Visually Believable Explosions in Real Time

Transcription

1 Visually Believable Explosions in Real Time Claude Matins Electonic Ats Canada 4330 Sandeson Way Bunaby, BC, Canada John Buchanan Electonic Ats Canada 4330 Sandeson Way Bunaby, BC, Canada John Amanatides Dept. of Compute Science Yok Univesity 4700 Keele Steet Toonto, ON, Canada Abstact The pape pesents a eal-time physically based simulation of object damage and motion due to a blast wave impact. An impoved connected voxel model is used to epesent the objects. The pape also exploes auxiliay visual effects caused by the blast wave that incease visual believability without being igoously physically based o computationally expensive. 1. Intoduction Explosions, and thei esultant blast waves, continue to be a popula phenomenon depicted in film, television, compute games, and othe visual media. Thee ae cetain advantages to simulating the appeaance and behavio of blast waves using compute gaphics, such as safety, epoducibility, customizability, and inteactivity. Blast waves, howeve, follow complex fluid dynamics ules, and modeling them vey accuately is computationally expensive. This is especially tue fo a game o a eal-time application, whee immediate visual feedback is paamount. Uses expect instant gatification with unpedictable and chaotic blast effects. Meticulous physical accuacy is less desiable hee than a fast simulation speed. This pape takes the blast wave simulato and connected voxel model pesented by Mazaak et al [MMA99] and extends its scope to eal-time gaphics. The petinent enhancements and simplifications necessay fo the impovement of computing time ae discussed. The functionality of the model is also enhanced by the intoduction of abitay voxel shapes. Futhemoe, cetain commonly expected visual cues ae added to the simulation to impove the visual believability of the explosion at low computational cost. 2. Pevious wok Pevious effots on explosion modeling in the field of compute gaphics have taditionally focused moe on the gaphical epesentation of an explosion, athe than its effects on objects in the envionment. Usually, the attibutes and motion of an explosion ae contolled explicitly by the use, o else the explosion follows a set of infomal behavioal ules [Reeves83]. Othe techniques concentate on cetain afte-effects of an explosion, such as fie [COMM94] and smoke. Inteest has ecently been ekindled in blast waves and thei effects. In his Maste s thesis, Bashfoth employs volume cell subdivision to model shock font popagation [Bashfoth98]. Neff and Fiume model the factuing of a plana suface into polygonal fagments by a spheical blast wave [NF99]. Mazaak et al use connected voxels to model objects beaking into solid debis when hit by a spheical blast wave [MMA99]. Yngve et al model blast wave popagation using a combination of spatial voxelization and finite elements [YOH00]. Except fo [MMA99], these appoaches eschew simulation speed in favo of igoous physical accuacy, which makes them inappopiate fo use in eal-time gaphics. Although papes discussing explosions and blast waves ae somewhat ae in the field of compute gaphics, it is impotant to note that this is not the case fo the disciplines of physics and chemisty. Thee have been numeous woks published in those aeas that delve with geat detail into the ceation and detonation of explosive mateials, the popagation of the geneated shock fonts, and thei effect on vaious mateials. Seveal compute methods fo the modeling of blast waves have also been poposed and implemented [Bake73]. These models, howeve, ae concened pimaily with pedicting and duplicating the behavio of explosions and explosion effects down to the smallest detail. They equie

2 substantial computational powe and time to handle the govening fluid dynamics equations. In eal-time compute gaphics, eplicating blast wave behavio in evey detail is simply not feasible. Instead, we cull some of the oveall elevant physical popeties, and make cetain simplifications and optimizations. In this way, it is possible to obtain a balance between accuate modeling and ealistic visuals without sacificing a geat deal of computing time. 3. Blast wave theoy An explosion in ai causes a blast wave to popagate outwads fom the souce at supesonic speed. Since the esugence of ecent inteest in blast wave modeling in compute gaphics, the fundamentals of blast wave theoy have been adequately coveed in seveal papes ([MMA99], [NF99], and [YOH00]). Ou blast wave model is a combination of simplified physical equations and expeimental data. The ai suounding the explosion is assumed to be still and homogenous, and the explosion souce is spheically symmetic. This esults in an ideal blast wave that is itself pefectly symmetical. The pessue pofile geneated by an ideal blast wave at a point at some fixed distance R emoved fom the cente of the explosion is as shown in the following Figue 1 [Bake73]. PRESSURE Figue 1. Pessue-time cuve of an ideal blast wave Befoe the shock font eaches the given point, the ambient pessue is p 0. At aival time t a, the pessue ises discontinuously to the peak value of p 0 s p0 P s p0 p0 - P s 0 0 P s. The quantity P is called the peak ovepessue. The pessue then decays to ambient in total time t a T, dops to a patial vacuum of value p 0 - P s, and eventually etuns to the ambient pessue p 0, in total time t a ta Positive phase ta T p(t) TIME Negative phase ta T T T T [Bake73]. Ou simulation models blast wave pofiles using the modified Fiedlande equation: p(t) = p 0 P s (1 t / T ) e bt / T (3-1) Time is measued fom time of aival