Beyond a Simple Physically Based Blinn-Phong Model in Real-Time

Transcription

1 Pactcal Physcally Based Shadng n Flm and Game Poducton: Beyond a Smple Physcally Based Blnn-Phong Model n Real-Tme. Intoducton Yoshhau Gotanda t-ace, Inc. We pesented ou mplementaton fo a physcally based Blnn-Phong model [Blnn 977] at SIGGRAPH 00, whch was: Rd f, x, F0 F shnness spec F0 n max n, n shnness, whee R d s the dffuse albedo and F spec f 0 s the Fesnel functon wth Schlck s appoxmaton usng f as the specula eflectance fo the nomal decton. n s the nomal vecto, s the outgong decton 0 and s the ncdent decton. Snce then, physcally based shadng models have been apdly adopted n the game ndusty. Thee ae and wll contnue to be many ttles that use enegy-consevng and/o nomalzed shadng models that nclude physcally based paametes. Ou physcally based Blnn-Phong has smlates to the Cook-Toance model n [Cook and Toance 98]. It s not enough, howeve, to epoduce the complex appeaances of mateals n the eal wold; fo example, tanslucent, ough, layeed, and eto-eflectve mateals. In ths couse, we would lke to ntoduce ou newe models that epesent moe complex appeaances, whch could not only be useful fo next-geneaton consoles but also cuent-geneaton consoles.. ayeed Blnn-Phong Model The fst model we mplemented s a layeed shadng model. ayeed mateals ae vey mpotant to epoduce ealstc esults because, n the eal wold, thee ae lots of mateals that have combnatons of dffeent popetes consstng of dffeent BRDFs. If atsts ty to epoduce these mateals wth a sngle physcally based shadng model, thee ae cases n whch t would be moe dffcult than usng an ad-hoc model. Ths s because n an ad-hoc model the atsts ae able to adjust the paametes fo the desed layeed appeaance wth non-layeed shadng models wthout physcal lmtatons. A smple soluton fo ths ssue s to mplement a layeed shadng model. Typcally, off-lne endees suppot vey flexble layeed shadng models that can be combnatons of any numbe of layes and BRDF models. Howeve, due to pefomance ssues, fo eal-tme endeng on not-so-poweful GPUs, we chose only dual-layeed and lmted shadng models. ven unde these estctons, a layeed model can epoduce much moe ealstc esults than any othe sngle-layeed shadng model. We efeed to [Wedlch and Wlke 009] and [Wedlch and Wlke 0] fo ou layeed model. The mplementaton was vey smple, even fo eal-tme endeng, and we wee able to appoxmate some elements to meet the pefomance equements fo cuent-geneaton consoles. In the ognal mplementaton,

2 they used the Bougue-ambet-Bee law to epesent one lght-absopton phenomenon by the top laye. Howeve, t uses an exponental functon and efacted dstances, whch ae computatonally expensve to evaluate n the shade. Theefoe, we fstly appoxmated them wth a lnea functon and non-efacted dstance and used ou own physcally based Blnn-Phong nstead of Cook-Toance. Accodng to the ognal mplementaton, the lght absopton can be computed as: I l I 0 e l d cos, cos I s the ncdent ntensty, s the absopton coeffcent, d s the thckness of whee I s the ntensty, 0 the laye, s the angle of efacted ncdent lght, and s the angle of outgong efacted lght. Ou mplementaton appoxmates these equatons wth the followng equaton: I I 0 max 0,, 3 whee s the nomal vecto, s the modfed absopton coeffcent epesentng a combnaton and adjustment of the ognal coeffcent and thckness, s the lght vecto, and s the eye vecto. Secondly, we appoxmated the Fesnel tem computaton n the bottom laye. Snce the bottom-laye BRDF s evaluated wth the lght passng though the top laye, the Fesnel tem n the bottom laye s computed wth the followng equaton: n, n n F n F F n n F bottom, 4 whee F n s the Fesnel equaton, n s the efactve ndex of the top laye and n s the efactve ndex of the bottom laye. Fgue shows an example gaph of the Fesnel component n the top and bottom layes. The ed lne epesents the component n the bottom laye. otce that t s almost a flat lne and can theefoe be appoxmated wth a constant such as: F tansmttance n n F 5 n F bottom n, n F0 F0, n n whee F0 n s the Fesnel equaton fo the nomal decton, F n tansmtta nce s the tansmttance fom the top laye by the Fesnel tem, and F n, n bottom s the eflectance of the bottom laye and the Fesnel tem. Fgue shows a compason between the ognal absopton mplementaton and ou appoxmated mplementatons.

