Publications

A realization of Dijkstra's idea of the diffusing computation. A deadlock cycle can be discovered by processes reading and writing messages on objects. (pdf)

This described an Antialiasing Module, a general routine for building an image by non-uniform sampling of a function. Specifically, a tile of blue-noise samples are used, along with a nonlinear reconstruction filter. (pdf, fig1, fig2, fig7)

The infamous "Mitchell filter" is derived by studying cubic filters, both mathematically and subjectively. Reconstruction with derivative values is also discussed. We wrote a simple ray tracer that returned image gradient values, but I only touched on it in the paper. (pdf, fig4, fig5, fig6, fig8, fig9, fig10, fig11, fig12, fig15, fig16)

Johnny and I wrote a ray tracer called FX for the AT&T Pixel Machine, and this movie was our demo. The ray tracer parsed lisp, and so the model was a small file with recursive CSG definitions. Here is a high-resolution rendering of the final scene, and here is a wmv of the video (22 MB).

The FX ray tracer had a powerful system of nonlinear solvers that used interval arithmetic and automatic differentiation. With only 256K of memory per node, the Pixel Machine encourage highly procedural and recursive approaches to texture and modeling. ( pdf, fig1, fig2, fig3, fig4 )

FX did careful book-keeping to avoid numerical intersection errors, even when rays were near the corners of transparent objects. (pdf, fig1, fig2, fig3, fig4 )

Generating interlaced video requires careful multidimensional filtering to avoid spatial, temporal and chroma aliasing. Interlacing images is a bad design, making these problems unnecessarily difficult. (pdf, fig5, fig6, fig8, fig10, fig11)

Even by 1990, it was necessary to start out by refuting erroneous claims that "jaggies" were not caused by aliasing! Of course, there are other causes of jaggies, like bad gamma correction or nearest-neighbor image enlargement. (pdf)

One of the first quasi-random solutions to distribution ray tracing, although based on spectral analysis, not low-discrepancy quasi-random numbers. (pdf, fig8 & 9, fig11 & 12, fig13 & 14,

More information about the techniques used by the FX ray tracer. (pdf)

One day, I told Pat that I knew how to do caustics: solve the Lagrange multiplier problem with interval solvers, and compute brightness from wavefront curvature. He said, "Let's visit the Geometry Center and program with no distractions!". We froze our asses off in Minneapolis, it was -25º F. (pdf, fig1, fig2, fig3, extra)

Arbitrary-edge discrepancy was introduced. Optimal sampling patterns were found by Monte Carlo estimation of discrepancy. (pdf)

Dobkin and I invented an algorithm for computing discrepancy. No need anymore for Monte Carlo estimation. (pdf)

Robert Morris Jr. and I modified my fast DES code to do fast UNIX password hashing. He later did something very naughty with that code, although I don't believe he intended the damaging effects of his internet worm. (pdf)

Pat and I had talked about this at Princeton, so they invited me to visit Stanford and help. I programmed the depth of field sampling on a lap-top I brought with me. (pdf)

A lot can be learned from text-based MUDS, but most VR enthusiasts were hostile to the idea that people could become immersed in a world without 3D graphics and head-mounted displays. I believe the people who designed Everquest understood this.

The ppt presentation is a talk at W.R.I.T.E. 95. (htm, ppt)

This was a weekend hack in the middle of the virtual worlds project at Microsoft. But of course I had been thinking about this for years, so it was a very focused weekend! (pdf, fig1)

Here you see a low-discrepancy pattern of 16 points. But I recommend blue noise, not low discrepancy. Discrepancy is too closely coupled to box-fitering. (pdf)

We rejected VRML and designed a more MUD-like object model. This project ultimately grew into a huge confused effort, unfortunately. (pdf)

After Keely and Hitchcock invented ClearType, I wrote up the first technical analysis of what I called RGB decimation. The scientific problem has been overshadowed by politics. (pdf, fig1)

Have I mentioned that I think blue noise works better than quasirandom sampling? (ppt)

We develop measures of quality for mappings from the plane to the sphere. A number of mappings are analyzed, including some used to represent spherical textures and environment maps in graphics. (pdf, figa, figb, figc, figd, fige)

Several years ago, I suggested to Michael that 3D ground cover would make multiuser game environments much more realistic. Jonathan found Wang tiles, which is a wonderful concept, making non-periodic expanses of texture from a finite set of square tiles. (pdf)