Gavin S. P. Miller

Rapid, stable fluid dynamics for computer graphics

We present a new method for animating water based on a simple, rapid and stable solution of a set of partial differential equations resulting from an approximation to the shallow water equations. The approximation gives rise to a version of the wave equation on a height-field where the wave velocity is proportional to the square root of the depth of the water. The resulting wave equation is then solved with an alternating-direction implicit method on a uniform finite-difference grid. The computational work required for an iteration consists mainly of solving a simple tridiagonal linear system for each row and column of the height field. A single iteration per frame suffices in most cases for convincing animation.Like previous computer-graphics models of wave motion, the new method can generate the effects of wave refraction with depth. Unlike previous models, it also handles wave reflections, net transport of water and boundary conditions with changing topology. As a consequence, the model is suitable for animating phenomena such as flowing rivers, raindrops hitting surfaces and waves in a fish tank as well as the classic phenomenon of waves lapping on a beach. The height-field representation prevents it from easily simulating phenomena such as breaking waves, except perhaps in combination with particle-based fluid models. The water is rendered using a form of caustic shading which simulates the refraction of illuminating rays at the water surface. A wetness map is also used to compute the wetting and drying of sand as the water passes over it.

A progressive multi-pass method for global illumination

A new progressive global illumination method is presented which produces approximate images quickly, and then continues to systematically produce more accurate images. The method combines the existing methods of progressive refinement radiosity, Monte Carlo path tracing and light ray tracing. The method does not place any limitation on surface properties such as ideal Lambertian or mirror-like. To increase efficiency and accuracy, the new concepts of light source reclassification, caustics reconstruction, Monte Carlo path tracing with a radiosity preprocess and an interruptible radiosity solution are introduced. The method presents the user with most useful information about the scene as early as possible by reorganizing the method into a radiosity pass, a high frequency refinement pass and a low frequency refinement pass. The implementation of the method is demonstrated, and sample images are presented.

GLOBULAR DYNAMICS: A CONNECTED PARTICLE SYSTEM FOR ANIMATING VISCOUS FLUIDS

Connected particle systems can depict many objects difficult to model in any other fashion. We present a method for animating viscous fluids by simulating the forces of such particles interacting with each other. This method allows for collision detection between the particles and obstacles, both stationary and mobile, and it allows solid objects to break and melt. An approximate method for covering the particles with an isosurface for efficient rendering is also presented.

Efficient algorithms for local and global accessibility shading

This paper discusses the use of two different approaches for computing the “accessibility” of a surface. These metrics characterize how easily a surface may be touched by a spherical probe. The paper also presents various acceleration techniques for accessibility. The idea of surface accessibility is extended to include “global accessibility” which measures the ability of a spherical probe to enter a structure from outside as well as to fit locally on the surface. The visual effect of shading using accessibility is shown to resemble the patina on certain tarnished surfaces which have then been cleaned.

Efficient techniques for interactive texture placement

This paper describes efficient algorithms for the placement and distortion of textures. The textures include surface color maps and environment maps. Affine transformations of a texture, as well as localized warps, are used to align features in the texture with features of the model. Image-space caches are used to enable texture placement in real time.