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Abstract
In this paper we summarize the technological advances in hair simulation for computer graphics. There are mainly three tasks in hair simulation - Hair Shape Modeling, Hair Dynamics and Hair Rendering. Various models developed for these tasks, fall mainly in the categories of particle systems, explicit hair models, cluster hair models and models based on volumetric textures. We discuss advantages and disadvantages of each of these approaches. We also introduce new hair shape modeling paradigm based on fluid flow. The proposed method provides a sound basis for modeling hairbody and hair-hair interaction. Keywords: hair shape modeling, hair animation, hair rendering, hypertexture
One of the many challenges in simulating believable virtual humans has been to produce realistic looking hair. The virtual humans, two decades ago, were given polygonal hair structure. Today, this is not acceptable. Realistic visual depiction of virtual humans has improved over the years. Attention has been given to all the details necessary for producing visually convincing virtual humans and many improvements have been done to this effect. On a scalp, human hair are typically 100,000 to 150,000 in number. Geometrically they are long thin curved cylinders having varying thickness. The strands of hair can have any degree of waviness from straight to curly. The hair color can change from white to grey, red to brown, due to the pigmentation, a nd have shininess. Thus, difficulties of simulating hair stem from the huge number and geometric intricacies of individual hair, complex interaction of light and shadow among the hairs, the small scale of thickness of one hair compared to the rendered image and intriguing hair to hair interaction while in motion. One can conceive three main aspects in hair simulation - hair shape modeling, hair dynamics or animation, and hair rendering. Often these aspects are interconnected while processing hairs. Hair shape modeling deals with exact or fake creation of thousands of individual hair - their geometry, density, distribution, and orienta-tion. Dynamics of hair addresses hair movement, their collision with other objects particularly relevant for long hair, and self-collision of hair. The rendering of hair involves dealing with hair color, shadow, specular highlights, varying degree of transparency and anti-aliasing. Each of the aspects is a topic of research.
Many research efforts have been done in hair simulation research, some dealing only with one of the aspects of simulation -shape modeling, dynamics or rendering. Several research efforts were inspired by the general problem of simulation of natural phenomena such as grass, and trees. These addressed a more limited problem of simulating of fur or short hair. We divide hair simulation models into four categories depending upon the underlying technique involved: particle systems, volumetric textures, explicit hair models and cluster hair model. We discuss models presented by researchers in each of these model categories and state their contribution to the three aspects of hair simulation, i.e. hair shape modeling, hair dynamics and hair rendering. We also introduce a new hair shape modeling paradigm based on fluid flow.
The paper is organized as follows. First we give the state of the art in hair shape modeling. The hair shape modeling research in each category of the imulation models is presented. Models for hair dynamics are briefly described in Section 3. Section 4 presents the problem of hair rendering and the various solutions proposed by different people. Finally, we summarize the effectiveness and limitations of models in the four categories related to each aspect of hair simulation in the form of a table. Some future avenues for research in hair simulation are also outlined.
2 Hair Shape Modeling
Intricate hairstyle is indeed a consequence of physical properties of an individual hair and complex hair-hair and hairbody interactions. As we will see in the next section, modeling complex hair dynamics, that too at interactive speeds, is currently impractical. For the reasons, it would be worthwhile to treat hair shape modeling as a separate problem and use some heuristic approach. Early attempts of styling long hair were based on explicit hair models. In the explicit hair model, each hair strand is considered for the shape and the dynamics.
Daldegan et al [5] proposed that the user could interactively define a few characteristic hair strands in 3D and then populate the hair style based on them. The user is provided with a flexible graphical user interface to sketch a curve in 3D around the scalp. A few parameters such as density, spread, jitter and orientation control the process that duplicates the characteristic hairs to form a hair style. Figure 1 illustrates the method of defining few characteristic curves and resulting hairstyles from the method. Similarly, even for the fur modeling, Daldegan et al [4], Gelder et al [8] and Bruderlin et al [1] took similar explicit hair modeling approach. Figure 12 illustrates a furry coat modeled by the explicit hair model.
The explicit hair models are very intuitive and close to reality. Unfortunately, they are tedious for hairstyling. Typically, it takes 5-10 hours to model a complex hair style, as in figure 1, using the method in [5]. They are also numerically expensive for hair dynamics. These difficulties are partially overcome by considering a bunch of hair instead of individual hair in the case of the wisp/cluster models. This assumption is quite valid as in reality. Due to effects of adhesive/ cohesive forces, hairs tend to form clumps. Watanabe introduced the wisp modeled in [24, 25]. Yan et al [26] modeled the wisps as generalized cylinders, see figure 2. One of the contributions of the work was also in rendering of hair using the blend of ray-tracing generalised cylinders and the volumetric textures. The wisp model is also evident in [2].
Surprisingly, till now, the wisp models are only limited to static hair shape modeling and we feel that it offers an interesting research possibility of modeling hair dynamics, effi-ciently. It would be interesting to model, how hair leave one wisp and join the other under dynamics.
Nature exhibits some interesting fuzzy objects such as clouds, fire, eroded rocks and fur for which it is hard to have explicit geometric definition. Using the volumetric texture approach, fur can be modeled as a volumetric density function. Perlin et al [18] introduced hypertextures, which can model fur, see figure 3. Here, fur is modeled as intricate density variations in a 3D space, which gives an illusion of the fur like medium without defining geometry of each and every fiber. The model is essentially an extension to procedural solid texture synthesis evaluated through out the region, instead of only in the surface.
They demonstrated that, combinations of simple analytical functions could de-fine furry ball or furry donut. They further used 3D vector valued noise and turbulence to perturb the 3D texture space.This gave the natural looks to the otherwise even fur defined by the hypertexture. A good discussion on the procedural approach to modeling volumetric texture and fur in particular is in [7]. Hypertexture method by Perlin et al is only limited to geometries that can be analytically defined. Kajiya et al [12] extended this approach to have hypertextures tiled on to complex geometry. They demonstrated this by modeling a furry bear, see figure 10. They used a single solid texture tile namely texel and mapped it repeatedly on the bear’s geometry. The texels automatically orient in the direction away from the surface and thus one has fuzzy volumetric density variation around the bear, which is the fur.
As evident from previous discussions, one of the strengths of the explicit hair models is their intuitiveness and ability to control the global shape of the hair. On the contrary, volumetric textures give a nice way of interpreting complexity in nature and they are rich in details. We notice that the fluid flow has both the characteristics, which we would like to exploit for hair shape modeling. We model hair shape as streamlines of a fluid flow. For complete details of the method, we refer to [10]. We choose the flow to be an ideal flow. User can setup few ideal flow elements around the body geometry to design a hairstyle, as shown in figure 2. The hair-body interaction is modeled using source panel method and hair-hair interaction is handled by the continuum property of fluid. Thus user can design complex hairstyles without worrying about hair-body and hair-hair interaction. Hairstyles in figure 5 and 6 are the examples of modeling hair as a fluid flow.
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