Animating Lava Flows

Transcription

1 Animating Lava Flows Dan Stora, Pierre-Olivier Agliati, Marie-Paule Cani, Fabrie eyret, Jean-Dominique Gasuel To ite this version: Dan Stora, Pierre-Olivier Agliati, Marie-Paule Cani, Fabrie eyret, Jean-Dominique Gasuel. Animating Lava Flows. Graphis Interfae (GI 99) Proeedings, 1999, Kingston, Ontario, Canada. pp , <inria > HAL Id: inria Submitted on 17 Aug 2010 HAL is a multi-disiplinary open aess arhivor the deposit and dissemination of sientifi researh douments, whether they are published or not. The douments may omrom teahing and researh institutions in Frane or abroad, or from publi or private researh enters. L arhive ouverte pluridisiplinaire HAL, est destinée au dépôt et à la diffusion de douments sientifiques de niveau reherhe, publiés ou non, émanant des établissements d enseignement et de reherhrançais ou étrangers, des laboratoires publis ou privés.

2 Animating Lava Flows Dan Stora Pierre-Olivier Agliati Marie-Paule Cani Fabrie eyret Jean-Dominique Gasuel imagis -GRAVIR / IMAG BP 53, F Grenoble edex 09, Frane Abstrat Animating lava flowing down the slopes of a volano brings several hallenges: modeling the mehanial features of lava and how they evolve over time depending on temperature; omputing, in a reasonable time, the interations inside thlow, and between thlow and a omplex terrain data-base; and lastly, rendering the visual aspet of thlow. The methods desribed rely on smoothed partiles governed by a state equation for animating the flow. We adapt this model to the animation of lava by linking visosity to a temperaturield and by simulating heat transfers. We propose partiular data-strutures that lead to linear omputational time with respet to the number of partiles. Lastly, we study a model based on a olor-and-displaement proedural texture ontrolled by thlow for the realisti rendering of lava. Key words: atural phenomena, animation of fluids, partile systems, proedural textures, impliit surfaes. 1 Introdution Modeling the rihness and omplexity of nature is a onstant hallengor Computer Graphis. In addition to realisti shapes and rendering, Computer Animation tehniques try to generate onsistent motion and deformations. A wide range of natural phenomena have been animated over the past few years. They inlude gaseous phenomena suh as fire or smoke [13, 18, 8, liquids from waves to droplets [9, 12, 16, 7, 10, and the simulation of soft terrains, from footprints to landslides [4, 19, 11. This paper addresses another omplex problem: the animation of lava flows. Our aim is to provide visual realism in both motion and rendering. In order to generate omplex trajetories due to the interations between lavaflows and a omplex terrain database, we need to model the main mehanial features of lava and the way they evolve over time. Another diffiulty is to ompute the simulation at aeptable rates. Lastly, we would like to provide a onvining visualization of lava skin appearane, even though we are not attempting to use a simulaimagis is a joint projet of CRS, IRIA, Institut ational Polytehnique de Grenoble and Université Joseph Fourier. tion approah for this part of the phenomenon. Reently, several movies featuring volanos have been launhed, showing the potential impat of lava animation in thield of speial effets. However, despite the advertising that announed the use of Computer Graphis tehniques, Dantes Peak and Volano mostly use regular speial effets, inluding sale models for lava. As far as we know, Computer Graphis was used for the 2D ompositing of these models with fire images, rather than for omputing a graphial simulation of thlows. Geologists have been interested for years in the simulation of volani explosions and lava flows. However their onern is not produing realisti images, but rather omputing a realisti aount of flow and ash oats (e.g. in a vertial setion), and measuring the way some global physial values vary over time. Thus, their models (see "!$#&%"%''')(*,+-/.&012)03.4*,- 5,%'6-,0"+ 7,%89 :!;/.<=>0 ) do not seem diretly usablor a Computer Graphis simulation. In terms of physially-based simulation, lava an be seen as a liquid whose visosity inreases exponentially when the material ools down. Previous solutions to the animation of liquids range into two main ategories: Eulerian approahes, that onsist of disretizing spae into a fixed 3D mesh and studying how physial fields evolve at the mesh nodes [12, 7; and Lagrangian approahes that onsist of following the motion of puntual mass elements, alled partiles, that sample the liquid. The seond approah seems more onvenient in the ase of lava-flows sine the use of partiles enables us to attah a deformable lava skin to thlow without introduing extra marker elements. In addition, partile systems have suessfully been used for modeling a wide range of behaviors that inludes very visous substanes, and for animating transitions between solid and liquid states, using a temperature parameter [20, 21. Among partile systems, the smoothed partile model introdued in [15, 6 plays an original part, sine inter-partilores are not tuned by hand, but are rather derived from a state equation that defines the marosopi behavior of the material. This model has been applied to the simulation of mud

