Spherical Billboards and their Application to Rendering Explosions

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1 Spherical Billboars an their Application to Renering Explosions Tamás Umenhoffer László Szirmay-Kalos Gábor Szijártó Department of Control Engineering an Information Technology Buapest University of Technology, Hungary Planar Spherical Planar Spherical Figure 1: Comparison of the classical planar an the propose spherical s ABSTRACT This paper proposes an improve renering metho that splats particles as aligne quarilaterals similarly to previous techniques, but takes into account the spherical geometry of the particles uring fragment processing. The new metho can eliminate clipping an popping artifacts of previous techniques, happening when the participating meium contains objects, or the camera flies into the volume. This paper also iscusses how to use spherical s to rener high etail explosions mae of fire an smoke at high frame rates. CR Categories: I.3.7 [Three-Dimensional Graphics an Realism] Keywors: Billboars, particle systems, shaer programming 1 INTRODUCTION Participating meia [2] or volumetric moels are often represente by particle systems [12]. The basic iea of particle systems is to buil complex moels from a large population of simple entities, whose geometric extent is small, but which possess certain properties use in animation (position, spee, acceleration) an in renering (e.g. color, opacity). Particle systems can be use to simulate an rener natural phenomena, incluing fire, smoke, explosions, fog, clou, etc [13, 17, 4, 10, 5, 9]. Formally, a particle system is a iscretization of a continuous meium, which allows us to replace ifferentials of the equations governing the motion an light scattering by finite ifferences uring simulation an renering. In this paper we focus on real-time renering such systems, which means the solution of the volumetric renering equation. In the continuous volume the optical properties on a single wavelength are escribe by the emission raiance, umitomi@fre .hu szirmay@iit.bme.hu szijarto.gabor@fre .hu ensity τ, i.e. the reciprocal of the expecte free run length of a photon, albeo a, i.e. the probability that the collie photon is not absorbe, an phase function P( ω, ω), i.e. the probability ensity of the photon irection ω after collision, provie that the photon came from irection ω before collision an is reflecte. To solve the volumetric renering equation efficiently, the omain is iscretize using a particle system. A particle represents a spherical neighborhoo where the volume is locally homogeneous, thus the particle neighborhoo can be represente by a single set of optical properties. Denoting the length of the ray segment intersecting the sphere of particle j by s j, an the ensity, albeo, an phase function of this particle by τ j,a j,p j, respectively, the iscretization of the volumetric renering equation leas to the following equation expressing outgoing raiance L( j, ω) of particle j at irection ω: L( j, ω)=i( j, ω) (1 α j )+α j a j C j +α j (1 a j ) L e j ( ω), (1) where I( j, ω) is the incoming raiance from irection ω, α j = 1 e s j τ(s)s = 1 e τ j s j (2) is the opacity, which equals to the ecrease of raiance cause by this particle ue to extinction (i.e. the sum of absorption an outscattering), L e j is the emission raiance, an C j = I( j, ω ) P j ( ω, ω) ω Ω is the total contribution of in-scattering from all possible irections ω of irectional sphere Ω. Equation 1 can be interprete as follows. Raiance I of the light ray in irection ω is ecrease because photons may collie with the meia. The probability that collision occurs in a particle sphere equals to opacity α j, which also expresses the amount of participating meia enclose by the particle. On the other han, the intensity is increase by the in-scattering term α j a j C j, which means that photons traveling in other irections ω collie an are scattere into irection ω, an by emission α j (1 a j ) L e j ( ω) of the participating meia enclose by the particle. Here a j P j ( ω, ω) is the subcritical probability ensity that

2 the photon is scattere into irection ω after collision, provie it came from irection ω. We have to consier all incoming irections, therefore the in-scattering term contains an integral in the irectional omain. Since particles are small, multiple scattering insie a particle sphere is ignore. Having approximate the in-scattering term somehow [19], the volume can efficiently be renere from the camera using alpha blening. The in-scattering term an the emission of a particular particle are attenuate accoring to the total opacity of those particles which are between the camera an this particle. This requires particles be sorte in the view irection before sening them to the frame buffer in back to front orer. At a given particle, the evolving image is ecrease accoring to the opacity of the particle an increase by its in-scattering an emission terms (equation 1). Particle system renering methos usually splat particles onto the screen [12, 21]. Splatting substitutes particles with semitransparent, camera-aligne rectangles, calle s [14]. Frame