Achieving curves in a piece of handwoven cloth has always been a difficult task given that the warp and weft intersect each other at right angles. The jacquard loom made curves possible because the manipulation of each individual warp thread allows designs to take place one thread at a time. Ethnic weavers have achieved it through skilled and time consuming hand manipulation of their warp and weft threads. But, for the floor loom weaver, curves were limited to optical illusions in designs.
In 1988 a pair of French mathematicians named Oliver Masson and Francois Roussel came up with a method of laying threading and treadling over a network. Their published work called Shaft Switching & Graph Design was pretty sophisticated for the mathematically challenged and the translation into English was less than perfect. An adventurous American weaver, Alice Schlein, analyzed the diagrams in the book and made the information accessible to handweavers around the world. Her book on the subject is called Network Drafting: An Introduction and was published by Bridgewater Press in 1994. Since that time, handweavers with multishaft looms have been weaving amazing curves and geometric designs using network drafting.
I started weaving network twills on my 24 shaft AVL as soon as I learned that my weaving software, WeavePoint, made it an easy task to do original designs. Fiberworks PCW also is adept at making the design work easy and it takes a different approach to the problem than WeavePoint does. I've woven some of my drafts and you can see examples in this Flickr slideshow. The joy for me, is that I have many more designs that I have yet to try on my loom and I expect to be busy for years to come weaving off drafts in my weaving software folders.
If you decide to weave curves and want more information, here are a few links to help you understand the process and enjoy the work of other weavers. And, if you find links to more information about this topic, please make a comment so that I can add them to this list.
Notes on Masson and Roussel's book For those who want to get into the meat of Masson and Roussel's work, here is a link with notes to help understand this complex treatise.
Weave Zine Network Twill Design Tutorial. Bonnie Inouye does a very complete drafting tutorial for eight and four shaft network twill designs. Once you have the procedure in mind, you are free to design for multishaft looms and let you imagination soar.
Alice Schlein's blog is full of adventures for a weaver who wants to design their own weaving drafts.
Complex Weavers has an extensive textile library. Members can join a wide variety of study groups and borrow materials from the library
Network Drafting for Double Weave written by Paul O'Connor can be downloaded for free and contains lots of useful information for adventurous weavers.