Tuesday, April 9, 2013

Beating Plowshares into Traveling Salesmen

Fabric making traditionally advances in a plowing (boustrophedonic) order, or a spiral order when worked in the round. These two working orders suffice, topologically speaking, to make any closed surface (after all, a closed surface is just a plane polygon with sewn-up edges,) but practically speaking these patterns are very restricting when we need to accommodate different densities of detail. (By the time a closed surface has been stretched out into a polygon there are always varying densities of detail.)

The solutions to the Traveling Salesman Problem are versatile in accommodating such variations in density, as proven by the image above, quoted from the Egg-Bot Wiki.

But, working in TSP order means we must be able to turn both left and right while working on the same side of the fabric...

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