A front plane Frame B fully visible fully invisible front plane 1.1 Billboar clipping an popping artifacts visible Frame A Frame B Figure 3: Billboar popping artifact. Where the gets to the other sie of the front clipping plane, the transparency is iscontinuous in time (the figures show two ajacent frames of an animation). object invisible Figure 2: Billboar clipping artifact. When the rectangle intersects an opaque object, transparency becomes spatially iscontinuous. Billboars are planar rectangles having no extension along one imension. This can cause artifacts when s intersect opaque objects making the intersection of the plane an the object clearly noticeable (figure 2). The core of this clipping artifact is that a faes those objects that are behin it accoring to its transparency as if the object were fully behin the sphere of the particle. However, those objects that are in front of the plane are not fae at all, thus transparency changes abruptly at the object intersection. On the other han, when the camera moves into the meia, s also cause popping artifacts. In this case, the is either behin or in front of the front clipping plane, an the transition between the two stages is instantaneous. The former case correspons to a fully visible, while the latter to a fully invisible particle, which results in an abrupt change uring animation (figure 3). The issue of clipping artifacts has been aresse in [6, 7] where the splitting of the intersecte s is propose. Instea of using the z-buffer to ientify the visible fragments, a back to front renering is execute, which raws two s instea of a single intersecte, one before, an the other after the object renering. While this approach eliminates artifacts in case of a single object, it gets unmanageable for many inclue objects. If pixels are either fully visible or fully opaque, then another possibility exists to mix s an conventional 3D objects. To avoi incorrect clipping, s are equippe with per pixel epth information as happens, for example in nailboars [15] an 2.5D impostors [18, 20]. In this paper we propose a novel solution for incluing objects into the participating meium without clipping an popping artifacts. The basic iea of spherical s is introuce in section 2. Unlike nailboars, the propose metho can also hanle semi transparent s neee for natural phenomena, such as fire, smoke, clous, an explosions. Instea of associating epth textures to s, we obtain two epth values analytically, one for the front, an another one for the back surfaces, an compute the opacity accoring to the real istance the light travels insie the particle. The propose iea is use then to rener realistic explosions in real-time in section 3. In our explosion renering system fire an smoke particles are animate an colore in a physically plausible way similarly to [10, 11]. 2 SPHERICAL BILLBOARDS Billboar clipping artifacts are solve by calculating the real path length a light ray travels insie a given particle since this length etermines the opacity value to be use uring renering. The travele istance is obtaine from the spherical geometry of particles instea of assuming that a particle can be represente by a planar rectangle. However, in orer to keep the implementation simple an fast, we still sen the particles through the renering pipeline as quarilateral primitives, an take into account the spherical shape only uring fragment processing. To fin out where opaque objects are uring particle renering, first these objects are rawn an the resulting epth buffer storing camera space z coorinates is save in a texture. Having renere the opaque objects, particle systems are processe. The particles are renere as quas perpenicular to axis z of the camera coorinate system. These quas are place at the farthest point of the particle sphere to avoi unwante front plane clipping. Disabling epth test is also neee to eliminate incorrect object clipping.

3 When renering a fragment of the particle, we compute the interval the ray travels insie the particle sphere in camera space. This interval is obtaine consiering the save epth values of opaque objects an the camera s front clipping plane istance. From the resulting interval we can compute the opacity for each fragment in such a way that both fully an partially visible particles are isplaye correctly, giving the illusion of a volumetric meium. During opacity computation we assume that the ensity is uniform insie a particle sphere. O x,y x f front clipping plane z F w Q Zs B r s P object particle sphere Figure 4: Computation of length s the ray segment travels insie a particle sphere of raius r an of center P. For the formal iscussion of the processing of a single particle, let us use the notations of figure 4. We consier the fragment processing of a particle of center P =(x p,y p,z p ) an of raius r. The particle is renere as a qua perpenicular to axis z. Suppose that the current fragment correspons to the visibility ray cast through point Q =(x q,y q,z q ) of the quarilateral. Although visibility rays start in the origin of the camera coorinate system an thus form a perspective bunle, for the sake of simplicity, we consier