Eighteen cleaned and degreased Perendale wool fibres, which were as free as possible from external and internal stresses, were photographed, the images scanned to computer, and their space curves reconstructed. Various relations between the fibres' curvature and torsion were discovered which point to the possibility of a statistical description of a free fibre's shape in terms of only a few easily measured quantities, including the mean and RMS curvature. An algorithm is given which allows the generation of realistic wool fibre shapes for use in computer simulations.
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