t a. The blast wave paametes P s, t a, T, and b allow feedom to customize the pessue pofile cuve fo any explosion, at vaious distances fom the souce. The modified Fiedlande equation impoves ove simple fomulae, which eithe have linea decay o fail to etun to ambient pessue [Bake73]. Moe complex equations given by Bode [Bode95] and Dewey [Dewey64] geneate blast wave pofiles that ae close to expeimental o theoetical models. Fo a eal-time simulation, howeve, the inceased accuacy does not justify the concomitant highe computational costs. Ou blast wave model employs Equation (3-1) to compute physically accuate pessue changes at any distance R fom the souce of the explosion. The blast wave paametes equied by Equation (3-1) ae obtained fom expeimental data fo a efeence explosion of one kilogam of TNT (tinitotoluene) in a standad atmosphee [KG85]. The expeimental data contains values fo peak ovepessue P s, expected aival time t a, positive phase duation T, and the pessue decay coefficient b, measued at cetain distances R 1, R 2,, R n, fom the souce. The coesponding paametes fo any abitay distance R ae obtained by linea intepolation. Time and distance elated paametes fo explosions with diffeent yields than one kilogam of TNT ae deived fom the efeence explosion data by using an appopiate scaling facto as detemined by the scaling laws [KG85]. This scaling facto is nomally equal to the invese of the cube oot of the enegy of the deived explosion: R Z = 1/ 3 (3-2) W whee Z is the scaled distance, R is the actual distance fom the cente of the explosion in metes, and W is the mass of the explosive conveted into an equivalent weight of TNT in kilogams. Since blast waves move at supesonic velocities, they popagate in a non-linea fashion. Envionmental inteactions fequently cause pessue inceases, iegula eflections, votices, and othe complex phenomena [Bake73]. These computationally intensive effects ae difficult to simulate in eal time, so we use a simple model that popagates blast waves outwads as if they wee in the open ai and not being affected by suounding objects. As a esult,

3 object damage occus that is not identical to a eal-life explosion. Factuing in ou simulation is moe accuate when thee ae no, o few, obstuctions between the explosion souce and a given object. 4. Modeling and animation Rigid bodies in the envionment ae affected by blast waves in two majo ways. Fistly, the blast wave ceates tensile stess within the object that can cause it to factue and beak apat. Secondly, the blast wave pessue exets foces on the object that can cause it to move and otate. Theefoe, a paticula object model must be chosen that takes both of these effects into account. 4.1 Connected voxels The objects in the simulation ae modeled with connected voxels [MMA99]. An object is decomposed into volume elements, o voxels, that make up its volume. Adjacent voxels ae connected to each othe with inflexible links that keep the voxels fimly attached togethe. The connected voxel appoach offes seveal advantages ove othe models. Fistly, it is volumetic- athe than suface-based, so factuing of an object s inteio is possible. Secondly, the model is scaleable. If a moe accuate simulation is desied, the voxel size can be educed, allowing a fine epesentation. Likewise, if simulation speed is moe impotant than pecision, a lage voxel size can be used. Thidly, the links connecting the voxels ae infinitely stiff, unlike the sping-mass paticle model [TPBF87]. This makes the object a tue igid body, and the simulation emains obust. Finally, suface association fo the objects is not equied when using connected voxels because each voxel aleady has a given shape assigned to it. This is an impotant benefit in a eal-time explosion simulation, because accuately computing new sufaces fo the dynamically ceated debis is non-tivial. In the oiginal implementation by Mazaak et al [MMA99], evey voxel was identical and homogenous. A basic voxel cube shape esulted in objects that wee blocky and unealistic. Ou simulation impoves upon this noticeably, though the intoduction of abitaily shaped voxels. The basic voxel cube shape can be scaled by any desied amount along any axis. As well, the voxel s vetices can be displaced by any amount in any abitay diection. Each voxel can also have unique popeties appopiate fo the mateial it epesents. This makes object modeling much moe flexible, and pemits the use to ceate voxel shapes that bette suit his o he needs fo a paticula application. Detemination of visible sufaces is tivial in the connected voxel model. Any voxel face that does not have a Figue 2. Flexible object modeling using abitay voxels. link attached to it is visible and must be endeed. Rendeing is thus linea on the numbe of bounday voxels. Regadless of the voxel shape, the simulation assumes that any given voxel has a constant density, which simplifies the foce and toque computations used in object animation. 