Filling a Hole in a Crease Pattern: Isometric Mapping from Prescribed   Boundary Folding
  Given a sheet of paper and a prescribed folding of its boundary, is there a way to fold the paper's interior without stretching so that the boundary lines up with the prescribed boundary folding? For polygonal boundaries nonexpansively folded at finitely many points, we prove that a consistent isometric mapping of the polygon interior always exists and is computable in polynomial time. 
Erik D. Demaine and Jason S. Ku
cs.CG