3 Fgue : A gaph showng the Fesnel components. The blue lne s the component of the top laye wth a efactve ndex of The ed lne s the bottom laye wth.5. Fgue : A compason wth dffeent shades. The pece on the left s endeed wth the ognal mplementaton takng 0.53ms on a PlayStaton 3 at 80x70 wth a sngle dectonal lght. The pece n the mddle s endeed wth ou appoxmated mplementaton, takng 0.37ms, and the pece on the ght s endeed wth ou appoxmated mplementaton and no absopton, takng 0.34ms. A sngle-layeed Blnn-Phong standad physcally based shade takes 0.33ms. These numbes demonstate that ou appoxmaton povdes good esults fo both endeng and pefomance. Suppotng mage-based lghtng fo layeed mateals s vey mpotant. In typcal cases, mage-based lghtng wth layeed mateals shows moe mpessve esults than a punctual lght wth layeed mateals. The absopton component must be ntegated wth a BRDF accodng to the endeng equaton. Howeve, because t s also computatonally expensve, t should be appoxmated. We used the same appoach as AmbentBRDF as descbed n [Gotanda 00]. Fo the specula component of the bottom laye, although the ntegal s dependent on the shnness value n ou Blnn-Phong model, we decded to coasely appoxmate the ntegal wth the followng equaton, whch

4 s equvalent to. egads the specula component as a pefect mo eflecton. In ths case, Theefoe, the ecpocal tem n ou appoxmated absopton equaton of quaton 3 becomes:, 6 Thus, the specula ntensty fom the bottom laye by mage-based lghtng can be computed wth: I IB max specula Fbottom n, n 0, s. 7 To compute the dffuse component, we analytcally ntegated the ecpocal tem n quaton 3 ove the hemsphee wth ambet as follows: cos cos cos d 0 ddd cos sn cos cos 8 d cos. cos As a esult, the dffuse ntensty fom the bottom laye by mage-based lghtng can be computed wth: I IBdffuse bottom F n, n max 0, d. 9 Fgue 3 shows the esults and pefomance of ou layeed mateal mplementaton fo mage-based lghtng. Fgue 3a: Images wth a mateal that epesents lacque and coatng. Ou layeed-mateal system epesents ths knd of a complex appeaance vey well, even wth mage-based lghtng.

5 Fgue 3b: A pefomance compason. The mage on the left s endeed wth the sngle-layeed Blnn-Phong model and mage-based lghtng, takng 3.00ms on a PlayStaton 3. The mage on the ght s endeed wth the dual-layeed Blnn-Phong model wth the same lghtng, takng 4.8ms. 3. Oen-aya Implementaton The second model we mplemented s an Oen-aya model, because pue ambetan dffuse sufaces nfequently exst n the eal wold. specally fo ough mateals e.g. when shnness s less than 30, a matte dffuse epesentaton s moe mpotant than the specula component. Oen-aya was ntoduced n [Oen and aya 994] and was desgned as a dffuse eflectance model wth a ambetan suface and Toance-Spaow V-cavty model. Cook-Toance s a specula model usng the Toance-Spaow V-cavty model and t only takes nto account eflectons fom the mcofacets towads the vewe. As a esult, Cook-Toance s a elatvely smple model than Oen-aya, because Oen-aya has to take nto account ambetan dffuse eflecton hemsphecal eflectons fom all mcofacets. Snce the ntegal becomes much moe complcated, the Oen-aya model was numecally ftted to the ntegal n the pape. The Oen-aya model quaton 7 n the ognal pape s too complcated to evaluate n eal-tme, so we used the Qualtatve Model offeed n quaton 30 n the pape as follows:,, ; cosa B Max0,cos sn tan 0 0 A 0.5, B 0.45, Max,, Mn,, whee and ae pojected angles onto the tangent plane, s the dffuse albedo, 0 s the ncomng adance, and s oughness. In ode to make ths equaton shade-fendly, the equaton can be ewtten wth famla expessons and dot poducts as follows: , Max, Mn, Max0, Max,