4.2 Factue simulation When a blast wave hits an object, pessue diffeentials cause the object to weaken and factue. We simulate this by weakening and beaking links and voxels in the object model. As the object beaks apat, new fagments may be ceated. Independent objects in the scene ae epesented by the connected components of the entie scene s connectivity gaph, whee the nodes ae individual voxels and the acs ae the links between voxels [MMA99]. Evey link has an associated yield limit, which is the maximum pessue that the link can withstand befoe beaking. A link is boken wheneve the absolute value of the pessue at that link s midpoint exceeds its yield limit. Any links that encounte a blast wave have thei yield limits weakened, making them vulneable to subsequent explosions. Additionally, links that ae paallel to the diection of the wave ae futhe weakened by an oientation facto, computed as a dot poduct of the wave s adius vecto R and the link vecto l. The inclusion of this oientation facto allows the simulation to bette mimic a eal explosion, whee tensile foces ceated by the blast wave inside an object ae much stonge in the diection paallel to the diection of the wave than nomal to it. An enhancement can be made to the factue model by adding a yield limit fo the voxels themselves. Pessue fom a blast wave is measued at the cente of each voxel. If the absolute value of the pessue at a voxel s cente exceeds its yield limit, that voxel is emoved and eplaced with a small paticle system. Linea momentum of the oiginal voxel is passed on to the individual paticles in the eplacement paticle system. This simulates the destuction of object fagments into paticulate dust if they undego sufficient stess due to the blast wave. As with damaged links, voxels that suvive a fist blast wave have thei yield limits weakened.

4 A significant benefit of eplacing voxels with paticle systems is that paticles ae easie to handle computationally, and ae also geneally quicke to ende. Futhemoe, allowing voxels to be destoyed helps cicumvent cetain poblems such as polonged intepenetation duing collision. Since the shock font pessue foces ae vey stong, objects in the envionment tend to stat tumbling eveywhee once the blast wave hits them. This is unealistic fo buildings that ae supposed to have foundations. Fo such fixed stuctues, the simulation tags voxels that ae in contact with the gound as foundation voxels. An object having these foundation voxels in it is defined as fixed, i.e., blast waves will affect voxel and link stength but will not impat any momentum to the stuctue. This allows debis to fly off the object and have momentum, but the oiginal stuctue emains stationay and does not tumble aound. customize objects fo a paticula game and oveide the basic vaiance values assigned in object configuation. 4.3 Animation The blast wave not only causes object factue and fagmentation; it also affects thei tanslation and otation though the application of foces and toques. Computing the foce at the voxel cente [MMA99] is insufficient since one-voxel bodies would not expeience toque. Futhemoe, foces exeted on abitay voxel shapes would be inaccuate. Theefoe, the foces exeted by the blast wave ae evaluated at the vetices of each voxel. The foce at a given vetex is computed as a poduct of the blast wave pessue and the aea of that voxel pojected onto the suface of the shock font. Assuming a spheical blast wave, the foce vecto is conguent to the blast wave adius vecto: R F = p( t) A (4-2) R Figue 3. Foundation voxels (shown shaded) stabilize the igid body. Of couse, blast waves can sometimes be stong enough to ip a building ight off its foundations. So, a foundation yield limit is intoduced fo each foundation voxel. As with voxel yield limits, the blast wave pessue measued at the cente of each voxel is used to diminish its foundation yield limit. Once a voxel s foundation yield limit dops to zeo o below assuming it hasn t been destoyed completely its foundation voxel status is emoved. If all of the foundation voxels in a stuctue evet to odinay voxels in this way, that object is no longe fixed. In effect, it has been blown off its foundations. Blast waves hitting the stuctue now impat momentum to it, as well as voxel and link damage. We assign vaiable yield limits by petubing some andom value, geneated within a cetain ange, aound some mean value [TF88]: yield_limit = mean_yield ± and(va_yield) (4-1) This allows the object to have a non-homogenous stuctue, with weake and stonge sections. The continual deteioation of the object s links and voxels also simulates patial, pesistent damage. It is possible that a simple vaiance in object stuctue might be insufficient. Fo example, a game designe may want a specific building wall to be easily destoyed. He o she can then alte link and voxel popeties explicitly to whee p(t) is a function that etuns the pessue value at a given voxel vetex at time t, A is the suface aea of the voxel pojected onto the spheical shock font, and R is a adius vecto fom the souce of the explosion to the voxel vetex. The pojected suface aea of a cubic voxel onto a spheical blast wave vaies mainly on its size and vey little depending on its oientation. Computing the actual pojected suface aea fo each voxel is too time-consuming in a eal-time simulation, so A is assumed to be constant, depending on the size of the voxel. Non-cubic voxels ae assigned the pojected suface aea of a cubic voxel with a side equal to the oiginal voxel s lagest dimension. This appoximation is impecise, with the accuacy deceasing as the diffeence inceases between the non-cubic voxel and the oiginal cubic voxel. The toque on the body is computed as the coss poduct of the elative position of a specific voxel vetex within the body, and the foce expeienced by that vetex: T = F (4-3) whee is the elative position of the voxel vetex to the cente of mass of the body. The foce and toque computation fo a single voxel vetex is shown in Figue 4. Noting that the body s bounday voxels appoximate its suface implies that the foce and toque vectos only need to be computed fo the bounday voxels. These foce and toque vectos ae then summed up to obtain the esultant foce and toque vectos fo the entie body.

