A mathematical foundation for foundation paper pieceable quilts

Foundation paper piecing is a popular technique for constructing fabric patchwork quilts using printed patterns. But, the construction process imposes constraints on geometry of pattern and order in which pieces are attached to quilt. Manually designing foundation pieceable patterns that meet all these challenging. In this work we mathematically formalize use formalization develop an algorithm can automatically check if input pieceable. Our key insight represent geometric design certain type dual hypergraph where nodes faces hyperedges seams connecting two or more nodes. We show determining whether equivalent checking acyclic, it apply leaf-plucking generate viable sewing orders geometry. implement tool allows quilt designers focus producing their let handle tedious task