*the model exhibits several important features of real clay, namely plasticity, mass conserva-
very simple and intuitive way to create complex shapes: even children use clay at
Graphical Models 66 (2004) 352369
1524-0703/$ - see front matter 2004 Elsevier Inc. All rights reserved.
* Corresponding author. Fax: +33 476615440.E-mail addresses: Guillaume.Dewaele@imag.fr (G. Dewaele), email@example.com (M.-P. Cani).tion, and surface tension eects. These features make the model intuitive, since the userobtains the shapes he expects, as demonstrated by our results. 2004 Elsevier Inc. All rights reserved.
Keywords: Virtual clay; Shape modeling
Compared to traditional tools for numerical shape modeling, real clay remains aGuillaume Dewaele, Marie-Paule Cani
GRAVIR-IMAG, GRAVIR is a joint lab of CNRS, INRIA, Institut National Polytechnique de
Grenoble and Universit Joseph Fourier, France
Received 4 February 2004; received in revised form 28 April 2004; accepted 23 June 2004Available online 17 September 2004
Making virtual modeling as easy and intuitive as real-clay manipulation is still an unsolvedproblem. This paper takes a step in this direction: in addition to oering standard featuressuch as addition and removal of material, it uses a new real-time plasticity model to let theuser apply local and global deformations such as those made in real clay by pressing with anger or bending a sculpture with one hand. Although not completely physically accurate,Interactive global and local deformationsfor virtual claydoi:10.1016/j.gmod.2004.06.008
G. Dewaele, M.-P. Cani / Graphical Models 66 (2004) 352369 353school. Many artists prefer expressing themselves with real materials instead of usinga computer.
If one could get the benets of real clay in a computer-based modeling system, onecould have the best of both worlds: virtual clay would neither dry nor crack; it couldbe mutated from softer to dryer states as needed; the artist could pause at any time,and return to work as convenient without worrying about material changes in theinterim. Furthermore, gravity would no longer be a problem, so shapes than cannotbe made easily with real material would become possible. Finally, the advantages ofany computer-based modeling tool would apply: the artist would be able to work atany scale and use any size of tool, simplifying the production of ne details as well asglobal features, and virtual modeling would allow copy/paste, undo, etc., as well asmore clay-specic ideas such as temporarily removing a part of the model to ease theediting of hard-to-reach areas.
Although previous virtual clay models oer real-time interaction and a number ofinteresting features, most were either restricted to carving and adding material, oradapted solely to surface deformation, not allowing topology modication. Andthe operations they supported often failed to provide an intuitive interface for mod-eling, because some of the dening features of clayits constant volume, its surfacetensionwere not simulated in the systems.
This paper proposes the rst volumetric, real-time virtual clay model which can beboth sculpted by adding and removing material, and deformed through interactionwith rigid tools. Either global or local, the deformations mimic the eects of the toolson real clay, due to plasticity, mass conservation, and surface tension.
1.1. Related work
Although an impressive number of computer graphics works have used the termsculpting [2,3,1214,16,18,20,22,23,30,31] or even clay [7,19], none has provided areal-time model that mimics the main feature of real clay, namely the ability to un-dergo plastic, constant volume deformations in addition to matter addition and re-moval. The previous approaches fall into three main categories: empirical surfacemodels, empirical volume models, and physically based models.
The rst group of interactive sculpting methods relies on surface representations[3,18,20]. Such representations ease the application of interactive deformations, butrequire the use of complex mechanisms for enabling topological changes. Moreover,these geometric models cannot easily provide the same features as the interactionwith a volumetric material, such as constant volume deformation.
