Real-time Rendering of Enhanced Shallow Water Fluid Simulations

Transcription

1 Real-tme Renderng of Enhanced Shallow Water Flud Smulatons Jesús Ojeda a, Antono Susín b a Dept. LSI, Unverstat Poltècnca de Catalunya b Dept. MA1, Unverstat Poltècnca de Catalunya Abstract The vsualzaton of smulated fluds s crtcal to understand ther moton, wth certan lght effects restrcted or wth added computatonal complexty n the mplementaton f real-tme smulaton s requred. We propose some technques that mprove the renderng qualty of an enhanced shallow waters smulaton. To mprove the overall appeal of the flud representaton, lower scale detals are added to the flud, couplng external non-physcal smulatons, and advectng generated surface foam. We smulate caustcs by raytracng photons n lght and screen-space, and apply refracton and reflectons also n screen-space, through a number of render passes. Fnally, t s shown how a reasonably szed flud smulaton s executed and rendered at nteractve framerates wth consumer-level hardware. Keywords: real-tme reflectons and refractons, real-tme caustcs, flud renderng Introducton Photorealstc renderng s stll qute demandng for nteractve applcatons due to ts computatonal complexty. Otherwse, gven enough tme, offlne renderers can easly generate ths knd of magery, usually usng some algorthm of the raytracng famly. In the real-tme feld, however, GPUs are used whch mplement rasterzaton algorthms. These algorthms rely on hgh coherency for the operatons executed, whch mpose some constrants to smulate lght as a raytracer could do, by smulatng each separate lght beam. For ths reason, photorealstc renderng s acheved at nteractve framerates by smplfyng the algorthms used or even usng trcks that are perceptually feasble. Ths smulaton of lght behavour s requred f a realstc flud vsualzaton s pursued. Lquds, n ther vast majorty, exhbt reflecton and refracton effects, whch n turn may also result n caustcs. Assumng a vsualzaton over the flud, for great volumes of water, as open sea scenes, the major vsual effects one could expect may be the refracton of the underlyng terran wth projected caustcs, as well as reflected scenery from above the flud. Wth present flud smulatons beng performed n GPUs at nteractve framerates, we also need realstc vsualzatons whch reproduce these effects of the lght. In our case, we start from a heghtfeld flud smulaton enhanced wth partcles for the smulaton of splashes n breakng wave condtons, lke the ones proposed n [1] or [2], whch are also fully coupled wth dynamc objects. From there, we am to provde these expected, lght-based effects, namely refractons, reflectons and caustcs. Emal addresses: jojeda@ls.upc.edu (Jesús Ojeda), ton.susn@upc.edu (Antono Susín) As the flud smulaton mesh may have lower resoluton than that expected for hgh qualty results, t s also mproved wth other technques as lower scale detals and surface foam advecton whch effectvely ncrease the general appeal of the rendered scenes. The key contrbutons we propose are An extenson of the technque from [3] to screen-space, followng an ntal photon search n lght-space, as well as some other modfcatons for the smulaton of caustcs. A screen-space technque to smulate refractons and reflectons, based n raycastng through depth-maps. Texture-based technques for addtonal surface effects usng FFT ocean smulaton or Perln nose, as well as the advecton of surface foam generated at the splash partcles rentroducton. The result of these contrbutons s exemplfed n Fgure 1, and how they are nterlaced as an overall algorthm can be seen n Fgure Related Work There are two common approaches to smulate fluds: euleran and laplacan. The frst smulate the flud nsde a grd. In the second, the flud s mplctly represented by a partcle system. For a full 3D flud smulaton we can fnd many references of both approaches but for brevty reasons we refer the reader to [4], [5] and references theren for greater flud overvews. In the specfc case of euleran flud smulaton, the flud s usually represented as a scalar feld and ts vsualzaton s done by raycastng the volume or by usng mesh-extractng technques lke marchng cubes for further use. Nevertheless, 3D full smulaton can be stll qute costly, so other solutons as Preprnt submtted to Computers & Graphcs June 13, 2013

