ABSTRACT

A typical way of characterizing rocks, composite materials, or human tissue is to extract aspect ratio histograms. A common assumption for this type of analysis is that the sample is composed of several grains or building elements that have a similar shape. Among various shapes, the ellipsoid is very common. In practice, such detailed analysis is performed on 2D cuts or slices through the material. It is intuitive that there is a difference between a 2D aspect ratio histogram and the corresponding 3D histogram. I have derived simple equations that can be used to transform from 3D to 2D and also from 2D to 3D, assuming that the two shortest axes in the ellipsoid were equal. For the general case, when all axes were different, an approximate equation was derived. All equations were compared with stochastic numerical simulations of cutting a 3D ellipsoid by an arbitrary random number of planes. It was determined that in the general case, the shortest aspect ratio would dominate the 2D histograms and that it was practically impossible to detect the highest aspect ratio from 2D planar cuts.

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