6 As ths equaton stll seems too expensve to evaluate n a shade at un-tme, typcally t s appoxmated o some tems ae baked nto textues. Howeve, befoe fallng back on these methods, we ty to smplfy the equaton nstead. In quaton, thee ae max and mn functons n the squae oot n the numeato of the last tem. When s geate than, the max chooses and the mn chooses. In the othe case, the max chooses and the mn chooses. Snce these functons always choose and, the equaton can be smplfed as follows:, Max Max0, Fo the late opeaton, the fst s expanded as follows:, Max Max0, The factonal tem excludng the squae oot tem can be smplfed as follows:, Mn, Max 4 Mn,. Substtutng ths fomula nto quaton 3, the equaton then becomes: Mn, Max0, Recallng the elaton of cos n quaton 0 and, the elatonal expesson becomes: cos. 6 In ode to smplfy the left sde of the equaton, we deve anothe elatonal expesson fom quaton 37 and 38 n the ognal pape as follows: cos cos sn sn cos cos. 7 Rewtng ths equaton usng vecto expessons, the equaton becomes: cos 8

7 cos. Ths elatonal expesson can be substtuted nto quaton 5: Max0, Mn, And then, snce 0, quaton 9 can be smplfed as follows: Max0, Mn, Fnally, ths equaton has been damatcally smplfed fom quaton and t seems smple enough to evaluate n eal-tme. The fst tem contanng s just a weghted ambet and the next tem s the key component of Oen-aya. The last mn functon s the same tem as n ou Blnn-Phong model, whch appeas n the eumann-eumann geomety attenuaton facto [eumann and eumann 999]. Theefoe, many tems n quaton 0 ae eused fom othe pats of the shade. As a esult, ths model s computatonally nexpensve enough fo eal-tme. Both the specula and dffuse components ae based on the same mcofacet model as the Toance-Spaow V-cavty model. So, f the same shnness oughness value can be used fo both components, both the data sze and computatonal tme ae educed at un-tme. When the szes of mcofacets ae close to the wavelengths of the vsble lght, the behavos of the specula and dffuse components ae dffeent. Howeve, fo othe cases, they behave the same way, so the shnness specula powe values can be conveted to oughness values n quaton 0 usng followng equaton: shnness Ths equaton can be substtuted nto quaton 0 to smplfy t futhe:. 0.5 sh 0.45 sh. 0 Max0, Mn, sh sh Then, ths equaton s agan smplfed to make t GPU-shade fendly as follows: 0 Max0, Mn, sh. 0.sh As a esult, all squaes and two multplcatons can be emoved fom quaton 0. quaton 3 has been smplfed enough to use n eal-tme. Howeve, t s based on the qualtatve model of Oen-aya. Fgue 4 shows the dffeence between the qualtatve and ognal models. Ths gaph eveals poblems n the qualtatve model. The fst poblem s that the qualtatve model behaves the same as the ambet model causng a flat appeaance n the case of backwad lghtng. The second poblem s that the