3 a X X slides [11. There has been no attempt yet, to the authors knowledge, to modify its mehanial features over time. The approah desribed in this paper relies on an extension of the smoothed partile model. We ontrol the evolution of the lava dynamis over time by providing eah partile with a visosity parameter, whih depends on temperature. During a simulation, heat transfers at the surfae of the lava and inside thlow auses the temperature to derease, enabling the transition from a lowvisosity behavior to a highly visous one. The visual aspet of the lava hanges aordingly, thanks to a oating of the partiles that ontrols loal olor and granularity of the lava skin as funtions of temperature. Setion 2 details the model we have designed for the physial features of lava. Implementation issues for the effiient omputation of a lava-flow, inluding the design of onvenient data strutures, are disussed in Setion 3. Setion 4 desribes our method for generating a visually realisti rendering of the animation. 2 Physially-based Modeling of Lava 2.1 Modeling Lava atural lava-flows present a wide diversity of morphologies and strutures. Among other fators, the topography of terrain, and thlow rate out of the rater affet the lava spread. Thesators will be onsidered in Setion 3 for the pratial omputation of lava-flows. Studies of the main mehanial features of lava [3 establish that: Visosity depends on the hemial omposition of the lava; For a given hemial omposition, visosity inreases exponentially when the temperature dereases (see Figure 1, from [3). The mass-density of lava remains quasi-onstant until it ommutes to the solid state. The value of massdensity for basalti lavas is BDC"EGF HJI>K. Figure 1: Visosity as a funtion of temperature, for lavas of different hemial omposition. Our aim is to simulate the lava flowing proess. We are looking for a general model of a visous fluid, robust enough for enabling high visosity hanges inside the material. These hanges will take plae in spae as visosity is not onstant along a lava flow at a given time and in time, sine lava is ooling down during the simulation. During the simulation, thlow s mass density should be maintained ABBLCE>F H I>K. The next setion presents the deformable model that we have used as the bakground for our simulations. This model uses a partile system for modeling thlow, whih is also onvenient for rendering lava skin as will be shown in Setion 4. Its main feature is that, ontrary to standard partile systems, it sets the material to a speified massdensity at rest, thanks to a state-equation that desribes the desired marosopi behavior. 2.2 Smoothed partiles maintaining a onstant restdensity Our model is an extension of the smoothed-partiles simulation method developed by Mathieu Desbrun 1 [6. This setion reviews this previous work. Smoothed partiles simulate a substane whose physial harateristis are governed by a state equation. The following equation states that the pressure 2 field M inside the material is proportional to the differene between the urrent mass-density and a given rest value ;O : MQPRCSTVUW OX where the parameter C represents a stiffness oeffiient. During a simulation, the material is sampled by smoothed partiles. Eah of them represents a sample of mater of fixed mass HZ whih is distributed in spae around its urrent loation [G aording to a smoothing kernel \^ (parameter _ ontrols the extend of the kernel s support). The partiles sample the values of ontinuous physial fields suh as pressure M and mass-density inside the material (so M and respetively denote pressure and density at partile ` ). Interpolation yield the value and gradient of these physial fields anywhere in spae: a S[ X P b S[ X P b a H a H \ S[dUW[ \^)ST[dU^[ where a is the value of field a at partile `. This an be used for deriving the expression of internal pressurores exerted on partile ` from the expression 1 Thormalism was originally inspired from works in astrophysis [15 on Smoothed Partiles Hydrodynamis (SPH). 2 As in [6, the term pressure we use is not totally adequate: g is rather a differene of pressure with a given referene value, thus it an take either positive or negative values.

