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This work concerns the realistic modeling, rendering and animation of water. Specifically, the paper surveys many of the most outstanding references on computer graphics techniques regarding this problem developed during the period 1989-97. The paper, which has been organized for clarity into two different periods, follows on from a previous one dedicated to the same topic during the period 1980-88 [11]. 1 Early nineties: 1989-92 Although the previous works [11] provided adequate models for waves hitting the beach, to quote just one example, a significant range of physical phenomena still remained unexplored. A major question was the accurate description of fluid dynamics. Great interest was also placed upon several physical phenomena related to water such as: – state of matter changes such as melting and freezing, – complex natural phenomena such as wetting and drying, – mass transport or flow including meandering, – the behavior of individual droplets and their streams, – interaction with static and dynamic buoyant obstacles, etc. On the other hand, a number of interesting rendering effects, such as the simulation of reflected waves, the interaction between light and water, the analysis of caustics, etc. had not yet been considered by the previous computer graphics techniques. Finally, water realistic animation was still in its infancy and it had to be greatly improved. To overcome these limitations, several new models were proposed. Roughly, they can be grouped into two different alternatives which are analyzed in the following sections. This research was supported by the CICYT of the Spanish Ministry of Education (projects TAP1998-0640 and DPI2001-1288). P.M.A. Sloot et al. (Eds.): ICCS 2002, LNCS 2330, pp. 191−200, 2002.  Springer-Verlag Berlin Heidelberg 2002 1.1 Interaction of a Large Number of Particles The first alternative tried to simulate the fluid dynamics by the interaction of a large number of particles [7, 17, 26, 27]. Thus, in [17] and [27] the authors studied the attraction and repulsion forces between particles to simulate various degrees of fluid viscosity and state of matter change such as melting. For example, the approach in [17] presented a particle based model for fluids, powders and gelatinous solids. This model was based on what the authors called globules, a term intended to avoid connotations with words such as particle or blob, and used to designate the elements of the connected particle system. Globules can be applied for the detection of soft collisions between the particles and obstacles, involving forces which vary gradually with distance, thus allowing globules to flow over one another. The forces acting on the particles depend on two scaling factors, one for attraction/repulsion, sr, and another one, sd, (drag) to attenuate the inter-globule force based on distance. For powders and fluids the globules interact with a short range repulsive force and drag. In the solid state the attraction term is also considered, so globules interact with a short range repulsion, a medium range attraction and long range indifference. The temperature values for a given pair of globules can be used to simulate changes in their interaction behavior, thus allowing the melting of solids and the freezing of liquids. This temperature effect was later analyzed by Tonnesen in [27], through a model describing the changes in geometry and movement of elemental volumes as a consequence of thermal energy and external forces. This model simulates both the liquid and solid states by varying the shape of the potential energy curve as a function of temperature. Objects at hot temperatures behave like fluids, with rapidly varying geometry. At cold temperatures they resemble solids, with a stable shape which can be modified, however, under the influence of appropriate external forces. Changes in topology are modelled by using particles to represent elemental volumes with potential energies between pairs of particles. Finally, another remarkable reference using this particle interaction scheme is due to Sims [26]. In his work, a waterfall was simulated by applying gravity to thousands of non-interacting water droplet particles and bouncing them off obstacles made of planes and spheres. The water droplets were created at the top of the waterfall, flowed over the last edge at the bottom and then recycled back to the top of the waterfall. These particles of different shapes, sizes, colors and transparencies were rendered by using a parallel rendering particle system incorporating some techniques for increasing the image quality, such as anti-aliasing, hidden surfaces and motion-blur. The combination of some ad hoc tricks (such as the combination of white and blue particles to avoid lighting calculations and exaggerated motion blur to give the flow a smoother look) allow realistic pictures of the waterfall to be obtained. Additional effects such as the deformations produced on a falling droplet as it enters in contact with a surface are also analyzed in [20]. 1.2 Partial Differential Equations for the Fluid Dynamics The second approach is to directly solve a partial differential equation (PDE) system describing the fluid dynamics [14]. Of course, this alternative is much 192 A. Iglesias

Computer Graphics Techniques for Realistic Modeling, Rendering and Animation of Water. Part II: 1989–1997