Multi-Layer Implicit Garment Models Roberto E. P´ erez-Urbiola Isaac Rudom´ ın G. Instituto Tecnol´ ogico y de Estudios Superiores de Monterrey Campus Estado de M´ exico Km. 3.5 Carretera Lago de Guadalupe Atizap´ an de Zaragoza, Estado de M´ exico, CP 52926. M´ exico rperez@campus.cem.itesm.mx rudomin@campus.cem.itesm.mx Abstract This paper presents a new way to model clothing worn by articulated implicit characters. A scalar field is produced using ellipsoids as primitives. Isosurfaces are then used to place garments in one or more layers. As each implicit sur- face is independent, collision detection is not needed. The cloth is a polygonal mesh whose vertices are in turn moved towards their destination isosurface using the gradient of the scalar field. In order to maintain the cloth’s shape and size a net of simple springs is used. We improve appearance by adding noise to simulate wrinkles and light wind. 1. Introduction Computer animations that we can see today consist mostly of rigid solid objects. Lately, however, we are start- ing to see flexible objects being used more often. Solid objects are usually described by a polygon mesh that is too complex to manage in a vertex by vertex way, as is often the case when dealing with flexible characters. Implicit surfaces can be used to model them. An implicit surface is defined as all the points that satisfy the condition in a given three dimensional scalar field. Different constants refer to separate isosurfaces. In order to create realistic articulated soft objects, we can use ellipsoids in combination with blending functions to shape the scalar field. Our articulated model is similar to Wilhelms’ [21] and includes a skeleton, joints and muscles. Many researchers are working in the cloth design, mod- elling and animation [4][10], with various approaches. Both physical and geometric methods have been used to model cloth. Geometric approaches try to imitate the shape of cloth. For example, Weil [20] uses catenary curves to ap- proximate the appearance of hanging cloth from its corners. Hybrid techniques combine geometric approaches with some sort of physical phase. Rudom´ ın [13] approximates the initial state of draping cloth on an object with its convex hull, then continues with physical simulation. Terzopoulos et al. [14] generalised deformable model was one of the first physical methods introduced. Neverthe- less, it requires solving a large system of simultaneous ordi- nary differential equations. Since then, physical methods have been commonly sim- ulated by calculating the actual forces and energies involved in a grid of particles. For static views of cloth, a minimum energy state is searched. For dynamics, it is necessary to in- tegrate the equations using Euler or Runge-Kutta. Breen et al. [5][9] employ an interacting-particle model which is based on the microstructure of woven cloth. The modelling of clothing worn by virtual actors has been investigated by Thalmann et al. [19]. Their algorithm is generic enough to handle cloth by itself (i.e. clothing with- out a person under it) [15]. They pursue physically accurate clothing coupled with an optimised algorithm for collision detection [16]. References to their hierarchical collision de- tection solution and other algorithms can be found in [17]. Their clothing systems [19][18] include a collisiondetection engine, a mechanical simulation engine, software for human body modelling and deformation, garment design and sim- ulation, and a graphical interface. Garments are first assem- bled from panels and latter placed on a human model. Baraff et al. [1] has dramatically reduced the time needed to perform implicit integration which allows the simulation to advance in larger steps that with either Euler or Runge- Kutta. Nevertheless, the issue of multiple layers of clothing has not yet been addressed. The problem is the large amount of time needed for calculating collision detection.