2 Fgure 1: Caustcs on the underlyng terran can be seen through the refractve surface of the flud. Flud Render Scene SS photonbased Caustcs Dynamc object couplng Lower scale detal effects Composton Heghtfeld Flud Partcles SS Raycasted Refracton & Reflecton Foam advecton Framebuffer Partcle Refracton Fgure 2: Ppelne of the dfferent parts nvolved n the renderng of enhanced shallow water smulaton wth partcles, provdng our screen space photon-based caustcs, screen-space raycasted refracton and reflecton, as well as other surface effects as lower scale detals and foam advecton heghtfeld representatons are more commonly used n the ndustry of real-tme applcatons. Such smulatons can come from procedural methods lke the FFT ocean smulaton [6], wave trans [7] or even physcal frameworks as the Shallow Water equatons [8, 2, 1]. Ther result, can be easly represented as a trangle mesh, where vertex heghts are provded by the own smulaton. As these grd-based approaches have a fxed resoluton, n order to ncrease the perceved level of detal, other technques have been appled as the advecton of addtonal textures to smulate flow [9], coupled wth normal mappng as n [2]. To fnally vsualze the flud, several lght-nduced effects have to be consdered. One of these effects are caustcs, whch are a very dstngushable effect from any refractve or reflectve surface. Startng from Kajya s work [10], caustcs have been tradtonally mplemented wth global llumnaton technques lke pathtracng, the metropols lght transport method [11] or photon mappng [12]. These technques requre a hgh count of rays or photons to acheve soft caustcs, whch relegate them to off-lne renderng, although there are already GPU mplementatons of some of them lke, e.g., [13, 14]. In the real-tme doman, [15] was the frst to explore caustcs usng synthetc texture maps; although naccurate, they were vsually compellng. Nevertheless, to acheve physcally realstc results, the more recent technques are nspred n pathtracng methods and can be generally classfed n two groups. In the frst group, technques lke, e.g, [16, 17, 3, 18], render from lght and create caustc maps, smlar to photon maps, but used lke shadow maps; reprojected n camera space n order to lt the vsble pxels that receve caustcs. In the second group, the caustcs are traced back from the recever object to the lght through lmted areas on the refractve surface as n [19, 20], whch usually requre the recever to be planar as a smplfcaton. Smlarly, for the smulaton of refractve or reflectve materals, the ground truth may be reached wth the usual pathtracng technques but n the real-tme doman trck technques, lke [21] whch apply a random offset to the refracted vector, are commonly used. [16] on the other hand reles on envronment maps as dstance mpostors to acheve approxmate refracton. However, for a more physcally accurate approach, the more complete technques nvolve tracng rays through depth maps. In ths sense, [22] smulated refracton usng front and back depth maps, whle later [23] mproved on the prevous technque by repeatng the search n between depth maps to smulate total nternal refracton. [24] also worked upon [22], mprovng t wth depth correctons, mpostors and caustcs. In contrast, we provde a full system for caustcs, reflectons and refractons as well as other effects to complete the flud renderng. For the caustcs, we mprove upon [3], addng a second raycast phase n screen space (from the camera) to the frst one used n lght space. Furthermore, we smplfy ther approach by not generatng a caustcs map, but splattng the photons on the recevng geometry. In the reflecton and refracton case, we specalze the refracton approach of [22, 23] to our flud scenes: we render the geometry over and below the flud separately and apply the same raycast algorthm to both buffers,

3 118 combnng the results usng Fresnel terms Flud smulaton In our case, we use the flud solver from [1], the smulaton algorthm s based on the the Lattce Boltzmann Method (LBM) for Shallow Waters. The flud s smulated n a grd and the nteractons between the flud molecules (descrbed as dstrbuton functons f ) are modeled as collsons. Usng the D2Q9 model, the LBM wth the popular BGK collson operator [25] can be defned wth the followng equaton: f (x + e t, t + t) = f (x, t) ω( f f eq ) + F, (1) where ω s the relaxaton parameter related to the vscosty of the flud, F are external forces and f eq s the equlbrum dstrbuton functon defned as f eq h ( (h, u) = gh 2 3 u2), = 0, λ h ( ) gh (2), 0, 6 + e u 3 + (e u) 2 2 u2 6 where λ = 1 for = 1..4 and λ = 1/4 for = g s the gravty and h and u are the flud propertes: heght level from the underlyng terran and velocty, respectvely. They are