5 souce of explosion F T shock font body = F bounday _ voxels body = T bounday _ voxels (4-4) (4-5) The dynamic simulato then updates the body s position using the esultant foce vecto and the body s oientation using the esultant toque vecto. The linea and angula momenta of any newly ceated body fagments ae computed as weighted potions of the linea and angula momenta of the oiginal body: m fagment P fagment = Poiginal (4-6) m oiginal m fagment L fagment = Loiginal (4-7) m oiginal whee P is the linea momentum, L is the angula momentum, and m is the mass. This agees with the law of consevation of momentum, and ensues accuate motion of the split fagments. Using a discete time step to simulate the continuous popagation of a shock font tends to lead to inaccuacy. It is possible fo the shock font to skip ove cetain voxels completely fom time t to next consecutive time t t. Reducing the size of the time step will educe this discetization eo at the cost of a slowe-unning simulation but will not emove it completely. Voxel size and aangement might still be such that the shock font skips ove paticula voxels. Using an adaptive time step size that ensued the shock font hit evey voxel would eliminate any such eo. Howeve, the simulation would need a lage numbe of tiny time steps wheneve the shock font passes ove voxels located in vey close poximity, which is the case fo any multi-voxel object. We cuently educe this eo by using shock font pecomputation. Evey time an explosion is intoduced into the envionment, the peak ovepessue (the most significant Figue 4. Foce and toque computation. T ω F pat of the blast wave pofile), aival time, and esultant shock font foce ae computed fo each voxel. These pecomputed values ae then stoed in a chonologically soted list fo that voxel. At each simulation time step, foces and toques ae computed fo a bounday voxel. In addition, that voxel s list of pecomputed values is checked to detemine if any of the pecomputed shock font foces ae set to occu. If the cuent simulation time is equal to the stoed aival time fo that enty in the list, this implies that the shock font is pecisely at that paticula voxel s cente. In this case, the pecomputed values ae used in place of the cuent foce and toque computation. If the cuent simulation time is geate than the stoed aival time, this implies that the shock font has skipped ove that voxel. So hee, the pecomputed values ae added to the cuent foce and toque computation. In both cases, the enty is emoved fom that voxel s list. This teatment of pecomputed shock font values is advantageous because it allows the simulation to maintain a constant time step while still taking into account the effect of the peak ovepessue fo each voxel. The method is not entiely accuate, howeve, since the stoed aival time is offset fom the cuent simulation time by a small amount. The magnitude of the eo is always smalle than the size of the time step: t cuent t aival < t (4-8) In pactice, this inaccuacy is negligible compaed to the oiginal discetization eo. It is impotant to note that only the blast wave s peak ovepessue is pecomputed. Pessue changes at othe points in the pessue-time cuve ae computed as they occu duing the simulation. 5. Collision detection Once objects ae in motion, thee is a possibility that they will intepenetate if appopiate checks fo collision ae not made. 5.1 Dynamic contact Dynamic contact occus when adjoining objects ae moving togethe with some positive velocity. We limit collision tests to bounday voxels, since they appoximate the object s suface. Additionally, a voxel will neve collide with othe voxels belonging to the same igid body because, by definition, a igid body s link stuctue coheently maintains the elative positions of all of its component voxels and pevents self-intesection. Hence, collision tests need only be done fo voxels fom sepaate bodies.

