Algebraic modelling of pattern design: the abelian pattern semi‐group

Pattern design is a transformation process from the design sketch to the final production pattern. In order to computerize such a process, a mathematical model is indispensable. When a garment is decomposed into components of pattern pieces, this decomposition process can be modelled by using semi‐group. Presents the construction of this semi‐group structure, which is called the abelian pattern semi‐group, and the associated lattice structure with proofs and examples. Illustrates the interpretation and application of this algebraic model with the optimal control problem of the production line.