them as being parallel with axis z. Note that it woul also be possible to trace rays not parallel with axis z, or even rotating s to be perpenicular at their centers with the viewing irection. However, we have foun that the orthographic projection approximation is acceptable if the perspective istortion is not too strong, an requires the simplest formulae to implement. If the visibility ray is parallel with axis z, then the z coorinates of P an Q are ientical, i.e. z q = z p. The istance between the ray an the particle center is = (x q x p ) 2 +(y q y p ) 2. The closest an the farthest points of the particle sphere on the ray from the camera are F an B, respectively. The istances of these points from the camera can be obtaine as F z p w, B z p + w, where w = r 2 2. The ray travels insie the particle in interval [ F, B ]. Taking into account the front clipping plane an the epth values of opaque objects, these istances may be moifie. First to eliminate popping artifacts, we shoul ensure that F is not smaller than the front clipping plane istance f, thus the istance the ray travels in the particle before reaching the front plane is not be inclue. Seconly we shoul also ensure that B is not greater than Z s which is the store object epth at the given pixel, thus the istance travele insie the object is not consiere. From these moifie istances we can obtain the real length the ray travels in the particle: s = min(z s, B ) max( f, F ). 2.1 Gourau shaing for spherical s Assuming that the ensity is homogeneous insie a particle an using equation 2 to obtain the respective opacity value correspon to piece-wise constant finite-element approximation. While constant finite-elements might be acceptable from the point of view of numerical precision, their application results in annoying visual artifacts Figure 5: The accumulate ensity of a ray (left) an its seen opacity (right) as the function of the istance of the ray an the center in a unit sphere with constant, unit ensity. Figure 5 epicts the accumulate ensity ( s j τ(s)s) an the respective opacity as a function of ray particle istance, assuming constant finite-elements. Note that at the contour of the particle sphere ( = 1) the accumulate ensity an the opacity become zero, but they o not iminish smoothly. The accumulate ensity has a significant erivative at this point, which makes the contour of the particle sphere clearly visible for the human observer Figure 6: The accumulate ensity of a ray as the function of the istance of the ray an the center in a unit sphere with ensity function linearly ecreasing with the istance from the particle center. This artifact can be eliminate if we use piece-wise linear rather than piece-wise constant finite-elements, that is, the ensity is suppose to be linearly ecreasing with the istance from the particle center. The accumulate ensity compute with this assumption is shown by figure 6. Note that this function is very close to a linear function, thus the effects of piece-wise linear finite elements can be approximate by moulating the accumulate ensity by this linear function. It means that instea of equation 2 we use the following formula to obtain the opacity of particle j: α j 1 e τ j(1 /r j ) s j where is the istance between the ray an the particle center, an r j is the raius of this particle. Note that this approach is very similar to the trick applie in raiosity methos. While computing the patch raiosities piece-wise constant finite-elements are use, but the final image is presente with Gourau shaing, which correspons to linear filtering.

4 2.2 GPU Implementation of spherical s The length the ray travels in a particle sphere an the corresponing opacity can be compute by a custom fragment shaer program. The fragment program gets some of its inputs from the vertex shaer: the particle position in camera space (P), the shae point in camera space (Q), the particle raius (r), an the screen coorinates of the shae point (scr). The fragment program also gets uniform parameters, incluing the texture of the epth values of opaque objects (Depth), the ensity (tau), an the camera s front clipping plane istance (f). The fragment program calls the following function to compute the particle opacity at the shae fragment: float Opacity(float3 P, float3 Q, float r, float2 scr) { float alpha = 0; float = length(p.xy - Q.xy); if( < r) { float w = sqrt(r*r - *); float F = P.z - w; float B = P.z + w; float Zs = tex2d(depth, scr); float s = min(zs, B) - max(f, F); alpha = 1 - exp(-tau * (1-/r) * s); } return alpha; } With this simple calculation the shaer program obtains the real ray segment length (s) an computes opacity alpha of the given particle that controls blening of the particle into the frame buffer. The consieration of the spherical geometry uring fragment processing eliminates clipping an popping artifacts (see figures 1 an 7). Figure 7: Particle system renere with spherical s. (figure 8). When renering ust an smoke we assume that these particles o not emit raiance so their emission term is zero. To calculate the in-scattering term, the length the light travels in the particle sphere, the albeo, the