Practical Implementation at tri-ace

Transcription

1 Physically Based Shadig Models i Film ad Game Productio: Practical Implemetatio at tri-ace 1. Itroductio Yoshiharu Gotada tri-ace, Ic. I this paper, we preset our practical examples of physically based shadig models that we implemeted. I the game idustry, traditioal ad-hoc shadig models are maily used because of performace, though recetly, physically based models have bee attractig more attetio. I our studio, artists had some difficulty settig parameters for physically correct materials usig the followig ad hoc shadig model: σ = R ( N L) + R F( f)( N L)( N H G, (1) d s ) where R d is the diffuse color, R s is the specular color, N is the ormal vector, L is the light vector, H is the halfway vector, F ( f ) is the Fresel fuctio, ad is the cosie power that is ofte called shiiess which represets the roughess of a surface. Lastly, G is the geometry atteuatio factor. Some of the above parameters are typically stored i textures. The huma eye does t perceive light liearly ad the brai recogizes the brightess of light i o-liear space (similar to logarithmic space) with a high dyamic rage. O the other had, display devices used for video games typically have a 8-bit color resolutio which is isufficiet to represet real world, high dyamic rage, light itesity. Due to these two reasos, artists ca set material parameters icorrectly via their ituitio, eve though the real world material properties have more dyamic variace. For example, if there is a object that has a 1, times stroger specular tha aother object, a artist may set oly a 1 times stroger specular parameter, because the artist felt that was the correct value. I our case, this problem ofte happeed by the Fresel parameter beig icorrectly set. For our implemetatio, we used Schlick s approximatio [1] as show i Equatio. The approximatio is faster tha the origial equatio ad produces a good shadig result. F( f = f + f E H. () 5 ) (1 )(1 ) f is the ormal specular reflectace. This ca be computed with: 1 f =, (3) 1+ where is the complex refractive idex 1. For typical dielectric materials, is betwee 1.3 ad 1.7. Usig the average value of 1.5, f evaluates to.4 ad Equatio evaluates to.4 i the ormal directio ad 1. i the directio perpedicular to the ormal. As a result, the reflectio ratio betwee the ormal ad glacig directios becomes 5. Sice such a large specular variace is ot ituitively acceptable for artists, they icorrectly set a value like.3 or.5 to f. This causes the specular i the ormal directio to become too 1 If is a complex umber, it is importat that this equatio be calculated usig as a complex umber.

2 strog compared to reality. The artist the seses somethig is t right ad reduces specular itesity to try ad compesate. Cosequetly, this leads to specular at glacig agles becomig too weak. As a typical example, because the specular at glacig agles is weak, the highlight o the edge of a back lit object caot be accurately represeted. As a solutio, we chaged parameters i our tool to use either complex refractive idices,, or prebuilt material templates such that artists do ot have the opportuity to provide icorrect iputs for the Fresel equatio. Compared with these issues, physically based shadig models allow us to easily maipulate the parameters. We ca reduce the umber of parameters or textures ad the shader still produces physically correct results.. Customized Bli-Phog model The followig equatio is our BRDF model based o the Bli-Phog model [] : R ( ) F ( f)( N H ) d + spec ρ = ((1 Fdiff ( f) ) +. (4) π max( N L, N E) 4π ( ) F diff ( f ) ad F spec f ) are Fresel fuctios. We used Schlick s approximatio for them: ( F diff F spec ( f = L, (5) 5 ) f + (1 f )(1 N ) ( f = H. (6) 5 ) f + (1 f )(1 E ) The BRDF show i Equatio 4 basically follows the laws of eergy coservatio. However, the fuctio violates reciprocity i the diffuse term for performace. The ormalizatio factor ( + ) / 4π ( ) is calculated with our specular BRDF with Neuma-Neuma BRDF [3] as: f r _ spec ( H N) =. (7) max( N E, N L) I order to acquire the ormalizatio factor, this BRDF with the cosie term is itegrated ad must satisfy the laws of eergy coservatio as follows: ( H N) ( N L) c dω 1. (8) Ω max( N E, N L) Choosig c i this iequality to satisfy the eergy coservatio requiremets, the ormalizatio factor ca be computed. Sice itegratig the itegral aalytically over all light ( L ) directios is impossible, we assume that the maximum reflected eergy occurs whe L = N. Therefore the iequality becomes: ( H N) c dω 1. (9) Ω max( N E,1)

