Structure analysis and surface simulation of woven fabrics using fast Fourier transform techniques

Fourier transform techniques are particularly suitable for modelling woven fabrics with periodic structures. These techniques allow us to analyse the periodicity and the directionality of repeated elements. In fact, while passing through the Fourier spectrum, each periodic element is characterised by a peak whose value and frequency are proportional to the magnitude, spacing, and orientation of this element in the spatial domain. So the shape of the spectrum and its composition depend on the fabric's structural parameters. In this paper we apply the two-dimensional fast Fourier transform (FFT) to two types of woven fabrics - plain and 2/1 twill weaves - whose surfaces were digitalised using an optical profiler. Then we link the typology of the obtained spectrum to the fabric characteristics in a particular pattern and yarn densities. This correlation is used to provide a new approach for the simulation of the original fabric, also rendering the simulation of other fabrics with new structural parameters using the inverse FFT. Indeed, the angular distribution deduced from the magnitude spectrum of these surfaces shows the existence of three privileged directions: horizontal, vertical and diagonal - corresponding respectively to the directions of warp, weft and diagonal periodic structure. The orientation of the diagonal direction is characteristic of the pattern type, warp and weft densities. Dominant peaks in each one of these directions are correlated to the periodicity of the corresponding structure. Thus, the characterisation of the fabric in the frequency domain can be reduced to several dominant elements of the spectrum. Consequently, a simple change of these elements will allow us to simulate fabric surfaces according to their characteristics using the inverse fast Fourier transform.