Disk packing for the estimation of the size of a wire bundle

Abstract

A heuristic method for packing disks in a circle is constructed, and is applied to the estimation of the sizes of holes through which given sets of electric wires are to pass. Modern intelligent machines such as planes and cars have a variety of electric systems, and consequently a lot of electric wires run in a complicated way. These wires should pass through holes opened in the walls of the body of a machine. Those wholes should be as small as possible because larger holes weaken the body. The problem of finding the smallest hole is reduced to the problem of finding the smallest circle containing all of given disks without overlap. In the proposed method, a sufficiently large circle is initially constructed, and it is shrunk step by step while keeping all the disks inside. For this purpose a Voronoi diagram for circles is used. Computational experiments show the validity and the efficiency of the method.

Adaptive and restarting techniques-based algorithms for circular packing problems

“…The algorithm iterates through two complementary steps which are dynamically coupled in search for the smallest circle. Sugihara et al [26] designed a shrink and shake strategy to pack disks into the smallest diameter wire bundle. They construct a sufficiently large circle that contains all circles, then reduce the radius of the containing circle by translating circles.…”

“…[22]. For instance, in the automobile industry, design engineers have to estimate the size of the hole to be drilled on the body of the car and through which they plan to pass the bundle of wires that connect a car's sensors to the display board [26]. The hole has to be large enough to allow all wires to pass, but as small as possible to avoid unnecessarily weakening the body [26].…”

Scandinavian Thins on Top of Cake: New and Improved Algorithms for Stacking and Packing

“…Disk packing was considered in Sugihara et al [57]; see [40,52] for combinatorial bounds. For a further packaging problempacking the cake into a box-see [56].…”

Split Packing: An Algorithm for Packing Circles with Optimal Worst-Case Density

“…This naturally occurring circle packing problem has numerous applications in engineering, science, operational research and everyday life. Examples include packaging cylinders [2,6], bundling tubes or cables [16,18], the cutting industry [17], the layout of control panels [2], the design of digital modulation schemes [14], or radio tower placement [17]. Further applications stem from chemistry [19], foresting [17], and origami design [9].…”