calculated as h(x, t) = f, (3) u(x, t) = 1 e f. (4) h Ths basc model s enhanced by applyng breakng wave condtons, an addtonal partcle system and two-way object couplng smlarly to [2]. Except the couplng wth external objects, smulated wth the Bullet Physcs lbrary, the whole smulaton s executed n CUDA and acheves nteractve tmerates. We refer the reader to [1] for a full revew on the smulated flud system, the breakng wave example shown n Fgure 3. As the flud s provded as a heghtfeld, ts basc vsualzaton can be a trangle mesh representng the whole doman, beng the vertces equally dsplaced n the xz plane and ther y coordnate the value of the heghtfeld at that pont. We use ths representaton, and apply some technques that enable more complex vsual effects as caustcs and refracton, whch aren t restrcted to ths Shallow Waters smulaton and may be appled to other refractve/reflectve surfaces. These technques are explaned n the next sectons. For the partcles, we render them as ponts, expanded to quadrlaterals and use depth and normal replacement, smlarly to [26]. For refracton, methods lke [21, 27] can be used. In our case we use the frst one, where an arbtrary offset s appled to the refracted vector from the partcle surface normal and used to look up at the framebuffer; although the results of ths arbtrary offset on the refracted vectors are not physcally correct, they are perceptually feasble and smpler to mplement than the latter one, for example (a) FFT ocean smulaton. (b) Nose, 4 octaves of a fractal sum. Fgure 4: Addng lower scale detals to the flud surface by normal mappng. Refracton and reflecton are deactvated. 3. Addtonal surface detal The heghtfeld smulaton has a fxed sze resoluton whch mposes a lmt on the detal scale that can be acheved. We can add other smulatons that mprove the detals by changng the surface normals locally. Furthermore, other advected propertes as, e.g., surface foam, can also be smulated and appled to the fnal vsualzaton. Ths secton wll ntroduce how these effects are accomplshed Lower scale detal From the heghtfeld of the flud surface we can extract approprate normals although they are restrcted to the smulaton resoluton. We can ncrease the detal of the flud just usng normal mappng. For example, [2] appled a normal map texture generated from the FFT ocean smulaton by [6] and advected t as n [9]. The FFT ocean smulaton from [6] s based on the computaton of the Fourer ampltudes of a wave feld. The fnal heghtfeld s obtaned from the nverse FFT to those ampltudes. In our case, we compute the FFT each frame and obtan a normal map from ts heghtfeld whch s then appled to the flud surface, as can be seen n Fgure 4a. An alternatve to the FFT approach s the use of nose textures wth the same goal at mnd. We can use gradent nose, beng Perln nose [28] the more popular, to obtan heghtfelds and compute normal maps from them to apply to the flud surface. Wth 3D nose, we can create the lluson of anmaton movng through one of the dmensons. However, nose textures have some nherent problems: t s not clear how to create a good water-lke functon and f tlng s requred, the pattern repettons are qute obvous, as shown n Fgure 4b Surface Foam In the real lfe stuaton where splashes are generated, lke n breakng waves, t s most probable that foam s generated when these splashes ht the flud bulk agan. In contrast to [2], where dffuse dsks are generated and advected wth the flud when partcles fall nto the surface flud agan, we smplfy the dea. Usng a floatng-pont sngle component texture mapped to the surface flud, we detect where a

4 Fgure 3: Breakng wave example from [1] Fgure 5: Foam s generated at partcle-surface ht ponts and advected n successve frames usng the flud s velocty. partcle has fallen and ntalze that texel to a certan maxmum tme-to-lve (TTL) for the foam. Ths texture s then advected usng the flud s velocty feld, tracng back as n [29]. Each frame, the values of the texture are decreased t untl they become 0. These values are then multpled wth the desred foam color and mapped to the flud mesh, resultng n the blended foam. Usng a texture for the foam ntroduces a constrant, however: ts resoluton should be dctated by the sze of the partcles as, t could happen that more than one texel should be ntalzed, dependng on the partcle to texel sze rato or, conversely, that the texels are too bg for the partcle sze. Overall, as seen n Fgure 5, the results are convncng and the computatons are faster due to the lmted requrements, whch make t deal n real-tme applcatons. 