8 model doesn t contan an nte-eflecton component, whch causes a slghtly dake appeaance. Fgue 4: The gaph of the dffeence between the qualtatve ed and the ognal models blue of the Oen-aya model. The hozontal axs s, whch means that the qualtatve model behaves the same as the ambet model n the case of backwad lghtng. To solve ths poblem, we adjust quaton 3 as follows: 0 Mn, sh. 0.sh We adjusted the coeffcent n the fst facton and emoved the fst max functon n quaton 3. Fgue 5 shows the dffeence between quaton 4 and the ognal Oen-aya model. Fgue 5: The gaph of the dffeence between ou slghtly mpoved ed and the ognal blue Oen-aya models. Ou slghtly mpoved model stll has a poblem on the left sde of the gaph. When caefully lookng at quaton 7 n the ognal pape, the coeffcent C s changed wth espect to the

9 sgn of cos -. Followng sut, quaton 4 can be modfed to: f 0 0 Mn, 0.65sh. 0.sh othewse sh. 0.sh Fgue 6 shows the esult of quaton 5. Compaed to the flat look wthn the qualtatve model, ou mpoved model can epesent smoothe appeaances close to those of the ognal Oen-aya model. 5 Fgue 6a: The gaph of the dffeence between ou mpoved ed and the ognal blue Oen-aya models. Ou model seems to be able to be futhe mpoved by adjustng the coeffcent n the fst facton n ode to get close to the ognal model. Howeve, ths gaph shows the value of functons n the case whee s 0.9. The amount of the nte-eflecton component changes wth espect to the albedo, so ths s plausble n pactce. Fgue 6b: A compason between the qualtatve left and ou mpoved ght models. It may be dffcult to dstngush the dffeence at a glance. Compaed to the qualtatve model on the left, the bottom sde of the oad wth ou mpoved model looks dake, as shown n the gaph n the Fgue 4a. ot only s thee a dffeence n bghtness, but ou mpoved model also makes the shadng esult che than the qualtatve model.

10 Fgue 6c: A pefomance compason between ou physcally based Blnn-Phong-ambet model left and ou Blnn-Phong-Oen-aya ght. Scenes ae endeed wth one dectonal lght on a PlayStaton 3 at 80x70. The left box s endeed n 0.97ms and the ght s endeed n.5ms. As mentoned n the layeed Blnn-Phong secton, mage-based lghtng fo Oen-aya s also mpotant because t s used wthn ou endeng ppelne to acheve aea lghtng. Howeve, t s dffcult to acheve mage-based lghtng fo Oen-aya usng envonment mappng, because quaton 5 s computed wth espect to, and. If t s mplemented usng envonment mappng wthn the shade, a mult-dmensonal cube map s equed. In ou case, snce dffuse shadng s appoxmated wth sphecal hamonc lghtng, we can use sphecal hamonc coeffcents to epoduce the behavo of the Oen-aya model. The Oen-aya model has some chaactestcs that ambet doesn t, such as a moe matte appeaance, vew-dependency, a shadowng/maskng facto, and an off-peak dffuse eto-eflectve component. We chose a few notable behavos that can be epoduced wth sphecal hamonc lghtng. A vew-dependent component s vey mpotant fo epesentng cetan dstnctve chaactestcs compaed to ambet, because t gves the feel of a vey ough specula component, despte beng only dffuse. The shadow and maskng factos change the bghtness of the shadng esult. A eto-eflectve component s dffcult to epesent wth low-ode sphecal hamonc coeffcents. If thee ae hgh-ode sphecal hamonc lghts, bendng the nomal vecto used fo fetchng the envonmental map would wok to epoduce the eto-eflectve chaactestc. Fstly, to epoduce the shadowng and maskng factos, a scale facto fo the DC component n the sphecal hamoncs s computed wth a late equaton. To that end, ntegatng the shadng model to analyze the behavo of shadowng and maskng factos s as follows: f, d 6