6 Associating bounding volumes to the objects can educe the numbe of compaisons even futhe. If two bounding volumes ae detemined to be disjoint, then thei contents must necessaily be non-intesecting, and no exta tests fo those specific objects ae needed. We use a two-level hieachical scheme with sphees as the bounding volumes. At the highe level, a igid body is assigned a bounding sphee with a adius equal to the distance between the cente of mass and the voxel vetex futhest fom the cente of mass. Since a body otates about its cente of mass, this ensues that the bounding sphee coves all possible body oientations at a given position. At the lowe level, each voxel is assigned a bounding sphee with adius equal to the distance between the voxel cente and the voxel vetex futhest fom the cente, fo a simila eason. Fo a eal-time simulation, unfotunately, vey accuate collision detection is too time-consuming. Theefoe, two bodies ae consideed to collide in the simulation when thei voxel-level bounding sphees intesect. If the voxels ae stationay o moving away fom each othe, no collision esponse is necessay since intepenetation will not occu. If the voxels ae moving towads each othe, a pope collision esponse is computed to pevent intepenetation of the bodies. The linea and angula momenta of the bodies is changed discontinuously ([BW97], [MC95]) to ensue that the collision occus with little to no defomation. Each voxel has an associated coefficient of estitution that detemines how bouncy a collision is. A coefficient of zeo coesponds to a pefectly inelastic collision whee all kinetic enegy is lost, wheeas a coefficient of one coesponds to a pefectly elastic collision whee all kinetic enegy is etained. p Bounding sphee Figue 5. Dynamic contact collision. Pecise suface econstuction is too time-consuming fo eal-time simulation, so the sufaces of the bodies ae assumed to be smooth. Thus, the collision nomal N is appoximately paallel to the distance vecto between the colliding voxels, and the collision point p is appoximately equal to the midpoint of the distance vecto [MMA99]. A blast wave can impat exceptionally high velocities to objects it hits, potentially causing some of them to intepenetate noticeably in a single time step. Objects may even N pass though each othe completely. In pinciple, this poblem can be solved by educing the time step adaptively until the intepenetation is kept within a cetain toleance. Howeve, this is not feasible fo a eal-time simulation because the time step may become pohibitively small. One appoach we use is the eduction of voxel stength by collision foces so that voxels that intepenetate fo too long ae eventually destoyed. This method has an additional advantage because it appoximates object damage due to collision. Anothe tactic is the ceation of dust -like paticle systems at collision points to mask intepenetation. This also adds visual infomation to the scene. A difficulty with collision esponse algoithms is that the esolution of one contact could lead to the ceation of new contacts. In theoy, this situation could loop indefinitely and cause a majo pefomance hit. In ou implementation, all contacts ae only esolved once in the cuent fame. Any new contacts ceated by collision esolution, as well as those that aise duing the nomal couse of the simulation, ae dealt with in the subsequent fame. Consequently, intepenetation is moe ponounced but the fame ate is kept easonable. 5.2 Static contact Objects ae defined to be at est i.e., in static contact when they ae in contact and ae not moving with espect to each othe. Finding static contact foces fo a multi-body system is a complicated pocess, equiing efficient quadatic pogamming algoithms, such as those descibed in [Baaff94]. In ode to facilitate static contact esolution, we intoduce two limitations to collision. Fistly, an object can only be at est when it is in static contact with the gound, not with othe objects. Objects that ae adjacent and have zeo elative velocity have no associated collision esponses. This means that objects ae kept fom intepenetating but tend to bounce, wobble, o slide when they fall atop one anothe with low velocities. Given that the blast wave fom an explosion usually causes objects to move vey fast, this is an acceptable estiction. Due to this limitation in ou simulation, howeve, lage debis piles eventually collapse towads the gound. Secondly, static contact with the gound is esolved not with the computation of balanced epulsive foces, but though a combination of dynamic collision esponse and a heuistic athe than physically based implementation of fiction that we call pseudo-fiction. When an object collides with the gound, the following assumptions ae made to simplify calculations: the gound has infinite mass; the collision nomal N is equal to the gound plane nomal; and the collision point p is at the colliding voxel vetex.