4 f P t M e e ˆ B H Ž H f \ \ t B B of pressure given by the state equation [6: e hji k bl m UnHoTH qp Mr "sut rv s e where 4\ is the gradient of \J6S[) Uw[ X. The density field is omputed by integrating pressure hanges over timrom its initial value "O (orresponding to the initial partile distribution) using the ontinuity equation: Vx`4yGSz X x x { P B The omponent of the interation fore 4\ e h i k whih is exerted between partile ` and partile } an be either positive or negative aording to the sign of the overpressures M and M. It has been shown in [6 that these fores are similar to Lennard-Jones attration-repulsion fores (ie. long-range attration and short-range repulsion) that are ommonly used in physially-based partile systems [14. One of the advantages of SPH is that no loal user-speified parameter is needed, sine they are diretly derived from the global state equation. As with any partile system, the animation is omputed by integrating, for eah partile, applied fores over time. on-onservativores that model visosity inside the material, as well as external fores suh as gravity and ollision fores with obstales, are added to pressure fores. The smoothed partiles representation provides an expression for the maximal time step at whih eah partile should be simulated, omputed from Courant s ondition [6. The use of an adaptive time-step based on this minimal rate ensures stability of omputations. The main benefits of this model is that the user defines the marosopi behavior of the material through the state equation. As a onsequene, the same substane may be simulated with variable auray, by simply tuning the number of partiles that sample it (this is not the asor partile systems based on Lennard-Jones interation fores, suh as those used in [20, 21, sine the material behavior then depends on both fores parameters and the sale at whih these speifi fores are used). Another advantage of this model is that we are able to ontrol the rest mass-density, whose value is well known for lava. In pratie, we model lava by taking the same smoothing kernel that in [6 and by setting the parameters of the state equation to 3 : O H IGK C~P B BB B The above model is not suffiient for modeling all the physial features of lava listed in Setion 2.1. In the next 3 the higher is, the more inompressible the material will be, but the required time step is smaller. two setions we extend the model to inlude variable visosity and to simulate heat transfers over time. 2.3 Modeling visosity inside a lava-flow Visosity plays a very important part in the dynamis of lava flows. The model for a visosity fore must be hosen with are. The expression of visosity fore used in [15, 6, originally designed for osmologi fluids, was: hj k PƒUnH bl m where ` and }, and of the distane between them: is a funtion of the relative speeds of partiles P &kš Œ kš Ž &ˆ k kš Œ O&O e š if y [ š if y [ where œ is the speed of sound 4 inside the material and y P y U^y, [) P [ U^[), PžST This expression is not onvenient for us, even for modeling visosity at a given temperature. Firstly, thore ontribution from a given neighbor partile } beomes zero when the distane between the two partiles inreases. Seondly, even when the speed vetors are not oriented along the segment between the partiles, this fore ontribution is always applied along this segment. Lastly, the parameters are not easy to alibrate due to the omplex formulation of. We rather use a more intuitive and simpler expression for visosity fores, aimed at modeling the variations of the veloity field at the neighborhood of a partile. The value of thore is proportional to the differene between the partile s speed and the mean speed around it: h k P H bl m y Sine the visosity of lava inreases exponentially when temperature dereases, we set the parameter to: P > ; S Ũ "ª X «d B «w B where ª is a new parameter representing temperature, whih is assoiated with eah partile (we B and wp B,F±A in our simulations). ext we have to design a simulation method for omputing the loal variations of the temperaturield during a simulation. 2.4 Simulation of heat transfers Two kinds of heat transfers should be taken into aount during a simulation: those that are internal to the lava flow, and those that are external (i.e. transfers with the air and with the ground). 4 i.e. the speed of thastest propagation wave.

