Conventional fashion designers adopt a linear, Euclidean geometry approach to pattern cutting and making. This involves the uses of single continuous rectangles of fabrics. However, linear measurements lack the potential to fully capture the three-dimensional curvature of the human body. In particular, individuals may have the same linear body measurement but completely different three-dimensional body measurement. The incapability to produce an accurate fit also mean that more fabrics may be used than needed, leading to potential wastage of fabrics.

Mark Liu is dissatisfied with the extensive needless use of fabric in conventional linear pattern making. During his PhD research, he sought to understand the underlying structure and function of fashion pattern making. Leveraging on the idea of modern mathematics of curved surfaces, he argued that a Non-Euclidean geometry approach to pattern cutting is needed. A Non-Euclidean geometry approach would help to accurately map the curvature of the unique human body, and hence minimise potential fabric pieces that are not necessarily needed. Moreover, he came up with a new device named the 'drape measure' which helped in the measurement of the curvature of a surface, giving an angle measurement that could be used in future pattern making and zero-waste garments. 

The introduction of a Non-Euclidean geometry approach to pattern cutting minimises fabric waste (by about 15% per garment!) through bridging the gap between fashion and science. It addresses systemic problems in conventional linear pattern making and the potential subjective judgment involved, allowing industrial players to rethink ready-to-wear sizing systems. With a Non-Euclidean geometry approach, it enables greater accuracy, control, efficiency, and creates new possibilities to pattern making, while being simple enough for fashion pattern makers to understand. It also creates new possibilities for technology, such as the building of more advanced 3D scanning algorithms for more accurately-fitted pieces of garments.

To help more industrial players reveal the potential of STEAM, Mark Liu also collaborated with Dr Mary Coupland from the University of Technology Sydney to provide a series of workshops that teach STEAM concepts through fashion and textile design.