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This paper proposes a simple and computationally inexpensive method for animation of clouds. The cloud evolution is simulated using cellular automaton that simplifies the dynamics of cloud formation. The dynamics are expressed by several simple transition rules and their complex motion can be simulated with a small amount of computation. Realistic images are then created using one of the standard graphics APIs, OpenGL. This makes it possible to utilize graphics hardware, resulting in fast image generation. The proposed method can realize the realistic motion of clouds, shadows cast on the ground, and shafts of light through clouds.

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Figure 1: Viscous fluids simulated with our implicit formulation. Left to right: caramel sauce coiling with a particle view in the inset; a dragon consisting of particles with different viscosities; melted chocolate buckling with a particle view in the inset. AbstractWe propose a stable and efficient particle-based method for simulating highly viscous fluids that can generate coiling and buckling phenomena and handle variable viscosity. In contrast to previous methods that use explicit integration, our method uses an implicit formulation to improve the robustness of viscosity integration, therefore enabling use of larger time steps and higher viscosities. We use Smoothed Particle Hydrodynamics to solve the full form of viscosity, constructing a sparse linear system with a symmetric positive definite matrix, while exploiting the variational principle that automatically enforces the boundary condition on free surfaces. We also propose a new method for extracting coefficients of the matrix contributed by second-ring neighbor particles to efficiently solve the linear system using a conjugate gradient solver. Several examples demonstrate the robustness and efficiency of our implicit formulation over previous methods and illustrate the versatility of our method.