Local vs. Global Illumination & Radiosity

Transcription

1 Local vs. Global Illumato & Radosty Last Tme? Ray Castg & Ray-Object Itesecto Recusve Ray Tacg Dstbuted Ray Tacg A ealy applcato of adatve heat tasfe stables. Local Illumato BRDF Ideal Dffuse Reflectace Ideal Specula Reflectace The Phog Model Why s Global Illumato Impotat? Radosty Equato/Matx Calculatg the Fom Factos BRDF Rato of lght comg fom oe decto that gets eflected aothe decto Bdectoal Reflectace Dstbuto Fucto 4D R(θ,φ ; θ o, φ o ) Icomg Radace Ideal Dffuse Reflectace The amout of lght eceved by a suface depeds o comg agle Bgge at omal cdece (Wte/Summe dffeece) By how much? db = da cos θ Same as: l. (dot poduct wth omal) θ da l db Assume suface eflects equally all dectos (a.k.a. Lambeta) A deal dffuse suface s, at the mcoscopc level, a vey ough suface Examples: chalk, clay, some pats 1

2 Ideal Specula Reflectace No-Ideal Reflectos Assume suface eflects oly mo decto Vew depedet Mcoscopc suface elemets ae oeted the same decto as the suface Examples: mos, hghly polshed metals θ θ l Real mateals ted to be ethe deal dffuse o deal eflectve Hghlght s bluy, looks glossy No-Ideal Reflectos The Phog Model Most lght eflects the deal eflected decto Mcoscopc suface vaatos wll eflect lght just slghtly offset How much lght s eflected? How much lght s eflected speculaly? Depeds o the agle betwee the deal eflecto decto ad the vewe decto α. Camea q L Lo = ks(cosα ) θ θ ks: specula eflecto coeffcet q : specula eflecto expoet v α l Effect of the q expoet The Phog Model Ambet Illumato Sum of thee compoets: dffuse eflecto + specula eflecto + ambet. I a typcal oom, eveythg eceves at least a lttle bt of lght Ambet llumato epesets the eflecto of all dect llumato L (ω ) = k a Ths s a total hack! vaatos Phog specula expoet

3 Asotopc BRDFs Questos? s wth stogly oeted mcogeomety Examples: bushed metals, ha, fu, cloth, velvet Souce: West et.al 9 Lghtscape Local Illumato Why s Global Illumato Impotat? The Coell Box Radosty vs. Ray Tacg Radosty Equato/Matx Calculatg the Fom Factos Why Global Illumato? Smulate all lght te-eflectos (dect lghtg) a oom, a lot of the lght s dect: t s eflected by walls. How have we dealt wth ths so fa? Ambet tem to fake some ufom dect lght ay tacg dect llumato ght aswe + = (o ambet tem) t s smooth, but ot costat! Hek Wa Jese Why Radosty? Radosty vs. Ray Tacg Sculptue by Joh Fee Dffuse paels photogaph: dagam fom above: Ogal sculptue by Joh Fee lt by daylght fom behd. Ray taced mage. A stadad Image edeed wth adosty. ay tace caot smulate the ote colo bleedg effects. teeflecto of lght betwee dffuse sufaces. eye 3

4 Readg fo : The Coell Box Caeful calbato ad measuemet allows fo compaso betwee physcal scee & smulato photogaph smulato Goal, Toace, Geebeg & Battale Modelg the Iteacto of Lght Betwee Dffuse s SIGGRAPH '84 photogaph smulato Lght Measuemet Laboatoy Coell Uvesty, Pogam fo Compute Gaphcs Two appoaches fo global llumato Vsualzg Ite-eflectos Radosty Vew-depedet Dffuse mateals oly Mote-Calo Ray-tacg Sed tos of dect ays dect llumato (0 bouces) 1 bouce bouces mages by Mcheal Callaha Radosty vs. Ray Tacg Ray tacg s a mage-space algothm If the camea s moved, we have to stat ove Radosty s computed object-space Vew-depedet (just do't move the lght) Ca pe-compute complex lghtg to allow teactve walkthoughs Local Illumato Why s Global Illumato Impotat? Radosty Equato/Matx Calculatg the Fom Factos 4

