Animation Based in Dynamic Simulation Involving Irregular Objects with Non-Homogeneous Roughness Luis A. Rivera Departamento de Inform´ atica, PUC-Rio, Marquˆ es de S˜ ao Vicente, 255, 22453-900, Rio de Janeiro, RJ, Brasil rivera@inf.puc-rio.br Paulo C. P. Carvalho Luiz Velho IMPA–Instituto de Matem´ atica Pura e Aplicada Estrada Dona Castorina, 110, 22460 Rio de Janeiro, RJ, Brasil pcezar,lvelho @visgraf.impa.br Abstract We propose a new technique that provides a unified framework for modeling the collision dynamics of objects having arbitrary shape and roughness. The technique as- sumes that boundary of the object is expressed by elemen- tary segments with some random distribution of perturba- tion. Collision detection and treatment is done considering this conceptual representation. In order to efficiently de- tect collision between irregular objects, we introduce the aumented oriented bounded box tree. 1. Introduction In order to be realistic, a simulation of the dynamic be- havior of a set of rigid objects should consider all possible characteristics of the objects and their environment. One of the characteristics to be considered is the geometry of the objects. Much of the work in the area concentrates on objects defined by poligonal aproximation, or on piecewise smooth objects described by either implicit or parametric surfaces, but does not consider objects of arbitrary shape with perturbation or roughness. Several techniques have been proposed to model ob- jects having arbitrary shapes, such as particle based mode- ling [28], variational methods [26, 27], direct manipulation [2, 3, 21], and free form deformation [4, 12], among others. All those techniques allow making objects of a desired form starting from a initial one. In this way we could represent a model that is an approximation to a real object. Usually, this approximation, however, is good only up to a certain level of detail, since the surface of real world objects is not completely smooth. Rather, it presents some irregular de- gree of roughness, which can affect the dynamic behavior of the objects in animation. Most simulation techniques treat collitions events using friction coefficients , that sumarize the effects of surface de- tails and material properties in contacts [11], considering this as being constant on all object surface; these conside- ration is not all true, because in the real word the surface details are not allways homogeneous, for that the friction coefficient must vary in each point of the object surface, so affecting dynamic behavour of contacts. In this work, we propose a new technique that provides a unified framework for modeling animation based in dy- namic simulation with objects having arbitrary shape and roughness. The technique consider the characteristic of sur- face details to treat the collision and then to produce real behavour of the objects in animation. In Section 2 we discuss the modeling of objects hav- ing arbitrary shape and roughness, using a multiresolution representation based on wavelets and statistical estimation techniques to deal with the finer levels of detail; in Section 3 we explain how to detect collisions between objects with roughs; in Section 4 we formalize the dynamic aspects of such a collision. Finally, in Section 5 we conclude and dis- cuss possible extensions of this approach. 2. Complex objects In this paper a complex object is an object of arbitrary shape with irregular distribution of detail representing its rough. The details could be expressed by a multiresolution representation that, conceptually, considers all levels of de- tail of the object, in such a way that it captures its rough. We say conceptually because it is not practical to repre- sent explicitly the finer levels of detail. Instead, explicit representation is given up to a certain level of detail. Be- yond that level, detail is seen as a perturbation applied to the surface, according to certain statistical laws.