5 f e S ¹ H H ª \ \ As in [20, 21, we model heat transfers inside the material by integrating the general heat equation: xª x{ P²C6³ ª However, the way we do this is different from previous works, sine we have to express it is the smoothed partiles formalism. Sine SPH annot be used for omputing seond derivatives due to the smoothing effet of the kernel \^, diretly omputing ³ ª (the Laplaian of temperature) is diffiult. In pratie, we ompute ³ ª for eah partile using: ªµP ³ ª P bl m bl m ª UWª Thanks to temporal oherene and very slow speed of the heat transfers inside the material, we an use the value of ª stored at a given time step for omputing ³ ª at the subsequent time step, in a single list traversal. ow we need to model heat transfers that take plae at the surfae of the lava flow, inluding both lava-air and lava-ground interfaes. The term representing the time variation of temperaturor a partile loated at the surfae of thlow should 5 be proportional to the differene between its temperature and the temperature of exterior medium, proportional to the size of the ontat surfae, and inversely proportional to the loal mass density: x ª x { X& k P C STªU^ª X¹ s where ¹, the approximate radius of the small sample of lava the partile models, is omputed from: º»¼ K P In our simulations, we set the temperature of basalti lava to 1200 ½¾ when it spreads out of the rater. It goes down to about 900 ½¾ during the simulation. H O 3 Computing animations of lava flows 3.1 Data strutures The bottlenek of any simulation of a partile system is the omputation, at eah time step, of the interations between neighboring partiles. In the smoothed partiles formalism, interations (through pressure and visosity 5 This is just a simple model onvenient for a Computer Graphis appliations. We do not pretend to simulate the real physis of lava ooling suh as degazing and radiative transfers. fores) take plae as soon as the distane between two partiles is smaller _, where _ is the radius of their smoothing kernel. Sine the model maintains the material around a given rest density, the number of neighbors always stays around a given small value (between 20 and 30 in our simulations). However, in a brutore implementation, the neighbor searh would be quadrati in the number of partiles, whih would lead to unaeptably low performanes. A well-known solution onsists of using a 3D grid that stores the onneted list of the partiles that lie inside eah voxel. In the speifi ase of lava spreading out of a volano, this solution annot be used diretly, sine the 3D grid would be too large. Our solution exploits that that while lava spreads far away from the rater, the loal vertial range of the flow always remains small ompared to the size of the terrain (see Figure 2 (a)). Thus, we use a predefined grid of a large size in the horizontal plane, but with only a few elements per vertial olumn. The vertial sope of eah olumn is adapted in order to over the loal vertial range of thlow over this preise point of the horizontal plane (seigure 2 (b)). During neighbor searh, only partiles lying in a grid voxel that is loser _ from the urrent partile are onsidered. Sine lava approximately maintains its rest density everywhere, alibrating the grid in order to have an almost onstant number of partiles per oupated voxel is easy. This strategy provides a simulation time whih is lose to linear with respet to the number of partiles. Figure 2: (a) Lava spreading out of a volano (ross setion). (b) Data struturor neighbors searh. The terrain is defined by a digital elevation model (DEM), i.e. a 2D grid where altitudes are stored. The use of a DEM makes easier the detetion of ollision between a partile and the terrain, sine it only requires the omputation of the terrain s altitude (through bilinear interpolation) at the partile s projetion onto the horizontal plane. In pratie, ollision detetion is performed only for partiles that are at the surfae of thlow. The omputation of this subset of partiles is also neessary to apply the heat transfer equations. The next setion proposes a riteria for performing this omputation. 3.2 Charaterization of partiles at thlow surfae An original feature of highly deformable materials ompared with solid deformable bodies, is that the set of small matter elements that lie near the surfae may hange over time. This is partiularly obvious when a

6 f e f e flow separates into several disonneted omponents, or when some omponents merge. In our simulations, the set of partiles lying near the surfae has to be reomputed at eah time step. We need a robust riteria for haraterizing these partiles. The gradient of mass-density at a partile loation indiates the diretion where the highest neighbor mass is found. So the border should be searhed for in the opposite diretion. Our riteria states that a partile : is on the surfae if the quotient between the mass of its neighbors loated in the half spae oriented by U and the total mass of all neighbors is under a threshold. Sine this riteria will not work when the lava has ompletely spread out (the gradient of mass-density is in the partile s plane when all the partiles are in ontat with a flat part of the terrain) we add a seond riteria: a partile is at the border if that partile and all its neighbors are approximately loated in the same plane. 3.3 Simulation proess for lava flows At eah integration time step: Generate some more partiles inside the rater, aording to the desired flow rate. For eah partile: 1. Compute the list of neighbors. 2. Use it to ompute, ª, and ³ ª. 3. Compute pressure and visosity fores. 4. Integrate the equation of motion aording to the set of external and internal fores. 5. If the partile is on the surfae of thlow: test for ollisions with the ground, ompute the heat transfer with the exterior. 