Holomorphic Mappings for Integrated Garment and Motif Design
Loe Feijs, Rong-Hao Liang, Holly Krueger, and Marina Toeters

Proceedings of Bridges 2025: Mathematics and the Arts
Pages 101–108
Regular Papers

Abstract

Today's fashion design is based on a separation of concerns such that the geometry of the fabric motif and the geometry of the pattern cut are unrelated. We challenge this approach by developing mathematical tools to morph the motif. The core innovation lies in the mathematical framework, based on holomorphic mappings and harmonic conjugate functions, to map motifs onto arbitrarily shaped panels. This approach, implemented via custom software, allows for seamless motif continuation across complex garment shapes, avoiding cutting through repeating designs. We demonstrate the technique's application through several garment examples, showcasing its potential for creative pattern design and efficient manufacturing.

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