4. Photon-based Caustcs In order to add caustcs to our real-tme flud smulaton, we follow the same path of [3] and extend ther work. They raycast a grd of photons, as ponts, through the scene n an orthographc space defned at the lght source, whch also allows them to easly add shadow mappng. One restrcton they have s that the depth map used n the raycast phase should be contnuous or, at least, wth no great jumps. Other lmtatons ths technque has are the same as mage-based renderng: the results depend on the resoluton of the textures used, whch n ths case restrcts where the photons can end wthn the scene. Our contrbutons to ther algorthm mply extendng the raycast of photons out of the lght space to screen space, splat tng them orented wth the surface of the recevng mesh. In contrast to [3], we do not generate a caustcs map; the splats are blended wth the scene, varyng ther ntensty dependng on the orentatons of the caustc generatng flud poston, as well as the dstance the photon has travelled nsde the flud. As our flud smulaton s represented just by ts surface, we restrct our approach to refracted photons whch wll fall n the underlyng terran and gnore reflected ones. The multpass algorthm can be summarzed n the followng steps: 1. Render the objects of the scene (excludng the flud) from the camera and store depth and normal maps. 2. Render the objects of the scene (excludng the flud) from lght wth an orthographc projecton and store the depth map. 3. Render the flud from lght wth the same orthographc projecton as before and store the world postons and refracted drectons at each pxel. 4. Render the grd of photons. The prmtves used are ponts whch wll be expanded to quadrlaterals when a fnal poston s found. Ths grd of ponts has the same resoluton as the orthographc projecton used prevously n Step 2. In a vertex shader, the vertces wll be raycast frst n lght space usng the depth map from Step 2. If there s no ntersecton found,.e., the photon exted through a wall of the frustum, the raycastng wll be repeated n camera space. If there s not an ntersecton yet, the pont s dscarded (rendered out of frustum). Otherwse, f an ntersecton s found at lght space, t s transformed to camera space and checked for correctness: If the pont s occluded n camera space, t s dscarded. Else, f the pont s not occluded and the depth does not match between lght and camera spaces, the raycastng contnues from the actual pont poston n camera space. Else, the pont s correct, that s, the depths match between lght and camera spaces, thus the pont s fnal. When a fnal pont s found, from the prevous condton or from the camera raycastng, the normal s looked up n the normal map from Step 1. In a geometry shader, the ponts are expanded to quads orented wth ther assocated normal. Fnally, n the fragment shader, the photons are textured wth a

5 Gaussan splat, and ther ntensty s regulated dependng on how they are facng the lght and the dstance they have trav258 elled through the flud untl fnally ht the recevng surface. At 259 last, they are blended to the contents of the framebuffer. 260 We have not mplemented shadows to keep the algorthm 261 smple but, as suggested n [3], shadow mappng s easly added 262 as the depth map from lght s already stored for the raycastng. 263 As can be seen n Fgure 6, the vsual results are good enough 264 for real-tme renderng and the photons are not restrcted to the 265 lght space. For a full physcally-based render, the precse rad266 ance of the photons should be computed. In order to make the 267 algorthm more approachable, we just regulate the photons con268 trbutons wth ther orentaton and user parameters as they are 269 just blended wth the framebuffer, whch allow the technque to 270 be faster n comparson, because we don t need the expensve 271 operatons for gatherng the photons Screen-space Refracton and reflecton Smlarly to the caustcs approach, we mplement refracton and reflecton raycastng through depth maps, n the same way 275 of [23]. 276 For smplcty, we want to be able to use the same raycastng 277 algorthm for both refractons and reflectons, so we mprove 278 upon prevous works by renderng n separate buffers what s 279 above and below the flud. Ths allows to, usng the same code, 280 just look for ray-depth ntersecton n the approprate buffer to 281 obtan the result and do a fnal composton wth both refrac282 tons and reflecton as needed. 