How to Solve a Cubic Equation, Part 2: The 11 Case

Jim Blinn discusses a good practical closed-form solution process for cubic equations and makes some observations about the relation between iterative and closed-form solutions.     

A trip down the graphics pipeline: grandpa, what does `viewport'mean?

The author describes how he extracted the desirable aspects of window-to-viewpoint transformation while discarding the disquieting ones. He examines the classic window-to-viewport transform, and discusses how it relates to the graphics pipeline he has discussed in the past. He then considers clipping and off-screen viewports     

Lines in space

Previously we came up with two algebraic representations for lines in 3D projective space: we got one from connecting two points and the other from intersecting two planes. In both cases the algebraic representation was an antisymmetric 4 /spl times/ 4 matrix, but these two matrices were not the same. In this paper, we try to understand these differences and see how to convert one to the other. We become more acquainted with the properties of these matrices and build up some intuition on the geometric meaning of their components. We do all the algebra using what we call conventional, or familiar, notation. This gives letter names to each element of a vector/matrix and gives a sense of concreteness to the calculations. This makes the reader really appreciate the newer Einstein index notation and its alternate representation, tensor diagrams.     

The 3D kaleidoscope

The author presents a method for constructing platonic solids that takes advantage of their symmetry. This works well with a coordinate transform system, since symmetry is based on coordinate transformations. He treats the cube and other related shapes, using a seed-triangle element that can be rotated and reflected to generate the shape. He shows that the seed triangle can be replaced with any shape whatever, and all the replications will generate a result that also shares the symmetry of the cube. By making the seed shape rotate and move about in some random way, a changing shape that generates the 3-D kaleidoscope patterns of the title can be animated. The tetrahedron is also treated     

How to attend a Siggraph conference

The author is one of the few people who has been to all 22 of the Siggraph annual conferences. In this article, he gives some historical nuggets and tips he has formulated over the years. He discusses time management, technical talks, panels, equipment shows, video shows, art shows, parties, name badges and the summer camp session     

The world of digital video

Digital video standards define byte-stream signal formats for transferring video over cables. The composite and component standards, two digital video standards that relate most closely to the NTSC broadcast standard used in North America and Japan, are discussed. The analog NTSC signal and the framework of digital video standards are reviewed. The horizontal timing, quantization, and TRS-ID used by the composite digital standard, and the vertical renaming, scan line timing, and pixel value quantizing used by the component digital standard are described     

Vectors and geometry and objects, oh my!

This paper describes the design of classes to represent geometric objects (such as points and transforms) and algebraic objects (such as vectors and matrices). I start out by reviewing some fairly basic math. I've included this just to provide context for the main topic, which is class design that implements the math. A truly bulletproof system for these objects might not even be achievable without an inordinate amount of complexity.     

A bright shiny future

We know from viewing past predictions that short term predictions tend to be overly optimistic and long term predictions tend to be overly conservative. The author presents some short-term predictions that he feels pretty sure of, mainly because most of them are almost here now. These predictions include computers, display technology, applications and computer graphics     

Floating-point tricks

The author discusses IEEE floating point representation that stores numbers in what amounts to scientific notation. He considers the sign bit, the logarithm function, function approximations, errors and refinements