A technique for rendering images of volumes containing mixtures of materials is presented. The shading model allows both the interior of a material and the boundary between materials to be colored. Image projection is performed by simulating the absorption of light along the ray path to the eye. The algorithms used are designed to avoid artifacts caused by aliasing and quantization and can be efficiently implemented on an image computer. Images from a variety of applications are shown.

An architecture is presented for fast high-quality rendering of complex images. All objects are reduced to common world-space geometric entities called micropolygons, and all of the shading and visibility calculations operate on these micropolygons. Each type of calculation is performed in a coordinate system that is natural for that type of calculation. Micropolygons are created and textured in the local coordinate sysem of the object, with the result that texture filtering is simplified and improved. Visibility is calculated in screen space using stochastic point sampling with a z buffer. There are no clipping or inverse perspective calculations. Geometric and texture locality are exploited to minimize paging and to support models that contain arbitrarily many primitives.

The A-buffer (anti-aliased, area-averaged, accumulation buffer) is a general hidden surface mechanism suited to medium scale virtual memory computers. It resolves visibility among an arbitrary collection of opaque, transparent, and intersecting objects. Using an easy to compute Fourier window (box filter), it increases the effective image resolution many times over the Z-buffer, with a moderate increase in cost. The A-buffer is incorporated into the REYES 3-D rendering system at Lucasfilm and was used successfully in the “Genesis Demo” sequence in Star Trek II.

Ray tracing is one of the most elegant techniques in computer graphics. Many phenomena that are difficult or impossible with other techniques are simple with ray tracing, including shadows, reflections, and refracted light. Ray directions, however, have been determined precisely, and this has limited the capabilities of ray tracing. By distributing the directions of the rays according to the analytic function they sample, ray tracing can incorporate fuzzy phenomena. This provides correct and easy solutions to some previously unsolved or partially solved problems, including motion blur, depth of field, penumbras, translucency, and fuzzy reflections. Motion blur and depth of field calculations can be integrated with the visible surface calculations, avoiding the problems found in previous methods.

Fractals are a class of highly irregular shapes that have myriad counterparts in the real world, such as islands, river networks, turbulence, and snowflakes. Classic fractals include Brownian paths, Cantor sets, and plane-filling curves. Nearly all fractal sets are of fractional dimension and all are nowhere differentiable.