3 However, N E is always less tha or equal to 1 ad the iequality ca be simplified to: The the reciprocal of c becomes: Ω c ( H N) dω 1. (1) ( H N) Ω π π π = dω θ (cos ) siθdθdϕ 4π ( ) =. (11) + This ormalizatio factor is a little expesive to compute i real-time, therefore we approximate it with a liear fuctio. The coefficiets of the liear fuctio are determied usig the least square method by fittig them i the rage of = to 1,: (1) 4π ( ) Figure 1 shows the differece betwee the origial ormalizatio factor ad the approximated oe. Figure 1: Normalizatio Factor Compariso. The blue lie is the origial factor ad the red lie is the approximated factor with the liear fuctio. The graph oly shows the factor betwee shiiess of ad 1. The error betwee shiiess of ad 1, is almost egligible. The diffuse term i our BRDF model is a approximatio of a more physically correct model. First we assume that the diffuse compoet is a perfect lambertia. The, the icidet light reflects as specular ad diffuse reflectios at the shadig poit. (I this case, we do t thik of other types of reflectios.) The amout of specular reflectio is decided by the Fresel equatio with respect to the reflectio agle. Due to eergy coservatio, the diffuse compoet ca be computed as the rest of specular reflectio. The reflectio agle is equivalet to the icidet agle, so the Fresel equatio i the diffuse term is calculated with respect to the icidet agle. This is obviously a wrog assumptio because it violates the reciprocity. It is ot a assumptio from physics, from simplicity for performace.

4 However, the diffuse term is a little expesive ad approximatig it oly produces subtle differeces. Therefore, the diffuse term is also approximated i our fial implemetatio as: R Fspec( f)( N H ) d ρ = (1 f) + ( ). (13) π max( N L, N E) Figure shows rederig results with our customized BRDF. Figure (a): A compariso oly with a shiiess map. The left steel frame is redered with a ad-hoc model ad the right oe is redered with our model. The right frame looks more atural compared to the left frame, though it looks a flat material. Figure (b): A compariso oly with a reflectace map. The steel frames from the top left are redered with a ad-hoc model, our model ad our spectral model. The texture is used as a specular color map for the ad-hoc model that looks like it is just varyig the desig of the steel frame. Compared with it, our model looks to have more varied surface materials. Moreover, spectral model represets rust well. The BRDF model show i Equatio 13 is isotropic. I order to cover other types of materials, we implemeted other variatios of models which are aisotropic, spectral ad metal versios. Because of the performace reasos, the basic model oly covers isotropic, moochrome (o-spectral) ad dielectric materials. The aisotropic model supports two differet shiiess parameters alog with the taget vector ad

5 biormal vector. The spectral model supports three differet f parameters, especially for materials which have differet refractive idices at differet wavelegths. The metal model[4] is desiged for materials which have a complex refractive idex especially with a large imagiary umber. The Fresel fuctio for these kids of metals has a distictive curve compared to other materials. Figure 3 shows rederig results of these variatio shaders. I additio to the BRDF model based o the Bli-Phog model, we also implemeted other BRDF models such as Ashikhmi-Shirley[5] model, Marscher[6] model ad Kajiya-Kay[7] model. Figure 4 shows rederig results of these shaders ad comparisos with our Bli-Phog based shaders. Figure 3(a): The left steel frame is redered with a ad-hoc model ad the right oe is redered with our spectral model. Both frames have all textures such as reflectace, shiiess maps, etc. With respect to the steel part ad rusty part of both steel frames, it s easier to otice the differece betwee the materials o the right oe. Figure 3 (b): From the left: (a) ad-hoc model vs. our model, (b) ad-hoc model vs. spectral model. The left object uses a ad-hoc model ad the right object uses our model i both images. I the image (a), reflectace is chaged with respect to the black ad yellow pigmets i the sig. However, with the ad-hoc model, the black ad yellow pigmets look like they use the same material. Differet materials are redered well for the drum o the right usig a reflectace map.