5 Radosty Ovevew Radosty Equato s ae assumed to be pefectly Lambeta (dffuse) eflect cdet lght all dectos wth equal testy The scee s dvded to a set of small aeas, o patches. The adosty, B, of patch s the total ate of eegy leavg a suface. The adosty ove a patch s costat. Uts fo adosty: Watts / steada * mete ω' x' L(x',ω') = E(x',ω') + ρ x '(ω,ω')l(x,ω)g(x,x')v(x,x') da Radosty assumpto: pefectly dffuse sufaces (ot dectoal) B x' = E x' + ρ x' B x G(x,x')V(x,x') Cotuous Radosty Equato Dscete Radosty Equato x eflectvty B x' = E x' + ρ x' G(x,x') V(x,x') B x fom facto Dscetze the scee to patches, ove whch the adosty s costat eflectvty A j B = E + ρ j=1 F j B j x G: geomety tem V: vsblty tem No aalytcal soluto, eve fo smple cofguatos A fom facto dscete epesetato teatve soluto costly geometc/vsblty calculatos The Radosty Matx Solvg the Radosty Matx B = E + ρ j=1 F B j j The adosty of a sgle patch s updated fo each teato by gatheg adostes fom all othe patches: smultaeous equatos wth ukow B values ca be wtte matx fom: 1 ρ1f11 ρ1f1 L ρ1f1 ρf1 1 ρf M O ρf 1 L L 1 ρf B1 B M B = E1 E M E A soluto yelds a sgle adosty value B fo each patch the evomet, a vew-depedet soluto. Ths method s fudametally a Gauss-Sedel elaxato 5

6 Computg Vetex Radostes Questos? B adosty values ae costat ove the extet of a patch. How ae they mapped to the vetex adostes (testes) eeded by the edee? Aveage the adostes of patches that cotbute to the vetex Vetces o the edge of a suface ae assged values extapolato Factoy smulato. Pogam of Compute Gaphcs, Coell Uvesty. 30,000 patches. Local Illumato Why s Global Illumato Impotat? The Redeg Equato Radosty Equato/Matx Calculatg the Fom Factos Calculatg the Fom Facto F j F j = facto of lght eegy leavg that aves at patch Takes accout of both: geomety (sze, oetato & posto) vsblty (ae thee ay occludes?) patch patch patch Calculatg the Fom Facto F j F j = facto of lght eegy leavg that aves at patch Fom Facto Detemato The Nusselt aalog: the fom facto of a patch s equvalet to the facto of the the ut ccle that s fomed by takg the pojecto of the patch oto the hemsphee suface ad pojectg t dow oto the ccle. A j θ θ j A j patch 1 cos θ cos θ j F j = V j da j da π A A A j = 1 da F da,a j 6

7 Hemcube Algothm A hemcube s costucted aoud the cete of each patch Faces of the hemcube ae dvded to "pxels" Each patch s pojected (astezed) oto the faces of the hemcube Each pxel stoes ts pe-computed fom facto The fom facto fo a patcula patch s just the sum of the pxels t ovelaps Patch occlusos ae hadled smla to z-buffe astezato Fom Facto fom Ray Castg Cast ays betwee the two patches s typcally betwee 4 ad 3 Compute vsblty Itegate the pot-to-pot fom facto Pemts the computato of the patch-to-patch fom facto, as opposed to pot-to-patch A Aj Questos? Readg fo Tuesday 3/4: A Two-Pass Soluto to the Redeg Equato: A Sythess of Ray Tacg ad Radosty Methods Wallace, Cohe, & Geebeg, SIGGRAPH 1987 Lghtscape Optoal Readg: The Redeg Equato Kajya, SIGGRAPH