283 In ths case, rays are cast from camera and reflected or re284 fracted (or both) when they ht the flud, as shown n Fgure Here, we also use a multpass algorthm that can be ex286 planed n the followng steps, always renderng from camera: Render the flud mesh and store the depth buffer. 2. Usng two render targets (RT) named over and below, whch wll store color and depth, we render the objects of the scene (dynamc objects and ground n ths case) and compare the depth wth the prevously stored. If the depth s greater, the fragment s stored n the below RT, otherwse n the over one. Ths pass can be thought as a stencl test, whch separates what s above o below the flud surface. 3. Render the flud agan, usng the RTs. For each fragment of the flud two rays are cast: one for refracton (usng RT below ), one for reflecton (usng RT over ). As the rays start from the camera, f the reflected/refracted rays should come back, they are dscarded. The results of both raycasts are combned usng Schlck s approxmaton [30] to Fresnel terms for smplcty. 4. Fnally, to avod the repeated render of the other objects of the scene, we just use a screen-szed quadrlateral textured wth the color buffer from the over RT. Fgure 6: Caustcs n the ground below the flud surface wth planar (boat) and nosy (buoy) terran. To reduce somewhat the need of the double raycastng, we can compute the Fresnel term from [30] pror to the raycastngs at Step 3 as F = F0 + (1 F0 )(1 θ)5, (5) 5

6 Reflectons Refractons Fresnel composton + Fgure 7: Reflectons and refractons are found from the raycastng two dfferent depth maps and fnally composed usng Fresnel for the fnal renderng. beng θ half the angle between the ngong and outgong lght drectons and F0 the known value of F when θ = 0, the re308 flectance at normal ncdence. As we use the value F for a 309 lnear nterpolaton between the refracted and reflected colors, 310 we can mpose a threshold such as: If F <, only the refracton raycastng s executed. 312 If 1 F <, only the reflecton raycastng s done. 313 Otherwse, both raycastngs are done. Addtonally, for zones where the flud heght s qute low, controlled by an user parameter, we get the color from the d316 rect vew ray and nterpolate from t to the combned color ob317 taned from the prevous algorthm, usng the depth dfference 318 between the flud and the ground below t. Ths allevates some 319 vsble artfacts caused by the trangular mesh used for the flud 320 renderng, as shown n Fgure Everythng s done n screen-space, so there may be zones 322 where there s not enough nformaton,.e., a ray should ht a 323 pont n space not vsble; n those cases we detect the jump n 324 the depth map and make use of the last pxel wth nformaton 325 n the texture. Although ths s really a problem due to lack 326 of nformaton, t may reman greatly unnotced wth the an327 mated lower scale detal technques of Secton 3.1 and the own 328 movement of the flud surface Results and Dscusson We have tested the prevous algorthms on an Intel Core2Duo E8400 wth 4GB of RAM and a Nvda GTX280 runnng Ubuntu The resultng averaged tmngs of the caustcs and re333 fracton/reflecton algorthms are shown n Table 1, as these are 334 the ones that tax more on the GPU by the use of raycastng. 335 An mprovement to the normal mappng for lower scale de336 tal technque could be provded by also applyng the technque 337 from [9], n whch multple sets of texture coordnates are used 338 and advected, already exploted n [2] Fgure 8: Artfacts from the flud s trangular mesh on the left, allevated on the rght by nterpolatng the color value between the flud s color and the ground color dependng on the vew dstance from surface to ground. 6

7 Vewport Caustcs Refracton & Caustcs Sze Resoluton Reflecton Table 1: Averaged tmngs n mllseconds for frame for the caustcs and refracton/reflecton algorthms. The Vewport column ndcates the vewport resoluton. Smlarly, the Caustcs Resoluton column ndcates the sze of the vewport used for the orthographc camera, and thus, the number of photons traced. The foam smulaton from [2] could solve the fxed-sze texture restrctons of our current soluton, as they smulate foam drectly wth advected dffuse dsks on the flud surface, although ths comes at the addtonal cost of generatng and mantanng these dsks on the fly. An alternatve we beleve would help our foam smulaton s the use of a pyramdal texture approach; when partcles fall to the flud they ntalze the correct level of the pyramd, beng the other levels ntalzed extrapolatng from that one. Nevertheless, the