6. Compute the heat transfers with neighboring partiles. If neessary, modify the value of the integrate step in order to maintain Courant s ondition. We have seen that in order to maintain lava in a quasiinompressible state, our simulations are omputed with a high valuor C. Courant ondition then leads to about 64 integration steps between two frames, using integral integration shemes for inreasing stability. Even in this ase, omputational time is reasonable: On a SGI s workstation, an image is generated every 20 seonds for a simulation of 1000 partiles, and every two minutes for a simulation of 6000 partiles. If we derease C to a less realisti value suh as CdPžÀ B B, less integration steps are needed between two images, so we obtain one image per seond for 1000 partiles. " Figure 4 shows some steps of a lava flow for our standard high valuor C. Partiles are displayed as spheres of radius ¹. Their olor varies with temperature. Displaying partiles as spheres is adequator arefully following eah partile s motion, but does not, however, yield the visually realisti rendering we need. 4 Visually realisti rendering 4.1 Trying to obtain the aspet of basalti lava Figure 7 depits a real basalti lava flow of type aa, whose partiularity is thormation of linkers during the slow transition between fluid and solid states. These linkers are made of the lava foam that has ooled down quiker that the rest of thlow, and merged into regularly spaed lusters. In this paper, we are trying to render this speifi kind of lava, whose roughness, size of linkers, and olor highly depend on temperature. At first sight, obtaining a similar visual aspet for our syntheti lava flows looks like a hallenge. The most urrent solution for defining a surfae around a set of partiles onsists of omputing an iso-surfae of a sum of salar fields generated by the partiles [1, 20, 21, 5. This solution easily deals with topology hanges (separations and fusions) but is not onvenient for our appliation sine impliit surfaes generate very smooth shapes [2. Motion and deformations of our lava flows are simulated at a relatively large sale, then it seems obvious that more geometri omplexity should be generated. Performing a miro-simulation of the lava skin mehanis would be diffiult, omputationally intensive, and is not really useful sine our only aim is visual realism. Thus we must deal with this smaller sale by providing a geometri dressing of the larger one. Perturbating the surfae with a stohasti ontinuous noise, suh as Perlin s noise [17, seems a good approah. A first idea would be to define a 3D noise depending on temperature in a loal frame linked to eah partile, and to use it to deform the impliit primitive defined by the partile. The surfae of thlow would then be omputed as an isosurfae for the sum of perturbated fields. However, this approah would be extremely time onsuming due to the resolution needed for polygonizing the surfae. Moreover, when two neighboring partiles move at different speeds, the addition of noise ontributions would probably produe aliasing artifats (suh as interferenes). Our approah onsists in generating a proedural displaement map, together with a olor texture, on the smooth impliit-surfae generated by a standard isotropi fields around the partiles. Both olor and roughness of the texture aruntion of the loal temperature of the flow. One of the hallenges is to maintain temporal oherene when an animation sequene is rendered: eah

7 surfae detail may ontinuously deform and hange its olor, but must onsistently follow thlow. 4.2 A lava skin that follows thlow Texture is going to be generated on triangles, so thirst point is to tessellate the impliit surfae. This annot be done by using a standard surfae tiling algorithm [2 at eah time step sine, beause of our need of temporal oherene, eah triangle should deform and move with the underlying flow. Our solution is thollowing: 1. We assoiate a sample point on the impliit surfae to eah partile that verifies thlow surfae riteria of Setion 3.2. This is done by searhing for the isosurfae in the diretion of thield s gradient on the partile. 2. We ompute the Voronoï diagram of these sample points: for eah of these points, we sort sample points that orrespond to neighboring partiles in ounterlokwise order with respet to the surfae s normal, and selet those that are ontributing to the Voronoï region. 3. We tessellate eah Voronoï region into triangles that turn around the sample point defining the region. This results into triangles that both tessellate thlow surfae, define the neighborhood of a partile on the surfae, and onsistently follow thlow (see Figure 3). Figure 3: Tesselated Voronoï regions on a flow surfae. 4.3 Generating a proedural texture The idea is to generate a lava skin linker into eah Voronoï region. Sine the sample point at the enter of the region follows a given flow partile, the linkers will be adequately arried by thlow. Clinkers and lava skin between them are modeled by a texture that inludes both loal olor and also a displaement map ontrolling surfae altitude and roughness. We ompute the displaement map as the sum of two terms (see Figure 6): a given 3D profile defining the shape of a linker, a stohasti altitude perturbation modeling the loal surfae s roughness. Continuity onditions at the border of triangles must be maintained arefully. This inludes both olor and displaement Á ontinuity (i.e. geometri ontinuity of derivatives). Modeling speifi profiles whose shape and altitude depend on temperature, and whose support is inluded into eah Voronoï region is straightforward. Color onsisteny and ontinuity an easily be obtained by assoiating a given olor to eah altitude, with a olor map depending on the loal temperature of thlow. The next paragraph onentrates on the most diffiult part of the proess, ie, defining a Á stohasti noise whih gives the desired visual effet. 4.4 Continuous Perlin s noise on a triangular mesh Perlin s noise [17 is a stohasti auto-similar Á noise that has beome a standard for generating objets that look like wood, marble, fog, or rok surfae. One of its main features is to maintain ontinuity of both noise and noise derivatives. The idea is to use it for defining a 2D displaement texture that will serve as a perturbation of altitude over eah lava skin triangle. However, we need to generate the noise on a 2D triangular mesh, sine it is easier to guarantee ontinuity through two adjaent texture pathes if the noise ontrol points fall exatly on their boundary. Perlin s standard model being defined on a quadrangular grid, we modify the algorithm in thollowing way: 1. we generate a pseudo-periodi noisuntion on a regular grid of equilateral triangles by: randomly assoiating a plane to eah grid node, defined by its elevation above the node and by its normal; defining the noise at any point inside the mesh as the baryentri interpolation of the distanes to the three planes assoiated to the verties of the triangle where the point lies. 2. we define thinal noise giving the altitude of a mesh point as the sum of instanes of the pseudoperiodi noise defined above, applied at different sales thanks to reursive subdivisions of the triangular mesh. This gives a fratal aspet to the noise. The olor and displaement texture we obtain is depited at the top right of Figure 6. Sine the noisuntion has been generated on a regular grid made of equilateral triangles, applying it on the non-equilateral triangles resulting from the tessellation of Voronoï regions may loally alter the isotropy of the noise. In pratie, we redue this problem by suppressing the very thin triangles (by merging their edges) that may appear around a sample point.