ensity, an the phase function (see equation 1) are neee. We use the Henyey-Greenstein phase function [8, 3]: P( ω, ω)= 1 4π 3(1 g 2 ) (1 +( ω ω) 2 ) 2(2 + g 2 ) (1 + g 2 2g( ω ω)) 3/2, where g ( 1,1) is a material property escribing how strongly the material scatters forwar or backwar. To spee up renering, these function values are fetche from a prepare 2D texture aresse by cosθ = ω ω an g, respectively. We have foun that setting g to constant zero gives satisfactory results for ust an smoke. The real length the light travels insie a smoke or ust particle is compute by the propose spherical metho. Figure 8: High albeo ust an low albeo smoke. In orer to maintain high frame rates, the number of particles shoul be limite, which may compromise high etail features. To cope with this problem, the number of particles is reuce while their raius is increase. The variety neee by the etails is ae by perturbing the opacity values compute by spherical s. Each particle has a unique, time epenent perturbation pattern. The perturbation is extracte from a grey scale texture, calle etail image, which epicts real smoke or ust (figure 9). The perturbation pattern of a particle is taken from a ranomly place, small qua shape part of this texture. This technique has been use for a longer time by off-line renerers of the motion picture inustry [1]. As time avances this texture is ynamically upate to provie variety in the time omain as well. Such animate 2D textures can be obtaine from real worl vieos an store as a 3D texture since inter-frame interpolation an looping can automatically be provie by the graphics harware s texture sampling unit [11]. 3 RENDERING EXPLOSIONS The propose spherical technique can replace planar s in all participating meia renering application. In this section, we consier a single example, the explosion renering. Explosions consist of ust, smoke, an fire, which are moele by specific particle systems. Dust an smoke absorb light, fire emits light. These particle systems are renere separately, an the final result is obtaine by compositing their renere images. 3.1 Dust an smoke Smoke particles are responsible for absorbing light in the fire. These particles typically have low albeo values (a = 0.2,τ = 0.4). High albeo (a = 0.9,τ = 0.4) ust that is swirling in the air, on the other han, is ae to improve the realism of the explosion Figure 9: Images from real smoke an fire vieo clips, which are use to perturb the fragment opacities an temperatures.

5 3.2 Fire Fire is moele as a black-boy raiator rather than participating meium, i.e. the albeo in equation 1 is zero, so only the emission term is neee. The color characteristics of fire particles are etermine by the physics theory of black-boy raiation. For wavelength λ, the emitte raiance of a black-boy can be compute by Planck s formula: L e (λ)= 2C 1 λ 5 (e C 2/(λT) 1) where C 1 = Wm 2, C 2 = m K, an T is the absolute temperature of the raiator [16]. Figure 10 shows the spectral raiance of black-boy raiators at ifferent temperatures. Note that the higher the temperature is, the more blueish the color gets. For ifferent temperature values, the RGB components can be obtaine by integrating the spectrum multiplie by the color matching functions. These integrals can be precompute an store in a texture. To epict realistic fire, the temperature range of T [2500 K,3200 K] nees to be processe (see figure 11). normalize intensity 1,0 0,8 0,6 0, K 4000 K 6000 K 8000 K The fragment program gets fire particle position in camera space (P), the shae point in camera space (Q), the particle raius (r), the screen coorinates of the shae point (scr), an the position of the etail image in the texture (etail) an the starting time of the animation in time. The fragment program also gets uniform parameters, incluing the texture of the fire vieo (FireVieo), the black boy raiation function of figure 11 (BBRa), the epth values of opaque objects (Depth), the ensity (tau), the camera s front clipping plane istance (f), an the temperature scale an bias in T1 an T0, respectively. The fragment program calls the Opacity function of subsection 2.2 an computes the color of the fire particle with the following Cg program: float alpha = Opacity(P, Q, r, scr); float3 etuvw = etail + float3(0,0,time); float T = T0 + T1 * tex3d(firevieo, etuvw); return float4(tex1d(bbra, T).rgb, 1) * alpha; 4 LAYER COMPOSITION To combine the particle systems together an with the image of opaque objects, a layer composition metho has been use. This way we shoul rener the opaque objects an the particle systems into separate textures, an then compose them. This leas to three renering passes: one pass for opaque objects, one pass for ust, fire, an smoke, an one final pass for composition. The first pass computes both the color an the epth of opaque objects. 