Anisotropy of a stationary fibre process in three dimensional space can equivalently be quantified by the directional measure (which is up to normalization the rose of directions), the rose of intersections and the associated zonoid. The best accessible quantity is the rose of intersections, as its values can be estimated by counting intersections of the fibres with lower dimensional test sets. Three non-parametric algorithms to estimate the directional measure, based on this information, are investigated. We also present estimators for the associated zonoid, which turns out to be an intuitive tool for visualization. The methods are applied to two different carbon fibre architectures and to simulated data.