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.