8 Figure 4: An example of lava-flow where partiles are displayed as spheres. About 3000 partiles have spread out of the volano in the last image. Figure 5: A textured lava flow. Figure 6: Top left: a linker s profile; top right: stohasti perturbation modeling the surfae s roughness; bottom: the resulting texture. Figure 7: A real lava flow for basalti lava of type aa. Computational time has been measured on a test sene ontaining one linker made of 6 triangles (seigure 6, bottom) overing a video-sized sreen and subdivided 32 times (so that 6144 very small triangles are drawn). Computing the texture takes about 0.15 seonds per frame on a SGI s workstation. As small triangles that sample the texture should always be of the same size (about a few pixels), the subdivision depth dereases when the number of polygons inreases, so the rendering time remains of the same order of magnitudor any sene (less than a seond per frame).

9 5 Conlusion This paper has foussed on the animation and rendering of lava flows. Figure 5 depits some steps of an animation where lava flows down the slopes of a volano. Animation sequenes are availablrom ÂÃÃÄÅÅ ÆÆÆ Ç>È " Å ÉÊËÊÅ. Lava flows represent a hallengor physially-based animation, sine the mehanial features of lava hange over time. This hange is governed by a temperature field, that needs to be animated. Thirst ontribution of this paper is to show that the smoothed partiles formalism is onvenient for performing this kind of simulation. In order to model lava, we extend the equations, and we propose an effiient way to simulate them. Internal fores inside thlow, and interations between thlow and a omplex terrain data-base are omputed in a reasonable time, by the implementation of adequate data-strutures. Performing an animation is made easier by the use of a marosopi model for the lava flow, whih only inludes a few intuitive parameters (mass, density, stiffness, initial visosity and temperature of lava, air and ground temperatures). In the ontext of searhing for visual realism, we also addressed the problem of rendering lava. Our solution, designed for a speifi type of basalti lava flow, onsists of rendering a moving texture ontrolled by thlow and generated on thly on an impliit surfae that surrounds the partiles. The texture ombines olor and displaement information. The displaement map is proedurally omputed as the sum of a large sale shape and of a Perlin s noise omponent. Texture moves and deforms with the underlying flow aording to the loal variations of thlow speed and temperature. In partiular, roughness of the texture inreases when the lava ools down, while its olor hanges. Our methods for defining the displaement map allows us to ontrol the visual aspet of the lava skin, and ensures spatial and temporal ontinuity during an animation. Future work inludes the modeling of other ategories of lavas, suh as blok lavas for whih an extra animation layer ould be used for animating large lava-rust bloks arried by thlow, or obsidian flows whose skin behaves as a smooth deformable surfae that folds and rolls during motion. The detailed modeling of a lava front, with for example liquid parts spreading out of the rigid rust, is also a hallenging work to be done. Aknowledgments: We wish to thank Mathieu Desbrun, whose researh work on the animation of highly deformable substanes served as a basis for this work. Thanks to Pierre-Olivier oirey for integrating Mathieu s work on our animation platform FABULE, and to Eugenia Montiel for re-reading this paper. Many thanks to Eri Ferley for whose pratial help was determinant for making the whole thing work. 6 Referenes [1 J. 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