Volumetric models [1,1114,22,23] are much closer to real clay: most of them aredened using a scalar eld, which is either stored in a grid or controlled throughprimitives such as B-spline volumes. The surface of the object is an isosurface of thiseld, which plays a similar role than a density of material. This representation is veryadequate to the application of volumetric operations, such as carving the object oradding material, performed through local editing of eld values. These volumetricrepresentations therefore handle any kind of topological change without the needof any specic mechanism. Only local deformations with no volume conservation
354 G. Dewaele, M.-P. Cani / Graphical Models 66 (2004) 352369were dened . Solutions using cellular automata have been purposed to computelocal deformations of a virtual clay [1,11] or sand . Interactive free-form model-ing with volume conservation and topological changes are possible. However, noneof these models provides the ability to deform the piece of clay, as an artist would dowhile putting the limbs of a model in the right posture.
Although physically based modeling is a good way to ensure intuitive results whendeforming shapes, it has hardly been applied to virtual clay models. Real clay liessomewhere between viscous uids  and plastic solids . All previous physicallybased clay models [19,28,30] relied on the plastic solid representation. A plasticbehavior can easily be obtained by extending an elastic model. Typically, an objectsrest shape is given the ability to locally absorb the deformations that exceed a giventhreshold . In such models, applying the very large deformations that real claycan undergo, including local matter displacement, would require frequent re-mesh-ing of the model. In particular, enabling topological changes (such as separationof matter into several pieces) appears incompatible with real-time performance, sincemost real-time deformable models exploit the materials internal structure for prein-verting matrices or pre-computing hierarchies [6,8,15,17]. Therefore, none of the pre-vious physically based clay models allows the simulation of very large deformations,including relative matter displacement inside the shape, carving, fusion, and separa-tion. Geometric topological changes were however made possible using a cleverlyadapted representation, i.e., subdivision solids . But these changes in topologystill required the user to specify which cells should be deleted or joined.
If we look upon the uid modeling side, some non-real-time particle-based modelswere used to represent very viscous material [5,27,29], somewhat similar to clay.Real-time performance was only obtained in Eulerian uid simulations [24,25], forwhich the uid was occupying the entire space (in contrast to clay, which is boundedby a time-varying surface).
As we just saw, none of the previous real-time deformable model exhibits the fea-tures of clay we would like to mimic. The main contribution of this paper is to de-scribe a new deformable model for virtual clay that does capture these features.Although it was inspired by the way real material behaves, our model does not fullycapture the physics of clay. We believe that its capability to exhibit the main char-acteristic of clayextreme plasticity, including enabling relative matter displacementinside the block of material, topological changes, constant volume, surface tensionwill be sucient for the user to recover the feeling he gets when interacting with realclay.
Our model exploits a layered approach for achieving this goal with real-time per-formance: based on a standard volumetric representation (i.e., mass density valuesstored in a grid), it uses the combination of three independent deformation layersfor providing the desired behavior. These three layers, respectively, model large-scaledeformations, mass conservation (which yields smaller-scale matter displacement),and surface tension. These layers are activated successively during each time step.
be easily implemented; we currently use the algorithms described in .
G. Dewaele, M.-P. Cani / Graphical Models 66 (2004) 352369 355The remainder of this paper focuses on our new contribution: the ability to de-form the clay in real time, without modifying the underlying quantity of material.
2.2. Deforming virtual clay
In our representation, deforming clay just requires decreasing the eld function insome regions, while increasing it in others. Since the quantity of material should notbe modied, we basically have to add to some cells the exact quantity of matter weare removing elsewhere, thus modeling matter displacement.Since they share the same underlying volumetric representation, coherence is en-sured, a layer being immediately aware of the changes of the clay state due to theaction of the other layers.
The remainder of this paper develops as follows: Section 2 describes our represen-tation for clay and motivates the use of multiple layers for the simulation. Section 3details our three layers. Section 4 deals with real-time rendering. Section 5 presentsresults. We conclude and discuss future work in the last section. This paper is a re-vised version of the work we presented at Pacic Graphics 03 .
2. Our clay model
2.1. Volumetric representation
Since we are working with a solid material, a volumetric representation is a nat-ural choice. It permits easy modeling of topological changes, whi