Beautification of Islamic Patterns via Constraint Satisfaction

Yongquan Lu and Erik D. Demaine
Proceedings of Bridges 2016: Mathematics, Music, Art, Architecture, Education, Culture (2016)
Pages 371–374 Short Papers


Islamic star patterns are traditionally drawn with compass-and-straightedge constructions, which yield geometrically precise results, but are often unintuitive to work out. We present a more declarative paradigm for construction, where users can draw patterns by hand and then apply constraints to improve and beautify the design. This system applies concepts from CAD systems like geometric constraint satisfaction and numerical optimization in a highly symmetric and aesthetic context. We exhibit some representative results generated by our system.