0, K wavelength (nm) Figure 10: Black-boy raiator spectral istribution 0 K 2500 K 3200 K K Figure 11: Black-boy raiator colors from 0 K to K. Fire particles belong to temperature values from 2500 K to 3200 K. The opacity of fire particles is calculate by the spherical s. High etail features are ae to fire particles similarly to smoke an ust particles. However, now not the opacity, but the emission raiance shoul be perturbe. We coul use a color vieo an take the color samples irectly from this vieo, but this approach woul limit the freeom of controlling the temperature range an color of ifferent explosions. Instea, we ecie to store the temperature variations in the etail texture (figure 9), an its store temperature values are scale an are use for color computation on the fly. A ranomly selecte, small quarilateral part of a frame in the etail vieo is assigne to a fire particle to control the temperature perturbation of the fragments of the particle. The temperature is scale an a bias is ae if require. Then the resulting temperature is use to fin the color of this fragment in the black-boy raiation function. Figure 12: Particles renere to rener targets of ifferent resolutions. Upper left: particle rener target with screen resolution (35 FPS). Upper right, lower left, lower right: rener target with half (60 FPS), quarter (110 FPS) an one eights (185 FPS) of the screen resolution. One great avantage of renering the participating meium into a texture is that we can use floating point blening. Another avantage is that this rener pass may have smaller resolution renering target than the final isplay resolution, which consierably spees up renering since blening nees a huge amount of pixel processing power to overraw a pixel many times (see figure 12). To enhance realism, we also simulate heat shimmering that istorts the image [11]. This is one by renering particles of a noisy

6 texture. This noise is use in the final composition as u,v offset values to istort the image (figure 13). With the help of multiple rener targets, this pass can also be merge in the pass of renering of fire particles. The final effect that coul be use through composition is motion blur, which can easily be one with blening, letting the new frame fae into previous frames. The complete renering process is shown in figure 14. Figure 13: Heat noise texture an the final istorte image. the smoke consist of 16, 135, an 112 animate particles, respectively. Note that these small number of larger particles can be simulate very efficiently, but thanks to the opacity an temperature perturbation, the high frequency etails are not compromise. The moele scene consists of triangles. The scene is renere with per pixel Phong shaing. During particle simulation we etecte collisions between particles an a simplifie scene geometry. Our algorithm offers real-time renering spee (70 FPS) in resolution winowe moe, proviing high etails (see figure 15). The frame rate strongly epens on the number of overwritten pixels. For comparison, the scene without the particle system is renere at 370 FPS, an the classic renering metho woul run at about 80 FPS. This means that the performance lost ue to the more complex spherical calculations can be regaine by ecreasing the rener target resolution uring particle system rawing. Frame rate ata measure with ifferent particle numbers are shown by table 1, having set the resolution of the rener target for the opacity to the half of the final image resolution. Note that when higher number of particles are use, the sizes are ecrease proportionally. This means that only the particle simulation an vertex processing time are proportional to the number of particles, the fragment processing time remains constant. particles Planar FPS 60 FPS 45 FPS 40 FPS Spherical FPS 56 FPS 40 FPS 35 FPS Table 1: Frame rates with ifferent particle numbers Pass1 Scene color Scene epth 6 CONCLUSION Dust Fire color Fire heat Smoke This paper propose to consier particles as spheres rather than planar s uring fragment processing, while still renering them as s. Spherical s eliminate clipping an popping artifacts. The paper also introuce an efficient metho to isplay explosions compose of fire, smoke, an ust. The iscusse metho also use post renering effects an runs at high frame rates. ACKNOWLEDGEMENTS Pass2 This work has been supporte by OTKA (T042735), GameTools FP6 (IST ) project, an by Hewlett-Packar an the National Office for Research an Technology (Hungary). REFERENCES Pass3 5 RESULTS Final Composite Image Figure 14: Renering algorithm The presente algorithm has been implemente in OpenGL/Cg environment on an NV7800GT graphics car. The ust, the fire, an [1] A. A. Apoaca an L. Gritz. Avance RenerMan: Creating CGI for Motion Picture. Acaemic Press, [2] J. F. Blinn. Light reflection functions for simulation of clous an usty surfaces. In SIGGRAPH 82 Proceeings, pages 21 29, [3] W. Cornette an J. Shanks. Physical reasonable analytic expression for single-scattering phase function. Applie Optics, 31(16):31 52, [4] R. Fekiw, J. Stam, an H. W. Jensen. Visual simulation of smoke. In ACM SIGGRAPH 2001, pages 15 22, [5] B. E. Felman, J. F. O Brien, an O. Arikan. Animating suspene particle explosions. In ACM SIGGRAPH 2003, pages , [6] M. Harris an A. Lastra. Real-time clou renering. Computer Graphics Forum, 20(3), [7] M. J. Harris. Real-time clou renering for games. In Game Developers Conference, 2002.

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