7 If the object is moving into the gound, the simulato computes the pope dynamic collision esponse to pevent intepenetation. As mentioned above, collision foces diminish voxel stength destoying the voxel and eplacing it with a paticle system if its stength dops to zeo o below and dust -like paticle systems ae spawned at collision points. Simulating igid body dynamics using the dynamic collision methods detailed above leads to the following difficulty. Objects tend to keep moving, spinning, and sliding aound on the gound. It takes a long time fo them to come to est, if eve. In ode to compel the objects to eventually come to est, the simulation uses a sot of pseudo-fiction. v T v Figue 6. Gound collision. An object in contact with the gound has an associated velocity v at the point of contact p. That vecto v can be decomposed into a nomal component v N and a tangential component v T. If v T is non-zeo, the pesence of tangential fiction needs to be taken into account. This is done by the addition of a tangential foce F T to the object in the opposite diection of the tangential velocity v T. The magnitude of F T is coelated to the magnitude of v T and the mass of the object m; i.e., a heavie object moving faste expeiences moe fiction than a lighte object moving slowe. Adding the above tangential fiction pevents objects fom sliding along the gound foeve. Howeve, objects still tend to oscillate. Subtacting a pat of an object s linea and angula momenta wheneve it comes into esting contact with the gound can minimize these oscillations. Resting contact is defined to occu wheneve an object in contact with the gound has a nomal velocity v N of zeo (within a cetain theshold). Futhemoe, if an object has thee o moe contact points with the gound, and eithe its linea o angula momentum appoaches zeo, it is clamped to zeo. Using this implementation of pseudo-fiction eliminates any small petubations to a body, and thus also helps maintain the stability of an object aleady at est. We chose a lowe limit of thee contact points fo the clamping of linea and angula momenta to zeo because an object usually needs at least thee gound contact points to emain at est (e.g., a tipod). In the eal wold, howeve, an N v N F T object whose cente of mass lies outside the convex hull of its gound contact points egadless of the numbe of contact points is unbalanced, and will theefoe topple ove. An object is in balanced est only when its cente of mass pojected onto the gound plane lies within the convex hull of its gound contact points. Computing the convex hull of an object s gound contact points poves to be too computationally expensive to justify in a eal-time simulation. Instead of the convex hull, an axis-aligned bounding box containing the gound contact points is computed. Pseudofiction is only applied if the pojected cente of mass lies within this ectangula base. Obviously thee ae cases whee this appoximation is invalid, but it yields bette esults than if no balancing condition is used, and is much quicke than using an accuate convex hull. 6. Acceleated visual cues In addition to object factue, a spectato viewing a eal explosion has numeous othe visual cues that convince him o he that the detonation is authentic. A cue is something that adds expected o peceived visual infomation to the scene, and ultimately makes the animation moe plausible. Any such cue need not be igoously physically deived as long as it satisfies the viewe s expectations. A simulato that endes vitual explosions needs to mimic as many of these cues as possible in ode to convince a viewe that the blast is believable. This is even moe obvious in eal time whee it is easie to duplicate simple, expected explosion effects than it is to meticulously simulate unfamilia phenomena. Since this is a eal-time simulation, all of the visual cues ae geneated concuently with the blast wave computation and object endeing, athe than as a post-pocessing step afte the animation is completed. Moe ealistic methods may be chosen povided they ae not too computationally intensive. A pimay visual cue is the explosion itself. Possibly influenced by films and television, a viewe expects to see a lage fieball at the explosion souce. A display like this is ceated in the simulation by spawning multiple flame-like paticle systems at the explosion souce. Adding a bight yellow-oange light to each explosion paticle system also maintains the illusion of an intense fieball. In eal life, the density changes acoss the shock font cause the index of efaction to be modified. Light ays passing though these egions of diffeent efaction indices ae bent by vaying amounts. The amount of efaction due to the blast wave is usually vey mino, and can baely be seen amidst the sound and fuy of the explosion unless a viewe knows exactly what to look fo. An accuate epesentation of light efaction by the shock font can be obtained by using ay-taced images in the simulation. Unfo-

