An algorithm to construct conformable tubular networks that occupy arbitrary regions in R3

We describe a general algorithm for the construction of networks of tubes which occupy a specified, and possibly quite complicated, region D⊂R3 as fully as possible. Such networks can be important in a variety of industrial applications ranging from heat exchangers to storage vessels. The algorithm is comprised of three fundamental steps: (i) decomposition of region D into subregions Di, (ii) packing of each subregion with a set of parallel tubes using appropriate circle-packing algorithms and finally, (iii) connection of the tubes, both within each subregion Di as well as between neighboring regions. Such a design problem is extremely ill-posed: For a given region D, our algorithm can produce an enormous number of networks, which generally requires that a much smaller number of “best” networks be isolated. Such isolation can be accomplished by ranking the networks based on some application-dependent properties. Some simple examples are presented to illustrate the procedure and output of the algorithm.