Digital Weaving Part 2 introduces and discusses Andrew's Weaving Language. This is a compact little notation I cooked up for describing weaves that can otherwise take a lot of numbers to specify. I based this on the language that ships with Corel Painter. This column also talks about how to infer your loom setup if all you have to start with a piece of woven fabric. You can download a parser in the C# language for my weaving language here.

Digital Weaving Part 3 talks about the structure and colors in the traditional Scottish patterns known as tartans. I also talk about my digital loom, and how to program your own.

Image Search and Replace is my technique that does for pictures what traditional search-and-replace functions do for text documents. You tell the system what to look for, and what you'd like to replace it with. It finds the targets, removes them, cleans up the background, and then puts in the new images transformed appropriately so that they look good. The tricks are finding an efficient way to search (otherwise it would take much, much too long) and then using modern texture-synthesis algorithms to fill in the holes after a piece has been removed.

Venn and Now talks about how to generalize Venn diagrams beyond the standard three-circle form that we're all used to. It turns out that you can't just draw four circles! Lewis Carroll had a go at the problem, and made some nice progress. In this column I talk about what other people have done, and I give my own technique for drawing these types of diagrams for large numbers of variatbles.

Bart Barenbrug has found a nice geometric alternative to my equations for finding the circles for the Edwards construction, shown in Figure 31 on page 95. Noting that C2 is on the line from C1 through M, write C2=C1+q(M-C1). Because the circles are perpendicular at A and B, C1-A is perpendicular to C2-A. Writing (X,Y) for the dot product of vectors X and Y, we have (C1-A,C2-A)=0. Plugging in the value for C2 from above, and simplifying, we get q=-(C1-A,C1-A)/(C1-A,M-C1) = -r1^2/(C1-A,M-C1). Plug this value for q back into the first equation to get C2, then find r2=|C2-A|. Done, and without any trig functions!

DMorph discusses my algorithm for smoothly blending one convex polyhedron to another. It's a refinement on my metamorphosis technique, described here. The basic idea is to take the planes that define the start and end shapes, move them all simulaneously, and then find the volume they define as their interior at each moment along the transition. It's really easy and fast to program, and the results look great because they're smooth and continuous.

In Everyday Computer Graphics I talk about some of the many ways that our lives could be improved when we have handy display devices at our disposal, and smart computers around us all the time that can remember where we put things, where we've been, and can talk to other computers to help us find friends and directions.