We present a fast and stable system for animating materials that melt, flow, and solidify. Examples of real-world materials that exhibit these phenomena include melting candles, lava flow, the hardening of cement, icicle formation, and limestone deposition. We animate such phenomena by physical simulation of fluids -in particular the incompressible viscous Navier-Stokes equations with free surfaces, treating solid and nearly-solid materials as very high viscosity fluids. The computational method is a modification of the Marker-and-Cell (MAC) algorithm in order to rapidly simulate fluids with variable and arbitrarily high viscosity. This allows the viscosity of the material to change in space and time according to variation in temperature, water content, or any other spatial variable, allowing different locations in the same continuous material to exhibit states ranging from the absolute rigidity or slight bending of hardened wax to the splashing and sloshing of water. We create detailed polygonal models of the fluid by splatting particles into a volumetric grid and we render these models using ray tracing with sub-surface scattering. We demonstrate the method with examples of several viscous materials including melting wax and sand drip castles.

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Both image textures and procedural textures suffer from minification aliasing, however, unlike image textures, there is no good automatic method to anti-alias procedural textures. Given a procedural texture on a surface, we present a method that automatically creates an anti-aliased version of the procedural texture. The new procedural texture maintains the original texture's details, but reduces minification aliasing artifacts. This new algorithm creates a pyramid similar to MIP-Maps to represent the texture. Instead of storing per-texel color, our texture hierarchy stores weighted sums of reflectance functions, allowing a wider range of effects to be anti-aliased. The stored reflectance functions are automatically selected based on an analysis of the different reflectances found over the surface. When the texture is viewed at close range, the original texture is used, but as the texture footprint grows, the algorithm gradually replaces the texture's result with an anti-aliased one.