11 Fgue 7: Results of the ntegal n quaton 6 wth dffeent 0.0:blue, 0.5:ed, 0.5:yellow,.0:geen. Fgue 7 shows the esult of ths ntegal. We looked fo an equaton to ft ths ntegal and the esult s as follows: SH accos f sh g sh, 7 DC SH DC whee f sh and g sh 0.65sh. 0.sh. Fgue 8 shows the esult of ths equaton. Though the esult of ou ftted model s good enough, t s computatonally expensve because of the accos n the equaton. The followng equaton can be used as a compomse fo a eal-tme mplementaton: SH DC f sh g sh SH DC. 8 Fgue 9 shows the esult of ths equaton. The ft s not as good compaed to that of quaton 7, but t s faste to evaluate and close enough to epoduce the chaactestcs of Oen-aya. Fgue 8: The gaph of the ntegal esult wth =0.5 left and =.0ght. The blue lne shows the ntegal esult and the ed lne shows the ftted model. When lookng at the fgue, you can ecognze that ths shadng model volates the law of enegy consevaton. Although you can adjust the coeffcents n the shadng model to follow t, as a physcally based shadng model, t may beak the elatonshp between eal oughness values and the shadng esult of the Oen-aya model. Ths gaph shows the ntegal esults wth =.0. Ths model volates the law of enegy consevaton wth hgh values and a naow ange of values fo. If you use physcally easonable values especally fo ths model doesn t volate the law of enegy consevaton.

12 Fgue 9: The gaph of the compomsed equaton ed lne wth =0.5 left and =.0ght compaed to the ntegal esult blue lne. Secondly, to epoduce the chaactestc of the matte appeaance of Oen-aya, we analyze the behavo shape of Oen-aya cuves wth dffeent paametes. Wth the analyss n Fgue 0, the vaance of Oen-aya changes fom ambet wth espect to = 0 to a flat cuve wth espect to = and =. In ode to epoduce ths chaactestc, we deve the followng equaton fo the lnea components n sphecal hamoncs: S H S sh, 9 lnea SH lnea f s x S s, x f s. Ths functon S has followng chaactestc; t becomes.0 n the case whee = 0 wth = 0 o =. It becomes 0.7 n the case whee = wth = 0. It becomes 0.4 n the case whee = wth =. The value s lnealy ntepolated between paametes. If the lnea coeffcents n sphecal hamoncs become zeo, sphecal hamonc lghtng becomes a constant, whch means that the shadng becomes flat and matte. Ths equaton contols how matte the esult of sphecal hamonc lghtng s wth espect to and. Theefoe, ths equaton can epesent the vew-dependent matte chaactestc of Oen-aya. Fgue shows the esults of ou mplementaton of Oen-aya wth mage-based lghtng. = = 0 = 0 quvalent to ambet quvalent to ambet = 0.7 * ambet Compaatvely Flat Fgue 0: Analyss of Oen-aya wth dffeent paametes. Ths table epesents the elatonshp between dffeent and values n the case whee - s small enough nsde the plane of ncdence. Ths table demonstates ths chaactestc n exteme cases. If the aveage case s equed, you can modfy quaton 9 to halve ts effect.