6 Figure ３ (c): Comparisos of our metal model ad spectral model. The top bolts are redered with our spectral model ad the bottom bolts are redered with our metal models. Materials from the left are alumium, copper ad titaium. Specular reflectio looks slightly differet. Figure 4 (a): The hair of the left character is redered with Marscher model ad the hair of the right character is redered with Kajiya-Kay model. Figure 4 (b): The wheel o the left is redered with Ashikhmi-Shirley model, the wheel o the right is redered with our aisotropic model. Our aisotropic model ca achieve the close result with a less computatioal cost tha Ashikhmi-Shirley model.

7 3. Ambiet Shadig Improvemet Implemetig the physically-based shadig models itroduced i the previous sectio, the quality of typical materials ca be drastically ad easily improved. However, i typical game egies, these BRDF models are used for direct (puctual) light sources such as directioal, poit ad spot lights. Although deferred based shadig or lightig techiques are becomig popular, multiple BRDF models do t get alog well with deferred based techiques because differet BRDF models icrease the umber of deferred shadig passes or require dyamic braches i the deferred shader. Whether usig forward shadig or deferred shadig, ambiet lightig is still importat for real-time rederig i games. However, because ambiet lightig has bee iveted for performace, ambiet lightig typically has a differet pass from direct light shadig. There are two stadard implemetatios for ambiet shadig. Oe is oly treatig oly the diffuse term with ambiet light. With this simplificatio, objects that oly have a specular compoet such as metals are redered completely black i a scee that oly uses ambiet lightig. The secod implemetatio solves the problem of the first by usig oe arbitrary costat betwee diffuse ad specular terms. I both implemetatios, the ambiet term is computed as a costat ad is view idepedet; though if it existed i the real world, it should be computed as spherical area lightig with a proper BRDF. As a result of the ambiet shadig simplificatio, rederig quality degrades i scees maily lit by ambiet light such as shadowed areas, the iside of a house lit oly by daylight (o artificial lights), cloudy outside areas, etc. Figure 5 shows a sample scee with this problem. Figure 5: A scee with oly ambiet lightig. Because there are o specular compoets, material differeces are difficult to see. O the other had, ambiet lightig has bee improved. I the past, ambiet light was a costat color vector i the scee ad the color vector was same for every pixel ad/or vertex. Recetly, ambiet lightig color has bee chaged to be depedet o locatio 3. Examples would be Hemisphere lightig, Spherical Harmoic (SH) lightig [8][9], ad Ambiet Occlusio [1]. Hemisphere lightig or SH are oe of the most reasoable approximatios of spherical area lightig ad are widely used for real-time rederig. SH coefficiets, 3 If the calculatio is doe o the CPU the the object locatio is used. If doe o the GPU the the vertex or pixel locatio is used.