8 tunately, ay tacing is too time-consuming to use in a ealtime simulation. Nevetheless, viewes still expect to see some visual indication of the shock font itself. Since the simulation assumes the blast wave is spheical, a viewe s expectations can be fulfilled in this case by endeing a semi-tanspaent sphee centeed at the explosion souce, and having a adius equal to the adius of the blast wave. Tanspaency is gadually inceased as the adius inceases. Since the blast wave itself is almost invisible, its popagation is notable mainly by the effect it has on the envionment. As the blast wave moves along the gound, it kicks up clouds of dust. We achieve this by adding dust-like paticle systems at the intesection of the expanding blast wave sphee and the gound plane. The blast wave also knocks dust off of the objects in its path. To imitate this effect, we geneate paticle systems at the intesection of the blast wave and the voxels. A visual indicato not limited to explosions is the dust thown off when objects hit the gound o each othe with sufficient foce. Again, the simulation epoduces this by spawning dust-like paticle systems at voxel collision points. The dust thown up at collision points also helps to mask any intepenetation that occus. Explosions poduce high tempeatue conditions that lead to neaby flammable objects getting set on fie. Fo the aveage viewe, thee is an inexticable link again, possibly einfoced by films and television between explosions and fie. Cuently, the simulation models the pessue changes acoss a shock font using physically deived methods. It is possible to emulate combustibility by using a simple, heuistic appoach. As with the yield limit, each voxel has a combustibility limit that is assigned in a simila fashion. Duing an explosion, the blast wave pessue measued at each voxel s cente is scaled by a use-definable paamete. This scaled pessue is then used to diminish the combustibility limit fo that voxel. Once a voxel s combustibility dops below zeo, it is set on fie, i.e., it spawns fie- and smoke-like paticle systems. Voxels that ae on fie have thei yield limits weakened continually as long as they ae aflame. Links that ae attached to buning voxels also have thei yield limits weakened. This simulates the destuctive natue of fie. In the eal wold, fie popagates based on the pesence of neaby flammable objects that ae affected by elevated tempeatues. Rathe than use a poximity appoach which is much moe computationally expensive the simulation takes advantage of the existence of links and popagates heat along them instead. Non-buning voxels attached to buning voxels have thei combustibility limits weakened in tun. Based on the obsevation that fie tends to spead upwads in a stuctue, an oientation facto is computed fo the position of the neighboing non-buning voxel. Voxels located diectly above the buning voxel ae accoded a lage oientation facto than voxels located to the side o below. This oientation facto is then used to scale deteioation of neighboing voxels so that fie popagation and damage tends to pogess upwads. When objects beak apat, the sides that wee hidden in the oiginal object usually have a diffeent appeaance than the exposed faces. Any voxel face not oiginally visible that subsequently appeas due to object beakage is assigned a geneic voxel damage textue. This effect can be impoved by having specific damage textues fo individual voxels. It can be genealized futhe by having appopiate damage textues painted on as a voxel diminishes in stength, o is affected by fie. Lastly, it is self-evident that footage of eal explosions is shot with eal cameas. What is less obvious, though, is that they ae as affected by the blast wave as othe objects. Unless the camea is locked down completely (and sometimes even then), it will shake as the blast wave passes it. Adding a simila wobble to the simulated camea when it encountes the blast wave helps to bing the vitual scene even close to its eal-wold countepat. 7. Results The simulation geneates animations that ae visually simila to eal-wold explosions, though the use of physically based methods and the pesence of paticula visual cues. Impotant aspects of the blast wave, such as the peak ovepessue and the negative phase, ae pesent in the simulation. Without collision detection, the simulation speed is dependent on the computation of connected bodies in the scene. This has an uppe bound of O(n), whee n is the total numbe of voxels in the scene. Pai-wise testing fo collision detection inceases the simulation time to O(m 2 ), whee m is the total numbe of bounday voxels in the scene. The addition of object-level bounding sphees educes the initial numbe of tests to O(k 2 ), whee k is the total numbe of objects in the scene. The basic blast wave simulation without gaphical output is vey fast (see Figue 7). In fact, the fame ate with no endeing is consistently about two odes of magnitude faste than simila tests with endeing. This demonstates that endeing each fame causes a lage pefomance hit. The fame ate can be impoved substantially using hadwae gaphics acceleation. The implementation pefoms easonably close to eal time (see Figue 8). Fo small (<200) numbes of voxels, the pefomance is nea 30 fames/sec. When the numbe of voxels inceases to 500 and moe, the pefomance dops below 20 fames/sec. Apat fom gaphical output, the main bottleneck fo the simulation itself is collision detection. As the numbe of independent objects in the scene inceases eithe due to a

