An Excel-Based Solution to the One-Cut Folding Problem

Abstract

Although the straight skeleton-based algorithm may in principle result in an infinite number of creases, for many patterns it is not only finite; it is also quite simple to implement. In this work, this famous one-cut problem is revisited with the description of an implementation of the straight skeleton using only angle bisectors and perpendiculars. The new method is simple enough to be implemented in Excel to automate the crease creation process.2 A New Implementation of the Straight Skeleton Among all possible folding creases, angle bisectors and perpendiculars are the most important. The angle bisectors allow two adjacent sides of a polygon to be folded into a single line. The perpendiculars, on the other hand, allow a single side to be folded toward itself into a single line. After many experiments it was concluded that the following algorithm, a variation of the straight-skeleton technique, solves the one-cut folding problem: