Application of Delaunay triangulation to the nearest neighbour method of strain analysis

The nearest neighbour method of strain analysis is re-evaluated and a method for objectively determining nearest neighbours, namely the Delaunay triangulation, is applied. A simulation study and application to a real set of data demonstrates that this approach makes the NNM of strain analysis a practical (and computationally more efficient) alternative to the Fry and associated methods. Once nearest neighbours are selected centre–centre distances can be processed by normalisation and enhancement and the best fit ellipse is determined using a steepest gradient non-linear least squares algorithm applied to the polar equation of a centred ellipse. A simulation study indicates that the technique is a valid one and estimates the strain ellipse well at the 95% confidence interval. Application to a set of natural oolite data shows that there is a systematic variation of error with selection factor and it is suggested that the best estimate of the strain ellipse is obtained by choosing the selection factor which minimises the error.