Subjectivity in visual selection of hinge and inflection points leads to significant errors in analyses of fold shapes in profile sections. This article gives a method for precise determination of these points. The method: (1) imports a fold image into Matlab, (2) digitizes points on the image, (3) increases the number of available points by using an interpolation algorithm, (4) fits a polynomial curve to the points, and (5) searches for the hinge and the inflection points mathematically. Tests on several folds confirm that the ‘HingeInflex’ is a rapid, robust and user-friendly method for precise selection of the hinge and inflection points.

Let jν, 1, jν,2, … denote the positive zeros of the Bessel function Jν(x), and similarly, let j'v,1, j'v,2, … denote the positive zeros of J'v(x), which are the positive critical points of Jv(x). It is well-known that when v is positive, both jν ,k. it and j'ν k are increasing functions of ν; see, e.g., [12, pp. 246 and 248]. Recently, Lorch and Szego [6] have attempted to show that the same is true for the positive zeros j″v,1, j″v,2, … of j″v(x), which are the positive inflection points of Jv(x).