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Smoothing algorithms provide a means of identifying significant patterns in sets of orientated data, eliminating local perturbations within the observations and predicting patterns of orientated data in places which lack observations. Here we present the smoothing of orientation data with a distance-related method of data weighting as an alternative to previous weighting algorithms. The data weighting and smoothing method presented here in theory and practice is developed on the basis of a statistical smoothing algorithm. The method can be applied to orientation data of 180 ~ periodicity such as maximum horizontal tectonic stresses (SH) as compiled in the World Stress Map database. Our smoothing algorithm enables discrimination between local (<250 km of lateral extent) and regional (c. 250-5000 km of lateral extent) stress fields, and allows comparison of SH with other directional data such as fault trends or strain data. We present smoothed stress maps for northeastern America, the Himalayas and western Europe. By varying the scale and smoothing parameters we illustrate their influence on the accuracy and smoothness. We give recommendations for the appropriate choice of these parameters.

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