Abstract
Mathematics remains an endless source of inspiration for both the conception and the fabrication of clothes and fashion products. Over the last century, the prominent role of mathematics in the fashion industry has evolved together with the progress in computational resources and fabrication technologies. Nowadays, mathematics not only provides useful theoretical and computational tools to assist design and fabrication, but also acts as a catalyst of creativeness. This survey discusses the latest advances on mathematical models and methods in the fashion industry, restricting our attention to clothing design and multi-scale modelling, and their applications for digital manufacturing of textiles and garments. Particular focus is given to the usage of mathematics to drive product innovation and to reduce the environmental impact of the fashion industry in order to meet the Sustainable Development Goals of the United Nations.
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