tmng results for both these technques combned, the lower scale detal and the foam advecton, never exceed the 2ms mark. For the caustcs, as shown n Table 1 and concluded n [3], the performance of the caustcs algorthm depends prmarly on the sze of the grd of photons, but n our case also on the drecton of the lght, whch can cause more photons to mss the lght space raycast and use the second camera space one, thus ncreasng the number of computatons and texture fetches needed to try to fnd a fnal poston for them. Also, as the raycastng s done n the vertex shader t s further slowed down because of the ncreased penalty of texture fetches n that shader stage. Although a drect comparson wth [3] s dffcult because of the dfferent hardware used, they reported to acheve about 200fps wth a photon grd, whch s the same that sayng that each frame costs 5ms to compute. Wth newer hardware but the dual lght and camera space raycasts we propose, the cost of computng caustcs s, n our case, below 2ms for the same confguraton. As the number of photons s lmted, there may be zones over or undersampled; a herarchcal soluton could help to solve ths problem as shown n [18, 31], but we would requre that t remans hghly dynamc, as we are adressng the vsualzaton of a movng flud. Another thng worth researchng would be to extend these caustcs, f possble, to volumetrc ones as those n [32]. The performance of the refracton/reflecton algorthm s qute varable, t depends on the sze of the vewport as well as the coverage of the flud n screen: the more vsble pxels, the more rays are cast. For far comparson, the results n Table were captured wth the flud coverng the whole vewport, and even n ths case, the whole algorthm does not cost more than 10ms for a reasonably szed vewport. In perspectve, [23] made total nternal refracton avalable although wthout surface reflecton whch, n the best case, reported 138fps,.e., 7.24ms per frame on a Nvda 8800 GTX, usng only one bounce for nternal refracton on a vewport of Although our GPU s newer than thers, n a smlar scenaro, we acheve less than half ther tme wth both refracton and reflecton. Evdently, the restrcton of the refracton/reflecton algorthm beng a screen-space technque lmts how much nformaton s avalable for such refractons and reflectons. The smplest soluton to ths would be the use of envronment maps, but, as the heght of the flud can be qute dfferent across the doman, the poston where the envronment maps were generated would constrant, and even clp, possble geometry for correct refractons or reflectons. Other alternatves should be consdered to solve ths lmtaton. Both algorthms, caustcs and refracton, may also suffer other performance penaltes dependng on the tessellaton of the objects of the scene n queston. Ths s due to the multpass character of the algorthms and the requrement of the renderng of the scene to obtan the depth maps for later raycastng. Although we have not encountered ths problem n our tests due to low polygonal complexty, t should be worth havng n mnd. As a note, the boat model has 300 trangles, the buoy has 11k, the dolphn has 4k and the flud and the ground have 32k trangles each. Fnally, the partcles have just been rendered as bllboards usng depth and normal replacement wth a sphere model. As they represent splashes, we want to mantan ther crsp representaton so, to mprove ther appeal, some addtonal tweakng could be done as applyng some nose to ther normals or deformng them n the drecton they are movng to smulate some moton blur. Fnally, we have only taken nto account the vsualzaton of the surface of the flud, as shown n Fgure 9, n the future t should be also a key pont to research water renderng as n, e.g., [33], n order to provde a full featured vsualzaton. 7. Conclusons In ths paper we have presented a full ppelne of dfferent algorthms for the renderng of heghtfeld-based flud smulatons coupled wth partcles, although the dfferent parts can be appled to other stuatons as well. The complex lght-related effects lke caustcs, refractons and reflectons have been adressed usng raycastng technques whch ensure a more realstc smulaton and the constrant of the algorthms to be n screen-space keeps the quantty of memory used low enough. Addtonally we have appled foam and lower-scale detal by applyng textures to the flud mesh; technques whch are very low demandng n comparson to the prevous ones and really help to enhance the fnal result. 7

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