9 Pefomance Pefomance Fames pe Second Fames pe Second Numbe of Voxels Figue 7. Pefomance without gaphical output Numbe of Voxels Figue 8. Pefomance with OpenGL endeing. lage initial set of objects o due to object fagmentation the fame ate deceases, as moe collision checks need to be made. The simulation tests wee pefomed on an Intel P3 900MHz machine with no hadwae optimization fo OpenGL. 8. Conclusions and futue wok This pape has extended the connected-voxel model used in [MMA99] fo the eal-time animation of a blast wave impact on solid objects. Visual ealism of the animation is achieved pimaily though the volumetic epesentation of an exploding object, esulting in convincing solid debis. Abitay voxel shapes pemit the ceation of objects that ae moe complex using fewe voxels. Seveal simplifications ae equied to achieve a simulation that uns in eal time. The blast wave model assumes that the shock font emains pefectly spheical as it popagates. Using shock font pecomputation minimizes the inaccuacy inheent in dynamic simulatos using discete time steps. The collision esponse algoithms fo both dynamic and static contact between objects ae also somewhat impecise. Moe accuate contact esolution would advesely affect the fame ate. Cetain simplifications, such as the use of pseudo-fiction in static contact esolution, ae employed to maintain an acceptable simulation speed. The addition of seveal key visual cues commonly associated with explosions impoves the visual believability of the scene. Each cue is not igoously physically deived o simulated in the inteest of speed. It is sufficient to have a specific cue looking easonably simila to its eal-wold countepat without it being a totally accuate facsimile. Wheeas ou simulato woks on a puely visual basis, it is notewothy that an obseve of an explosion also elies on auditoy cues to povide authenticity. Adding immediate explosion sound effects to the simulation would enhance its believability consideably. The use has a high level of contol in most aeas of the implementation. The design of an initial object can be customized to a lage extent, fom the way it looks (using abitay voxel shapes) to the way it behaves unde a blast wave impact (using non-homogenous link and voxel popeties). The level of accuacy in the simulation can also be chosen depending on the use s goals. The main challenge would be to simulate moe complex wave inteactions with both objects and the envionment in eal time. Examples of this ae eflection, efaction, Mach stem fomation, and votices [Bake73]. Yngve et al [YOH00] model these complex blast wave inteactions faily accuately, but unning times fo thei simulation anged fom seveal hous to seveal days. A elated poblem is the simulation of shock wave popagation within an object itself. The implementation can also be enhanced with moe efficient collision detection to impove simulation speed, and moe advanced object factue modeling (such as [OH99], [SWB00]) to incease accuacy and visual believability. 9. Refeences [Bake73] Wilfed E. Bake, Explosions in Ai, Univesity of Texas Pess, [Baaff94] David Baaff, Fast Contact Foce Computation fo Nonpenetating Rigid Bodies, SIGGRAPH 94, pp , [BW97] David Baaff and Andew Witkin, Physically Based Modeling: Pinciples and Pactice, SIGGRAPH 97 Couse Notes, [Bashfoth98] Byon Bashfoth, Physics-Based Explosion Modelling fo Compute Gaphics, M.Sc. thesis, Univesity of Saskatchewan, 1998.

10 [Bode95] [COMM94] [Dewey64] [KG85] [MMA99] [MC95] [NF99] H.L. Bode, Numeical Solutions of Spheical Blast Waves, Jou. Appl. Phys., 26, N. Chiba, S. Ohkawa, K. Muaoka, and M. Miua, Two-dimensional Visual Simulation of Flames, Smoke and the Spead of Fie, The Jounal of Visualization and Compute Animation, Vol. 5, No. 1, John M. Dewey, The Ai Velocity in Blast Waves fom TNT Explosions, Poc. Roy. Soc., A, G. F. Kinney and F. J. Gaham, Explosive Shocks in Ai, 2 nd Ed., Spinge-Velag, Oleg Mazaak, Claude Matins, and John Amanatides, Animating Exploding Objects, Gaphics Inteface 99, pp , B. Mitich, J. Canny, Impulse-based Simulation of Rigid Bodies, 1995 Symposium on Inteactive 3D Gaphics, pp , Michael Neff and Eugene Fiume, A Visual Model fo Blast Waves and Factue, Gaphics Inteface 99, pp , [OH99] [Reeves83] [SWB00] [TF88] James F. O Bien and Jessicca K. Hodgins, Gaphical Modeling and Animation of Bittle Factue, SIGGRAPH 99, pp , William T. Reeves, Paticle Systems A Technique fo Modeling a Class of Fuzzy Objects, ACM Tansactions on Gaphics, Vol. 2, No. 2, Jeffey Smith, Andew Witkin, and David Baaff, Fast and Contollable Simulation of the Shatteing of Bittle Objects, Gaphics Inteface 00, pp , D. Tezopoulos and K. Fleische, Modeling Inelastic Defomation: Viscoelasticity, Plasticity, Factue, SIGGRAPH 88, pp , [TPBF87] D. Tezopoulos, John Platt, Alan Ba, and K. Fleische, Elastically Defomable Models, SIGGRAPH 87, pp , [YOH00] Gay D. Yngve, James F. O Bien, and Jessica K. Hodgins, Animating Explosions, SIGGRAPH 00, pp , (a) (b) (c) (d) (e) (f) Figue 9. House destuction (single object of ~150 voxels).

11 (a) (b) (c) (d) (e) (f) Figue 10. Building damage (single object of ~4300 voxels). (a) (b) (c) (d) (e) (f) Figue 11. Logo destuction (multiple objects of ~70 voxels). The 00 in 2001 was specified as moe flammable than the othe objects.