13 Fgue : A compason of mage-based lghtng wth ou physcally based Blnn-Phong-ambet left and Blnn-Phong-Oen-aya ght. It may be dffcult to dstngush the dffeence wth ths sceenshot. The esult vaes wth espect to the vew angle, so you would be able to see the dffeence as the vew angle changes. The pefomance s.35ms left and.6ms ght on a PlayStaton 3 at 80x Applcatons A layeed shadng model, Oen-aya, and the combnaton of these models s both vey useful and pactcal to epesent the ealstc appeaance of eal-wold mateals. Fo example, though ou physcally based Blnn-Phong has smla chaactestcs to those of Cook-Toance and s enough to epesent human skn, some subsuface scatteng methods such as textue-space o sceen-space dffuson ae stll useful to epesent human skn shadng. These methods have become vey popula fo vdeo games ecently. Howeve, n the eal wold, human skn has a much oughe look than ambetan sufaces. If atsts ty to epesent ths matte appeaance just wth ambet and subsuface scatteng, they may apply too much tanslucency, causng a bluy appeaance. The esult looks lke a wax fgue. Fgue shows an exteme example of ths case. Ou layeed shadng model and the Oen-aya model both easly solve ths poblem. As a smple method to smulate human skn, the top laye s used to epesent sweat o ol, whch can poduce a shny appeaance, and the bottom laye s used to epesent the matte appeaance of human skn tself, wth a matte specula component and matte vew-dependent dffuse components due to the ough suface. ven though ths model can acheve moe natual esults than wth only ou physcally based Blnn-Phong-ambet o wth heavy subsuface scatteng, addng a small amount almost nvsble of subsuface scatteng helps add moe ealsm. Fgue 3 shows these esults. Fnally, Fgue 4 shows a pefomance compason wth dffeent confguatons of shades among ou poposed shadng models.

14 Fgue : A compason of ou physcally based Blnn-Phong model left and sceen-space subsuface scatteng ght. Too much tanslucency seems too bluy and much lke a wax fgue. Ths s an exteme example, exaggeated fo ease n ode to dstngush the poblem. Fgue 3: A compason of ou layeed model wth ou modfed Oen-aya model left, addng a small amount of subsuface scatteng ght. Both have moe natual esults than the esults n Fgue, and f savng computatonal tme s necessay, no subsuface scatteng left s moe acceptable than too much subsuface scatteng the mage on the ght n Fgue.

15 Blnn-Phong-ambet Blnn-Phong-Oen-aya ayeed Blnn-Phong-ambet ayeed Blnn-Phong-Oen-aya 6.87ms 7.7ms 7.55ms 7.8ms Fgue 4: A compason of ou layeed model and ou modfed Oen-aya model wth dffeent confguatons. The scene s endeed wth one dectonal lght and one mage-based lght on a PlayStaton 3 at 80x Concluson Ou poposed appoxmated laye model and modfed Oen-aya model ae both vey pactcal even fo cuent-geneaton consoles, whch mples that these models could be used as default models fo next-geneaton consoles. The combnaton of these models wth many lght methods and mage-based lghtng can dastcally mpove the ealsm of endeng esults wth an nexpensve endeng cost. Moeove, ou methods ae vey easy to mplement. Acknowledgements The autho would lke to thank Tatsuya Shoj fo helpng wth the eseach and mplementaton of these physcally based shadng models, and llott Davs, Shawn Wlcoxen and Stephen Hll fo evewng the pape and sldes.

16 Refeences [Blnn 977] James F. Blnn. Models of ght Reflecton fo Compute Syntheszed Pctues. Poceedngs of the 4th annual confeence on Compute gaphcs and nteactve technques, 977. [Cook and Toance 98] Robet. Cook and Kenneth. Toance. A eflectance Model fo Compute Gaphcs. SIGGRAPH, 98. [Oen and aya 994] Mchael Oen and Shee K. aya. Genealzaton of ambet s Reflectance Model. SIGGRAPH, 994. [eumann and eumann 999] ászló eumann, Attla eumann, ászló Szmay-Kalos. Compact Metallc Reflectance Models. Compute Gaphcs Foum, 999 [Wedlch and Wlke 009] Andea Wedlch, Alexande Wlke. xplong the Potental of ayeed BRDF Models. SIGGRAPH Asa, 009. [Gotanda 00] Yoshhau Gotanda. Pactcal Implementaton of physcally based shadng models at t-ace. SIGGRAPH, 00. [Wedlch and Wlke 0] Andea Wedlch, Alexande Wlke. Thnkng n layes: modelng wth layeed mateals, SIGGRAPH Asa, 0. Yasuho Fuj. A tny mpovement of Oen-aya eflectance model. 0.