptch I compute rdosty usg orgl x equtos updte rdostes of sub-ptches l l,,, ptch s subptch s s s s s s
24 Progressve Rdosty or trdtol rdosty soluto, ech terto s of O^ Gtherg rdosty updtes, oe for ech pth ech updte gthers the rdosty vlues of ll ptches
25 ,,, l l,,,
26 0 bouce bouce bouces
27 Shootg rdosty updtes ll ptches usg the rdosty vlue of sgle ptch,,
28 Oe terto voles O updtes orm fctors of oe ptch eed be ept Oly the prt of rdosty tht ws ot processed before eed be shot,, l,
29 Trde-off Most ccurte for dffuse lghtg Photorelstc mge Soft shdow, color bleedg Lrge computtol effort orm fctor computto
30 Combg Ry Trcg d Rdosty rst compute vew depedet, globl dffuse llumto wth rdosty The compute vew depedet, globl speculr llumto usg ry trcg
31 xmple
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