  Modeling folding surfaces with nonzero thickness is of practical interest for
mechanical engineering. There are many existing approaches that account for
material thickness in folding applications. We propose a new systematic and
broadly applicable algorithm to transform certain flat-foldable crease patterns
into new crease patterns with similar folded structure but with a
facet-separated folded state. We provide conditions on input crease patterns
for the algorithm to produce a thickened crease pattern avoiding local self
intersection, and provide bounds for the maximum thickness that the algorithm
can produce for a given input. We demonstrate these results in parameterized
numerical simulations and physical models.