8 irradiace [11], or values similar to irradiace are stored i a voxel structure ad lightig vectors are iterpolated accordig to shadig positio. These kids of techiques are widely used i pseudo real-time global illumiatio. However, these improvemets for ambiet lightig oly chage icomig light accordig to the shadig poit. Eve if physically correct material parameters are set for every object, they seem to have the same material i a scee domiated by ambiet lightig. Figure 6 shows objects with variety of materials usig ambiet lightig ad ambiet occlusio. Figure 6: Screeshots redered with oly ambiet lightig. Compared to other screeshots with direct lightig, it is difficult to distiguish material differeces. I the real world, though it is also difficult to distiguish. Artists oticed this problem from the begiig. I oe project, eve though they tried paitig ambiet occlusio or ormal mappig textures carefully, quality oly margially improved. Therefore, they solved the problem by placig secodary lights, like rim lights or fill lights, maually. I aother project, a artist built a origial shader that improved quality usig our highly flexible shader system [1] [13]. However, both solutios were based o artists ituitio ad were ot physically correct. For solvig the previously metioed problem, we came up with a ovel BRDF model called Ambiet BRDF. After implemetig this model, ambiet shadig computes the specular ad diffuse compoets properly ad the ambiet term is o loger a costat. I other words, ambiet lightig is regarded as area lightig i our shader. I practice, first we itegrated a BRDF itegral as: f, f, ω ) = ρ(, f, ω, ω )( N L) dω Ω (, (14) where ρ is a BRDF model, is shiiess, f is ormal specular reflectace, ω is the eye vector ad ω is the light vector. I our case, the specular term i Equatio 13 is used for computig the specular compoet of the fuctio ρ. Sice this itegral is difficult to itegrate aalytically, we itegrated it umerically offlie ad stored it i a liear (o-swizzled) volume texture. For creatig the texture, we developed a applicatio that was firstly used for the experimet of our ambiet BRDF models. After that, we tried both a liear texture ad swizzled texture, ad the liear texture was faster. With our texture, the U coordiate represets E N, the V coordiate represets shiiess, ad W coordiate is used for f. Figure 7 shows the volume texture computed by our implemetatio. The volume texture stores the specular term itself ad is directly used as the specular term i a pixel shader. The diffuse term computatio is approximated with R ( 1 d specular term) but ideally, it should be stored i aother texture because due to

9 geometry atteuatio, (specular term + diffuse term) does ot always equal oe. If this approximatio is used, the reflectace gets too strog at glacig agles; however, we used it for performace. Figure 7: Part of the volume texture computed by our applicatio. With the itegral, oly specular ad diffuse terms ca be computed. Therefore, the ambiet shadig result will vary due to material parameters ad viewig agle. For a more realistic result, we computed the color terms of ambiet light. Whe usig Spherical Harmoics, the diffuse lightig color vector is evaluated with a ormal vector ad the specular lightig color vector is evaluated with a reflectio vector. For both vectors, the color could be approximated depedig o the umber of SH coefficiets. Sice the specular compoet requires a lot of coefficiets ad o specular cosie lobe is take ito accout, the specular color i ambiet shadig is coarsely approximated. Whe usig image based lightig (eviromet map), the diffuse lightig color vector is computed with a diffuse cube map or SH coefficiets which are calculated from a eviromet map. The specular color vector is computed with a pre-filtered mipmapped eviromet map. For spectral materials, we fetch the texture three times with differet f. For aisotropic materials, we fetch the texture with the average of two differet shiiesses. If we implemet aisotropic ambiet BRDF with texture, we eed 4D texture. Therefore, we decouple the 4D texture to two 3D textures. However, compared to the differece betwee this experimet ad the average versio, we thought that it was too costly. As a result, we decided to use the curret implemetatio. Figure 8 shows results of rederig with Ambiet BRDF ad Figure 9 shows a performace compariso. Figure 8: The image o the left was redered without Ambiet BRDF ad the image o the right was redered with Ambiet BRDF. The both images were redered with oly ambiet lightig. I the right image, the shadig result from the specular compoet was added o the edges of the tire or wheel. As a result, the right image s material differeces are slightly more recogizable tha the left image.

10 Ad-hoc model Customized model Aisotropic model Spectral model Metal model Ashikhmi Ambiet BRDF off Ambiet BRDF o N/A Figure 9: Performace of differet shaders is compared with the scee show o the image. The umbers idicate rederig times i millisecod o GPU for PlayStatio 3. Each object has a albedo map, ormal map ad combied map (R: Reflectace, G: Shiiess). The scee is redered by 18x7. 4. Limitatios ad future work Our customized physically-based Bli-Phog model does t hadle reciprocity ad roughess i the diffuse compoet. The diffuse roughess compoet is very importat for some materials. Ore-Nayer or other approximatio models would be ecessary to achieve higher quality results. Additioally, multi-layered BRDF is ot supported. A sigle layer BRDF is ot eough to represet objects with coatig, orgaic materials, ad so o. We will eed to implemet multi-layered BRDF models i real-time. Our Ambiet BRDF model is oly a approximatio; i the future we ca compute more accurate real time represetatios o more powerful GPUs. 5. Coclusio With physically based shadig models, artists ca easily maipulate parameters ad textures compared to ad-hoc models. Physically based shadig models are fast eough to ru i real-time, allow us to reder realistic images, ad give us true HDR images. The Ambiet BRDF model automatically improves image quality i a scee domiated by ambiet lightig istead of usig ad-hoc methods such as placig secodary lights. As a result secodary lights like rim lights or fill lights ca be used for their origial purposes. Lastly, Figure 1 shows rederig results.

11 Ackowledgemets The author would like to thak to Tatsuya Shoji for helpig with the research ad implemetatio of physically based shadig models, Bart Sekura ad Elliott Davis for reviewig the paper ad slides, Keichi Kaekura, Kazuki Shigeta, Keichi Kaeko ad Ryo Mizukami for creatig beautiful graphics samples, ad my fellow course speakers, especially Nathaiel Hoffma for reviewig. Refereces [1] Christophe Schlick. A Iexpesive BRDF Model for Physically-based Rederig. Computer Graphics Forum, 13(3):33-46, [] James F. Bli. Models of Light Reflectio for Computer Sythesized Pictures. Proceedigs of the 4th aual coferece o Computer graphics ad iteractive techiques, [3] László Neuma, Attila Neuma, László Szirmay-Kalos. Compact Metallic Reflectace Models. Computer Graphics Forum, 1999 [4] Istvá Lazáyi, László Szirmay-Kalos. Fresel Term Approximatio for Metals. I Short Paper Proceedigs of WSCG, pp.77-8, 5. [5] Michael Ashikhmi ad Peter Shirley. A Aisotropic Phog BRDF Model. UUCS--14,. [6] Stephe R. Marscher, Herik Wa Jese, Mike Cammarao, Steve Worley ad Pat Haraha. Light Scatterig from Huma Hair Fibers. ACM Trasactios o Graphics,, 3(July), 81-9, 3. [7] James T. Kajiya. Aisotropic Reflectio Models. I Proceedigs of SIGGRAPH 85, ACM Press, 15 1, [8] Robi Gree. Spherical Harmoic Lightig: The Gritty Details [9] Peter-Pike Sloa, Ja Kautz, Joh Syder. Precomputed Radiace Trasfer for Real-Time Rederig i Dyamics, Low-Frequecy Lightig Eviromets. ACM Trasactios o Graphics 1, 3, ,. [1] S. Zhukov, A. Ioes, G.Kroi. A ambiet light illumiatio model. I Rederig Techiques 98 (Proceedigs of the Eurographics Workshop o Rederig), 45 55, [11] Gee Greger, Peter Shirley, Philip M. Hubbard, Doald P. Greeberg. The Irradiace Volume. IEEE Compute Graphics & Applicatios, 1998 [1] Yoshiharu Gotada, Tatsuya Shoji. Shader Karijirei Jiyudoto Hikikaei (Postmortem of Shader Maagemet). I CESA Developers Coferece, 8.

12 [13] Yoshiharu Gotada. STAR OCEAN 4: Flexible Shader Maagemet ad Post-Processig. I Game Developers Coferece, 9. Figure 1: The images o the left are redered with our physically based shadig models ad the other images o the right are redered with ad-hoc models. Due to our artists good work, the right images still look very good. The left images keep cosistet material appearace with all kids of lightig such as daylight, suset, or uder shadow.

13 Appedix Shiiess 1 Shiiess 1 Shiiess 1 Shiiess 1 Shiiess Map Box (AB OFF) Box (AB ON) Sphere (AB OFF) Sphere (AB ON) Teapot (AB OFF) Teapot (AB ON) Table 1: Ambiet BRDF compariso with differet settigs. Each colum shows differet shiiess settigs. Each row shows differet objects ad Ambiet BRDF settigs (ON or OFF). Images with Ambiet BRDF look surrouded by the area light.